Fatigue behaviour of composite tubes under multiaxial loading

Fiifth IInternatiionall Conference 

on Fatiigue of Composiites 

Editor in Chief: W-X Yao 

16-19 October 2010, Nanjing, China 

Nanjing University of Aeronautics and Astronautics

Contents 

Fatigue behaviour of composite tubes under multiaxial loading ............................................................ 1 

M Quaresimin, R Talreja 

Damage mechanism and fatigue behaviour of uniaxially and sequentially loaded wound tube 

specimens ......................................................................................................................................................... 8 

Frank Schmidt, Peter Horst 

An effective method for P-S-N curve fitting of composite laminates ................................................... 21 

D Guan, Q Sun 

Constant Fatigue Life Diagrams for a Woven CFRP Laminate at Room and High Temperatures 25 

M Kawai, Y Matuda, R Yoshimura, H Hoshi, Y Iwahori 

Effect of stress ratio on fatigue transverse cracking in a CFRP laminate ........................................... 44 

K Ogi, R Kitahara, M Takahashi, S Yashiro 

Fatigue damage characterisation for wind turbine blade GFRPs using computed tomography .... 54 

J Lambert, A R Chambers, I Sinclair, S M Spearing 

Cyclic interlaminar crack growth in unidirectional and braided composites .................................... 63 

S Stelzer, G Pinter, M Wolfahrt, A J Brunner, J Noisternig 

Effect of Water Uptake on the Fatigue Behavior of a Quasi-Isotropic Woven Fabric 

Carbon/Epoxy Laminate at Different Stress Ratios ............................................................................... 76 

M Kawai, Y Yagihashi, H Hoshi, Y Iwahori 

Influence of thermal and mechanical cycles on the damping behaviour of Mg 

based-nanocomposite ................................................................................................................................... 94 

Z Trojanová, A Makowska-Mielczarek, W Riehemann, P Lukáč 

Delamination during fatigue testing on carbon fiber fabrics reinforced PPS laminates ................ 103 

J Bassery, J Renard 

A residual stiffness – residual strength coupled model for composite laminate under fatigue 

loading .......................................................................................................................................................... 131 

W Lian 

An Innovative Energy-Based Fatigue Approach for Composites Combining Failure Mechanisms, 

Strength and Stiffness Degradation ......................................................................................................... 147 

H Krüger, R Rolfes, E Jansen 

Experimental characterization and analytical modeling of material non-linearity in fatigue 

analysis of polymer matrix composites ................................................................................................... 158 

M Magin, N Himmel 

Calorimetric Analysis of dissipative Effects associated with the Fatigue of GFRP Composites.... 161 

H Sawadogo, S Panier, S Hariri 

Fatigue-driven Residual Life Models Based on Controlling Fatigue Stress and Strain in Carbon 

Fibre/Epoxy Composites............................................................................................................................ 172 

J J Xiong, J B Bai, R A Shenoi 

Prediction of transverse crack initiation of CFRP laminates under fatigue loading ....................... 186

A Hosoi, K Takamura, N Sato, H Kawada 

Interfacial Fatigue Crack Propagation in Microscopic Model Composite using Bifiber Shear 

Specimen ...................................................................................................................................................... 194 

M Hojo, Y Matsushita, M Tanaka, T Adachi 

Experimental analysis and modelling of fatigue behaviour of thick woven laminated composites 

....................................................................................................................................................................... 209 

P Nimdum, J Renard 

Fatigue life assessment via ply-by-ply stress analysis under biaxial loading .................................... 230 

F Schmidt, T J Adam, P Horst 

Fatigue Damage initiation of a PA66/glass fibers composite material ............................................... 241 

B Esmaeillou, P Fereirra, V Bellenger, A Tcharkhtchi 

Fatigue life prediction of off-axis unidirectional laminate................................................................... 250 

F Q Wu, W X Yao 

Post-Impact Fatigue Damage Monitoring using Fiber Bragg Grating Sensors ............................... 264 

C S Shin, S W Yang 

Delamination detection in CFRP laminates using A0 and S0 Lamb wave modes ............................. 273 

N Hu, Y L Liu, H Fukunaga, Y Li 

Effect of Temperature on Fatigue behavior in nylon 6-clay hybrid nanocomposites ...................... 288 

S J Zhu, M Kichise, A Usuki, M Kato 

Fatigue Behavior of Unidirectional Jute Spun Yarn Reinforced PLA ............................................... 291 

H Katogi, Y Shimamura, K Tohgo, T Fujii 

An evaluation on thermal shock fatigue damage of SiC composite using nondestructive technique 

....................................................................................................................................................................... 302 

J K Lee, S P Lee, J H Byun 

Fabrication of ti/apc-2 nanocomposite laminates and their fatigue response at elevated 

temperature ................................................................................................................................................. 308 

M-H R Jen, Y-C Sung, C-K Chang, F-C Hsu 

Fatigue and Fracture of Elastomeric Matrix Nanocomposites ........................................................... 317 

C Bathias, S Y Dong 

Correlation between crack propagation rate and cure process of epoxy resins ............................... 327 

V Trappe, S Günzel 

Thermal fatigue of AX41 magnesium alloy based composite studied using thermal expansivity 

measurements.............................................................................................................................................. 331 

Z Drozd, Z Trojanová, P Lukáč 

Fatigue behaviour of woven composite joint ...................................................................................... 339 

J Y Zhang, Y Fu, L B Zhao, X Z Liang, H Huang, B J Fei 

Damage in thermoplastic composite structures: application to high pressure hydrogen storage 

vessels ........................................................................................................................................................... 355 

C Thomas, F Nony, S Villalonga, J Renard 

Residual life predictions of repaired fatigue cracks.............................................................................. 367 

H Wu, A Imad, N Benseddi 

Monotonic and cyclic deformation behavior of ultrasonically welded hybrid joints between light

metals and carbon fiber reinforced polymers (CFRP) ......................................................................... 376 

F Balle, D Eifler

Fatigue behaviour of composite tubes under multiaxial loading 

Abstract 

M Quaresimin a, *, R Talreja b 

a Department of Management and Engineering - University of Padova, Stradella S. Nicola, 3 36100 Vicenza, ITALY 

b Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77843, USA 

The paper illustrates the results of an extensive investigation on the damage evolution in composite glass/epoxy tubes 

subjected cyclic tension-torsion loading. S-N fatigue curve, stiffness trends and microscopic damage evolution for 

different values of biaxiality ratio are discussed. 

1. Introduction 

In spite of its importance in the design of structural components that are subjected to complex load 

histories with variability of loading direction and intensity, the fatigue behaviour of composite materials 

under multiaxial loading has received only little attention by the scientific community. A recent 

review by the authors, [1], indicated the deep lack of information about the damage evolution during the 

fatigue life: only few papers in fact report quantitative analysis and damage growth data [2], qualitative 

information and stiffness trends can be found in [3-7]. A strong influence of the shear stress on the 

multiaxial fatigue strength was also shown. Eventually, the analysis of reliability of some criteria 

available for life prediction, done again in [1], clearly suggested the need of a physically based model 

suitable to describe and account for the actual fatigue damage. 

This paper illustrates the preliminary experimental results of a project aimed at investigating the 

problem through the following steps: study of fatigue damage evolution under multiaxial loading 

conditions, analysis of the mutual influence of the stress components and understanding of the 

associated damage mechanisms and, eventually, development of a life prediction model suitable to 

incorporate these mechanisms. 

2. Materials and specimens 

Tubular samples to be tested under combined tension-torsion loading were considered as the optimum 

solution to avoid free-edge effects on the damage evolution. Moreover by varying the ratio between 

external tension and torsion loading the mutual influence of the stress components on the damage 

evolution can be investigated. Samples were produced by wrapping of 4 layers of glass/epoxy UD 

pre-pregs at 90 o with respect to the longitudinal axis and then autoclave moulding. To compare the use 

of different alternative clamping set-ups, tubes with different external diameter (38 mm or 22 mm) and 

* Corresponding author. 

E-mail address: marino.quaresimin@unipd.it

2 

Fifth International Conference on Fatigue of Composites 

the same thickness (1.5 mm) were produced. Samples with a different lay-up were also manufactured, 

by replacing the inner layer of UD tape with a balanced fabric layer. In this way, the initial [90]4 lay-up 

became [0T/90UD,3]. The [90]4 lay-up allowed us to quantify the influence of the shear stress component 

on the transverse fatigue strength, in the absence of the longitudinal (fiber-direction) stress. The 

[0T/90UD,3] facilitated instead a stable and measurable growth of the fatigue damage. The following 

prepregs were considered: UD tape UE400-REM produced by SEAL-Italy, area weight = 645 g/m 2 , 

Balanced fabric VV345T-DT107A produced by Deltatech-Italy, area weight 345 g/m 2 ). 

3. Experimental testing and damage investigation 

The tensile properties of the prepregs used for manufacturing the tubes were first measured by testing 

flat coupons under tension loading. The average values of elastic and strength properties measured for 

the UD and fabric tape are summarised in table 1. 

The multiaxial fatigue behaviour of the tubes was investigated by means of pulsating tension- torsion 

fatigue loading. Fatigue tests were carried out on a MTS 809 axial-torsional machine, under 

load/torque control at a frequency of 10 Hz. S-N fatigue curves for [90]4 tubes are shown in figure 1, 

for pure tensile loading and for biaxiality ratio 12 (6/2) equal to 1.0 and 2.0. 

Table 1. Average in-plane properties of the materials used for tubes manufacturing 

EL (MPa) ET (MPa) GLT (MPa) LT L (MPa) T (MPa) LT (MPa) 

UD400-REM 34860 9419 3193 0.326 973 50 98 

VV345T-DT107A 21700 20800 3351 0.159 448 431 85 

Fig. 1. Fatigue results for [90]4 glass/epoxy tubes under tension (12=0) and tension-torsion loading (12= 1 and 2) (L denotes tube of 38 mm 

external diameter, S for 22 mm external diameter; thickness= 1.5 mm). 

The presence of a shear stress component turned out to have indeed a significant influence, with a 

40% drop in the fatigue strength at 2 million cycles for a biaxiality ratio equal to 2 . 

As shown again in figure 1, tubes with 38 or 22 mm diameter turned out to behave similarly and 

therefore it was decided to continue testing with the smaller diameter tubes which can be clamped

M Quaresimin, R Talreja / Fatigue behaviour of composite tubes under multiaxial loading 

directly by the hydraulic grips of the testing machine (see figure 2). 

Figure 2 shows the specimen mounted on the axial-torsional testing system as well as the internal 

LED light illumination built up to investigate the damage evolution and, in particular, the crack onset 

and growth. This is made possible by the transparency of the glass-epoxy tubes. 

Fig. 2. Testing set-up and details of the internal lighting of tubes for observation of damage. Example of multiple cracking in a [0T/90U,3] tube. 

During the testing of [90]4 tubes the absence of stable crack propagation was observed, with cracks 

nucleating and propagating almost instantaneously (few cycles) to the whole section of the sample, 

causing the complete separation into two parts. This behaviour could be expected due to the particular 

lay-up investigated and was clearly indicated even by the sample stiffness. In fact, both axial and 

torsional stiffness were found not to change significantly during the fatigue life of the samples, showing 

a sudden drop only close to the final failure. Therefore from these tests we can derive only the influence 

of the shear stress component on the transverse fatigue strength. However, the change of the slope of 

fatigue curves shown in figure 1 seems to suggests a change in the damage mechanics as the shear stress 

increases. Further data are indeed needed to clarify this situation and also to increase the statistical 

significance of the results, in particular at high number of cycles. 

It still remains to identify how the damage evolves during the fatigue life of the tubes. Under pure 

tension a crack nucleates after a certain number of cycles and then grows under pure mode I condition. 

The simultaneous presence of shear stress together with the transverse stress changes the scenario 

completely and one can speculate that the crack nucleates at the external surface and then propagates to 

the inner surface under I + III mixed mode loading. Then the crack grows along the tubes circumference 

under I + II mixed mode condition, as sketched in figure 3. In view of modeling this damage evolution 

it is important to verify and quantify these speculations and this can be done experimentally only 

slowing down the crack initiation and growth process. 

3

4 


Fig. 3. Schematic of the damage process in a [0F/903UD] tube under tension-torsion loading. 

Thus, in the attempt to better investigate the damage evolution it was decided to slightly change the 

lay-up from [90]4 to [0T/90U,3]. As said before, the [0T/90U,3] lay-up facilitates a stable growth of the 

damage, suitable to be observed, measured and, eventually, correlated with the applied stress-state. In 

this configuration, the limited amount of longitudinal fibers provided enough strength to let the 

transverse cracks to nucleate and growth reasonably slowly during the sample fatigue life. Examples 

of cracks identified on the samples are shown in figure 2, 4 and 5. From figure 2 and 4 it is rather clear 

that the internal led light system works pretty well in showing the presence of the cracks. For the 

[0T/90U,3] tubes, the cracking process can be tracked even on axial stiffness curve, where rather evident 

drops can be identified in correspondence of the nucleation and growth of transversal cracks. 

Fig. 4. [0T/90U,3] glass/epoxy tube after failure under tension-torsion fatigue loading (12=2). Internal light makes the transverse cracks outside the 

failure zone clearly visible. 

Fig. 5. Micrographs of longitudinal sections of the [0T/90U,3] glass/epoxy tube shown in fig. 3.


Figure 6 shows the fatigue curves for the [0F/903UD] tubes. To allow a comparison with the previous 

results on [90]4 tubes to be made, the life to initiation of the first crack was taken as reference. 

Although the behaviour under pure tension needs to be further clarified, the effect of the shear stress on 

the fatigue life is comparable with that shown in figure 1 and this may suggest a similar damage 

scenario in the two cases. With this new [0F/903UD] lay-up it was possible to monitor the evolution of the 

damage during the fatigue life. This was done by taking again advantage of the internal light system and 

visually observing by naked eyes the samples during testing. For the longer tests, a continuous digital 

acquisition system controlled by a in-house developed Labview tool was used. 

tubes with one inner layer of fabric and three layer of 90 UD Tapes 

transverse stress 2 in 90°plies [MPa] 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

10 100 1000 10000 100000 1000000 10000000 

cycles for nucleation of the first visible crack 

12=0 

12=05 

12=1 

12=2 

L. 

(12=05) 

L. 

(12=1) 

L. 

(12=0) 

L. 

(12=2) 

Fig. 6. Fatigue results for [0F/903UD] glass/epoxy tubes under tension (12=0) and tension-torsion loading (12= 0.5, 1 and 2). 

With reference to figure 3, it can be confirmed first of all that the hypothesis made on the damage 

onset and evolution was correct: the cracks actually nucleated at the external surface, propagated to the 

inner radius and then grew along the tube circumference. However the fraction of fatigue life spent in 

the different phases is rather different: in fact, the onset and propagation under Mode I+ Mode III is, in 

general, very fast when compared to the lower circumferential growth. 

° 

N = 350 cycles 

x 

y 

z 


α 

z 

y 

α = 33° 

ΔN = 150 cycles 

β 


z 

y 

α = 30° 


5

6 

β 


z 

y 

α = 117° 



α 

z 

y 

α = 21° / β = 13° 


α 


α 


z 

y 

α = 39° 



z 

y 

α = 95° 


α 


z 

y 

α 

α = 12° 


Fig. 7. Crack growth during the fatigue life of a [0F/903UD] tube under tension-torsion loading (12 = 1, transverse stress 2= 30 MPa). 

An example of the complete evolution for one of the cracks observed and measured during their 

growth is reported in figure 7. 

crack growth [degrees] 

360 

315 

270 

225 

180 

135 

90 

45 

0 

0 10000 20000 30000 40000 50000 60000 70000 

number of cycles of crack propagation 

12=0 

12=0.5 

12=1 

12=2 

Fig. 8. Crack growth data for [0F/903UD] tubes under tension-torsion loading (nominal tensile stress= 30 MPa). 

Being now available the crack "length" (measured in degrees of propagation along the tube 

circumference) against the number of cycles it is possible to assess the possible influence of the


multiaxial loading conditions on the crack growth rate. This is made, for the data available so far, in 

figure 8 where crack propagation data for pure tension and tension/torsion tests are plotted. All the tests 

were done with the same external tensile stress (30 MPa) and progressively increasing the shear stress 

from 0 to 60 MPa. The effect of the shear stress in accelerating the growth of the cracks along the tube 

circumference is still dramatically evident. 

4. Conclusions 

The results of an experimental investigation on the fatigue behaviour of glass/epoxy tubes under 

cyclic tension-torsion loading has been presented and discussed. The shear stress components associated 

to the torsion load (quantified by the biaxiality ratio 12) was found to have a dramatic influence on the 

fatigue strength of [90]4 and [0T/90U,3] tubes, with a reduction in the high cycle fatigue strength up to 

40% in the case of the [90]4 tubes. The slower rate of damage propagation obtained for [0T/90U,3] tubes 

allowed the monitoring of the damage evolution to be made. Even the crack growth rate turned out to be 

affected by the shear stress, with a significant increase in the average rate of crack propagation as the 

shear stress increased. 

References 

[1] Quaresimin M., Susmel L., Talreja R., Fatigue behaviour and life assessment of composite laminates under multiaxial loadings, 

International Journal of Fatigue, 32, 2-16, 2010. 

[2] Adden S, Horst P. Damage propagation in non-crimp fabrics under bi-axial static and fatigue loading. Composites Science and Technology 

33, 626-633, 2006. 

[3] Smith E. W., Pascoe K. J., Biaxial fatigue of glass-fibre reinforced composite. Part 1: fatigue and fracture behaviour. Biaxial and 

Multiaxial Fatigue, Edited by M. Brown and K. J. Miller, EGF 3, Mechanical Engineering Publications, London 1989: 367-396. 

[4] Takemura K., Fujii T. Fatigue strength and damage progression in a circular-hole-notched GRP composite under combined tension/torsion 

loading. Composites Science and Technology, 52, 519-526, 1994. 

[5] Fujii T., Lin F. Fatigue behavior of a plain-woven glass fabric laminate under tension/torsion biaxial loading Journal of Composite 

Materials 29, 573-590, 1995. 

[6] Kawakami H., Fujii T., Morita Y. Fatigue degradation and life prediction of glass fabric polymer composite under tension/torsion biaxial 

loadings. Journal of Reinforced Plastics and Composites, 15, 183-195, 1996. 

[7] Inoue A., Fujii T., Kawakami H. Effect of loading path on mechanical response of a glass fabric composite at low cyclic fatigue under 

tension/torsion biaxial loading. Journal of Reinforced Plastics and Composites 19,111-123, 2000. 

7

Damage mechanism and fatigue behaviour of uniaxially and 

sequentially loaded wound tube specimens 

Abstract 

Frank Schmidt *, Peter Horst 

Institute of aircraft design and lightweight structures, Technische Universität Braunschweig, 

Hermann-Blenk Straße 35, 38108 Braunschweig, Germany 

In mechanically loaded composites various damage types occur depending on different external load cases. One aspect 

of this paper is to show the differences in damage and fatigue behaviour under pure tension/compression and pure shear 

fatigue loading. For this purpose, fatigue tests with nominally defect-free wound tube specimens and non-destructive tests, 

i.e. thermography, optical fracture analysis with high-speed camera and discrete damage monitoring are performed. Based 

on the experimental data a comprehensive analysis of the successive failure mechanisms (matrix cracking, delamination 

and final failure) is conducted. Thereby, the location of final failure can be found in an early stage of the fatigue life 

observing high temperature areas (hot-spots). In the following, the effects of two different uniaxial load directions under 

sequence loads, which mean a sequently change from pure shear load to pure tension/compression load after several life 

cycles, are investigated. 

Keywords: Polymer matrix composites; fatigue test methods; experimental data; non-destructive testing 


The increasing application of composite materials in several industries, e.g. automobile and aircraft 

industry or wind-energy plants, demands a deeper understanding of the fatigue behaviour and its 

modelling for different load cases. Thereby, the range of fatigue loadings is varied. Concerning the high 

realistic complexity of load histories and arbitrary load ratios or intensities (e.g. aerodynamic loads of 

aircraft wings or rotor blades of a wind-energy plant) investigations of multiaxial cyclic loading 

conditions are required. Additionally, the sequence of different load directions and amplitudes is also 

crucial for the occurrence and interaction of complex damage mechanisms and the fatigue behaviour of 

composites. 

Although constant-amplitude tests under uniaxial loading hardly represent realistic fatigue loading 

conditions, mostly these simplified types of fatigue loading experiments are performed. However, these 

investigations lead to a good understanding of the basic influences of fatigue damages and are essential 

for the interpretation of further researches with multiaxial and sequence loadings. 

The fatigue damage scenarios of 0/90 laminates show the initiation and progress of transverse cracks 

with sharp tips (stage I), the development of local delaminations caused by the transverse cracks (stage 

II) and the consolidation of local delamination surfaces with the final failure (stage III) [1-3]. Analysing 

* Corresponding author. Tel: 0049-531-391-9921, Fax: 0049-531-391-9904 

E-mail addresses: frank.schmidt@tu-bs.de, p.horst@tu-bs.de

F Schmidt, P Horst / Damage mechanism and fatigue behaviour of uniaxially and sequentially loaded wound tube specimens 

of stiffness behaviour shows an inverted behaviour. The initial stage I consists of a steep decrease in 

stiffness (triggered by matrix cracks), stage II shows a weak, quasi-linear decrease of the stiffness which 

is followed by a rapid decrease caused by fibre ruptures and the overall laminate failure in the final 

stage III. These damage mechanisms and fatigue behaviours are used for fatigue models. Similar 

damage evolutions and stiffness degradations can also be shown in multiaxially and sequentially loaded 

composites. Quaresimin et al. [4] give an up-to-date review of current approaches on fatigue behaviour 

under multiaxial loading and distinguish the influence of factors such as biaxial stress ratios and damage 

mechanisms. Furthermore, a ply-by-ply stiffness degradation model, which describes the first and 

second stage of the stiffness behaviour, based on experimental results of multiaxial fatigue tests is 

developed by Adden et al. [5]. The authors show the application of this modelling approach for 

composites with arbitrary layers provided that the discrete damage states (crack densities) are known. 

Using this approach and experimental test methods Schmidt et al. [6] reveal the transferability of the 

stiffness behaviours to sequentially loaded specimens. Thereby, the differences in crack development 

under pure shear loads and pure tension loads are considered and used as input for modelling the 

stiffness behaviour under sequence loading (different loading directions). Further researches lead to a 

fatigue life assessment via ply-by-ply stress analysis [7] and a resulting single lamina-based S-N curve 

of the critically stressed layer formed by stress redistributions in multiaxial fatigue. An enhancement to 

this model for calculating the stress redistributions under sequence loading is conceivable. A further 

modelling approach for the effects of block loading and load sequence is presented by Paepegem et al. 

[8]. The authors propose a phenomenological residual stiffness model incorporating a modified static 

Tsai-Wu failure criterion. This fatigue damage model is used to simulate the effect of block loading 

fatigue tests. Nevertheless, a literature survey on load sequence effects and block loading presented in 

this paper shows that the opinions on the load sequence effect are strongly divided. Thus, further 

researches for a deeper understanding of the damage accumulation under sequence loading and for the 

validation of fatigue damage theories are required. 

Concerning the monitoring of damages and the fatigue process several approaches can be used. 

Applications of different non-destructive test methods are required for the interpretation of the 

correlation between the damage mechanisms and the fatigue behaviour (stiffness degradation and final 

failure). Adden et al. [9] show fatigue damage characterization in GFRP tube specimens by means of 

circumferential plate waves. The results demonstrate a positive relation between fatigue induced 

ultrasonic damping and stiffness degradation. Therefore, using simple measurements of circumferential 

plate acoustic wave amplitude variations leads to observation of fatigue damage. Another possibility of 

monitoring fatigue is the use of air-coupled lamb waves [10]. Thereby, the change in wave velocity and 

the attenuation parallel to the axial direction of the specimens throughout fatigue correlated closely with 

the development of matrix cracks and measured stiffness degradation. In order to detect the location of 

final failure in an early stage of fatigue life of composite structures, Gagel et al. [11] apply 

thermography as a non-destructive test method. By means of uniaxial fatigue tests with flat specimens 

the authors show the development of spots of increased temperature correlating with the final failure. 

Similar results are also shown by Schmidt et al. [12] investigating nominally defect-free wound tube 

9

10 

specimens under biaxial stress ratios. 


The current paper contains the experimental results of uniaxially and sequentially loaded tube 

specimens. Thereby, the occurring damage mechanisms (matrix cracking, delamination and final failure) 

measured with different non-destructive test methods and the fatigue behaviour for different load cases 

are shown. Additionally, these phenomenological results can be used as input for future models 

describing the fatigue behaviour of composites under sequence loading. 

2. Material 

Matter of the investigation is a nominally defect-free wound tube specimen made of E-Glass-fibre 

rovings from Owens-Corning (OC 111A) and a resin/hardener-combination of RIM135/ RIMH137 from 

Hexion. In order to produce these specimens at a high quality standard a self-designed winding machine, 

which enables the manufacturing of arbitrary lay-ups is used. The winding process and one tube 

specimen are shown in figure 1. As in a previous investigation of the fatigue behaviour under biaxial 

loading [12] the specimens used in the current research consist of 8 layers with a symmetric lay-up of 

[0 o /45 o /90 o /-45 o ]S. The applied mass per unit area and the relative mass fractions are shown in talbe 1. 

Using resin transfer moulding (RTM) the wound tube specimens are manufactured in the way that the 

plies orientated in 0 o -direction (identical to the axial direction of the specimens) are the inner and outer 

plies. 

Fig. 1. Winding process (left) and nominally defect-free wound tube specimen (right). 

Table 1. Lay-up of the wound tube specimens 

Orientation ( o ) Mass per unit area (g/m 2 ) Relative mass fraction (%) 

0 638 49 

45 301 23 

90 63 5 

-45 301 23 

The testing specimens are tubes of 46 mm outer diameter, a length of 328 mm and a wall thickness of 

approximately 2.0 mm. Due to the wall thickness the fibre volume fraction is about 50 %. After having 

completed the RTM-process both ends of the tube specimens are strengthened by a GFRP-doubler of 

70 mm length and bonded steel inserts which prevent failure due to the fixing pressure of the testing 

machine. Such a configuration of wound tube specimens makes it possible to


(1) manufacture arbitrary lay-ups with the winding process, 

(2) investigate biaxial (tension/compression and torsion) or sequence loads with arbitrary load ratios, 

(3) prevent the so-called free edge effect, which occurs when using coupon specimens. 

The material lay-up promises high intra- and interlaminar stresses depending on the magnitude of the 

loading and the fraction of fibres in the different layers, which are not orientated in global load-direction. 

As a consequence fibre-resin-interface cracks will develop and a load transfer inside and between 

different layers will occur depending on the amount of damage in each layer. Furthermore, these matrix 

cracks lead to a decrease of the material stiffness of the wound tube specimens and to the initiation of 

delaminations. Concerning the active fatigue damage mechanisms, the current work presents the 

differences in the development of damages under different uniaxial and sequence loads. 

3. Experiments (uniaxial and sequence loading) 

The aim of the work is to consider the relation between the mechanical properties, the fatigue damage, 

the surface temperature and the final failure of mechanically loaded wound tube specimens. Thereby, 

different load cases are chosen in the current experiments. Two uniaxial loading directions (pure 

tension/compression and pure shear) and a combination of both load cases (sequence loads) are 

investigated. Sequence loading means the change from pure shear load to pure tension/compression load 

after several life cycles. These changes of loads are conducted sequently after 1000 (the first interval 

length) or 2500 (the second interval length) loading cycles for different specimens. Independent of the 

sequence interval length the tube specimens are firstly loaded with torsion moments in the current work. 

Other interval lengths and changes of the initial load cases will be conducted in further works. 

Furthermore, a change from sequence loads with pure tension/compression and pure shear loads to 

sequence loads with arbitrary biaxial load ratios are conceivable. 

The experimental tests are similar to a recent research [12] and are performed on a servohydraulic 

tension-torsion machine, which provides tensional (up to ±250 kN) as well as torsional (up to 

±2200 Nm) loads. All fatigue tests discussed in this paper are conducted in a force-controlled manner 

with R = -1 and a frequency of 3 Hz. Different uniaxial/biaxial and sequence load ratios are enabled by 

using different ratios of tension/compression forces and torsional moments. 

A constant ambient temperature of 20 o C is assured by means of a cooling chamber installed between 

the grips of the testing machine. A small opening at the front side of the cooling chamber enables the 

application of different non-destructive tests during all uniaxially and sequentially loaded fatigue tests. 

So, a thermographic camera is used for investigation of the thermal development of the specimen 

surface and a high speed camera is applied for examining the failure progress. Furthermore, aluminium 

reflectors are installed to observe the rear side of the tube specimen. Applying these reflectors the 

thermal infrared emission as well as the optical reflection of the rear side of the tube specimens is 

visible. 

In order to calculate the material stiffness and to observe the fatigue behaviour, all fatigue tests are 

divided into three main parts (see figure 2): 

11

12 


Fig. 2. Protocol of fatigue loading. 

(1) Characterization step: In this step, quasi-static tests are performed with force-controlled ramps 

(discrete pure tension/compression force and positive/negative torsion moments). These 

characterization loads are chosen in a way that no further damage occurs and they are considerably 

smaller than the applied cyclic loads in the fatigue damage steps. Nevertheless, all quasi-static 

loads are adequate for calculating the Young‟s (tangent modulus of elasticity) and shear modulus. 

(2) Fatigue damage step: After each characterization step, the fatigue damage step with cyclic loads 

(sinus wave form) of constant amplitudes follows. Here, the different uniaxial and sequence fatigue 

loads are performed. These steps introduce the fatigue damages like matrix cracking, delamination 

and fibre failure. For recording the surface temperature of the tube specimen during the fatigue 

damage steps, the thermographic camera (CEDIP Titanium) is applied. Furthermore, a photo 

camera (CASIO Exilim Pro EX-F1) with integrated ring buffer and high-speed-mode is used for 

observing the qualitative development of matrix cracks and for an optical fracture analysis 

(recording the location and type of final failure). Consequently, an analysis of the location of high 

surface temperatures (so-called hot-spots) and the location of the fracture is conducted. 

(3) Discrete damage monitoring: Matrix cracking indicated by the crack density is the first occurring 

type of fatigue damage and can be monitored with a light microscope (ZEISS Stemi 2000-C). 

Based on the nearly similar refraction index of resin and glass fibre used for the tube specimens, 

the specimen is transparent and matrix cracks are observable via transmitted light method. 

Therefore, the fatigue test is stopped after several fatigue damage steps and the specimen is taken 

out of the testing machine. Subsequently, photos of several areas (up to 15) of the specimen are 

taken and matrix cracks are counted using the photographically documented cracking states. 

Differentiating the cracks by their orientation angle leads to the numbers of cracks in each single 

layer direction (0 o , 45 o , 90 o and -45 o -direction). Additionally, referencing of these crack numbers to 

the fixed monitoring areas is conducted in order to calculate the specific crack densities, which are 

average values of all observed areas. Beside the matrix crack monitoring close-up digital photos of 

occurred damages such as delaminations are taken. 

Concerning the different parts of the fatigue tests, the heating and cooling of the tube specimens


repeats continuously during the fatigue damage steps and the characterization steps in the uniaxially and 

sequentially loaded fatigue life tests. Due to the external mechanical loads, the experiments reveal a 

uniform heating of the tube specimens during each fatigue damage step. Due to the cooling to a constant 

temperature of 20 o C during each characterization step the same initial state of the surface temperature of 

the tube specimens is ensured at the beginning of each fatigue damage step. Then, the maximum surface 

temperatures increase up to 30 o C (except for the occurring hot spot) during the fatigue damage steps, 

although the ambient temperature remains at 20 o C. Another advantage of controlling the surface 

temperatures is the prevention of potential thermal damage of the matrix during all fatigue life tests. 

Fig. 3. typical surface distribution with evaluation areas (left) and development of surface temperature during the fatigue life (right). 

In order to compare the surface temperatures of each tube specimen under different load cases, the 

surface temperature development during 100 sinus cycles of each fatigue damage step is analysed. For 

this purpose, the average and maximum temperatures of two different areas are determined in several 

thermographic pictures. On the left hand side of figure 3 a typical surface temperature distribution at the 

end of the fatigue life (occurred hot-spot) with the measurement areas is shown. The picture illustrates 

the increase of the surface temperature, which is the subtraction of the initial one from the measured 

temperature (T-T0). Firstly, the average temperature is used to represent the main surface temperature 

and secondly, the maximum temperature is required for detecting the highest temperature along the tube 

specimens (at the end of the fatigue life for detecting the hot spot temperature). Moreover, a diagram 

with the calculated temperature T-T0 of selected fatigue damage steps versus the normalized lifespan is 

plotted on the right hand side of figure 3. Higher values of T-T0 imply a faster and higher heating of the 

specimens during the analyzed 100 sinus cycles of the selected fatigue damage steps. Investigating 

different load cases reveals differences in the surface temperature development and in the development 

of high-temperature areas (hot-spots), which is presented in section 4. The comparison of thermographic 

pictures of different specimens at the same time of several fatigue damage steps (after exact 100 sinus 

13

14 


cycles of each fatigue damage step) is enabled by using a digital output of the testing machine, which 

always triggers the thermography camera. 

4. Experimental results 

Firstly, a differentiation between uniaxially loaded and sequentially loaded tube specimens is 

conducted showing the basic damage mechanisms and fatigue behaviour under uniaxial loadings 

separately. Afterwards the interaction of the different fatigue behaviours under sequence loadings 

(combination of pure shear loads and pure tension/compression loads) is presented. 

4.1 uniaxial pure shear loads 

As mentioned above, the crack densities, the Young‟s modulus, the shear modulus and the 

development of the surface temperatures are measured throughout cyclic loading. The following 

investigations are shown by reference to an exemplary tube specimen under pure shear loads. However, 

the results are generally observed for all tested specimens. In figure 4 the crack densities and the 

stiffness degradation (Young‟s modulus E/E0 and shear modulus G/G0) are shown. The results are 

plotted versus the normalized lifespan of the specimen. A quite usual increase of the layer-specific crack 

densities within the first 10-15 % of the fatigue life is followed by saturation of the crack densities. 

During the first part of the fatigue life the stiffnesses show the typical behaviour of a high degradation 

caused by matrix cracking. The magnitude of stiffness degradations depends on the highest values of 

respective crack densities. After crack density saturation the specimen exhibits only a minor further 

decline of the stiffnesses till failure. However, differences in the decrease of Young‟s and shear modulus 

are monitored. The specimen shows a significantly steeper decrease in the shear modulus caused by the 

crack densities of the 0 o -layers (high relative mass fraction of 49 % leads to high influence on the shear 

modulus degradation). This interaction of the reached crack density of the 0 o -layers and the degradation 

of the shear modulus is also visible comparing the results of the pure shear loaded and pure 

tension/compression loaded specimens mentioned below. 

Fig. 4. crack densities (left) and moduli + temperature development (right) under pure shear loads. 

Additionally, the development of average and maximum surface temperatures T-T0 (analyzed after 

exactly 100 sinus waves of selected fatigue damage steps) are illustrated in the diagram on the right 

hand side of figure 4. The results show a decrease of the occurring temperatures within the first 10-15 %


of the fatigue life, which is very similar to the stiffness degradation. Consequently, a higher and faster 

surface temperature development is measured within the first 10-15 % of the fatigue life or more 

precisely during the increase of matrix cracking. Hence, the initiation of matrix cracks dissipates more 

energy and leads to higher surface temperatures. Following these temperature decreases an almost 

uniform development of the surface temperature is measured. During that part the development of 

delaminations begins. The distribution of delaminations along tube specimens appears randomly and 

leads to local damages increasing local temperatures. This temperature increase caused by 

delaminations at the end of the fatigue life is also plotted in figure 4 (right). The maximum surface 

temperatures at the location of delaminations can reach twice the values for T-T0 as the average 

temperatures. On the left hand side of figure 5 the infrared image with the surface temperatures shortly 

before final failure is shown. Only one separated spot of higher thermal activity (hot spot) caused by 

cyclic loading develops after approximately 90 % of the fatigue life (at the left upper front side of the 

specimen, whereas the average temperature is similar to the rest of the specimen). This location is equal 

to the initiation of final failure (figure 5 right). 

Fig. 5. infrared image with local hot-spot shortly before final failure (left) and high speed image at failure initiation (right) under pure shear loads. 

4.2 uniaxial pure tension/compression loads 

Analogous to figure 4 the crack densities (left), the stiffness degradations (Young‟s modulus E/E0 and 

shear modulus G/G0) and the surface temperature development (right) of one exemplarily pure 

tension/compression loaded tube specimen are shown in figure 6. The development of the crack 

densities and the stiffness behaviour is very similar to the pure shear loaded specimens. Within the first 

10-15 % of the lifespan, matrix cracks develop in the different layers and lead to high degradation of 

stiffness. Compared to the pure shear loaded specimens two differences are observed. Firstly, the shear 

15

16 


modulus shows a lesser decrease under pure tension/compression loads caused by the very low crack 

density of the 0 o -layers and secondly, a rapid decrease in Young‟s modulus starting at 75 % of lifespan 

caused by fibre breaking in the extensively delaminated 0 o -layers is observed. These delaminated layers 

also lead to different final failure as mentioned below. The crack density of the 0 o -layers reaches lower 

values under pure tension/compression loads than under pure shear loads, which results from the 

different intralaminar stresses of these layers. External pure tension/compression loads lead to fibre 

parallel stresses explaining the lower values of crack density. In contrast to this load case the 0 o -layers 

obtain higher transverse tension stress leading to a higher crack density of the 0 o -layer under pure shear 

loads. 

Fig. 6. crack densities (left) and moduli + temperature development (right) under pure tension/compression loads. 

Fig. 7. infrared image with local hot-spot shortly before final failure (left) and high speed image at failure initiation (right) under pure 

tension/compression loads. 

Looking at the temperature developments throughout tension/compression cyclic loading similar 

decreases are measured within the first 10-15 %, whereas the maximum temperatures increase at an 

earlier stage of fatigue life (at 50 % of lifespan). At this point of fatigue life delaminations initiate along


the 0 o -layers, which leads to small hot spots at the tips of the delaminations influencing the measured 

maximum temperatures. Due to the huge number of delaminations the infrared image shows many areas 

with higher thermal activity caused by cyclic loading (see figure 7, left) shortly before final failure. The 

location of final failure is located in this region of higher temperatures (figure 7, right). 

4.3 sequence loading 

The interaction of damage mechanisms and the fatigue behaviour under sequence loading (sequently 

change of pure shear load and pure tension/compression load) is investigated. Thereby, two different 

interval lengths (1000 cycles and 2500 cycles) are distinguished. The constant load amplitudes are 

selected from the experiments described above. Consequently, the following results show the changes in 

fatigue behaviour under sequence load directions and further tests will reveal the influence of different 

load amplitudes combined with varying load directions. 

Fig. 8. crack densities of two specimens under sequence loading with interval length 2500 cycles (left) and interval length 1000 cycles (right) 

(limitation max. 10000 cycles). 

Fig. 9. Moduli and temperature development of two specimens under sequence loading with interval length 2500 cycles (left) and interval length 

1000 cycles (right). 

The monitoring of matrix cracking reveals the step-like increase of the layer-specific crack densities 

at the beginning of fatigue life. For a better visualisation of this effect the crack densities versus the load 

cycles are shown in figure 8 with a limitation of maximum 10000 cycles. The crack densities increase 

under pure shear loads and partly reach saturation, before the first change of load direction is conducted. 

In the following pure tension/compression loads several crack densities show a new steeper increase (in 

particular the crack densities of the 45 o -layers). Thus, the crack densities of the 45 o -layers reach the 

17

18 


maximum crack density measured for specimens under pure tension/compression loads. This steeper 

increase is not measured for the crack densities of 0 o - and 90 o -layers, because these layers reach higher 

maximum crack densities under pure shear loads than under pure tension/compression loads. 

Consequently, these crack densities show saturation and no further development of matrix cracks in the 

first pure tension/compression load interval. These results reveal the influence of sequence loadings on 

the damage evolution. The correlation to the stiffness behaviour and surface development is illustrated 

in figure 9. The stiffness behaviour under sequence loads is very similar to the behaviour under pure 

tension/compression or pure shear loads. Within the first 10-15 % of lifespan the Young‟s and shear 

modulus rapidly decrease followed by a slow, almost linear decline. During these phases of the fatigue 

life the average and maximum surface temperatures show a step-like behaviour which is explained in 

detailed below. 

After approximately 90 % of the lifespan, a further steeper decrease of the Young‟s modulus is 

measured ending in the final failure, which is equal to the results of the specimens under pure 

tension/compression loads. The reason for this behaviour is the initiation and increase of huge 

delamination areas and occurring fibre breaking in the 0 o -layers within the tension/compression load 

intervals of the sequence loading. Conducting a change from pure tension/compression loads to pure 

shear loads leads to an interruption of the stiffness decrease (see figure 9, right, at the end of fatigue life). 

Due to this load direction change the size of delaminations remains unchanged and no further increase 

of delaminated areas or fibre cracking is observed under pure shear loads. The influence of the load 

direction on the damage increase is also revealed by the thermographic changes under sequence 

loadings. On the left hand side of figure 10 the occurring hot spots (correlated with delaminations) and 

fibre breaking under pure tension/compression loads is illustrated. The infrared image of the directly 

following pure shear load interval (middle of the figure 10) shows a uniform heating of the specimen 

without any hot spots, whereas the 0 o -layers are extensively delaminated (see digital picture on the right 

hand side of figure 10). Subsequently, the final failure occurs under pure tension/compression load. 

The differences in surface temperature development under sequence loading are also shown in figure 

11. Besides the sequentially loaded specimens the surface temperature development T-T0 of two other 

specimens loaded under pure shear or pure tension/compression are plotted. Firstly, the surface 

temperature developments of specimens under pure shear loads and pure tension/compressions loads are 

different. During the pure tension/compression loads the average and maximum surface temperatures 

reach lower values of T-T0 than under pure shear. This trend is also observed for sequentially loaded 

specimens. The temperatures show a step-like behaviour and change using different uniaxial load cases. 

This effect is independent of the interval length and the sequence of loads (see figure 11). Starting at 

60-70 % of lifespan the surface temperatures increase individually due to the occurrence of hot-spots 

during the pure tension/compression loads. As already stated, the final failure is only caused by the 

initiation and development of delaminations in the pure tension/compression load intervals.


Fig. 10. thermographic changes under sequence loading during pure tension/compression load interval (left), the direct following pure shear load 

interval (middle) and digital picture at the beginning of showed pure shear load interval (right). 

Fig. 11. surface temperature development of two specimens under sequence loading with interval length 2500 cycles (left) and interval length 

1000 cycles (right). 

5. Conclusion 

The experimental procedures and results of uniaxially and sequentially fatigue loaded tube specimens 

are presented. Due to the application of non-destructive test methods such as crack monitoring and 

thermography the fatigue behaviour is related to the damage mechanisms (development of matrix cracks 

and initiation of delaminations). During the last few percentages of the lifespan hot-spots caused by 

cyclic loading develop and the location of the later final failure is detected in early stage of fatigue life. 

A correlation of the located hot-spots and the final failure is proved by means of a high-speed camera. 

The two uniaxial load cases (pure tension/compression and pure shear load) lead to different damage 

mechanisms and surface temperature developments, which are applicable to sequentially loaded 

specimens. In ongoing work, it is attempted to investigate sequentially loaded specimens with different 

biaxial load cases and load amplitudes. 

19

20 

Acknowledgements 


The authors gratefully acknowledge the support by the German Science Foundation (DFG) within the 

project PAK267 (Effects of Defects). 

References 

[1] Schulte K. Baron C., Neubert N.: Damage development in carbon fibre epoxy laminates: cyclic loading, Composites, 1985, pp. 281-285 

[2] Talreja R.: Damage and fatigue in composites – a personal account, Composites Science and Technology 68, 2008, pp. 2585-2591 

[3] Nairn J.A., Hu S.: The initiation and growth of delaminations induced by matrix microcracks in laminated composites, International 

Journal of Fracture 57, 1992, pp. 1-24 

[4] Quaresimin M., Susmel L., Talreja R.: Fatigue behaviour and life assessment of composite laminates under multiaxial loadings, 

International Journal of Fatigue 32, pp. 2-16, 2010 

[5] Adden S., Horst P.: Stiffness degradation under fatigue in multiaxially loaded non-crimped-fabrics, International Journal of Fatigue 32, 

2010, pp. 108-122 

[6] Schmidt F., Adden S., Möhle E., Horst P.: Description and modelling of the multi-axial stiffness degradation in fatigue loaded NCFs under 

sequence loading, 13th European Conference on Composites, ECCM-13, Stockholm, 2008 

[7] Schmidt F., Adam T. J., Horst P.: Fatigue modelling of a nominally defect-free GFRP composite under multi-axial loading, submitted to 

Composites Science and Technology, 2010 

[8] Paepegem W., Degrieck J.: Effects of load sequence and block loading on the fatigue response of fiber-reinforced composites, Mechanics 

of Advanced Materials and Structures 9, 2002, pp. 19-35 

[9] Adden S., Pfleiderer K., Solodov I., Horst P., Busse G.: Characterization of stiffness degradation caused by fatigue damage using 

circumferential plate acoustic waves, Composite Science and Technology 68, 2008, pp. 1616-1623 

[10] Rheinfurth M., Schmidt F., Solodov I., Busse G., Horst P.: Air-coupled Lamb waves combined with thermography for monitoring fatigue 

in biaxially loaded composite tubes, submitted to Composites Science and Technology, 2010 

[11] Gagel A., Lange D., Schulte K.: On the relation between crack-densities, stiffness degradation and surface temperature distribution of 

tensile fatigue loaded glass-fibre non-crimp-fabric reinforced epoxy, Composites Part A 37, 2006, pp. 222-228 

[12] Schmidt, F., Geier M., Horst P.: Characterization of the fatigue behaviour of nominally defect-free wound tube specimens under biaxial 

loading, submitted to Composites: Part A, 2010

Abstract 

An effective method for P-S-N curve fitting of composite 

laminates 

D Guan *, Q Sun 

School of Aeronautic, Northwestern Polytechnical University, Xi’an 710072, China 

A method for P-S-N curve fitting of composite laminates is presented, which is based on the heteroscedastic regression 

analysis theory. The results of two groups of carbon fiber laminates fatigue test show that P-S-N curve with high 

confidence and high reliability can be obtained by this method. The presented method consider all the test data of an S-N 

curve in different stress levels as a whole, not only make use of test data more fully, but also has higher precision than 

traditional methods. 

Keywords: P-S-N curve; Regression analysis; Fatigue test; Confidence; Reliability 


P-S-N curve has important significance in structural fatigue properties description and fatigue life 

estimation. Commonly used methods for measuring P-S-N curve in engineering is single-specimen test 

method and group test method, the former belongs to the field of homoscedastic regression analysis, 

without considering the changes in variance of log fatigue life under different stress levels, On the 

contrary, the latter consider the changes in variance, but the effect of the number of specimen on its 

precision is great. 

The dispersivity of fatigue test data of composite is so large that the single-specimen test method is 

not applicable, and the group test method needs a large number of specimens to ensure its precision. 

Reference [1] proposes a method of linear variance regression analysis. A small sample test method for 

S-N and P-S-N curves is established in reference [2], which can obtain S-N and P-S-N curves of metal 

materials by scattered test. A method for P-S-N curve fitting of composite based on the heteroscedastic 

regression analysis theory is presented in this paper, and two groups of carbon fiber laminates P-S-N 

curve test has been performed to validate the efficiency of this method. 

2. Heteroscedastic regression analysis theory 

The S-N curve of materials can be described by power function formula 

* Corresponding author. Tel / Fax: +86-29-88492850 

E-mail addresses: guanfei@mail.nwpu.edu.cn 

 

S N = C 

(1)

22 


Where, N is fatigue life, S is stress, and C is undetermined constants. Using log function on both 

sides of Eq. (1) 

When 

Eq. (2) can be written 

lg N = lgC - lg S 

(2) 

y = lg N, x = lg S, a = lg C, b = - 

(3) 

y = a + bx 

(4) 

Eq. (4) shows that there exists linear log relationship between the structural fatigue life and the stress. 

A larger number of fatigue test data suggest that lgN obey normal distribution and the standard 

deviation of it will linear increase with the stress decrease if the S-N or P-S-N curves are linear in log 

coordinate. The relationship between and the stress is expressed as 

Where, 0, , x0are 

undetermined parameters [1]. 

( x) = [1 + ( 

x - x )] 

(5) 

0 0 

Independence fatigue test of single specimen was performed for ni times in the same stress S i and 

the fatigue life is denoted by Nij ( i = 1,2, , m; j = 1,2, , ni 

), transform Nij to a set of data 

[ x , y ]( i = 1,2, , m; j = 1,2, , n ) by using Eq.(3), then the formula of P-S-N curve with high 

i ij i 

confidence and high reliability can be obtained by method of heteroscedastic regression analysis [2]. 

And 

yp = ap + bp x 

(6) 

u ˆ c0 0 ( c2x + 2 c3) 

a ˆ ˆ p = a + c00(1 -x0) u p - 

2 c x + c x + c 

2 

1 2 3 

ˆ 

ˆ 

u c0 0 (2 c1x + c2 

) 

b ˆ 

p = b + c0 0 u p - 

2 c x + c x + c 

0 

n i= 

1 

2 

1 2 3 

(7) 

(8) 

1 m 

x = n x 

(9) 

x = 

i i 

nx 

( ) 

m 

i i 

2 

i= 1 I xi 

m ni 

2 

i= 1 I xi 

( ) 

0 

(10) 

I( x) = 1 + ( 

x - x ) 

(11) 

2 

-1 

m 

- u 

 

i 

- w 

i= 

1 

21 c0= 1 - , = n - 3 

(12) 

22 

2 2 2 

u p 1 u 

c1 

= + 1- w l 

 

xx w 

 

2 2 

2 (1 -x0) 

up 2x 

u 

c2 

= - 1- w l 

 

xx w 

 

(13) 

(14)

Where, ˆ, , ˆ0 

deviator [3]. 

D Guan, Q Sun / An effective method for P-S-N curve fitting of composite laminates 

2 2 2 

2 

(1 - x0) u m 

p u 

-2 

x 

 

c3 = + 1 niI( xi) 

+ 1- (15) 

w i= 1 l 

xx w 

 

l 

xx 

2 

n ( x - x) 

= (16) 

( ) 

m 

i i 

i= 1 

2 

I xi 

1 

w= 2+ u-0.64- 

 

+ u 

-0.64 

 

a bˆ are the estimated value of undetermined parameters, u , uare standard normal 

3. P-S-N curve test 

The grade of carbon fiber laminates is CYCOM 970/PWC T300, the ply orientations is 

[45/0/0/0/-45/90/45/0/0/-45]S and the single thickness is 0.155mm. All laminates were divided into two 

groups (named A and B) for P-S-N curve test, Table.1 shows the results of test. 

Table 1. Results of P-S-N curve test 

No. Stress ratio/R Frequency / HZ Smax / MPa Fatigue life /cycle 

A1 0.1 5 404 7270 23134 32204 15480 

A2 0.1 5 388 13875 

A3 0.1 5 357 18936 75687 12713 70427 15971 26340 

A4 0.1 5 334 106155 685025 940843 82132 322380 

A5 0.1 5 303 1102374 404326 1076982 997271 

B1 -1 5 605 1584 175 144 

B2 -1 5 557 2757 9942 1088 1431 5574 

B3 -1 5 478 41174 38049 25092 29197 41621 

B4 -1 5 414 126022 145341 234957 203935 215949 

B5 -1 5 366 420749 803786 798668 572645 811787 

Table 1 shows that the P-S-N curve with high precision can‟t be obtained from the data of group A by 

group test method unless complementary test [2,4], however, by the method of heteroscedastic 

regression analysis, all the test data of an S-N curve in different stress levels can be analyzed as an 

integration, so its information quantity is much bigger than group test method, which is equivalent to 

reduce the number of specimens test needed. 

The formula of P-S-N curve with 95% confidence and 95% reliability can be obtained by Eq. (6~17). 

Group A 

Or 

Group B 

p 

23 

(17) 

yp, A = 45.9851- 16.5397xA 

(18) 

N 10 S - 

= (19) 

45.9851 16.5397 

p, A A 

yp, B = 46.0492 - 15.8161xB 

(20)

24 

Or 


N 10 S - 

= (21) 

46.0492 15.8161 

p, B B 

N95/95 is the structural safe life with 95% confidence and 95% reliability in different stress levels and 

it can be calculated by Eq. (18~21) or obtained from P-S-N curve which was measured by traditional 

group test method, in addition, the test value of N95/95 can be obtained from fatigue test data by 

probability-based method [4] as log fatigue life lgN obey normal distribution. Table.2 shows the value 

of N95/95,B given in different ways. 

Group Smax / MPa 

B 

Table 2. N95/95,B given in different ways 

Heteroscedastic 

regression analysis 

N95/95,B 

Group test 

method 

Test value 

(the control group) 

605 112 0 / 

557 417 6 61 

478 4689 571 13251 

414 45547 41081 57767 

366 319835 1605342 193566 

Selected the test value of N95/95,B as reference value, results of table 2 suggest that compared with 

traditional group test method the P-S-N curve given by the method of heteroscedastic regression 

analysis has higher precision. 


1)By the method of heteroscedastic regression analysis, all the test data of an S-N curve in different 

stress levels can be analyzed as an integration, the use of test data is more fully than traditional methods. 

2)Fitting the group test data by the presented method can obtain the P-S-N curve with high precision. 

3)To the fatigue test data with large dispersivity, P-S-N curve with high confidence and high 

reliability can be given by this method also. 

References 

[1] FU HuiMin. Linear variance regression analysis[J]. Acta Aeronautica et Astronautica Sinica, 1994, 15(3):295~302. 

[2] FU HuiMin, LIU ChenRui. Small sample test method for S-N and P-S-N curves[J]. Journal of Mechanical Strength, 2006, 28(4): 552~555. 

[3] GAO ZhenTong. Fatigue reliability[M]. Beijing: Beijing University of Aeronautics and Astronautic Press, 2000. 

[4] WU FuMin. Structural fatigue strength[M]. Xi‟an: Northwestern Polytechnical University Press, 1985.

Constant Fatigue Life Diagrams for a Woven CFRP Laminate 

at Room and High Temperatures 

Abstract 

M Kawai a, *, Y Matuda a , R Yoshimura a , 

H Hoshi b , Y Iwahori b 

a Department of Engineering Mechanics and Energy, University of Tsukuba, Tsukuba 305-8573, Japan 

b Japan Aerospace Exploration Agency, Mitaka 6-13-1, Japan 

The effect of temperature on the constant fatigue life (CFL) diagram for a woven fabric carbon/epoxy quasi-isotropic 

laminate has been examined. Constant amplitude fatigue tests are first performed at different stress ratios on coupon 

specimens at room temperature (RT), 100 and 150 o C, respectively. The experimental results show that the CFL diagram 

for the woven CFRP laminate, which is plotted in the plane of mean and alternating stresses, becomes asymmetric about 

the alternating stress axis, and the CFL envelope for a given constant value of life can be described using a curve over a 

range of fatigue cycles, regardless of test temperature. The CFL envelopes for all these test temperatures take their peaks 

approximately at the same stress ratio “critical stress ratio” that is given by the ratio of compressive strength to tensile 

one. Then, these experimental CFL diagrams are compared with the predictions using the anisomorphic CFL diagram 

approach that allows constructing the asymmetric and nonlinear CFL diagram for a given composite on the basis of the 

static strengths in tension and compression and the reference S-N relationship for the critical stress ratio. It is 

demonstrated that the anisomorphic CFL diagram approach can successfully be employed for predicting the CFL diagram 

and thus for predicting the S-N relationships for the woven CFRP laminate at any stress ratios regardless of test 

temperature. 

Keywords: CFRP; S-N curve; Stress Ratio; Constant Fatigue life (CFL) Diagram; Anisomorphic CFL Diagram; High Temperature; Critical Stress 

Ratio 


Accurate prediction of constant amplitude fatigue lives of composites for any stress ratios as well as 

for any amplitude levels is a vital prerequisite to a successful fatigue life analysis of composite 

structures. The fatigue load that should be withstood by the structural components made of composites 

is characterized by changes in the amplitude, mean, frequency and waveform of stress cycling during 

service. These mechanical factors characterizing fatigue load are well known to have significant 

influences on the fatigue lives of glass and carbon fiber-reinforced polymer matrix composites [1-3]. 

For evaluation of the effect of loading mode on the sensitivity to fatigue of composites, however, a large 

number of fatigue experiments for many different kinds of cyclic loading are needed. They consume 

considerable time and cost. From a practical point of view, therefore, it is required to develop a time - 

and cost-saving procedure for identifying the loading mode dependence of the fatigue strength of 


E-mail addresses: mkawai@kz.tsukuba.ac.jp

26 


composites with reasonable accuracy on the basis of a limited number of tests. Establishment of a 

theoretical method for predicting the S-N curves for composites under constant amplitude fatigue 

loading at any stress ratios is a definite contribution to this demand. 

To predicting the S-N curve for constant amplitude fatigue loading at a given stress ratio, there are 

two kinds of approaches developed so far: (1) the approach using a master S-N relationship; (2) the 

approach using a constant fatigue life (CFL) diagram, typically plotted in the plane of alternating and 

mean stresses. 

The master S-N curve approach has successfully been applied, for example, by Ellyin and El Kadi [4] 

and Kawai et al. [5-9] to prediction of the off-axis fatigue lives of unidirectional composites not only for 

different fiber orientations but also for different values of stress ratio. In the master S-N curve approach, 

a fatigue failure criterion for composites is formulated on the basis of a master S-N curve into which the 

S-N curves for different cyclic loading conditions collapse with the aid of an effective measure of 

fatigue strength. The master S-N curve approach thus relies on an effective fatigue strength measure that 

makes the effect of mechanical factors on the S-N curves for composites invisible. Ellyin and El Kadi [4] 

prescribed the master S-N curve using the elastic strain energy associated with fatigue loading. Kawai et 

al. [5-9] defined the master S-N curve by taking advantage of a non-dimensional effective stress based 

on the Tsai-Hill static failure criterion [10]. A different measure to define a fatigue master curve for 

composites has also been proposed and validated by Caprino and D‟Amore [11], Caprino and Giorleo 

[12], and D‟Amore et al. [13]. However, it is not straightforward in general to define an effective 

measure of fatigue strength by which the fatigue data for a given composite material at different stress 

ratios collapse into a single master S-N relationship. 

Incidentally, it is interesting to view a similar approach for conventional materials in a historical 

perspective. Different forms of equivalent stress amplitudes to identify a single controlling S-N 

relationship have been given, for example, by the Goodman equation [14], the Smith-Watson-Topper 

(SWT) parameter [15], and the Walker parameter [16]. These equivalent stress amplitudes yield the 

fatigue models based on the master S-N curve approach. The use of these equivalent stress amplitudes 

in fatigue modeling implicitly assumes that the master S-N curve is identified with the S-N curve for R 

= -1. In the case for composite materials, however, these effective stress amplitudes and the underlying 

assumption that the master S-N relationship always corresponds to a single stress ratio should be 

probed. 

In contrast to the master S-N curve approach, the CFL diagram approach allows easily 

accommodating itself to the mean stress sensitivity observed by experiment. Therefore, it is considered 

that the CFL diagram approach is a more practical method especially for the problems dealing with a 

non-Goodman type of fatigue behavior of composites. Harris et al. [17-21] examined the CFL diagrams 

for CFRP laminates for various stress ratios, and showed that the CFL envelopes for different values of 

life are asymmetric and nonlinear, and their peak positions are slightly offset to the right of the 

alternating stress axis. The experimental results obtained by Ramani and Williams [22] indicated that 

the maxima of the asymmetric CFL envelopes they observed are associated with a stress ratio which is 

not equal to R = –1 but almost equal to the ratio of compressive strength to tensile one. In fact, Boller

M Kawai, Y Matuda, etc. / Constant Fatigue Life Diagrams for a Woven CFRP Laminate at Room and High Temperatures 

[23, 24] had already reported all these features of the CFL diagrams for composites in the early days of 

composite fatigue exploration. These experimental observations suggest that the mean stress sensitivity 

in fatigue of composites often deviates from that predicted on the basis of the Goodman‟s assumption. 

A method for describing the full shape of the asymmetric and nonlinear CFL diagram for CFRP 

laminates has been developed by Harris et al. [17-21]. They found that the asymmetric and nonlinear 

CFL diagrams for the CFRP laminates can approximately be described using nested bell-shaped curves, 

and developed a formula for describing the bell-shape CFL diagram for composites. Kawai et al. [25, 26] 

also discussed the same issue and proposed an asymmetric and piecewise nonlinear CFL diagram for 

CFRP laminates; it was called an anisomorphic CFL diagram. The anisomorphic CFL diagram approach 

takes into account the gradual change in shape of CFL curves as well as the occurrence of peak of 

alternating stress amplitude at a non-zero mean stress, and it was shown to be valid for the 

fiber-dominated fatigue failure in quasi-isotropic [45/90/-45/0]2S and [0/60/-60]2S carbon/epoxy 

laminates and in a cross-ply [0/90]3S carbon/epoxy laminate [26]. The anisomorphic CFL diagram has a 

great advantage in efficient identification of the mean stress sensitivity in fatigue of composites over 

existing methods, and it can be built using only the static strengths in tension and compression and the 

reference S-N relationship fitted to the fatigue data obtained at a particular stress ratio which is equal to 

the ratio of compressive strength to tensile one; it is called the critical stress ratio. 

Recently, the anisomorphic CFL diagram approach was shown to be applicable to prediction of the 

matrix-dominated fatigue life of carbon/epoxy angle-ply laminates [27]. However, the validity of the 

anisomorphic CFL diagram approach to prediction of S-N curves for any stress ratios has been 

evaluated only for the fatigue failure in non-woven carbon/epoxy laminates at room temperature. In the 

fatigue design of composite structures, we often need to predict the fatigue lives of composites that are 

exposed to different temperatures. From a view to developing it to an engineering tool for fatigue 

analysis of composites, therefore, the anisomorphic CFL diagram approach should further be checked 

for applicability not only to different kinds of composites with different sensitivities to fatigue but also 

to a given composite at different temperatures. 

In the present study, the anisomorphic CFL diagram approach [24-27] is tested for applicability to 

prediction of fatigue life of a woven fabric carbon/epoxy quasi-isotropic laminate at different 

temperatures. First, constant amplitude fatigue tests at different stress ratios are performed at room and 

high temperatures; T = RT, 100 and 150 o C. By using the fatigue test results, the stress ratio sensitivity in 

fatigue and the effect of temperature on the shape of the CFL diagram for the woven fabric laminate are 

elucidated. Then, for each of the test temperatures, the anisomorphic CFL diagram is constructed using 

the static strengths in tension and compression and the reference S-N relationship for the critical stress 

ratio, and compared with the experimental CFL diagram. Finally, the S-N curves for different stress 

ratios are predicted using the anisomorphic CFL diagram and compared with S-N data to assess the 

theoretical method in regard to its applicability to S-N curve prediction. 

27

28 

2. Material and testing procedure 

2.1 Material and specimen 


The material used in this study was the plain weave roving fabric carbon/epoxy composite 

QFC133-6E01A manufactured by TORAY. The woven fabric composites were laid up by hand to 

fabricate the quasi-isotropic laminates with the 12-ply lay-up sequence of [(±45)/(0/90)]3S, and then 

they were cured in an autoclave at 350 o F (176.6 o C). The nominal thickness of as-received laminates was 

about 2.4 mm. 

Two kinds of coupon specimens with different nominal dimensions were utilized. For static tension 

tests and tension-tension (T-T) fatigue tests in which only tensile load is applied to specimens, the long 

specimens based on the testing standards JIS K7073 [28] and JIS K7083 [29] were employed; as shown 

in Fig. 1(a), the dimensions were gauge length LG = 100 mm and width W = 20 mm. For static 

compression tests and compression-compression (C-C) and tension-compression (T-C) fatigue tests, 

short specimens were used to reduce the risk of buckling of specimens due to compressive loading 

involved; as shown in Fig. 1(b), the dimensions were gauge length LG = 10 mm and width W = 10 mm. 

The nominal dimensions of the compressive specimens were determined on the basis of the testing 

standards JIS K7076 [30] and the report of Harberle and Matthews [31] that discussed compression test 

methods suitable for composite laminates. 

20 

10 

50 100 

50 

(a) Gauge length 100 mm 

45 10 45 

(b) Gauge length 10 mm 

Fig. 1. Specimen geometry (dimension in mm). 

For testing at room temperature (RT), rectangular-shaped aluminum alloy tabs were glued on both 

ends of specimens with epoxy adhesive (Araldite) in order to protect their gripped portions. The 

thickness of end-tabs was 1.0 mm for the tensile specimens and 2.0 mm for the compressive specimens. 

In the T-T fatigue tests at 100 o C and the T-T and T-C fatigue tests at 150 o C, however, untabbed 

specimens were finally employed, since slipping of end-tabs happened during fatigue tests and it could 

not be avoided. The test data for untabbed specimens were used for discussion of this study; since the 0 o 

layers of the laminate used in this study are protected by the ±45 o layers on the surface, a harmful effect


of directly gripping of the ends of specimens is not much significant. 

2.2 Testing procedure 

Constant amplitude fatigue tests were performed under load control at room temperature (RT) and at 

high temperatures (100 and 150 o C). Fatigue load was applied to specimens in a sinusoidal waveform 

with a constant frequency of 10 Hz; the fatigue loading condition is based on the testing standard JIS 

K7083 [29]. Most specimens were fatigue tested for up to 10 6 cycles, and the fatigue tests that lasted 

over this limit were terminated prior to fracture. In this study, fatigue tests were first performed for five 

kinds of stress ratios: R = 0.1, 0.5, 10, -1 and to elucidate the effect of stress ratio on fatigue life. 

A particular value of stress ratio , which is called the critical stress ratio [25-27], is defined as the 

ratio of compressive strength C (< 0) to tensile one T 

(> 0); i.e. = / . In order to identify 

the tensile and compressive strengths of the woven carbon/epoxy quasi-isotropic laminate, static tension 

and compression tests were performed at the test temperatures (RT, 100 and 150 o C) prior to fatigue 

testing. The static tests were carried out at a constant rate of 1.0%/min until the specimens fractured, 

following the testing standards JIS K7073 [28]. 

C T 

Static and fatigue tests were conducted in a servo hydraulic MTS-810 testing machine. For raising the 

temperature of a specimen, a heating chamber with a precise digital control capability was employed. 

Each specimen was clamped in the heating chamber by the high temperature hydraulic wedge grips 

fitted on the testing machine, and it was heated up to a prescribed test temperature in air without 

applying load and preconditioned in the test environment for 1 h prior to testing. Variation of specimen 

temperature in time from the prescribed value was less than 1.0 o C. Humidity in the heating chamber 

was not controlled. The longitudinal and lateral strains of each specimen were measured using strain 

gauges that were mounted back to back at its center. Measurement of the longitudinal strain of a 

specimen was complemented by a linear variable differential transformer (LVDT) on the testing 

machine and by a two-camera video extensometer (DVE-201, SHIMAZU). 

3. Experimental results and discussion 

The in-plane specimen coordinate system is denoted as (x, y). The x-axis is taken in the loading 

direction. 

3.1 Static tensile and compressive behavior 

The axial stress-strain relationships for the woven CFRP laminate that were obtained from tension 

tests at RT, 100 and 150 o C are shown in Fig. 2. Since only the displacement measurement using DVE 

was available in testing at 150 o C, Fig. 2 adopted nominal strain in common for all the test temperatures. 

The stress-strain relationships at RT and 100 o C are linear until ultimate fracture. In contrast, the 

stress-strain relationship at 150 o C has a knee point and thus its overall shape becomes nonlinear. The 

reproducibility of the yielding behavior at 150 o C has been confirmed. In Fig. 2, it is also seen that as 

temperature increases, the axial tensile modulus becomes smaller and the fracture strain tends to become 

29

30 

larger. 

Axial stress x , MPa 


1000 

800 

600 

400 

200 

Woven CFRP laminate 

[(±45)/(0/90)] 3s 

Experimental 

1.0%/min 

DVE 

0 

0 0.5 1 1.5 2 

Axial strain x , % 

RT 

Tension 

100¼C 

150¼C 

Fig. 2. Tensile stress-strain relationships at different temperatures. 

No significant difference was found between the ultimate tensile failure modes at RT and 100 o C. 

The tensile specimens tested at RT and 100 o C failed at a right angle to the loading direction, and they 

accompanied neither remarkable pull-out of fibers nor delamination. In contrast, the tensile specimens 

tested at 150 o C failed in a shear mode, and they accompanied local delamination that developed in the 

45 o direction or in the ±45 o directions to the loading direction. These observations suggest that the 

interlaminar and in-plane shear strengths of the woven CFRP laminate were significantly reduced by the 

exposure to the high temperature of 150 o C. It is thus considered that the stress level of the knee point 

observed in the stress-strain relationship at 150 o C corresponds to the onset of local deformation and 

failure due to the reduction in strength. 

Fig. 3 shows the compressive stress-strain relationships at RT, 100 and 150 o C. The axial compressive 

strains shown in this figure are based on the longitudinal displacement of actuator that was measured 

with LVDT on the testing machine. The reason is that the displacement measurement using DVE was 

not successful for the short specimens used in the compression tests. In Fig. 3, it is seen that the tangents 

of the compressive stress-strain relationships monotonically decrease with increasing strain, regardless 

of temperature, and thus they exhibit small but clear nonlinearity over the range of deformation until 

failure. In the compression test at 150 o C, the yielding behavior that appeared in the tension test at the 

same temperature was not observed. The compressive elastic modulus decreased with increasing test 

temperature, in line with the temperature dependence observed in the tension test results. However, the 

fracture strain in compression decreased with increasing test temperature in contrast to the increasing 

tendency in tension. The comparison of the results in Fig. 2 and Fig. 3 reveals that the reduction in 

compressive strength with increasing temperature is more significant than the reduction in tensile 

strength. No appreciable difference was observed between the fracture modes in compression at 

different temperatures. All the specimens failed in an out-of-plane shear mode under compression, 

regardless of test temperature.


Axial stress x , MPa 

-600 

-500 

-400 

-300 

-200 

-100 

0 

0 


[(±45)/(0/90)] 3s 

Experimental 

1.0%/min 

LVDT 

-1 

-2 

150¼C 

-3 

Axial strain x , % 

100¼C 

Compression 

-4 

RT 

Fig. 3. Compressive stress-strain relationships at different temperatures. 

3.2 Temperature dependence of tensile and compressive strengths 

The ultimate tensile and compressive strengths of the woven CFRP laminate are plotted in Fig. 4 as a 

function of test temperature. The tensile and compressive strengths at RT, 100 and 150 o C are listed in 

Table 1; they are the averages of two or three samples. 

Table 1. Tensile and compressive strengths of [(±45)/(0/90)]3s woven fabric carbon/epoxy laminate at different temperatures 

Temperature T (MPa) C 

(MPa) (= / ) 

RT 840.98 –464.69 –0.55 

100ºC 813.30 –371.43 –0.46 

150ºC 611.95 –215.75 –0.35 

Fig. 4 demonstrates that both the tensile and compressive strengths decrease with increasing 

temperature. The reduction in strength at high temperature is more significant in compression than in 

tension. The ratios of compressive strength to tensile one at RT, 100 o C and 150 o C were C / T = 0.55, 

0.46, and 0.35, respectively. The reduction in tensile strength in the range from RT to 100 o C is small, 

but it turns much larger than before as temperature exceeds 100 o C. By contrast, an appreciable 

decreasing tendency can be seen in compression over the whole range from RT to 150 o C. The gradual 

decrease in compressive strength with increasing temperature suggests that the compressive strength of 

the woven composite is more sensitive to temperature, and it was more significantly affected by the 

decrease in stiffness and strength of the matrix material due to exposure to high temperature. 

A change in the ratio of compressive strength to tensile one with temperature means that the critical 

stress ratio (i.e., = / ) changes with temperature accordingly. In the construction of the 

C T 

anisomorphic CFL diagram for the woven composite, which will be discussed later, the S-N relationship 

for the critical stress ratio is used. Therefore, the above observation of the change in strength with 

temperature suggests that the anisomorphic CFL diagram is affected by temperature. 

-5 

C T 

31

32 

3.3 Fatigue behavior 


Fig. 4. Temperature dependence of tensile and compressive strengths. 

The fatigue data for the stress ratios R = 0.1, 0.5, 10, -1.0, -0.553 (= ) that were obtained from 

constant amplitude fatigue tests at RT are shown Fig. 5, as plots of maximum fatigue stress level against 

the logarithm of number of reversals to failure log(2 N f ) . Note that while the values of max are 

plotted for T-T loading and T-C loading at R = , the absolute values of minimum fatigue stress min 

are plotted for C-C loading and T-C loading at R =- 1. 

The static tensile strength T and compressive 

strength C that were obtained at the same test temperature are plotted at 2N f = 1 as points of the 

ordinate in the S-N diagram, respectively. The dashed lines in the figure indicate the S-N curves fitted to 

the fatigue data. A nonlinear function of the same form as Eq. (8), which is presented later, was used to 

describe these S-N curves. The S-N curves fitted to the fatigue data help us not only to observe the 

similarity and difference in shape between the S-N relationships for different stress ratios, but also to 

evaluate the maximum fatigue stress levels for different constant values of life that are required to 

identify the experimental CFL diagram for the woven CFRP laminate; the construction of CFL diagram 

is discussed later. 

In Fig. 5, it is seen that the S-N relationships at RT greatly depend on stress ratio. The overall 

features in the sensitivity to mean stress are similar to those reported so far, e.g. [17-27]. The 

sensitivity to fatigue becomes highest under T-C loading at R = , suggesting that a larger value of 

alternating stress amplitude has a more degrading effect on the fatigue of the composite. It is also seen 

in Fig. 5 that the S-N data for the stress ratios in the range R 1 can approximately be described 

by means of the smooth dashed curves that are connected with the point indicating the tensile strength. 

By contrast, the S-N curves fitted to the fatigue data for T-C ( R = -1 ) and C-C ( R = 10 ) fatigue 

loading can smoothly be connected to the compressive strength. The specimens are apt to fail in a 

compressive mode under the completely reversed loading condition at R = -1.0 since = -0.55 - 

1


and thus the distance from the minimum fatigue stress to the compressive strength C- is less 

min 

than the distance from the maximum fatigue stress to the tensile strength T- . max 

(| |), MPa 

min 

max 

1000 

800 

600 

400 

200 

0 

10 0 

Woven CFRP laminate [(±45)/(0/90)] 3s 

UTS 

UCS 

Experimental 

RT 10 Hz 

○ R = 0.1 ▲ R = 0.5 

◆ = -0.55 

□ R = 10 ▼ R = -1 

10 1 

10 2 

10 3 

2N f 

10 4 

10 5 

Fig. 5. S-N relationships at room temperature. 

The fatigue data presented in Fig. 5 are normalized using the static strengths, in which the tensile 

strength is used for R = 0.1, 0.5, and -0.55 ( ) and the compressive strength for R = -1 and 10. The 

normalized S-N data, which are plotted in Fig. 6, demonstrate that stress ratio has a marked influence on 

the slope of S-N relationship. A largest gradient of S-N relationship is accompanied by fatigue loading 

at the critical stress ratio R = . This suggests that fatigue damage develops most rapidly under fatigue 

loading at the critical stress ratio. 

max / T (| min / C |) 

2 

1.5 

1 

0.5 

0 

10 0 


Experimental 

RT 10 Hz 

○ R = 0.1 ▲ R = 0.5 

◆ = -0.55 

□ R = 10 ▼ R = - 1 

10 1 

10 2 

10 3 

2N f 

10 4 

Fitted 

10 5 

Fitted 

10 6 

10 6 

Fig. 6. Normalized S-N relationships at room temperature. 

Obviously, the slope of the S-N relationship for T-T loading at R = 0.1 is steeper than that for C-C 

loading at R = 10. This feature indicates that the reduction in fatigue strength under C-C loading is less 

than that under T-T loading, and thus fatigue damage develops more slowly under C-C loading. These 

features of fatigue failure for the woven CFRP laminate are similar to those for non-woven CFRP 

10 7 

10 7 

33

34 


laminates [10-17]. The above observations, i.e. the different strengths in tension and compression and 

the different sensitivities to fatigue under T-T and C-C loading conditions, reveal that a CFL diagram 

which is given as a plot of alternating stress against mean stress becomes asymmetric about the 

alternating stress axis. 

The fatigue data obtained at 100 o C and 150 o C are shown Fig. 7 and Fig. 8, respectively. The effect of 

stress ratio on the S-N relationship at high temperature is similar to that observed at RT, except the case 

for R = 10 at 150 o C. A significant reduction in fatigue strength can be seen at 150 o C under fatigue 

loading at R = 10 in the range of life 

4 

N f 10 . The large reduction in fatigue strength under C-C 

loading at R = 10 is consistent with a significant decrease in compressive strength at 150 o C that was 

observed above. The large reduction in static and fatigue strengths in compression suggests a severe loss 

of load bearing capability of the woven CFRP laminate at 150 o C under compression, in contrast to a 

moderate capability left to sustain static and fatigue loads in tension at the same high temperature. 

These observations suggest that an allowable maximum temperature for the woven CFRP laminate 

should be determined on the basis of the temperature dependence of compressive fatigue strength, 

especially when it is applied in the design of composite structures that are required to sustain 

compressive fatigue load at elevated temperature. 

(| |), MPa 

max min 

1000 

800 

600 

400 

200 

0 

10 0 


UTS 

UCS 

Experimental 100¼C 10 Hz 

○ R = 0.1 ▲ R = 0.5 

◆ = -0.46 

□ R = 10 ▼ R = -1 

10 1 

3.4 Temperature dependence of S-N relationship 

10 2 

10 3 

2N f 

10 4 

Fig. 7. S-N relationships at 100 o C. 

The normalized S-N relationships for the woven CFRP laminate at RT, 100 and 150 o C are compared 

10 5 

Fitted 

in Fig. 9 and Fig. 10 for T-T loading at R = 0.1 and C-C loading at R = 10, respectively. 

Comparing the normalized S-N relationships at RT and 100 o C, we can see that the relative fatigue 

strength at 100 o C is smaller than that at RT, regardless of stress ratio. This suggests that the fatigue 

resistance at 100 o C is lower than that at RT, and thus the fatigue resistance of the composite is lowered 

by the increase in test temperature. In contrast, the relative fatigue strength at 150 o C for T-T loading at R 

= 0.1 tends to slightly exceed the relative fatigue strength level at 100 o C for the same stress ratio of R = 

0.1. 

10 6 

10 7


(| |), MPa 

max min 

max / T 

800 

600 

400 

200 

0 

1.5 

1 

0.5 

0 

10 0 

10 0 


UTS 

UCS 

Experimental 150⎫ C 10 Hz 

○ R =0.1 ▲ R =0.5 

◆ =-0.35 □ R =10 ▼ R =-1 

10 1 

10 2 

10 3 

2N f 

10 4 

Fig. 8. S-N relationships at 150 o C. 

10 5 


Experimental 

10 Hz R = 0.1 

○ RT 

● 100⎫C 

× 150⎫C 

10 1 

10 2 

10 3 

2N f 

10 4 

10 5 

Fitted 

Fitted 

Fig. 9. Comparison of the normalized S-N relationships at different temperatures (R = 0.1). 

max / C 

1.5 

1 

0.5 

0 

10 0 


Experimental 

10 Hz R = 10 

○ RT 

● 100⎫C 

◇ 150⎫ C with Tab 

× 150⎫ C without Tab 

10 1 

10 2 

10 3 

2N f 

10 4 

10 5 

10 6 

10 6 

Fitted 

Fig. 10. Comparison of the normalized S-N relationships at different temperatures (R = 10). 

10 6 

10 7 

10 7 

10 7 

35

36 


As seen in Fig. 10 for C-C loading at R = 10, on the other hand, the relative fatigue strength 

monotonically decreases with increasing temperature. Only a degrading effect of temperature on fatigue 

failure is involved by C-C loading at R = 10, in contrast to the difference in temperature dependence 

between the range from RT to 100 o C and the range from 100 to 150 o C for fatigue loading at R = 0.1. 

It is worth recalling the observation [32] that the relative fatigue strength of CFRP laminate with a 

ductile matrix becomes larger than that of CFRP laminate with a more brittle matrix. The above 

observations in the present study along with the earlier observation just recalled suggest that the 

increase in ductility and the decrease in strength for the matrix of a given composite with increasing 

temperature might have a qualitatively different influence on the fatigue failure of the composite under 

T-T and C-C loading. 

The experimental results obtained in this study suggest that the maximum temperature below which 

the relative fatigue strength of the composite monotonically decreases with increasing temperature 

should lie between 100 o C and 150 o C. It is also expected that the temperature below which the 

compressive strength does not rapidly reduce may be found in the range from 100 o C to 150 o C. 

The fatigue failure mode was similar to the observation in the previous study [17]. More significant 

pull-out of fibers, fracture into small pieces, and delamination were observed in the specimens that 

failed in fatigue, compared with those failed in static load. No clear difference was seen between the 

fatigue failure modes at RT and 100 o C. In the specimens fatigue failed at 150 o C, however, a little more 

significant fiber fracture into small pieces and a more extensive delamination were observed. 

4. Fatigue life prediction using anisomorphic CFL diagram 

A constant fatigue life (CFL) diagram, in which alternating stress a is plotted against mean stress 

m for different constant values of life, is a useful engineering tool for efficient fatigue analysis of a 

given material. The experimental results for the fatigue failure of non-woven CFRP laminates [17-21, 

26] reveal that (1) the shape of CFL envelope gradually changes from a straight line to a nonlinear curve 

as the constant value of fatigue life increases, and (2) the CFL diagram is often asymmetric about the 

alternating stress axis in the m a -plane. These experimental facts elucidate that a linear and 

symmetric CFL diagram, i.e. the Goodman diagram [14], which is based on the S-N relationship for R = 

-1 cannot always be applied with good accuracy to the fatigue life analysis of composites. In order to 

establish a theoretical CFL diagram that is suitable for composites, therefore, challenging studies have 

been attempted [17-21, 25-27]. 

The anisomorphic CFL diagram approach, which was recently proposed by Kawai and coworkers 

[25-27] with a view to developing an efficient engineering tool for preliminary fatigue life analysis of 

composites, enables us to take into account all these characteristics of the CFL diagrams for carbon fiber 

composites. This engineering method was shown to be valid not only for the fiber-dominated fatigue [26] 

but also for the matrix-dominated fatigue [27] in non-woven carbon/epoxy laminates. In this study, the 

anisomorphic CFL diagram approach is further tested for the fatigue failure of the woven CFRP 

laminate at different temperatures.


4.1 Anisomorphic CFL diagram 

The anisomorphic CFL diagram is the first to consider a family of piecewise nonlinear fatigue failure 

envelopes for different constant values of life in the -plane. m a The anisomorphic CFL envelope for a 

given constant value of life N f is composed of two smooth curves that are independently defined in 

the two segments of mean stress. It is assumed that these two domains of mean stress are associated 

with the T-T and C-C dominated fatigue failure of a given composite, respectively. The two smooth 

curves are smoothly connected with each other at a point 

the constant amplitude ratio 

a 1- 

 

= 

1+ 

 

m 

( ) ( ) 

( m , a ) 

on the radial straight line with 

Note that the critical stress ratio = / always takes a negative value, i.e. 0 . The 

coordinates 

and 

( ) 

a 

( ) 

m 

C T 

correspond to the peak point of the anisomorphic CFL envelope for a 

given value of life N f . They designate the alternating and mean stresses during constant amplitude 

fatigue loading at the critical stress ratio , and the values at a given value of life N f can be 

calculated as 

where 

37 

(22) 

( ) 1 ( ) 

a = ( 1- 

) max 

(23) 

2 

( ) 1 ( ) 

m = ( 1+ 

) max 

(24) 

2 

( ) 

max is the maximum fatigue stress associated with a constant value of life f 

fatigue loading at the critical stress ratio , and it conforms with the following relation: 

( ) ( ) ( ) 

max m a 

N under T-C 

= + 

(25) 

The nested equi-life envelopes of the anisomorphic CFL diagram depend on the value of life, and 

they are different in shape. Mathematically, the CFL envelopes are described by means of the following 

piecewise-defined function [25-27]: 

k 

( ) 

2 T 

 

- 

 

m 

 

- m 

( ) 

, 

( ) 

( ) m m 

T 

a - 

a T 

-m 

 

- = ( ) k 

( ) 

2 C 

 

 

a 

 

- 

m - 

m 

( ) 

, ( ) 

C mm C -m 

 

where T (> 0) and C (< 0) are the tensile and compressive strengths of a given composite, 

respectively. 

The scalar quantity in Eq. (5) is defined as 

T 

(26) 

( ) 

max = (27)

38 


It is important to note that is not a constant but a variable. In fact, is the fatigue strength ratio 

[9] for cyclic loading at the critical stress ratio , and it takes a value in the range [0, 1]. The fatigue 

strength ratio is described as a monotonic continuous function of N f ; i.e. 

2 Nf= f( ) 

(28) 

The function given by Eq. (7) defines the normalized S-N curve for fatigue loading at the critical 

stress ratio, which is obvious from the definition of given by Eq. (6). The normalized S-N curve 

defined by Eq. (7) is an essential prerequisite for constructing the anisomorphic CFL diagram, and thus 

it is called the (normalized) reference S-N curve for a given composite laminate. The reference S-N 

-1 

curve can be identified by fitting the function = f (2 N ) to the experimental normalized plot of 

max / T versus f 

 

f 

N for fatigue loading at the critical stress ratio R = . To this end, we can 

conveniently use a function of the following form: 

2N 

1 1 

= 

K 

1- 

( ) -( 

L) 

f n b 

 

where the angular brackets denote the singular function defined as x max0, x 

 

a 

= , ( L) 

(29) 

is a 

normalized fatigue limit, and it is determined, as in the other constants K , n , a and b , by fitting 

Eq. (8) to the reference fatigue data for the critical stress ratio. 

The exponents T k and k C in the formulas play a role to adjust the rate of change in the shape of 

CFL curves from a straight line to a parabola for the right and left CFL curves, respectively. This 

function of the anisomorphic CFL diagram, which was added in [27] allows us to describe the CFL 

envelopes that remain almost linear over a range of fatigue life. Incidentally, Eq. (5) can be reduced to 

the formulas that define the original anisomorphic CFL diagram if the adjusting function is made off by 

taking as k = k = 1. 

If k = k = 0 , then Eq. (5) predicts the inclined Goodman diagram [18]. 

T C 

T C 

4.2 Comparison with experimental CFL diagrams 

Applicability of the original form of the anisomorphic CFL diagram ( k = k = 1) 

is first discussed. 

T C 

The anisomorphic CFL diagram for the woven CFRP laminate at RT is shown in Fig. 11 by dashed lines, 

together with the experimental CFL data indicated by symbols. The material constants involved by the 

approximate function [i.e. Eq. (8)] that represents the reference fatigue data at the critical stress ratio 

were determined as listed in Table 2. The coordinates of the experimental CFL data in the -plane 

m a 

were calculated using the maximum fatigue stresses for the selected values of life f N = 101 , 10 2 , 10 3 , 

10 4 , 10 5 , and 10 6 ; those maximum fatigue stresses were evaluated using the approximate curves fitted to 

fatigue data that are shown in dashed line in Fig. 5. The solid line in Fig. 11 is obtained by connecting 

peak peak 

the maximum stress point ( , ) = ((1/ 2)(1 + ) , (1/ 2)(1 - ) ) on the radial line 

m a 

T T 

associated with the critical stress ratio and two points ( C, 

0) and ( T , 0) on the m -axis.


a , MPa 

1000 

500 

Experimental 

RT 10 Hz 

◆ N f =10 1 

△ N f =10 2 

■ N f =10 3 

◇ N f =10 4 

▲ N f =10 5 

□ N f =10 6 

R = 10 

R = -1 

= -0.55 

R = 0.1 

0 

-1000 -500 0 500 1000 

m , MPa 

Fig. 11. Anisomorphic CFL diagram at room temperature. 


[(±45)/(0/90)] 3s 

Predicted 

R = 0.5 

Table 2. Material constants involved by the approximate functions for the reference S-N curves at different temperatures 

Temperature 2 K n a b ( L) 

RT 7.0×10 -3 8 1.35 0.3 0.29 

100 o C 2.0×10 -2 7.8 1.5 0.4 0.25 

150 o C 0.1 1.5 1 4 0.265 

From Fig. 11, it is seen that the anisomorphic CFL diagram agrees well with the experimental CFL 

diagram in the tested range of fatigue life. Therefore, this observation proves that the anisomorphic 

CDL diagram approach can be applied to the woven CFRP laminate at RT as well as to the non-woven 

CFRP laminates at RT [25, 26]. The experimental results obtained from this study elucidate that the CFL 

diagram for the woven CFRP laminate at RT is asymmetric about the alternating stress axis, and the 

peaks of the CFL envelopes for different constant values of life appear under fatigue loading at a stress 

ratio close to the critical stress ratio =- 0.55 . These features in the woven CFRP laminate are similar 

to those for the non-woven CFRP laminates that were observed in the previous study [25, 26]. 

The S-N relationships predicted using the anisomorphic CFL diagram are compared with the 

experimental results. Figs. 12(a) and (b) show comparisons between the predicted and experimental S-N 

relationships for different stress ratios at room temperature; in these figures, predictions are indicated in 

solid lines. Except for slightly conservative predictions of fatigue lives for R = 0.5, the predicted S-N 

curves agree well with the observed S-N relationships. Note that the calculations for R = 0.1, 10, 0.5, 

and -1 give pure predictions using the anisomorphic CFL diagram, since the fatigue data for these stress 

ratios are not used for the construction of the anisomorphic CFL diagram. Therefore, we can evaluate 

the predictive accuracy of the anisomorphic CFL diagram approach by comparing the predictions with 

the fatigue data for these stress ratios. 

 

39

40 

max , MPa 

| min |, MPa 


1000 

800 

600 

400 

200 

0 

600 

500 

400 

300 

200 

100 

0 

10 0 

10 0 


Experimental 

RT 10 Hz 

○ R = 0.1 

▲ R = 0.5 

10 1 

10 2 

10 3 

2N f 

(a) R = 0.1, 0.5 

10 4 

Predicted 

10 5 


Experimental 

RT 10 Hz 

□ R = 10 

▼ R = -1 

10 1 

10 2 

10 3 

2N f 

(b) R = -1, 10 

10 4 

10 5 

10 6 

Predicted 

Fig. 12. Comparison between the predicted and experimental S-N relationships at room temperature. 

The anisomorphic CFL diagram for fatigue loading at 100 o C was also compared with the 

experimental results. From the comparisons, it was found that the asymmetric and nonlinear CFL 

diagram for the woven CFRP laminate at 100 o C can adequately be predicted by the anisomorphic CFL 

diagram approach. 

The test results reveal that as far as the range of temperature from RT to a certain temperature 

between 100 o C and 150 o C is concerned, the woven CFRP laminate tested in this study exhibits 

monotonic reduction in static and fatigue strength with temperature and no significant collapse in 

compressive fatigue strength. In that temperature range, the anisomorphic CFL diagram approach allows 

adequately predicting the CFL diagram for any temperature and S-N relationships for any stress ratios. 


The CFL diagrams for a woven fabric carbon/epoxy quasi-isotropic [(±45)/(0/90)]3S laminate at 

10 6 

10 7 

10 7


different temperatures, i.e. RT, 100 and 150 o C, were identified. For each test temperature, the CFL 

diagram was predicted using the anisomorphic CFL diagram approach, and the predicted CFL diagram 

was compared with the experimental CFL diagram. The S-N relationships for different stress ratios were 

also predicted using the anisomorphic CFL diagram approach and the accuracy of prediction was 

evaluated by comparing with the experimental S-N relationships. The results obtained can be 

summarized as follows: 

(1) The CFL diagram for the woven CFRP laminate at RT is nonlinear and asymmetric about the 

alternating stress axis. The CFL envelope gradually changes in shape from a straight line to a 

nonlinear curve as the constant value of life increases. The peaks of nested CFL envelopes 

correspond to fatigue loading at the critical stress ratio. The appearance of the peaks of CFL 

envelopes at the critical stress ratio indicates that fatigue deterioration in the woven CFRP laminate 

occurs most significantly under fatigue loading at the critical stress ratio. All these features are in 

line with those observed for non-woven CFRP laminates at RT [26]. 

(2) Similar features are exhibited by the CFL diagrams that were identified by fatigue testing at high 

temperatures: 100 o C and 150 o C. 

(3) The experimental CFL diagram shrinks as temperature increases since the tensile and compressive 

strengths decrease with increasing temperature. The CFL diagrams at different temperatures are 

thus nested. 

(4) The absolute value of the critical stress ratio decreases with increasing test temperature. This 

results in the CFL diagram inclining toward the right segment of positive mean stress. 

(5) The anisomorphic CFL diagram can successfully be employed to predict the experimental CFL 

diagrams for the woven CFRP laminate at the three test temperatures (RT, 100 and 150 o C), except 

the case for R = 10 at 150 o C. The S-N relationships predicted by the anisomorphic CFL diagram 

approach agree well with the experimental results for those cases accordingly. 

(6) The disagreement between the predicted and experimental results for R = 10 at 150 o C may be 

ascribed to a significant reduction in the compressive fatigue strength of the woven CFRP laminate. 

In contrast, the tensile fatigue strength is reduced moderately even at 150 o C, and thus no serious 

deterioration in the accuracy of prediction of life occurs for tension-dominated fatigue loading. 

(7) The relative fatigue strength of the woven CFRP laminate under T-T loading is reduced by 

increasing temperature from RT to 100 o C, regardless of the value of stress ratio. In contrast, the 

relative fatigue strength for T-T loading at R = 0.1 at 150 o C tends to slightly exceed the level for R 

= 0.1 at 100 o C. Therefore, the fatigue strength of the woven CFRP laminate exhibits the normal 

temperature dependence in the range from RT to a certain temperature between 100 o C and 150 o C. 

No significant collapse in compressive fatigue strength is likely to occur in the temperature range. 

Therefore, it is considered that the anisomorphic CFL diagram approach can be applied to the 

woven CFRP laminate for adequately predicting the CFL diagram and the S-N relationships for 

any stress ratios at any temperature in that range. 

41

42 

Acknowledgement 


This study was supported in part by the Ministry of Education, Culture, Sports, Science and 

Technology of Japan under a Grant-in-Aid for Scientific Research (No. 20360050). 

References 

[1] Hertzberg, R.W., Deformation and Fracture Mechanics of Engineering Materials, (1989), p. 467, Wiley. 

[2] Sendeckyj, G.P., Life prediction for resin-matrix composite materials, (Reifsnider, K.L., editor), Fatigue of Composite Materials, (1990), 

pp. 431-483, Elsevier Science Publishers. 

[3] Harris, B., Ed., Fatigue in Composites, (2003), Woodhead Publishing Limited, Cambridge UK. 

[4] Ellyin, F. and EL-Kadi, H., A fatigue failure criterion for fiber reinforced composite laminae, Composite Structures, 15, (1990), 61-74. 

[5] Kawai, M., Damage mechanics model for off-axis fatigue behavior of unidirectional carbon fiber-reinforced composites at room and high 

temperatures, in Massard, T. and Vautrin, A., Proc. of 12th Int. Conf. on Composite Materials (ICCM12), Paris, France, July 5-9, (1999), p. 

322. 

[6] Kawai, M., Yajima, S., Hachinohe, A. and Takano, Y., Off-axis fatigue behavior of unidirectional carbon fiber-reinforced composites at 

room and high temperatures, Journal of Composite Materials, 35(7), (2001), 545-576. 

[7] Kawai, M., Yajima, S., Hachinohe, A. and Kawase, Y., High-temperature off-axis fatigue behaviour of unidirectional carbon 

fiber-reinforced composites with different resin matrices, Composites Science and Technology, 61, (2001), 1285-1302. 

[8] Kawai, M. and Suda, H., Effects of non-negative mean stress on the off-axis fatigue behavior of unidirectional carbon/epoxy composites at 

room temperature, Journal of Composite Materials, 38 (10), (2004), 833-854. 

[9] Kawai, M., A phenomenological model for off-axis fatigue behavior of unidirectional polymer matrix composites under different stress 

ratios, Composites, Part A, Vol. 35, No. 7-8, (2004), 955-963. 

[10] Azzi, V.D. and Tsai, S.W., Anisotropic strength of composites, Experimental Mechanics, 5, (1965), 283-288. 

[11] Caprino, G. and D‟Amore, A. Flexural fatigue behaviour of random continuous-fibre-reinforced thermoplastic composites, Composites 

Science and Technology, Vol. 58, (1998), pp. 957-965. 

[12] Caprino, G. and Giorleo, G., Fatigue lifetime of glass fabric/epoxy composites, Composites Part A, Vol. 30, (1999), pp. 299-304. 

[13] D‟Amore, A., Caprino, G., Stupak, P., Zhou, J. and Nicolais, L., Effect of stress ratio on the flexural fatigue behaviour of continuous 

strand mat reinforced plastics, Science and Engineering of Composite Materials, Vol. 5, No. 1, (1996), pp. 1-8. 

[14] Goodman, J. Mechanics Applied to Engineering, 1899, Longman Green, Harlow, UK. 

[15] Smith, R.N., Watson, P., Topper, T.H., A stress strain function for the fatigue of metals, Journal of Materials, JMLSA, 1970, 5(4); 

767-778. 

[16] Walker, K., The effect of stress ratio during crack propagation for 2024-T3 and 7075-T6 aluminum, In: Effects of environment and 

complex load history on fatigue life. ASTM STP 462, 1970, pp.1-14. 

[17] Harris, B., Reiter, H., Adam, T., Dickson, R.F., Fernando, G., Fatigue behaviour of carbon fibre reinforced plastics, Composites, Vol. 21, 

No. 3, (1990), pp. 232-242. 

[18] Adam, T., Gathercole, N., Reiter, H., Harris, B., Fatigue life prediction for carbon fibre composites, Advanced Composites Letter, Vol. 1, 

(1992), pp. 23-26. 

[19] Gathercole, N., Reiter, H., Adam, T., Harris, B., Life prediction for fatigue of T800/5245 carbon-fibre composites: I. constant-amplitude 

loading, Fatigue, Vol. 16, (1994), pp. 523-532. 

[20] Harris, B., Gathercole, N., Lee, J.A., Reiter, H., Adam, T., Life-prediction for constant-stress fatigue in carbon-fibre composites, Phil. 

Trans. R. Soc. London, Vol. A355, (1997), pp. 1259-1294. 

[21] Beheshty, M.H., Harris, B., Adam, T., An empirical fatigue-life model for high-performance fibre composites with and without impact 

damage, Composites Part A, Vol. 30, (1999), pp. 971-987. 

[22] Ramani, S.V. and Williams, D.P., Notched and unnotched fatigue behavior of angle-ply graphite/epoxy composites, (Reifsnider, K.L. and 

Lauraitis, K.N., editors), Fatigue of Filamentary Composite Materials, ASTM STP 636, (1977), pp. 27-46. 

[23] Boller, K.H., Fatigue properties of fibrous glass-reinforced plastics laminates subjected to various conditions. Modern Plastics, Vol. 34, 

(1957), pp.163-186, 293. 

[24] Boller, K.H., Fatigue characteristics of RP laminates subjected to axial loading. Modern Plastics, Vol. 41, (1964), pp.145-150, 188. 

[25] Kawai, M., A method for identifying asymmetric dissimilar constant fatigue life diagrams of CFRP laminates, Proceedings of the Fifth 

Asian-Australasian Conference on Composite Materials (ACCM-5), Hong Kong, November 27-30, 2006. 

[26] Kawai, M. and Koizumi, K., Nonlinear constant fatigue life diagrams for carbon/epoxy laminates at room temperature, Composites Part A, 

Vol. 38, (2007), pp. 2342-53.


[27] Kawai, M. and Murata, T., A three-segment anisomorphic constant life diagram for the fatigue of symmetric angle-ply carbon/epoxy 

laminates at room temperature, Composites Part A, 2010. 

[28] JIS K7073, Testing method for tensile properties of carbon fiber-reinforced plastics, Japanese Industrial Standard, Japanese Standards 

Association, 1988. 

[29] JIS K7083, Testing method for constant-load amplitude tension-tension fatigue of carbon fibre reinforced plastics, Japanese Industrial 

Standard, Japanese Industrial Association, 1993. 

[30] JIS K7076, A compression examination method in a respect of CFRP, Japanese Industrial Standard, Japanese Industrial Association, 1991. 

[31] Haberle, J.G. and Matthews, F.L., An improved technique for compression testing of unidirectional fibre-reinforced plastics; development 

and results, Composites Part A, Vol. 25, No. 5, (1994), pp. 358-371. 

[32] Kawai, M., Morishita, M., Fuzi, K., Sakurai, T. and Kemmochi, K., Effects of matrix ductility and progressive damage on fatigue strengths 

of unnotched and notched carbon fiber plain woven roving fabric laminates, Composites Part A Vol. 27A, (1996), pp. 493-502. 

43

Abstract 

Effect of stress ratio on fatigue transverse cracking 

in a CFRP laminate 

K Ogi a, *, R Kitahara a , M Takahashi a , S Yashiro b 

a School of Science and Engineering, Ehime University, 3, Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan 

b Faculty of Engineering, Shizuoka University, 3-5-1, Johoku, Naka-ku, Hamamatsu 432-8561, Japan 

This paper presents the effect of stress ratio R on the transverse cracking behavior through theoretical consideration 

and experiment results. Firstly, the three subcritical crack growth (SCG) models were formulated in association with the 

Weibull's probabilistic failure concept for transverse cracking in a cross-ply laminate. The transverse crack density was 

expressed as a function of R , the maximum stress in the transverse ply and the number of cycles. Next, cyclic fatigue 

tests were performed for various R to analyze the applicability of the three models. Thirdly, the new crack growth law, 

that covers the whole range of R including R = 1, 

was proposed. Finally, constant fatigue life diagrams are simulated, 

based on the new Paris law. 

Keywords: Transverse cracking; Slow crack growth; CFRP 


Since carbon fiber reinforced plastic (CFRP) laminates have been employed in a variety of industrial 

fields as structural components, long-term structural reliability has become increasingly important. 

Transverse cracking is the first microscopic damage appeared in CFRP laminates during fatigue loading. 

This damage leads to reduction of modulus and residual strength of the laminates. Furthermore, 

delamination is initiated from the tips of transverse cracks for high-cycle fatigue loading. Therefore, it is 

important to quantitatively predict transverse cracking behavior under fatigue loading. 

A lot of work has been conducted on modeling of fatigue of composites. A review on modeling of 

fatigue in composites was reported by Kaminski [1]. In contrast, the models for transverse cracking 

behavior, under static loading as well as fatigue loading, are reviewed by Berthelot [2]. In order to 

predict the stable growth of transverse cracks under fatigue loading, a subcritical crack growth (SCG) 

model is employed. Ogin and coworkers [3, 4] proposed a fracture mechanics model for fatigue 

transverse crack propagation, based on the Paris law. In their model, the stress intensity factor for a 

transverse crack depends on the thickness and average applied stress of the transverse ply. In addition, 

they assumed that the crack propagation rate, as well as the stress intensity factor, is independent of 

crack length. The authors have recently developed probabilistic SCG models for predicting transverse 

crack evolution under static [5] and cyclic loading [6, 7] for cross-ply laminates with thick transverse 


E-mail addresses: kogi@eng.ehime-u.ac.jp

plies. 

K Ogi, R Kitahara, etc. / Effect of stress ratio on fatigue transverse cracking in a CFRP laminate 

The SCG models proposed for general materials to date are classified into two models. In the first 

model (Model I), the crack propagation rate d a/ dN 

is given by the Paris law using the stress intensity 

factor range I K . In the second model (Model II), the crack velocity d a/ dt 

is given by the power law 

using the stress intensity factor K I . Here, the effect of stress ratio R (the ratio of minimum stress 

min to maximum stress max ) on transverse cracking behavior under cyclic loading is considered. In 

Model I, d a/ dN 

decreases with increasing R while d a/ dt 

increases with an increase in R in 

Model II. As a result, the effect of the stress ratio on the crack propagation rate is quite different 

between the two models. 

For CFRP laminates, Hojo et al. [8, 9] proposed the third model (Model III). They demonstrated that 

Model I is dominant as the resin becomes tougher in the case of Mode I delamination of CFRP 

laminates. Then, they introduced the equivalent stress intensity factor range eq K as a controlling 

parameter for varying stress ratio R . Their model offers a solution to the effect of R on fatigue 

delamination, however, the effect of R on fatigue transverse cracking has not been clarified yet. 

In fact, the comparison among the above three models has been made by the authors [10]. Moreover, 

they proposed a modified Paris law that covers the whole range of R , by introducing the modified 

equivalent stress intensity factor range. They assumed that the crack propagation exponent n is a 

linear function of R . This assumption enables good agreement with experiment result. 

This paper presents the effect of R on the transverse cracking behavior through theoretical 

consideration and experimental results. Firstly, the above three SCG models were formulated in 

association with the Weibull's probabilistic failure concept for transverse cracking in a cross-ply 

laminate. The transverse crack density was expressed as a function of R , the maximum stress in the 

transverse ply 2,max and the number of cycles N . Next, cyclic fatigue tests were performed under 

various R to discuss the applicability of the three models. Thirdly, the new crack growth law (Model 

IV), that covers the whole range of R , was proposed. The SCG law in Model IV was obtained by 

adding the effect of R to Model II. Finally, constant fatigue life diagrams, based on Model IV. 

2. SCG-based transverse cracking model 

as 

In Model I, the crack propagation rate d a/ dN 

is given using the stress intensity factor range I K 

nI 

K I = AI 

 

IC 

da 

dN 

K 

where a denote the crack length, N the number of cycles, I A a material constant, I 

45 

(1) 

n a crack 

propagation exponent and K IC the mode I fracture toughness. In Model II, the crack velocity d a/ dt 

is given using the stress intensity factor K I as

46 

where II A and II 


= 

KI 

II 

IC 

nII 

 

 

da 

A 

dt 

K 

n denote a material constant and a crack propagation exponent, respectively. In 

Model III, the Paris law is expressed as 

nIII 

Keq 

= AIII 

 

IC 

da 

dN 

K 

where III A denotes a material constant and n III a crack propagation exponent. It is proven in the 

previous work [10] that the crack propagation exponent is identical among the three models. Thus, 

hereafter, the crack propagation exponent is simply denoted by n . In addition, we assumed that n is a 

linear function of R [10]. 

First, Model I is considered. The stress intensity factor range is given by 

( ) 

K = Y - a 

(4) 

I max min 

where Y represents a constant that depends on the geometry of the crack. Integrating Eq. (1) using Eq. 

(4), we have 

where 0 a and f 

n-2 n-2 

n 

- - n-2 Y 

2 2 

n n 

0 - f = I ( 1- 

) max f 

2 KIC 

a a A R N 

 

a are respectively referred to as the initial crack length and the crack length at the 

number of cycles to failure N f . These crack lengths are related to the fracture toughness and the static 

(or inert) strength S i . Then, we obtain 

with 

N 

n-2 

1 

S 

i 

f = 1 

2 - 

hI( R) max max 

 

n-2 Y 

hI R AI R 

2 K 

( ) = ( 1- 

) 

2 

IC 

Through the manipulation of equations similar to the above, the number of cycles to failure for 

Models I, II and III is expressed in a unified form as 

with 

Here, ( ) 

n-2 

1 

S 

i 

f 2 

hi( R) max max 

is the equivalent period defined as 

e R 

n 

( ) 

N = - 1 i = I, II, III 

 

n-2 Y 

hII R = AII e R 

2 KIC 

( ) ( ) 

n-2 Y 

hIII R AIII R 

2 K 

( ) = ( 1- 

) 

2 

IC 

2 

( 1- 

) n 

(2) 

(3) 

(5) 

(6) 

(7) 

(8) 

(9a) 

(9b)


( ) 

n n 

( t) 21+ 

R 1-R 

 

d sin d 

0 0 

(10) 

e R = t = + 

2 2 2 

max 

where is the period of cyclic stress. The equivalent period equals the period for R = 1 

The probabilistic expression of transverse crack density for each model is then given by [5-7] 

m 

m 

 

= 1- exp - Ve 1+ h 2,max N i = I, II, III 

S 

S 

 

2 n 2 2,max 

( i 

- ) ( ) 

where S represents the saturated transverse crack density, e V the volume of a unit element, 2,max 

the maximum stress in the transverse ply, and m and S the shape and scale parameters associated 

with the Weibull distribution of the transverse strength. The maximum stress in the transverse ply 

includes residual thermal stress [5-7, 10]. 

Equation (11) is rewritten as 

where ( I, II,III ) 

plotted against 

i 

 

y = = + h N 

1 

m 

S 1 S 1 

ln ln ln 1 

2,maxVeS- n-2 

 

2 ( 2,max ) 

h i= is replaced by h . After the experiment data on the left side of Eq. (12) are 

x= N for the various maximum stresses, the values of n and h are provided 

2 

2,max 

through curve fitting of these plots to the equation ( ) 

3. Experiment 

y = ln 1 + h x / ( n - 2) . 

The material used in the experiment was a [0 / 90 6 / 0 ] cross-ply laminate of carbon/epoxy 

(T700S/#2521R, Toray). Coupon specimens with end tabs were fabricated for cyclic fatigue tests. The 

specimens are 210 mm long, 0.76 mm thick, and 8.5mm wide. The dimensions of the specimen are 

presented in Table 1, where W denotes the width, and 2b 1 and 2b 2 the thicknesses of the 

longitudinal and transverse plies. The gage length for transverse crack density was 60 mm. Both edges 

of the specimens were polished for counting the number of transverse cracks within the gage length. 

First, the static tensile tests at low ( 

47 

(11) 

(12) 

4 

6 10 - 

mm/min) and standard (0.5 mm/min ) loading rates were 

conducted to determine the saturated crack density S , and the shape and scale parameters m and S . 

The cyclic fatigue tests were then performed at room temperature, at the stress ratio R of 0, 0.2, 0.4, 

0.6 and 1, and at the frequency of 10 Hz. Three or four specimens were tested for each value of R . The 

ratio of maximum applied stress 0 to static strength B , denoted by s 0 B 

( = / ) , was chosen to be 

0.60. The measured material properties are listed in Table 1. The residual thermal stress in the transverse 

ply 

[10]. 

T 

2 is computed based on the lamination theory. Other properties are presented in the literature

48 

4. Results and discussion 


Table 1. Material properties and geometrical parameters of the specimen [10]. 

W ( mm) 

8.5 

1 

( ) 

2b mm 

0.19 

2 

( ) 

2b mm 

0.57 

m 5.03 

S (MPa) 186.4 

B (MPa) 

562 

K IC ( MPa m ) 1.4 

I III IV (m) 

A A A = = 7 

5.85 10 - 

 

II (m/s) A 

4.1 Comparison among the models 

n 

R = 0.0 

19.1 

R = 0.2 

23.8 

R = 0.4 

28.4 

R = 0.6 

33.0 

R = 1.0 

5 

4.57 10 - 

 

42.3 

S (mm -1 ) 1.40 

V e (mm 3 ) 3.47 

T 

2 (MPa) 24.4 

Figure 1 presents the effect of stress ratio on transverse crack density in the fatigue tests. The average 

values are plotted in the figure for readability. It is clear that the transverse crack density becomes larger 

with decreasing stress ratio. This implies that transverse cracking behavior obeys the SCG law of Model 

I rather than Model II. However, Model I is inapplicable to the case of R = 1. 

Figure 2 depicts the experiment results of n and h against R , obtained by curve-fitting using Eq. (12). 

The value of h decreases with R whilst n increases linearly with R . Figure 3 (a) presents the 

value of h against R in each model. The value of in Model III is a fitting parameter [8, 9] empirically 

determined. 

Model III gives the best predictions except for the case of R = 1. 

More detail discussion is give in the 

literature [10].


n 

Transverse crack density (/mm) 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

50 

45 

40 

35 

30 

25 

20 

0 

10 1 

R = 0.0 

R =0.2 

R = 0.4 

R = 0.6 

R = 1.0 

10 2 

10 3 

Number of cycles 

10 4 

Fig. 1. Transverse crack density in fatigue tests. 

n 

15 

0 0.2 0.4 0.6 0.8 1 

R 

Fig. 2. The values of n and h against stress ratio. 

Next, we propose a new model (Model IV), which is applicable to the whole range of R . The crack 

propagation rate is assumed to be the following empirical formulation as 

da 

K 

= - 

dN 

K 

n 

h 

p ( ) 

AIV 

I 

 

IC 

exp k R 

where k and p are material constants. Based on Model IV, the transverse crack density is expressed 

as 

with 

10 -5 

10 -6 

10 -7 

10 -8 

m 

m 

 

2 2 2,max 

= 1- exp - Ve ( 1+ 

h n 

IV 2,max N - ) 

S 

S 

 

10 5 

h 

49 

(13) 

(14)

50 


n-2 Y 

hIV R AIV e R k R 

2 KIC 

p 

( ) = ( ) exp( 

- ) 

Equation (15) is rewritten, using the value for R = 0 , denoted by h 0 , as 

( ) 

( R) 

( 0) 

2 

p ( ) 

IV 

e 

e 

0 

Putting R = 1 into Eq. (16), we obtain the value of k as 

h/h 0 

h/h 0 

10 2 

10 0 

10 -2 

10 -4 

10 -6 

10 -8 

10 -10 

10 -12 

10 -14 

1 

0.8 

0.6 

0.4 

0.2 

(15) 

 

h R = exp - k R h 

(16) 

( 1) 

( 0) 

h k = = 

e 0 

ln 7.00 

e h 

1 

Experiment 

h I 

h II 

h III (= 0.9) 

0 0.2 0.4 0.6 0.8 1 

R 

(a) Models I, II and III 

Experiment 

h III ( = 0.9) 

h IV (p = 1.9) 

0 

0 0.2 0.4 0.6 0.8 1 

R 

(b) Models I, II and IV 

Fig. 3. Comparison of the value of hi/ h .0 against stress ratio among the models and experiment results. 

(17)

where 1 


Transverse crack density, (/mm) 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

10 1 

R = 0.0 measured 





R = 0.0 calculated 





10 2 

10 3 

Number of cycles, N 

Fig. 4. Comparison of transverse crack density between the experiment results and the predictions calculated by using Model IV. 

h denotes h ( ) . The value of p is estimated through the curve-fitting. Figure 3 (b) presents 

IV 1 

the value of h against stress ratio in Models III and IV. It is demonstrated that the results for k = 1.9 

gives the good agreement with the experiment result over the whole range of R . As a result, it can be 

said that Model IV is the most successful among the four models. Figure 4 plots the transverse crack 

density predicted using Model IV. The agreement between the predictions and the experiment results is 

fairly good although the model overestimates at the small number of cycles. 

4.2 Constant fatigue life diagrams 

When the transverse crack density is expressed as a function of stress ratio R , the number of cycles 

N , and the maximum stress 2, max , constant fatigue life diagrams or fatigue limit diagrams are derived. 

The mean stress 2,m and stress amplitude 2,a in the transverse ply are then given by 

where 

10 4 

1+ R * 1-R 

* 

2,m = 2,max ( R, Nf , ) , 2,a = 2,max ( R, Nf 

, ) 

(18) 

2 2 

* 

2, max denotes 2, max that satisfies Eq. (14). Figure 5 depicts the constant fatigue life diagrams 

for transverse crack density. The experimental data are in reasonably good agreement with the 

predictions. It should be noted that the mean stress for R = 1, 

represented by the x-intercept, is not 

constant, but is shifted to the left with increasing the fatigue life. This is because the static fatigue 

strength depends on fatigue life and failure probability or transverse crack density. In addition, the 

diagrams exhibit nonlinearity, unlike the modified Goodman's diagram. The diagram becomes 

approximately linear only for short fatigue life. 

5 Conclusions 

This paper presents the effect of stress ratio R on the transverse cracking behavior in a CFRP 

cross-ply laminate. The transverse crack density was expressed as a function of R , the maximum stress 

10 5 

51

52 


in the transverse ply and the number of cycles based on the probabilistic SCG model. Model III is the 

most successful among the conventional three models. However, the three conventional models cannot 

predict the behavior for the case of static fatigue loading ( R = 1). 

In contrast, the newly developed 

model, Model IV, that covers the case of R = 1 gives the best predictions over the whole range of R . 

In addition, Model IV enables us to obtain the constant fatigue life diagrams for transverse cracking. 

2,a (MPa) 

2,a (MPa) 

70 

60 

50 

40 

30 

20 

10 

198 

595 

1150 

4200 

N f = 10 

N f = 10 3 

N f = 10 5 

Experiment 

0 

0 50 100 150 

(MPa) 

2,m 

70 

60 

50 

40 

30 

20 

10 

1490 

N f = 10 

N f = 10 3 

N f = 10 5 

(a) 

3720 

Experiment 

9600 

0 

0 50 100 150 

(MPa) 

2,m 

(b) 

Fig. 5 Constant fatigue life diagrams for a variety of fatigue lives at transverse crack density ratio / S of (a) 0.4 and (b) 0.6. The figures 

besides the plots represent the fatigue life in the experiment. 

References 

[1] Kaminski M. On probabilistic fatigue models for composite materials. International Journal of Fatigue 2002; 24: 477-495.


[2] Berthelot JM. Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: Static and 

fatigue loading. Applied Mechanics Reviews 2003; 56: 111-147. 

[3] Ogin SL, Smith PA, Beaumont PWR. A stress intensity factor approach to the fatigue growth of transverse ply cracks. Composites Science 

and Technology 1985; 24: 47-59. 

[4] Boniface L, Ogin SL. Application of the Paris equation to the fatigue growth of transverse ply cracks. Journal of Composite Materials 

1989; 23: 735-754. 

[5] Ogi, K., Yashiro, S., Takahashi, M. and Ogihara, S., A probabilistic static fatigue model for transverse cracking in CFRP cross-ply 

laminates, Composites Science and Technology, 2009, 69 (3-4), 469~476. 

[6] Ogi, K., Ogihara, S. and Yashiro, S., A probabilistic SCG model for transverse cracking in CFRP cross-ply laminates under cyclic loading, 

Advanced Composite Materials, 19 (2010), 1-17. 

[7] Ogi, K., Yashiro, S. and Niimi, K., A probabilistic approach for transverse crack evolution in a composite laminate under variable 

amplitude cyclic loading," Composites Part A, Vol. 41 (2010), 383-390. 

[8] Hojo, M., Tanaka, K., Gustafson, C.-G., Hayashi, R., Effect of stress ration on near-threshold propagation of delamination fatigue cracks 

in unidirectional CFRP, Composites Science and Technology, 1987, 29, 273~292. 

[9] Hojo, M., Ochiai, S., Gustafson, C.-G. and Tanaka, K., Effect of matrix resin on delamination fatigue crack growth in CFRP laminates, 

Engineering Fracture Mechanics, 46 (1994), 35~47. 

[10] K. Ogi, M. Takahashi, Subcritical crack growth models for predicting effects of stress ratio on fatigue transverse cracking in a CFRP 

laminate, submitted to International Journal of Fatigue. 

53

Fatigue damage characterisation for wind turbine blade GFRPs 

using computed tomography 

J Lambert *, A R Chambers, I Sinclair, S M Spearing 

(Engineering Materials, School of Engineering Sciences, University of Southampton, Highfield Campus, Southampton, Hampshire, SO17 1BJ) 

Abstract 

The aim of the research was to investigate microdamage mechanisms with a view to informing micromechanical 

models. The material was first characterised using computed tomography (CT). This enabled a detailed 3-dimensional 

view of microstructure. Coupons were then fatigue tested at R=-1 to 40% of the material tensile UTS. Some tests were 

conducted to failure to obtain S-N data and to establish failure modes. Other tests interrupted at various fractions of the 

predicted coupon lifetime were subjected to CT scanning to gain an insight into the fatigue damage mechanisms present. 

The pre-test material characterisation scanning revealed details of the material microstructure, including fibre tows and 

voids. The interrupted tests identified the presence of transverse matrix microcracking. This appeared to originate 

predominantly from the free edges of the specimen, and in some cases extended into the specimen bulk in the form of 

delaminations. Fewer transverse microcracks were found towards the centre of the specimen width. The absence of any 

fibre breaks or evidence of microbuckling was also noteworthy, further suggesting that the main compressive damage 

mechanisms for the material were matrix cracking and delamination. 

1 Introduction 

This recent emergence of longer wind turbine blades to increase efficiency has resulted in an absence 

of long-term in-service data. With expected lifetimes of around 20 years, the long-term integrity of the 

blade material has thus become an important area of research. More accurate fatigue models are thus 

required to use material in a structurally efficient and fatigue tolerant fashion. In order to establish a 

physically-based fatigue model based on microdamage evolution, it is first critical to understand the 

micromechanisms themselves. Three main types of damage occur within composites; fibre damage, 

interfacial damage, and matrix damage. Fibre based damage encompasses fibre breaks and, in 

compression, fibre failure by microbuckling or kink band formation. Interfacial damage includes 

fibre/matrix debonding and fibre pullout, while matrix damage mechanisms are matrix cracking and 

delamination. Difficulties arise with the coupling of two or more different mechanisms, for instance 

delaminations caused by matrix cracking in neighbouring plies.[1] Another example of damage 

interaction relevant to tension-compression testing is the presence of fibre/matrix debonding causing 

either microbuckling [2] or transverse matrix cracking.[3] The affect of material microstructure is also a 

key consideration. Material layup, fibre volume fraction, voids and their location are of critical 

importance to fatigue performance. Structural and geometrical considerations must also be made, as 


E-mail addresses: j.w.lambert@soton.ac.uk

J Lambert, A R Chambers, etc. / Fatigue damage characterisation for wind turbine blade GFRPs using computed tomography 

features such as ply drops, holes, joints and free edges all act as load concentrators. As a result, 

extensive fatigue databases for different materials and loading conditions have been compiled in recent 

years. 

The recent thesis of Nijssen [4] gives a detailed analysis of fatigue life prediction methods both for 

constant amplitude and variable amplitude testing. The paper includes discussions of scatter sources and 

fatigue limits in composites. Damage accumulation was modeled in two ways and a comparison was 

made: these were the Miner‟s Sum method, and a strength-based method, which calculated the effect of 

each load cycle on the material strength. Mandell, who prior to 1992 conducted much relevant work 

concerning fatigue performance of a variety of composite materials, has since published a large body of 

work almost exclusively on testing, feature characterisation and life prediction methods for fibreglass 

wind turbine blade materials. His original work in the field included a large fatigue test matrix for 

unidirectional and triaxially [0,±45] reinforced glass fibre composites, their characteristic S-N curves, 

and their failure modes. [5] More recent works include Mandell et al., 2002 [6]; a detailed review of the 

work performed by the Montana State University (MSU) Composite Materials Fatigue Program from 

1997 to 2001. Extensive testing at coupon and substructure level is reported, including material studies 

with detailed experimental method definition, spectrum and very high cycle fatigue testing, and strain 

rate effects. Further recent collaborative work has been focused on analytical lifing methods and CLD 

refinement. [7]-[9] These approaches however require a large experimental effort to generate the data 

required for fitting parameters, and also lack an appreciation of the underlying mechanisms occurring. 

Correspondingly, a great number of micromechanical models for composites exist, however these are 

often limited to a specific loading condition or material lay-up and geometry. 

Notable models include Ogin et al.,[10] who related transverse crack spacing to stiffness degradation 

for a cross-ply GFRP. Dimant [11][12] developed a model linking matrix cracking and delamination. 

The compliance change resulting from the propagation of each of the two mechanisms was modelled 

with the outputs being a modified modulus E, and a value for the strain energy release rate G. 

Experimental values for G were obtained by performing fracture mechanics tests, and it was found that 

the onset of delamination cracking could be reliably predicted. The model is attractive as it uses two 

different mechanisms to predict the critical strain energy release rate required for delamination cracking. 

The critical element model, developed by Reifsnider and Stinchcomb, is an important representation of 

composite fatigue damage [13]. It could be argued however that despite the introduction of 

micromechanic metrics, in the form of critical and subcritical elements, the model is primarily residual 

stiffness based and lacks a true mechanism based formulation approach. 

One of the fundamental considerations in the development of a micromechanical model is the means 

by which the mechanisms are observed. The capture of the damage was in this project, achieved by 

using micro-scale Computed Tomography (µCT). µCT implies an x-ray source spot size in the range of 

5-100μm, giving comparable spatial resolution. µCT machines are becoming more common in 

engineering laboratories due to their “benchtop” dimensions, continuing advances in the resolution 

attainable, and the increasing ease associated with handling of large amounts of data. Despite this there 

is still very limited µCT work in the field of composite damage characterisation. A notable paper is that 

55

56 


of Schilling,[14] who used CT to examine internal damage in a number of different composite specimen 

types. Two studies were performed for glass/epoxy composites, one attempting to identify voids, and the 

other matrix cracking and delaminations. Spherical voids in the order of 0.25-0.5 mm were observed 

from a scan of unidirectional s-glass/epoxy specimen, using a pixel size of 26 μm. In the other 

glass/epoxy study, large (>25 μm) matrix cracks and delaminations were observed. The specimen 

geometry did however contain a centre hole, facilitating the locating of the damage, and the specimen 

had been destructively prepared. 

2. Experimental Procedure 

2.1 Mechanical testing 

The coupons were glass-fibre/epoxy with 6 stitched triaxial plies each containing 0 o , +45 o and -45 o 

layers; representative of wind turbine blade material. The rectangular coupons measured 120x25x7 mm 

with a 40 mm gauge. The tab material was woven +/-45 o glass/epoxy 2 mm thick and was adhesively 

bonded to the coupons. The mechanical testing was performed using an Instron 8872 servo-hydraulic 

test machine with a +/- 100 kN dynamic range. Static testing was performed to give an ultimate tensile 

strength (UTS) figure. The fatigue testing was then conducted to a stress level equal to 40% of this UTS 

value. As it was fully reversed (R=-1), the applied stress also extended into compression to -40% of the 

tensile UTS. Load controlled testing was used as it provided more relevant S-N data and was in 

agreement with the majority of the literature. Testing was conducted at a frequency of 2 Hz and a fan 

was used to cool the specimen surfaces, as autogenous heating was a concern due to the relatively thick 

coupon dimension. A clip-type extensometer with a 20mm gauge section was attached throughout 

fatigue testing, connected to a datalogger recording the dynamic strain readings at a sample rate of 50 

Hz. Some of the tests were run to failure, while others were interrupted to undergo CT investigation into 

the damage mechanisms. Failure was defined by a >6mm crosshead deflection from the unloaded, 

gripped state in either tension or compression. 

2.2 Computed Tomography 

The CT was performed using an XTek Benchtop 160i µCT scanner. CT prior to testing of the coupons 

was conducted in order to characterise the microstructure, in particular the voids, so that quantitative 

void analysis could be conducted. For the coupon size and density it was found that a voltage of ~85 kV 

and a beam current of ~95 μA gave the best results. This allowed sufficient penetration of the specimens 

whilst still maintaining a high contrast. The resolution for a scan of the entire specimen cross section 

was found to be 25 μm. 

Higher resolution scanning of destructively prepared “matchstick” specimens was also performed. 

The coupons were cut into 20 mm long specimens with a 3x3 mm cross section. This enabled a much 

higher magnification in the CT scanner, which in turn permitted resolutions of up to 6µm to be achieved. 

A voltage of 73 kV and a current of 123 µA was used for scanning these smaller specimens.


Fig. 1. µCT setup of a complete test specimen. 

The XTek system uses two main scan types, “slow” and “fast”. During a slow scan, the specimen 

stage stops rotating while each radiograph is taken, whereas with a fast scan the specimen is rotated 

continuously. It was found that fast scans, taking 1910 different projection during the 360 o rotation, 

offered the most efficient option. Scans took 1 hour and 7 minutes to perform. The reconstruction was 

performed using the Metris CT Pro software, and the reconstructions were visualised using VGStudio 

Max. 

3 Results 

3.1 Mechanical test results 

The static test results yielded an average failure stress of 440 MPa with a standard deviation of 27 

MPa. The fatigue tests that were conducted to failure gave the following results. All tests were 

performed at 352 MPa alternating stress, corresponding to -/+ 40% UTS. 

Fig. 2. Fatigue test results in the form of a single load level S-N plot, including the failure mode. 

Two different failure mechanisms were observed as shown in Fig.3. The compressive failures, Fig 

3.(a) were characterised by multiple large-scale delaminations along the whole gauge length between 

many, if not all the plies (discussed further in section 3.3). 

57

58 


Fig. 3. (a) Example of compressive failure showing delaminations and global buckling. (b) Example of tensile failure in the tabs showing multiple 

fibre breaks. 

The tensile failures, shown in Fig 3.(b) were all found to be within the tabbed region, at the point 

along the coupon length where the specimen entered the machine‟s grips. The average life of the 

specimens that failed in compression was 62,638, while the tensile failure coupons sustained on average 

25,402. The scatter in results, and limited number of tests performed implied, however, that this 

difference in average life could not be used to reliably predict failure type. 

3.2 Computed Tomography results 

The CT imaging provided useful insight into the material behaviour in both the untested and tested 

specimen scans. Fig 3. shows the three planes of view for the CT reconstruction. The scan was of the 

entire specimen cross section, thus allowing a voxel resolution of 25µm. 

Fig. 4. Orientation of CT reconstruction planes, showing micrographs of a slice from each of the three planes. 

For orientation, the 25mm scale bar on the upper left hand image is the specimen width. The lower 

left hand image is taken parallel to the fibre direction, in a resin rich region between fibre plies. The 

randomly orientated fibres and large voids present in the matrix can be seen. The middle set of images 

shows the through-thickness plane of view with the corresponding micrograph slice. The different ply 

orientations are visible, the 0 o plies discernable as they are parallel to the page thus lack the tow gaps


visible in the +/-45 o plies. The right hand images show the cross-sectional view of the specimen. The 

tow gaps in all the plies are visible. The large matrix voids present in the resin rich regions can be seen, 

as well as smaller voids between the fibre tows. 

The interrupted-test scans were conducted in order to gain an insight into damage evolution. It was 

hoped that full-cross section scans could be used, so that the specimens could continue to be fatigue 

tested after scanning. The 25µm voxel size associated with the intact specimen scans was however 

unable to resolve any ongoing damage, therefore cutting down of the specimens to the 3x3mm cross 

section was required. This enabled a resolution of up to 6µm, and was able to resolve matrix 

microcracking and partial delamination. 

Shown in Fig 5 is the scan from a specimen that sustained 77,505 fatigue cycles before the test was 

stopped for CT analysis. The figure shows the entire scanned region, measuring 3x3x5 mm. This 

corresponded to half the original coupon thickness, hence the three “front” triaxial plies are visible. The 

specimen was taken from the corner of coupon, so the two surfaces in the image were free surfaces 

during the test. Transverse matrix cracks, highlighted in red by using their greyscale histogram range, 

can be seen, the longest of which propagates from the free edge. The voids that interact with the cracks 

have been highlighted using the same method in blue. 

Fig. 5. 3D reconstructed view of a tested 3x3.8mm cross-section “matchstick” specimen 5 mm in length containing a transverse matrix crack. 

Fig 6(a) shows the same view of the same specimen, but now cutting the reconstructed CT image 

further through the thickness, as shown by the lower value in the scale bar. The matrix has also been 

removed by hiding the corresponding greyscale values, to aid the visualisation of the crack in three 

dimensions. The previously transverse fatigue crack has, at this depth, changed direction to propagate at 

45º; in line with the first fibre layer orientation. The crack can be seen extending through voids in 

between 45º tows. A second transverse crack in the upper left hand region can also be seen. Fig 6(b) cuts 

further into the specimen bulk, this time at the interface between +45º and the -45º layers. The crack 

continued to extend along the edge of a 45º tow, interacting with the only void at this depth, but also 

59

60 


formed a partial delamination, shown by the red region extending from the specimen edge. 

Fig. 6. (a) 3D reconstructed view taken 0.2mm from the front face of the specimen. (b) 3D reconstructed view taken 0.6mm from the front face of 

the specimen. 

The other three “corner” specimens from this coupon also revealed transverse matrix cracking 

extending from the specimen free edge across the outer resin rich region. One of these, from the 

opposite side width-wise, also showed a partial delamination between the +45/-45 interface, again 

extending from a crack in the outer resin rich region. The specimens from the centre of the coupon were 

also scanned but revealed no transverse matrix cracking near the surface, however, longitudinal matrix 

cracking between 0º fibre tows was observed. A key finding was the absence of any fibre breaks within 

any of the scans, despite the 8µm resolution of 15µm diameter fibres. 

Further transverse matrix cracking was found in a specimen that sustained 46,500 cycles prior to 

scanning. Again this appeared to be confined to a region near the coupon surface and originated from 

the free edge of the specimen. It must be noted that at the point when the test was stopped it was 

unknown whether these coupons would ultimately fail in compression or tension. However considering 

the failure modes it seems that the mechanism was relevant to the compressive failure mode, as 

discussed in the next section. 

3.3 Failure Modes 

The two very different modes of failure (tensile failure within the tabs and compressive), provide key 

area of discussion. The strain data, corresponding to the longitudinal stiffness degradation in the gauge 

section, was similar throughout the test for both types of failure. This suggests similar mechanisms 

occurring within each, and the cause for the marked difference in final failure remains unknown. Shown 

in Fig 7. is the cross-sectional CT image of a specimen which sustained 59,697 cycles and failed in 

compression.


Figure 7. Cross sectional view of a coupon that had failed in compression after 59697 cycles, showing multiple delaminations. 

Delaminations can be seen extending across the specimen width between the +45º and -45º layers in 

each ply. An additional delamination between the two central plies at their 0º/0º is also present. The 

+45º/-45º interface represents the highest interfacial shear stress within the specimen, causing it to be 

the most likely site for delamation.[15] These delaminations corroborate the importance of the partial 

+45º/-45º delamination found in the interrupted test as seen in Fig 6(b). A sequence for damage 

evolution for compressive failure can thus be hypothesised: 

(1) Transverse matrix cracks propagate from the corners of the specimen cross section across the outer 

resin rich region. 

(2) Some critical cracks propagate into the bulk of the specimen through the outer 45º fibre layers. 

(3) The cracks cause delaminations at the +45º/-45º interface, which then in turn propagate inwards 

from the edges of the coupon. 

(4) When the outer plies have delaminated, the increased stresses in the remaining plies causes further 

delamination between the +45º/-45º interfaces in the following plies. 

(5) The delamination rate continues to accelerate as the stress on the remaining plies increases, until 

compressive failure occurs with the onset of delamination between all the plies. 

4 Conclusions 

(1) µCT is an efficient and method for examining composite microstructure, capable of resolving 

fibres, voids and ply detail in 3-dimensions. 

(2) The fully reversed fatigue testing yielded two distinct failure modes. 5 out of 12 specimens failed 

in compression, while 7 out of 12 failed in tension within the tabbed region. 

(3) The compressive failures were governed by multiple delaminations between +45º/-45º fibre layers. 

The tensile failures within the tabbed region were characterised by fibre breaks extending 

transverse to the loading direction throughout the specimen cross section. 

(4) Scans of interrupted tests revealed transverse matrix cracking. The cracking originated 

predominantly from free edges and at the surface. Smaller scale transverse and longitudinal 

cracking was found in the bulk of the specimen. 

(5) No fibre breaks or fibre microbuckling were found in any of the interrupted-test CT scans. 

61

62 


(6) A fatigue damage sequence for compressive failure was hypothesised, involving first the formation 

of transverse matrix cracks from the free edges. These propagate to form delaminations between 

the outer +45º/-45º interface, which in turn propagate inwards resulting in ply failure. The loss of 

the outer plies result in increasing rapid delamination failures of the inner +45º/-45ºinterfaces. 


The authors would wish to extend thanks to the Engineering and Physical Sciences Research Council 

(EPSRC) for financial support of the project. 

References 

[1] SA Salpekar, TK O‟Brien. Analysis of matrix cracking and local delamination in (0/ θ/- θ)s graphite epoxy laminates under tensile load. 

ASTM Journal of Composites Technology and Research 15 (2), 95–100. (1993) 

[2] PT Curtis The Fatigue Behaviour of Fibrous Composite Materials. Journal of Strain Analysis, Vol 24, No 4/198. (1989) 

[3] EK Gamstedt, BA SjoÈgren. Micromechanisms in tension-compression fatigue of composite laminates containing transverse plies. 

Composites Science and Technology 59. 167-178 (1999) 

[4] RPL Nijssen. Fatigue Life Prediction and Strength Degradation of Wind Turbine Rotor Blade Composites. SAND2006-7810P. Unlimited 

Release. 2007 

[5] JF Mandell, RM. Reed, DD Samborsky. Fatigue of Fiberglass Wind Turbine Blade Materials. CONTRACTOR REPORT SAND92–7005. 

Unlimited Release UC–261. Printed August EN ISO 527: Plastics. Determination of tensile properties (1994). 

[6] JF Mandall, DD Samborsky, DS Cairns. Fatigue of composite materials and substructures for wind turbine blades. SANDIA REPORT 

SAND2002-0771. Unlimited Release. Printed March 2002 

[7] HJ Sutherland and JF Mandell. Optimized Constant-Life Diagram for the Analysis of Fiberglass Composites Used in Wind Turbine Blades. 

Journal of Solar Energy Engineering. NOVEMBER 2005, Vol. 127 / 563 

[8] HJ Sutherland and JF Mandell. Updated Goodman Diagrams for Fiberglass Composite Materials Using the DOE/MSU Fatigue Database. 

Sandia National Laboratories (2004) 

[9] HJ Sutherland and JF Mandell. The Effect of Mean Stress on Damage Predictions for Spectral Loading of Fibreglass Composite Coupons. 

Wind Energ. 8:93–108 (DOI:10.1002/we.125) (2005) 

[10] SL Ogin, PA Smith and PWR Beaumont. Matrix cracking and stiffness reduction during the fatigue of a (0/90)s GFRP laminate. 

Composites Sci Tech. 22(1), 23-31. 1985 

[11] RA Dimant. Damage mechanics of composite laminates. Cambridge University Engineering Department PhD Thesis. 1994 

[12] RA Dimant, HR Shercliff and PWR Beaumont. Evaluation of a damage-mechanics approach to the modeling of notched strength KFRP 

and GRP. Composites Sci Tech 62, 255-263. 2002 

[13] KL Reifsnider and WW Stinchcomb. 'Composite Materials: Fatigue and Fracture' (Ed. H,T. Hahn), ASTM STP 907, American Society for 

Testing and Materials, pp. 298-303. Philadelphia, (1986) 

[14] PJ Schilling, BhanuPrakash R. Karedla, AK. Tatiparthi, A Melody. Verges, PD Herrington. X-ray computed microtomography of internal 

damage in fiber reinforced polymer matrix composites. Composites Science and Technology 65 2071-2078 (2005) 

[15] TK O‟Brien. Characterization of delamination onset and growth in a composite laminate. NASA Langley Research Center (1981)

Cyclic interlaminar crack growth in unidirectional and braided 

composites 

S Stelzer a, *, G Pinter a , M Wolfahrt b,d , A J Brunner c , J Noisternig d 

Abstract 

a Institute of Materials Science and Testing of Plastics, University of Leoben, Franz-Josef-Strasse 18, A-8700 Leoben, Austria 

b Polymer Competence Center Leoben, Roseggerstrasse 12, A-8700 Leoben, Austria 

c EMPA, Swiss Federal Laboratories for Materials Science and Technology, CH-8600 Dübendorf, Switzerland 

d FACC AG, Fischerstrasse 9, A-4910 Ried im Innkreis, Austria 

Since there is still no standard test method for the investigation of the fatigue delamination propagation behavior of 

fiber reinforced composites, this paper aims at examining some of the parameters that can influence this kind of 

measurements. Therefore unidirectionally reinforced composites were tested under displacement control and double 

cantilever beam specimens were used to realize mode I tensile opening loads in the material. A comparison of the effect 

of different parameters on this type of measurements was carried out including machine parameters (frequency, control 

mode, type of machine) and specimen parameters (initial crack length, thickness, material). The comparison of the results 

with the results from a second laboratory yielded promising results. Furthermore the damage tolerance of braided 

composites with different braid architectures (i.e. braiding angle) was studied. 

Keywords: Braid; fracture mechanics; fatigue crack growth; crack branching; fractography 

1 Introduction 

High performance fiber composites feature outstanding specific properties and therefore have an 

indisputable potential for applications in design of lightweight structures. Nevertheless their application 

is limited especially because of their susceptibility to delamination. Delaminations can grow to a critical 

size under cyclic loading conditions, even at loads below the static strength of the material and can thus 

trigger the failure of the structure. To be able to avoid such a failure key data to describe the initiation 

and growth of delaminations for design purposes have to be created and approaches for the 

enhancement of the material performance have to be found. 

In ASTM D 6115 a standard test method for the mode I fatigue delamination growth onset of 

unidirectional fiber reinforced (UD)-polymer matrix composites was introduced [1]. But for estimating 

the behavior of existing delaminations under fatigue loads or for comparing different laminates with 

respect to their delamination propagation under fatigue loads and for design purposes, this is not 

sufficient. Therefore it is an aim to establish a test method for the characterization of the delamination 

growth under mode I fatigue loads. In order to allow its application in an industrial environment short 

test durations below 24 hours are desired. To be able to receive threshold values however, the test 

duration has to be increased significantly. For this reason the determination of the threshold value 

* Corresponding author. phone: +43 3842 402 2103; fax: +43 3842 402 2102 

E-mail addresses: steffen.stelzer@unileoben.ac.at

64 


should not be the main goal, but an option of a test procedure [2]. 

Due to the possibility to automatically manufacture large structures with complex shape and high 

production rates, braided composites produced with liquid resin infusion technology are increasingly 

considered for structural commercial aircraft components. Furthermore by using braided structures the 

impact and delamination resistance can be improved [3,4]. Biaxial braids consist of two yarns located at 

an angle of ±θ to the longitudinal direction along the mandrel axis. By adding fibers in the longitudinal 

direction a triaxial braid can be achieved [5]. Since the braid geometry has an influence on the 

mechanical properties of a part it is imperative to evaluate the differences in the performance of 

different braid geometries. In a previous study the effect of different braid geometries on the mechanical 

properties of specimens loaded in tension, without holes, and compression, with and without holes, 

applying standardized test methods, were examined [6]. So far there are no reported fundamental 

fracture tests for braided composites [7]. 

The overall objective of the present work was to create a test protocol for mode I delamination testing 

of UD-laminates which is applicable in an industrial test environment (short test duration, automated 

data acquisition and analysis) and to study the damage tolerance of braids by fatigue crack growth tests 

and classical CAI tests. 

2 Experimental 

2.1 Materials and test specimens 

The tests were carried out in two laboratories which will be further referred to as laboratories A and B. 

For the UD-laminates used at laboratory A prepreg type materials were used. A 180 o C-cureable 

interleaf-type toughened epoxy resin system, Rigidite 5276-1 (R5276), supplied by BASF AG 

(Ludwigshafen, Germany) and a 380 o C-processable thermoplastic poly(ether-ether-ketone) (PEEK) 

matrix supplied by ICI (Östringen, Germany) were utilized. The epoxy resin was reinforced with carbon 

fibers of the type Celion G30-500 from BASF Structural Materials (Charlotte, USA) and the PEEK 

matrix with carbon fibers of the type AS4 from Hercules Inc. (Magna, USA). The two types of carbon 

fibers were similar in terms of fiber diameter, modulus and ultimate fiber strength and strain. In order to 

initiate interlaminar crack growth, a Teflon film with a thickness of 20 µm was placed at the laminate 

mid thickness at one end of the specimen. The epoxy resin was cured in an autoclave using vacuum bag 

technique and the PEEK laminates were produced using a diaphragm forming process. Double 

cantilever beam (DCB) specimens, 145 mm long and 20 mm wide, were machined from the laminates 

with a diamond saw so that the fibers were oriented along the specimen length. The specimens had a 

thickness (2h) of 4 mm [8]. 

The UD-specimens tested at laboratory B were made of a 180 o C-cureable highly toughened epoxy 

resin system, Cycom 5276-1 (C5276), reinforced with carbon fibers of the type G40-800. The material 

was supplied by Cytec Engineered Materials (Anaheim, USA). A polymer film with a thickness below 

13 µm and a length of 50 mm, as required by ISO 15024 [9], was used to create a crack at specimen 

mid-thickness. The DCB specimens had a width of 20 mm, a length of 150 mm and a thickness of 3.5

S Stelzer, G Pinter, etc. / Cyclic interlaminar crack growth in unidirectional and braided composites 

mm. The unidirectionally reinforced epoxy resins tested at laboratories A and B had similar mechanical 

properties. 

In laboratory A the procedure was additionally applied to braided composites. A high-tenacity, 

standard modulus carbon fiber from Toho Tenax Europe GmbH (Wuppertal, D) was used for all braided 

preforms which were formed over a cylindrical mandrel. Afterwards the braids were removed from the 

mandrel, slit along the 0 o fiber direction, flattened and placed in a mold. To obtain the final thickness (4 

mm) of the test panels, the biaxial preforms consisted of 8 layers, while the triaxial preforms were made 

of 6 layers. Laminates with 300 mm in width and 500 mm in length were infused with the epoxy resin 

RTM 6 from Hexcel Composites (Dagneux, F) using Vacuum-Assisted Resin Transfer Molding 

(VARTM). All test panels were inspected ultrasonically and found to be free of voids and micro cracks. 

DCB specimens in the dimension of 250 x 25 mm were cut out from the laminate plates for the fracture 

tests using a cutting machine with a diamond-coated cutting blade. To be able to examine the influence 

of the crack growth direction on the delamination behavior, the specimens were cut out in 0 o 

(longitudinal) and 90 o (transversal) direction. A Teflon film was placed at laminate mid-thickness as 

starter crack at one edge of the specimens. For the compression after impact tests specimens with a 

length of 150 mm and a width of 100 mm were cut out of the test panels. The specimens with triaxial 

braid geometry were cut out in longitudinal and transversal direction like the specimens for the 

delamination testing. The biaxial samples, however, were only cut out in longitudinal direction. 

2.2 Test methods 

At laboratory A the fatigue crack growth measurements under mode I loading conditions were carried 

out on a servo-hydraulic test machine (MTS 858, MTS Systems Corporation, Berlin, Germany) and on 

an electro-dynamic test machine (ElectroForce 3200, Bose Corporation, Eden Prairie, USA) using the 

DCB specimens. The servo-hydraulic test machine had a 15 kN load cell calibrated in a load range from 

0 to 400 N. The electro-dynamic test machine had a load cell with a load capacity of 450 N. An R-ratio 

of 0.1 was used in all the measurements and the tests were carried out under displacement control. To be 

able to start the measurements at high crack growth rates just below GIC a quasi-static mode I test for 

pre-cracking was carried out as a GIC-test at a testing velocity of 3 mm/min. The displacement value at 

which pre-cracking was stopped, was then taken as the δ max value for fatigue loading (Figure 1). 

Furthermore potential influences of resin-rich areas at the end of the Teflon foil were avoided by 

performing this quasi-static test. The initial crack length for the cyclic test, a0, equals the crack length 

reached after the quasi-static test. The cyclic test was started at 5 or 10 Hz using the pre-cracked 

specimens and continued until a crack growth rate of about 10 -6 mm/cycle was reached. The crack 

length was obtained via visual observation of the crack through a traveling microscope (magnification 

40x). The tests were carried out in a laboratory environment of 23 o C and 50% relative humidity. 

The tests at laboratory B were performed on a servo-hydraulic test machine (Instron type 1273, 

Instron, High Wycombe, United Kingdom) with a 1 kN load cell calibrated in the load range from 0 to 

100 N. The tests were performed under displacement control with a frequency of 3 Hz and an R-ratio of 

0.1. No quasi-static mode I pre-cracking was done since the polymer film of the specimens used in 

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laboratory B was sufficiently thin. Hence the initial crack length for cyclic testing, a0, equaled the length 

of the polymer film insert. The delamination lengths were monitored with a traveling microscope and 

the tests were done in a climate controlled laboratory (+23 o C, 50% relative humidity). 

Fig. 1. Force over displacement curve of a quasi-static pretest to determine δmax. 

At both laboratories the strain energy release rates were calculated using the modified compliance 

calibration (MCC) [10] and additional crack lengths were computed from the compliance data recorded 

during the measurements by using the calibration equation of the MCC method. By plotting da/dN over 

GImax in a double logarithmic scale a so called Paris plot was achieved [11, 12]. GImax was used instead 

of ∆GI in order to avoid an influence of facial interference on the results of the measurements [13]. All 

the calculations were made using an Excel-VBA-Macro provided by laboratory A. 

Compression after impact tests on braided composites were carried out at laboratory A using an 

universal test machine (Z250, Zwick GmbH & Co. AG, Ulm, Germany) after the specimens were 

subjected to impacts at defined ranges of impact energies with a falling weight impact tester (Fractovis 

Plus S.p.A, CEAST, Pianezza, Italy). The residual compressive strengths of the specimens were 

assessed [14]. 

3 Results and discussion 

3.1 Fracture testing 

In Figure 2 a comparison of two types of crack length determination is depicted. On the one hand the 

crack lengths were measured optically by using a traveling microscope. On the other hand the crack 

lengths were computed from compliance data which was recorded by the test machine automatically. It 

is shown that the two calculation methods give crack growth curves with the same significance. 

Therefore in the following diagrams only compliance calibration is applied for the calculation of the 

crack growth curves in order to avoid overloading of the diagrams.


Fig. 2. Effect of crack length determination (optical vs. compliance calibration) on interlaminar fatigue crack growth. 

According to the literature [2, 7, 15, 16] a scatter of the data of up to one decade of the crack growth 

rate can be expected, when an interlaminar crack growth curve is recorded. Figure 3 shows the amount 

of scatter that was received without varying any test parameters at laboratory A. 

Fig. 3. Reproducibility of interlaminar fatigue crack growth tests. 

The length of the starter crack has an influence on the crack opening displacement, on the compliance 

of the specimen and on the amount of fiber bridging occurring during the test [17]. Considering this it is 

very important to examine the influence of the length of the starter crack on the results of t he 

measurements. In Figure 4 the fatigue crack growth curves for starter cracks with 30 and 50 mm can be 

found. To receive longer starter crack lengths, the quasi-static mode I test was carried on until the 

desired crack length was reached. During the measurements it was found that an increase of the length 

of the starter crack made it necessary to decrease the test frequencies, because a higher piston stroke 

was required. Hence the test frequency for the specimens with a starter crack length of 50 mm was 

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limited to 5 Hz. Additional problems with the 50 mm starter crack occurred at crack growth rates below 

10 -4 mm/cycle. The forces fell below a level that made it difficult to record them at the 15 kN 

servo-hydraulic test machine. This led to a big scatter in the recorded forces. 

Fig. 4. Effect of the length of the starter crack on interlaminar fatigue crack growth. 

An increase of the test frequency can, on the one hand, have a negative influence on the results of the 

measurements by leading to hysteretic heating of the specimen. On the other hand an increase of the test 

frequency, such as from 5 to 10 Hz, leads to a drastic reduction in the testing time and therefore reduces 

costs. In earlier tests on another type of CF-epoxy, 10 Hz did not result in hysteretic heating of the 

sample [2]. In Figure 5 it is shown that there was no significant influence of the test frequency on the 

results of the measurements, when the frequency was raised from 5 to 10 Hz. 

Figure 6 shows the influence of the thickness of the specimens on the results of the measurements. 

Through doubling the thickness of the specimen the bending stiffness is increased eight-fold. This leads 

to smaller crack opening displacements and makes it difficult to read the crack lengths with the 

traveling microscope. It is assumed that these circumstances led to the bigger amount of scatter when 

testing the thicker specimens. On the other hand the smaller crack opening displacements made it 

possible to test at higher frequencies. Thus test frequencies of 10 Hz were used for the thicker 

specimens. Nevertheless these effects need to be examined in more detail and exclude the use of 

specimens with a thickness of 8 mm for the characterization of the interlaminar fatigue crack growth 

behavior for now. 

In Figure 7 the results of the measurements under displacement control are compared to the results 

achieved from testing in load control. Therefore all other test parameters were kept constant. It can be 

seen that the two test control modes yielded similar results. Testing in displacement control had the 

following advantages compared to testing in load control: 

(1) Fast crack growth occurred at the beginning of the measurements.


(2) There was no need to be present all the time and the tests could be left alone over night or even for 

a couple of days. Crack lengths could be computed from the compliance data recorded 

continuously by the test machine. 

(3) The detection of the threshold was just a matter of testing time (given that no fiber bridging 

occurred and that the plastic zones remained small). 

Because the reproducibility of the results of standardized tests is enormously important, it was 

examined whether this test method can be carried out on other test machines. The results of this 

intra-laboratory comparison of the tests carried out on different types of test machines can be seen in 

Figure 8. Both machines yielded similar results, although the electro-dynamic test machine had some 

problems with the tuning. The low load capacity of the machine made it necessary to regularly adjust 

the tuning of the machine due to the change of specimen compliance during crack growth. 

Fig. 5. Effect of frequency on interlaminar fatigue crack growth. 

Fig. 6. Effect of specimen thickness (2h) on interlaminar fatigue crack growth. 

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Fig. 7. Effect of control mode (displacement control and load control) on interlaminar fatigue crack growth. 

Fig. 8. Effect of machine type (servo-hydraulic and electro-dynamic) on interlaminar fatigue crack growth. 

The results of an ongoing inter-laboratory comparison of this type of measurements in the framework 

of the European Structural Integrity Society, Technical Committee 4 (ESIS TC4) are not yet available. 

First results of tests on similar materials at Empa (s. Figure 9), however, indicate, that an 

inter-laboratory comparability of this type of measurements is given. 

This kind of measurements worked very well with other materials too, as can be seen in Figure 10, 

Figure 11 and Figure 13. Figure 10 shows the interlaminar fatigue crack growth behavior of UD-PEEK. 

In Figure 11 the fatigue crack growth behavior of a biaxial braid is depicted in the log da/dN versus log 

GImax-diagram. This figure shows some scatter in the values of GImax, which can be ascribed to two 

mechanisms. On the one hand, the crack growth is stopped at fibers not oriented in growth direction and 

the crack is deflected from its nominal growth plane (crack deflection). On the other hand a second 

crack plane is created (crack branching). In Figure 12 these mechanisms are shown in a picture taken


during the measurements on the biaxial braids. It has to be mentioned, that the results shown here were 

calculated based on formulas that require the ideal case of one single and even crack plane. Hence, the 

results are not fully valid. Nevertheless they were reproducible and could be well used for the 

comparison of the two different braid architectures. 

Fig. 9. Comparison of the results from laboratory A with results from laboratory B. 

Fig. 10. Interlaminar fatigue crack growth behavior of UD-PEEK laminates. 

In Figure 13 the fatigue crack growth behavior of the triaxial braids is illustrated both for the 

longitudinal and transversal test direction. The triaxial braids tested in longitudinal direction showed a 

smaller influence of both crack deflection and crack branching on the fatigue crack growth data (less 

scatter) than those tested in transversal direction. The difference between the two different test 

directions was within the scatter of the data. Compared to the biaxial braids, the triaxial braids showed 

no significant difference in the mode I fatigue crack growth behavior. 

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Fig. 11. Interlaminar fatigue crack growth behavior of biaxial braids. 

Fig. 12. Crack deflection and crack branching in the biaxial braid. 

Fig. 13. Interlaminar fatigue crack growth behavior of triaxial braids.


3.2 Compression after impact testing 

In Figure 14 the residual strength of the braided composites is plotted as a function of the impact 

energy. Similar results were obtained for the triaxial braids tested in transversal direction and the biaxial 

braids which were tested in longitudinal direction. The values of the triaxial braids which were tested in 

the longitudinal direction, however, were found to be at a significantly higher level than the triaxial ones 

tested in transversal direction. Hence the addition of 0 o yarns leads to an increase of the compressive 

strength after impact values when specimens are loaded in longitudinal direction. 

4 Conclusion 

Fig. 14. Effect of braid architecture on the residual compressive strength of braided composites. 

The procedure for the characterization of the interlaminar crack growth in fiber reinforced composites 

proved to be an appropriate way to measure the growth of delaminations. The fatigue crack growth 

behavior of unidirectionally reinforced polymer laminates with matrices made of either 

polyetheretherketone (PEEK) or epoxy resin could be well compared. The machine parameters 

frequency, control mode and type of machine showed no significant influences on the results of the 

measurements on UD-reinforced epoxy resins. When varying the specimen parameters initial crack 

length and thickness, however, the results indicate the need for guidelines concerning these parameters 

to be able to receive reproducible results. An inter-laboratory comparison of the results of this kind of 

measurements provided promising results. Round robin measurements were initialized to prove these 

findings and will be carried out by members of the ESIS TC4. [2, 18]. The interlaminar crack growth 

behavior of UD-PEEK samples could be measured reproducible and the PEEK samples proved to be 

much tougher than the epoxy resin samples. 

Furthermore an experimental investigation of the interlaminar crack growth in braided composites 

under fatigue loading conditions showed that crack branching occurs, which increases the dissipation of 

fracture energy in the specimen. All the braided samples showed stick slip effects, leading to crack 

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74 


growth curves with a greater amount of scatter compared to the unidirectional reinforced laminates. This 

can be ascribed to the delamination crack interacting with the braid structure, especially with transverse 

fibers [19]. Nevertheless no significant difference in the fatigue delamination behavior of biaxial and 

triaxial braided composites could be found. Compression after impact measurements were made to 

study damage tolerance of the braided composites. It was found that the fiber orientation has a great 

influence on the compression after impact behavior. 

In all cases the mode I fatigue delamination propagation measurements under displacement control 

provided very reproducible results and seem to be a promising tool to characterize the delamination 

behavior of polymer laminates under mode I fatigue loading conditions. 


The research work of this paper was performed at the Polymer Competence Center Leoben GmbH 

(PCCL, Austria) within the framework of the Kplus-program of the Austrian Ministry of Traffic, 

Innovation and Technology with contributions by the Montanuniversität Leoben (Institute of Materials 

Science and Testing of Plastics) and FACC AG (Ried im Innkreis, A). The PCCL is funded by the 

Austrian Government and the State Governments of Styria and Upper Austria. The authors would like to 

thank Mr. M. Stuart and Cytec (New Jersey, USA) for supplying UD-specimens for the measurements at 

Empa and Toho Tenax Europe GmbH (Wuppertal, D) for providing the carbon fibers for the braids. Test 

set-up, test performance and data acquisition by Mr. D. Völki at Empa is also acknowledged. 

References 

[1] ASTM E 647–00, Standard test method for measurement of fatigue crack growth rates, West Conshohocken, USA: American Society for 

Testing and Materials International (2008). 

[2] A.J. Brunner, N. Murphy, G. Pinter, Development of a standardized procedure for the characterization of interlaminar delamination 

propagation in advanced composites under fatigue mode I loading, Engineering Fracture Mechanics 76 (2009) 2678-2689. 

[3] J.E. Masters, P.G. Ifju, A phenomenological study of triaxially braided textile composites loaded in tension, Composites Science and 

Technology, 56 (1996) 347-358. 

[4] L.V. Smith, , S.R. Swanson, Strength design with 2-D triaxial braid textile composites, Composites Science and Technology, 56 (1996) 

359-365. 

[5] C. Ayranci, J. Carey, 2D braided composites: A review for stiffness critical applications, Composite Strucures, 85 (2008) 43-58. 

[6] M. Wolfahrt., G. Pinter, S. Zaremba, T. von Reden, C. Ebel, Effect of preform architecture on the mechanical and fatigue behavior of 

braided composites for generating design allowables. in „Proceedings of SAMPE Europe. Paris, France‟, Vol. 30 (2009) 277-282. 

[7] J. Chen, E. Ravey, S. Hallett, M. Wisnom, M. Grassi, Prediction of delamination in braided composite T-piece specimens, Composite 

Science and Technology 69 (2009) 2363-2367 

[8] M.-K. Cvitkovich, Polymer matrix effects on interlaminar crack growth in advanced composites under monotonic and fatigue mixed-mode 

I/II loading conditions, PhD Thesis, University of Leoben, Austria (1995) 56-57. 

[9] ISO 15024, Fibre-reinforced plastic composites – Determination of mode I interlaminar fracture toughness, GIC, for unidirectionally 

reinforced materials (2001). 

[10] K. Kageyama, M. Hojo, Proc. 5th Japan-US Conference on Composite Materials (1990) 227-234 

[11] P.C. Paris, F. Erdogan, A critical analysis of crack propagation laws, Journal of Basic Engineering 85 (1963) 528-534 

[12] D.J. Wilkins, J.R. Eisenmann, R.A. Camin, W.S. Margolis, R.A. Benson, Characterizing delamination growth in graphite-epoxy, in K.L. 

Reifsnider (Ed.) Damage in Composite Materials, ASTM Publications, Philadelphia, USA, 1982, pp. 168-183. 

[13] R.H. Martin, G.B. Murri, Characterization of mode I and mode II delamination growth and thresholds in graphite/peek composites, NASA 

technical memorandum 100577 (1988) 1-52. 

[14] AITM 1-0010: Determination of compression strength after impact, Blagnac, France (2003).


[15] R.H. Martin, G.B. Murri, Characterization of Mode I and Mode II delamination growth and thresholds in AS4/PEEK composites, in S.P. 

Garbo (Ed.) Composite Materials: Testing and Design, Vol.9, ASTM Publications, Philadelphia, USA, 1990, pp. 251-270. 

[16] A. Argüelles, J. Vina, A.F. Canteli, M.A. Castrillo, J. Bonhomme, Interlaminar crack initiation and growth rate in a carbon-fibre epoxy 

composite under mode-I fatigue loading, Composite Science and Technology 68 (2008) 2325-2331 

[17] M. Hojo, S. Ochiai, T. Aoki, H. Ito, New simple and practical test method for interlaminar fatigue threshold in cfrp laminates, 2nd 

ECCM-Composites, Testing & Standardization, (1994a) 553-561 

[18] A.J. Brunner, I. Paris, G. Pinter, Fatigue Propagation Test Development for Polymer-Matrix Fibre-Reinforced Laminates, in „Proceedings 

of 12th International Conference on Fracture Ottawa, Canada‟, (2009). 

[19] N. Alif, L.A. Carlsson, L. Boogh, The effect of weave pattern and crack propagation direction on mode I delamination resistance of woven 

glass and carbon composites, Composites Part B: Engineering 29B (1998) 603-611 

75

Abstract 

Effect of Water Uptake on the Fatigue Behavior of a 

Quasi-Isotropic Woven Fabric Carbon/Epoxy Laminate 

at Different Stress Ratios 

M Kawai a, *, Y Yagihashi a , H Hoshi b , Y Iwahori b 

1 Department of Engineering Mechanics and Energy, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan 

2 Japan Aerospace Exploration Agency, Mitaka, Tokyo 181-0015, Japan 

The effect of absorbed moisture on the fatigue strength of a plain weave roving fabric carbon/epoxy quasi-isotropic 

laminate under constant amplitude loading at different stress ratios has been examined. First, constant amplitude fatigue 

tests are performed at room and high temperatures, respectively, on the specimens immersed in hot water until saturation 

as well as on the specimens kept in a dry place. The results indicate that the fatigue lives of wet specimens are shorter 

than those of dry specimens, regardless of stress ratio as well as test temperature. The reduction in fatigue strength due to 

water absorption at room temperature is about eleven percent, regardless of stress ratio. A similar reduction in fatigue 

strength of wet specimens occurs at high temperature. Then, the full shapes of the constant fatigue life (CFL) diagrams 

for the woven CFRP laminate in dry and wet environments are identified using the fatigue test data obtained at different 

stress ratios and at different test temperatures. The results show that the experimental CFL diagrams are asymmetric and 

nonlinear, and the shape of CFL envelope gradually changes. Finally, those CFL diagrams are predicted using the 

anisomorphic CFL diagram approach for composites that was developed in an earlier study. Comparison with 

experimental results demonstrates that the theoretical method allows successfully predicting the CFL diagram for the 

woven CFRP laminate not only in a dry environment but also in a wet environment, regardless of test temperature. 

Keywords: CFRP; Woven fabric; Fatigue; Moisture; Temperature; S-N Relationship; Constant Fatigue Life Diagram 


Key application areas that benefit from the high specific stiffness and strength of carbon 

fiber-reinforced plastics (CFRPs) are rapidly growing, not only in the aerospace sector but also in wind 

energy [1], offshore [2] and high performance vehicle [3] sectors. A larger-sized wind turbine is required 

to enhance efficiency. The diameter of a wind turbine rotor that allow generating more than 5 MW of 

power, for example, exceeds the length of 100 m [1]. As the length of wind turbine blades increases, a 

lighter and stiffer material is needed. In deepwater offshore applications, a target water depth of oil and 

gas drilling is increasing to exceed 3000 m [4]. When they are made of steel, the riser pipes for the 

target deep sea may suffer from their increased weight and decreased axial rigidity. Such a large riser 

pipe for deepwater exploration thus requires selecting a material with low weight and high stiffness, in 

line with a large wind turbine blade. A strong demand for reducing the emissions of carbon dioxide 


E-mail addresses: mkawai@kz.tsukuba.ac.jp

Effect of Water Uptake on the Fatigue Behavior of a Quasi-Isotropic Woven Fabric Carbon/Epoxy Laminate at Different R 

pushes automotive industries to replace conventional materials with composites and to redesign vehicles 

accordingly [3]. 

For reliable application of CFRPs to those structures, it is a prerequisite to establish a method for 

accurately evaluating their fatigue lives under cyclic loading. Fatigue load that CFRP structures are 

required to withstand differs depending on application. In general, it is characterized by variable 

amplitude, mean, frequency and waveform. Above all, careful consideration of the mean stress 

component of cyclic load is the key to accurate evaluation of the fatigue lives of CFRPs and CFRP 

structures. This has been proved by many experimental results for various kinds of CFRP laminates that 

show the significant influence of stress ratio on their fatigue lives: e.g. [5-13]. In the fatigue design of 

composite structures, furthermore, it is essential to evaluate the maximum stress level below which the 

fatigue life of a given composite under constant amplitude cyclic loading becomes longer than a 

specified number of cycles to failure. This is because a fatigue limit defined as a stress level below 

which fatigue life becomes infinite cannot clearly be identified in the S-N curves for most continuous 

carbon fiber composite laminates, especially for the laminates in which some constituent plies are most 

favorably orientated in the direction of fatigue load. 

The effect of mean stress on the fatigue strength of a given composite laminate for a given value of 

life can conveniently be described using a constant fatigue life (CFL) diagram. In the CFL diagram, 

alternating stress amplitude is plotted against mean stress for different numbers of cycles to failure. 

Harris et al. [5-11] have examined the CFL diagrams for various kinds of CFRP laminates, and showed 

that the CFL envelopes are nonlinear in shape and asymmetric about the alternating stress axis, and the 

peak positions are slightly offset to the right of the alternating stress axis. The experimental results 

obtained from their systematic studies, along with the fatigue data from the other sources [14-17], 

suggest that the maxima of the CFL envelopes correspond to fatigue loading at a stress ratio almost 

equal to the ratio of compressive strength to tensile one. 

These experimental observations suggest that the linear Goodman diagram [18], which has 

successfully been employed in the fatigue analysis of metals, is not always valid for CFRP laminates. 

For design purposes, therefore, it is required to establish an engineering method for constructing a CFL 

diagram that is suitable for CFRP laminates. Adam et al. [7] assumed similar curves for different 

constant values of fatigue life and proposed an asymmetric parabolic representation of CFL diagram for 

a composite. Harris et al. [6] found a more general representation of CFL diagram by means of a 

bell-shape function. Recently, Kawai et al. [16, 17] have proposed a different method for efficiently 

constructing a nonlinear CFL diagram for a given composite on the basis of the static strengths in 

tension and compression and the reference S-N relationship for a particular stress ratio equal to the ratio 

of compressive strength to tensile one. This method was called anisomorphic CFL diagram approach, 

and shown to be valid for different types of CFRP laminates at room temperature in a dry environment. 

Accurate evaluation of the fatigue lives of CFRP structures needs consideration of the effects of 

temperature and moisture, since hygrothermal environments are often unfavorable for the properties of 

polymer matrices, especially epoxy resins, in CFRPs [19, 20]. The static and fatigue strengths of CFRP 

at high temperature are usually lower than those at room temperature; this tendency has been reported 

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for unidirectional carbon/epoxy laminates [21, 22] and for woven fabric carbon/epoxy laminates [23]. A 

similar reduction in static and fatigue strengths due to temperature has also been observed for carbon 

fiber-reinforced thermoplastic matrix composites [24]. Regarding the effect of moisture mainly 

absorbed by the polymer matrices in composites, many experimental studies have revealed that it 

reduces the tensile strengths of unidirectional carbon/epoxy laminates not only in the transverse 

direction [25] but also in the fiber direction [25, 26]. The reduction in tensile strength due to moisture 

has also been observed for multidirectional carbon/epoxy laminates of different lay-ups [27]. Ray [28] 

showed that the interlaminar shear strength of a carbon/epoxy laminate is lowered by water absorption. 

Patel and Case [29] examined the effect of water absorption on the fatigue damage and strength of 

woven fabric carbon/epoxy laminates, and found that fiber/matrix decohesion and interlaminar 

delamination develop more markedly in the specimens that absorbed water, and accordingly the 

resistance to fatigue is degraded. 

These experimental results prove that the fatigue failure of a given CFRP laminate in a wet 

environment differs from that in a dry environment. Therefore, it is required to establish an engineering 

method for accurately evaluating the fatigue lives of composites for a variety of hygro-thermal loading 

that is characterized by the combination of loading waveform, absorbed water content and temperature. 

If the anisomorphic CFL diagram approach that was developed to predict the fatigue lives of composites 

for different mechanical loading conditions is extended to a model that can consider the effect of 

hygro-thermal environments, it becomes a more useful and powerful tool for engineering fatigue life 

analysis of composites. 

In this study, therefore, the anisomorphic CFL diagram approach to prediction of fatigue life of 

composites is further tested for its applicability, respectively, to fatigue of a different kind of CFRP 

laminate (i.e., a woven fabric carbon/epoxy laminate) in dry and wet environments and to fatigue at 

different test temperatures. For this purpose, the effects of water absorption on the fatigue lives of the 

woven CFRP laminate at different stress ratios and at different test temperatures are first elucidated. 

Constant amplitude fatigue tests at different stress ratios are performed at room and high temperatures, 

respectively, on the specimens that were immersed in hot water until saturation as well as on the 

specimens that were not exposed to water environment but kept in a dry place. By comparing the S-N 

relationships for the dry and wet specimens that are obtained from testing at different temperatures, the 

effects of water uptake and temperature on the fatigue lives of the woven CFRP laminate under constant 

amplitude loading at different stress ratios are elucidated. The effect of these factors on the shapes of the 

CFL diagrams in dry and wet environments is also examined. Finally, the S-N relationships for different 

stress ratios at different temperatures in dry and wet environments are predicted using the anisomorphic 

CFL diagram approach, and compared with experimental results. 

2. Materials and Testing Procedure 

2.1 Material and Specimen 

The material used in this study was a plain weave roving fabric carbon/epoxy composite. The woven


fabric carbon/epoxy composite was supplied by TORAY in the form of prepreg sheets 

(QFC133-6E01A). Twelve-ply quasi-isotropic laminates were fabricated from the prepreg tapes with the 

stacking sequence of [(±45)/(0/90)]3S. The woven CFRP laminates were cured in an autoclave at 350 o F 

(176.6 o C). The nominal thickness of as-received laminates was about 2.4 mm. 

Two kinds of coupon specimens with different nominal dimensions were prepared. For static tension 

tests and tension-tension (T-T) fatigue tests, the long specimens based on the testing standards JIS 

K7073 [30] and JIS K7083 [31] were employed; as shown in Fig. 1(a), the dimensions were gauge 

length LG = 100 mm and width W = 20 mm. For static compression tests and compression-compression 

(C-C) and tension-compression (T-C) fatigue tests, on the other hand, short specimens were used to 

reduce the risk of buckling of specimens due to compressive load; as shown in Fig. 1(b), the dimensions 

were gauge length LG = 10 mm and width W = 10 mm. The nominal dimensions of the compressive 

specimens were determined on the basis of the testing standards JIS K7076 [32] and the report of 

Harberle and Matthews [33] for suitable compression testing on composite laminates. 

20 

10 

50 100 

50 

(a) Gauge length 100 mm (tensile specimen) 

45 10 45 

(b) Gauge length 10 mm (compressive specimen) 

Fig. 1. Specimen geometry (dimension in mm). 

A set of tensile and compressive specimens were immersed in hot water of 71±1 o C until saturation, 

and they are referred to as wet specimens. A water bath with a digital temperature control capability and 

an automatic water supply function was used for preparing wet specimens. Another set of tensile and 

compressive specimens were kept in a dry place, and they are called dry specimens. 

On both ends of dry specimens, rectangular-shaped aluminum alloy tabs were glued with epoxy 

adhesive (Araldite) in order to protect their gripped portions. The thickness of the end-tabs was 1.0 mm 

for tensile specimens and 2.0 mm for compressive specimens. To wet specimens, however, end-tabs 

were not attached to avoid drying during their cure process. Since the 0 o layers of the laminate used in 

this study are protected by the ±45 o layers on the surface, it would not be much hazardous to grip the 

ends of wet specimens directly. 

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2.2 Testing Procedure 


Constant amplitude fatigue tests were carried out on dry and wet specimens under load control at 

room temperature (RT~23 o C) and at high temperature (HT = 80 o C). Fatigue load was applied to 

specimens in a sinusoidal waveform with a constant frequency of 10 Hz; the fatigue loading condition is 

based on the testing standard JIS K7083 [31]. 

Fatigue tests were performed at three different values of stress ratio R = 0.1, 10, and , where 

= / and it designates the critical stress ratio that is equal to the ratio of compressive strength 

C T 

C (< 0) to tensile one T (> 0). Wet specimens were vaselined except for the gripped portions and 

then wrapped in a cling film in order to prevent them from drying during fatigue test. Most specimens 

were fatigue tested for up to 10 6 cycles. Prior to fatigue testing, static tension and compression tests 

were performed on the dry and wet specimens at room and high temperatures to identify the tensile and 

compressive strengths of the woven CFRP laminate in the testing environments. The static tests were 

carried out at a constant rate of 1.0%/min until ultimate failure occurred, following the testing standards 

JIS K7073 [30]. 

Static and fatigue tests were conducted in 100 kN servo hydraulic MTS-810 machine. For raising the 

temperature of a specimen, a heating chamber with a precise digital control capability was employed. 

Each specimen was clamped in the heating chamber by the high temperature hydraulic wedge grips 

fitted on the testing machine, and it was heated up to a test temperature in air without applying load and 

preconditioned in a test environment for 1 h prior to testing. Variation of specimen temperature in time 

from the prescribed value was less than 1.0 o C. Humidity in the heating chamber was not controlled. 

The longitudinal and lateral strains of dry specimens in static tests were monitored with two-element 

L-type rosette strain gauges; the gauge length of the rosettes was 2.0 mm for tension tests and 1.0 mm 

for compression tests. The strain gauges were mounted back to back at the center of each specimen. 

3. Experimental Results and Discussion 

3.1 Water absorption behavior 

The moisture absorption behavior of the woven CFRP laminate is first observed. A set of tensile 

and compressive specimens were immersed in hot water of 71 o C, and the weight of the specimens was 

measured periodically. The immersion of the specimens in hot water was continued until near saturation 

of water absorption. The weigh gain M t in percent was calculated using the following equation: 

where 0 

M 

W -W 

t 0 

t = 100 

(1) 

W0 

W is the initial weight of a dry specimen, and W t is the current weight of the specimen after 

t hours of immersion. 

Fig. 2 shows the relationships between the weight gain and the square root of immersion time for the 

long and short specimens of the woven CFRP laminate. The solid and dashed lines indicate the 

absorption curves that were obtained by fitting the following simplified equation [34, 35] of the solution


of the Fick equation [34] to the experimental data: 

M t 4 Dt 

= tanh 

M 

h 

 

where M is the weight gain at saturation, D is the diffusion coefficient, and h is the thickness of 

specimens. The value of the diffusion coefficient was 2.0 x 10 -7 mm 2 /s for the long specimen and 2.5 x 

10 -7 mm 2 /s for the short specimen. In Fig. 2, it is seen that the water absorption process of the woven 

carbon/epoxy laminate is well described by the Fickian diffusion model. The approximate saturation 

value of water absorption was about M 1.0% , and it took 2500 hours (104 days) to reach the 

approximate value of saturation. The values of diffusion coefficient that were obtained in this study are 

close to the value of 1.9 x 10 -7 mm 2 /s for the IM7/8551-7 epoxy laminate [36]. 

3.2 Static strength 

Moisture Content by Weight (%) 

1.5 

1 

0.5 

Woven CFRP quasi-isotropic 

[(±45)/(0/90)] 3s 

Water temperature 71⎫C 

△ Short specimen 

◆ Long specimen 

0 

0 10 20 30 40 50 60 

Square root of time (h 1/2 ) 

Fig. 2. Water absorption curve. 

Comparison of the tensile strengths for dry and wet specimens at room and high temperatures is 

shown in Fig. 3 (a). Similar comparison of the compressive strengths is also presented in Fig. 3 (b). In 

these figure, the average values of two or three samples are compared. The number of samples is limited, 

but it seems that the possible range of scatter of the static strengths in tension and compression is very 

small. This feature affects us favorably, and allows us to qualitatively discuss the effects of temperature 

and moisture on the static and fatigue strengths of the woven CFRP laminate on the basis of the limited 

number of data. 

81 

(2)

82 

3.2.1 Effect of temperature 

UCS, MPa 

UTS, MPa 

1000 

800 

600 

400 

200 

-600 

-500 

-400 

-300 

-200 

-100 

0 

0 


Woven CFRP quasi-isotropic [(±45)/(0/90)] 3s 

841.0 

832.0 

835.9 

790.0 

Dry-RT Dry-HT Wet-RT Wet-HT 

(a) Tensile strength 

Woven CFRP quasi-isotropic [(±45)/(0/90)] 3s 

-464.7 -422.0 -435.9 -382.0 

Dry-RT Dry-HT Wet-RT Wet-HT 

(b) Compressive strength 

Fig. 3. Comparison of static strengths under different hygro-thermal conditions. 

The tensile strengths at room temperature (RT) and high temperature (HT) are compared. The ratio of 

dry dry 

the tensile strength at HT to the tensile strength at RT was (HT) / (RT) = 0.99 for dry 

UTS UTS 

wet wet 

specimens and (HT) / (RT) = 0.95 for wet specimens. These comparisons suggest that while it 

UTS UTS 

has no influence on the tensile strength of a dry specimen, the increase in temperature has a slightly 

unfavorable influence on the tensile strength of a wet specimen. A similar comparison of compressive 

dry dry 

wet wet 

strengths led to (HT) / (RT) = 0.91 for dry specimens and (HT) / (RT) = 0.88 for wet 

UCS UCS 

UCS UCS 

specimens. The latter observation reveals that the compressive strength of the woven CFRP laminate is 

reduced by the increase in temperature, regardless of moisture content. The ratio of tensile strength to


dry dry 

compressive one, which gives the critical stress ratio, was / = 0.55 (RT) and 0.51 (HT) for 

UCS UTS 

wet wet 

dry specimens, and / = 0.52 (RT) and 0.48 (HT) for wet specimens. Obviously, the 

UCS UTS 

compressive strength of the woven CFRP laminate is lower than the tensile strength, regardless of 

temperature and water absorption. 

3.2.2 Effect of water absorption 

The strengths of dry and wet specimens that were obtained from static tests at the same test 

temperature are compared to extract the effect of water absorption. The ratio of the compressive strength 

wet dry 

of wet specimens to the compressive strength of dry specimens was (RT) / (RT) = 0.94 at RT 

UCS UCS 

wet dry 

and (HT) / (HT) = 0.91 at HT. Namely, the compressive strength of wet specimens at RT was 

UCS UCS 

about 6% smaller than that of dry specimens, and the compressive strength of wet specimens at HT was 

about 9% smaller. Thus, the water absorption is apt to moderately reduce the compressive strength of 

the woven CFRP laminate, regardless of test temperature. 

The effect of water absorption on the tensile strength at room temperature is considered to be 

wet dry 

negligible since (RT) / (RT) = 0.99 . In contrast, the ratio at HT became 

UTS UTS 

wet dry 

(HT) / (HT) = 0.95 , thus suggesting that the tensile strength at high temperature is apt to be 

UTS UTS 

reduced by water absorption. A similar tendency of the reduction in tensile and compressive strengths of 

composites due to water absorption has been reported in literature [26, 28, 34]. Incidentally, it is 

considered that the reduction in static strength due to water absorption is caused by the reduction in 

interlaminar adhesion strength as well as the reduction in the strength of matrix according to the 

increase in ductility due to water absorption. 

3.2 Fatigue Strength 

The S-N relationships at room temperature are shown in Fig. 4 and Fig. 5 for dry and wet specimens, 

respectively. Each figure includes fatigue data for different stress ratios R = 0.1, 10 and , where 

=- 0.55 for dry specimens and =- 0.52 for wet specimens. The maximum fatigue stress max is 

plotted against the logarithm of the number of reversals to failure 2N f in the case R = 0.1 and , 

while the absolute value of minimum fatigue stress min is plotted in the case R = 10. From these 

figures, it can clearly be observed that the S-N relationship for the woven CFRP laminate significantly 

depends on the shape of load waveform (i.e. stress ratio), regardless of the degree of water absorption. 

83

84 

max (| min|), MPa 

max (| min|), MPa 

1000 

800 

600 


UTS 


[(±45)/(0/90)] 3s 

400 

200 

0 

100 101 102 103 104 105 106 107 UCS 

Experimental 

Dry-RT 10 Hz 

○ R = 0.1 

◆ R = = -0.55 

□ R = 10 

Fitted 

2N f 

Fig. 4. S-N relationships for dry specimens at room temperature 

1000 

800 

600 

UTS 


[(±45)/(0/90)] 3s 

400 

200 

0 

100 101 102 103 104 105 106 107 UCS 

Experimental 

Wet-RT 10 Hz 

○ R = 0.1 

◆ R = = -0.52 

□ R = 10 

Fitted 

2N f 

Fig. 5. S-N relationships for wet specimens at room temperature 

It has been reported that the gradient of the S-N relationship becomes largest under fatigue loading at 

the critical stress ratio [16, 17]. Observing the results in Fig. 4 for dry specimens and Fig. 5 for wet 

specimens, we can confirm that also for the woven CFRP laminate tested in this study, the gradient of 

the S-N relationship becomes largest under fatigue loading at the critical stress ratio, regardless of 

moisture content. 

Comparisons of the S-N relationships for dry and wet specimens are shown in Figs. 6 (a), (b), (c) for 

different stress ratios R = 0.1, 10 and , respectively. We can clearly observe that the fatigue lives of 

wet specimens are shorter than those of dry specimens, regardless of stress ratio. While the number of 

fatigue data is limited, it is suggested that the fatigue strength of wet specimens is about 11% lower than 

that of dry specimens, regardless of stress ratio. 

The reduction in fatigue strength is affected by the reduction in static strength in general. It was


wet dry 

observed above that (RT) / (RT) = 0.99 , and thus the difference between the tensile strengths of 

UTS UTS 

the dry and wet specimens at room temperature is negligible. This fact reveals that a lower fatigue 

strength of wet specimens for R = 0.1 and that can be seen in Figs. 6 (a) and (b) was caused by the 

wet dry 

absorption of water. On the other hand, it was observed above that (RT) / (RT) = 0.94 , 

UCS UCS 

indicating that the compressive strength is reduced by water absorption. Therefore, it is suggested that 

the difference between the S-N relationships for dry and wet specimens fatigue loaded at R = 10 that 

was observed in Fig. 6(c) is affected by the reduction in compressive strength due to water absorption. 

max, MPa 

max, MPa 

1000 

800 

600 

400 

200 

0 

100 101 102 103 104 105 106 107 Experimental 

RT 10Hz 

R = -0.52 (Wet), -0.55 (Dry) 

○ Dry 

△ Wet 

1000 

800 

600 

400 

200 

UTS 

UTS 

Experimental 

RT 10Hz 

R = 0.1 

○ Dry 

△ Wet 


[(±45)/(0/90)] 3s 

(a) R = 

2N f 

Fitted 


[(±45)/(0/90)] 3s 

0 

100 101 102 103 104 105 106 107 (b) R = 0.1 

2N f 

Fitted 

85

86 

| min|, MPa 

600 

500 

400 

300 

200 

100 

3.3 Experimental CFL Diagram 


UCS 

Experimental 

RT 10Hz 

R = 10 

○ Dry 

△ Wet 


[(±45)/(0/90)] 3s 

0 

100 101 102 103 104 105 106 107 (c) R = 10 

2N f 

Fitted 

Fig. 6. Comparison of S-N relationships for dry and wet specimens at room temperature. 

The effect of moisture absorption on the CFL diagram for the woven CFRP laminate is examined. 

The experimental CFL diagram can be constructed by plotting alternating stress against mean stress. 

Figs. 7 and 8 show the experimental CFL diagrams for dry and wet specimens at RT, respectively. In 

these figures, the experimental data points for different constant values of life were evaluated using the 

S-N curves fitted to the experimental S-N data; they are indicated by dashed lines in Figs. 4 to 6. 

Observing the results for dry specimens shown in Fig. 7, we can see that the CFL diagram for the woven 

CFRP laminate at room temperature becomes asymmetric about the alternating stress axis. The CFL 

envelope changes in shape as the number of cycles to failure increases. It is linear in the range of a short 

life but it turns nonlinear in the range of a longer life. The peak of the CFL envelope is slightly offset to 

the right of the alternating stress axis, and it is associated with a stress ratio close to the ratio of 

compressive strength to tensile one, i.e. = -0.55. It is also seen that the maximum alternating stress 

is accompanied at the critical stress ratio. 

The shape of the CFL diagram for wet specimens is similar to that for dry specimens, as can be 

observed in Fig. 8. The difference between the CFL diagrams for dry and wet specimens is small, since 

the critical stress ratio for wet specimens is = -0.52, and it is close to = -0.55 for dry specimens, 

along with a small difference between the absolute values of the tensile and compressive strengths. 

The experimental findings can be summarized as follows: (1) the CFL diagram for the woven CFRP 

laminate is asymmetric about the alternating stress axis, (2) the shape of CFL envelope changes in shape 

from a straight line to a nonlinear curve as the number of cycles to failure increases, (3) the peaks of 

CFL envelopes correspond to fatigue loading at the critical stress ratio, and (4) all these features are 

common to the fatigue failure in dry and wet environments.


a, MPa 

a, MPa 

900 

600 

300 

900 

600 

300 


[(±45)/(0/90)] 3s 

Experimental 

Dry-RT 10Hz 

◆ N f = 10 1 △ N f = 10 2 

■ N f = 10 3 ◇ N f = 10 4 

▲ N f = 10 5 □ N f = 10 6 

R = 10 

= - 0.55 

R = 0.1 

0 

-900 -600 -300 0 300 600 900 

m, MPa 

Fig. 7. Anisomorphic constant fatigue life diagram for dry specimen at room temperature 


[(±45)/(0/90)] 3s 

Experimental 

Wet-RT 10Hz 

4. Prediction of CFL Diagram 

◆ N f = 10 1 △ N f = 10 2 

■ N f = 10 3 ◇ N f = 10 4 

▲ N f = 10 5 □ N f = 10 6 

R = 10 

= - 0.52 

Predicted 

R = 0.1 

0 

-900 -600 -300 0 300 600 900 

m, MPa 

Fig. 8. Anisomorphic constant fatigue life diagram for wet specimen at room temperature. 

Predicted 

If the CFL diagram for a composite that is exposed to a hygrothermal environment is identified over 

the whole range of mean stress C m T 

, one can efficiently predict the fatigue life of the 

composite for any constant amplitude fatigue loading in the given hygrothermal environment. 

Therefore, it is a practical demand to establish such a CFL diagram approach in the form that is suitable 

for composites. The experimental results obtained from this study, along with the results from other 

sources [6-11, 14-17], have shown not only that the symmetric and linear Goodman diagram is not 

always valid for CFRP laminates, but also that modeling a CFL diagram by assuming the equi-life 

envelopes of similar shape for different constant values of life cannot be justified for all composite 

systems considered. 

87

88 


The anisomorphic CFL diagram, which was recently proposed by Kawai et al. [16, 17], takes account 

of all the fundamental requirements suggested by the experimental results. The anisomorphic CFL 

diagram approach was shown to be valid for different types of non-woven CFRP laminates in a dry 

environment at room temperature. If the anisomorphic CFL diagram approach is applicable to woven 

CFRP laminates not only in a dry environment but also in different mechano-hygro-thermal 

environments, the potential usefulness of this approach for evaluating the fatigue life of composites can 

be justified further. In order to answer this question, the anisomorphic CFL diagram approach is applied 

to the woven CFRP laminate tested in this study for different hygro-thermal environments. 

4.1 Anisomorphic CFL Diagram 

The anisomorphic CFL diagram [16, 17] is a theoretical CFL diagram that can be constructed for a 

given composite using only the static strengths in tension and compression and a single reference S-N 

relationship for the critical stress ratio . It allows predicting the S-N curves for the composite for any 

stress ratios in a given environment. 

The CFL envelope for a given constant value of life is composed of two smooth members defined in 

the two intervals of mean stress that are associated with tension and compression dominated failure 

modes, respectively. The two member curves are connected with each other on the radial straight line 

with a particular constant value of amplitude ratio 

= = - + that is 

( ) ( ) 

a / m a / m (1 ) / (1 ) 

associated with the critical stress ratio . The theoretical CFL curves are described by means of a 

piecewise nonlinear function that is defined by different formulas depending on the position of mean 

stress m in the interval [ C, T] 

as follows: 

( ) 

2- 

 

m - 

m 

( ) 

, 

( ) 

m m 

T 

a - a T -m 

 

- = ( ) 

( ) 

2- 

 

a m - 

m 

( ) 

 

, ( ) 

C mm C 

-m 

 

where C ( 0) and T ( 0) are the compressive and tensile strengths of the composite considered, 

respectively. The key quantities 

of the maximum fatigue stress 

and 

( ) 

a 

loading at the critical stress ratio = / ; 

represent the alternating and mean stress components 

( ) 

m 

( ) 

max , respectively, for a given constant value of life f 

C T 

(3) 

N on fatigue 

( ) 1 ( ) 

a = (1 - ) max 

(4) 

2 

( ) 1 ( ) 

m = (1 + ) max 

(5) 

2 

The variable in Eq. (3) denotes the fatigue strength ratio for loading at the critical stress ratio , 

and it is defined as 

( ) 

max = (6) 

 

T


Note that 0 1. 

 

The reference S-N curve for the critical stress ratio is described in a normalized form by means of a 

continuous monotonic function of the number of cycles to failure 2 Nf= f( ) . It is fitted to the 

fatigue data for the critical stress ratio. It is useful to assume a particular form of the function that is 

given by 

2N 

1 1 

= 

K 

1- 

( ) -( 

L) 

f n b 

 

where the angular brackets denote the singular function defined as x max0, x 

 

a 

= , ( L) 

89 

(7) 

is a 

normalized fatigue limit, and it is determined, as in the other constants K , n , a and b , by fitting 

Eq. (7) to the reference fatigue data for the critical stress ratio. 

Incidentally, if the exponent in the piecewise-defined function is replaced with a constant value of 

unity, the anisomorphic CFL diagram can be reduced to the following form [37]: 

- 

a - 

( ) 

a 

( ) 

m m 

( ) 

T 

-m 

( ) 

a 

( ) 

m 

-m 

( ) 

C -m 

 

- = 

 

, 

, 

( ) 

m m T 

C m 

( ) 

m 

which represents the asymmetric Goodman diagram. If the exponent is eliminated, the formulas 

for the anisomorphic CFL diagram become 

( ) 

2 

 

m - 

m 

( ) 

, 

( ) 

( ) m m 

T 

a - a T -m 

 

- = ( ) 

( ) 

2 

a m - 

m 

( ) 

 

, ( ) C mm C 

-m 

 

which is equivalent to the asymmetric Gerber diagram [37]: 

4.2 Comparison with experimental results 

The dashed lines in Figs. 7 and 8 indicate the anisomorphic CFL diagrams predicted. The solid line in 

each figure by which the anisomorphic CFL diagram is bounded corresponds to static failure = 1. 

In these figures, it is seen that for both dry and wet specimens, the experimental CFL data for R = 0.1 

and 10 are in good agreements with the predicted CFL envelopes, regardless of temperature and 

moisture content. Note that the fatigue data for R = 0.1 and 10 were not used for predicting the 

anisomorphic CFL diagrams. The fatigue data used in constructing the anisomorphic CFL diagram are 

those only for the critical stress ratio. Thus, we can use the fatigue data for R = 0.1 and 10 in order to 

verify the theoretical method. Consequently, the good agreements observed for these stress ratios 

suggest that the anisomorphic CFL diagram approach has great potential as a preliminary tool for 

visualizing the mean stress dependence of the fatigue life of the woven CFRP laminate in different 

hygro-thermal environments. 

(8) 

(9)

90 


Using the anisomorphic CFL diagrams, we can predict the S-N relationships for constant amplitude 

fatigue loading at any stress ratios in the combined temperature and moisture environments. The 

predicted S-N curves for dry and wet specimens at room temperature are shown in Fig. 9 and Fig. 10, 

respectively, along with the corresponding experimental data. It is clearly seen that the predicted S-N 

curves for R = 0.1 and 10 agree well with the experimental results, regardless of moisture content, 

which is consistent with the good agreements between the predicted and experimental CFL diagrams. 

These comparisons thus prove that the anisomorphic CFL diagram approach allows adequately 

predicting the fatigue lives of the woven CFRP laminate in a wet environment as well as in a dry 

environment at room temperature. We obtained good predictions for dry and wet environments also at 

80 o C. 

max, MPa 

max, MPa 

1000 

800 

600 

400 

200 

Experimental 

Dry-RT 10 Hz 

○ R = 0.1 

□ R = 10 


[(±45)/(0/90)] 3s 

0 

100 101 102 103 104 105 106 107 2N f 

Predicted 

Fig. 9. Predicted S-N relationships for dry specimens at room temperature. 

1000 

800 

600 

400 


[(±45)/(0/90)] 3s 

200 

0 

100 101 102 103 104 105 106 107 Experimental 

Wet-RT 10 Hz 

○ R = 0.1 

□ R = 10 

Predicted 

2N f 

Fig. 10. Predicted S-N relationships for wet specimens at room temperature.



The effect of water absorption on the constant amplitude fatigue strengths of a plain-weave roving 

fabric carbon/epoxy quasi-isotropic laminate at different stress ratios was examined. Furthermore, the 

anisomorphic CFL diagram approach was tested on the woven CFRP laminates that were exposed to 

different hygro-thermal environments. The results obtained can be summarized as follows: 

(1) At room temperature, the fatigue lives of wet specimens tend to become shorter than those of dry 

specimens, regardless of stress ratio. The reduction in fatigue strength due to water absorption was 

about 11 percent. 

(2) A similar reduction in fatigue strength due to water absorption occurred at high temperature 

(80 o C). 

(3) The S-N relationship for the woven CFRP laminate significantly depends on stress ratio, regardless 

of temperature and moisture content. 

(4) The slope of S-N relationship became largest for fatigue loading at the critical stress ratio, 

regardless of temperature and moisture content. Similar feature was observed in the results for dry 

specimens at room temperature. 

(5) The experimental CFL diagram for the woven CFRP laminate exhibits asymmetry and nonlinearity, 

regardless of test temperature and moisture content. The peaks of CFL envelopes are accompanied 

by fatigue loading at the critical stress ratio. The difference between the values of critical stress 

ratio for dry and wet specimens is small because of small difference between the static strengths in 

tension and compression. Accordingly, no significant difference in shape was observed between the 

CFL diagrams for dry and wet specimens. 

(6) The anisomorphic CFL diagrams predicted for different moisture-temperature conditions agree 

well with the experimental results. Accordingly, the S-N curves for the woven CFRP laminate that 

were predicted using the anisomorphic CFL diagram are in good agreements with the experiment 

S-N curves, regardless of water content, temperature and stress ratio. The successful agreements 

between the predicted and observed results suggest that the anisomorphic CFL diagram approach is 

potentially applicable to prediction of fatigue life of the woven CFRP laminates at different 

temperatures not only in a dry environment but also in a wet environment. 


This study was supported in part by the Ministry of Education, Culture, Sports, Science and 

Technology of Japan under a Grant-in-Aid for Scientific Research (No. 20360050). 

References 

[1] Kensche, C., Fatigue of composites for wind turbines, International Journal of Fatigue, Vol. 28, 2006, pp. 1363-1374. 

[2] Gustafson, C. and Echtermeyer, A., Long-term properties of carbon fibre composite tethers, International Journal of Fatigue, Vol. 28, 2006, 

pp. 1353-1362. 

[3] Feraboli, P. and Masini, A., Development of carbon/epoxy structural components for a high performance vehicle, Composites Part B, Vol. 

35, 2004, pp. 323-330. 

91

92 


[4] Watanabe, Y., Ito, N., Suzuki, H., Tamura, K., Optimization of a multiple traplock structure of CFRP riser pipe for deep sea drilling, 

proceedings of the 17th International Offshore and Polar Engineering Conference, Lisbon, July 1-6, 2007, pp.864-870, ISOPE. 

[5] Harris, B., editor, Fatigue in composites. Cambridge, UK: Woodhead Publishing Limited, 2003. 

[6] Harris, B., Reiter, H., Adam, T., Dickson, R.F., Fernando, G., Fatigue behaviour of carbon fibre reinforced plastics, Composites 

1990;21(3):232-242. 

[7] Adam, T., Fernando, G., Dickson, R.F., Reiter, H., Harris, B., Fatigue life prediction for hybrid composites, International Journal of 

Fatigue 1989;11(4):233-237. 

[8] Harris, B., Gathercole, N, Lee JA, Reiter H, Adam T. Life-prediction for constant-stress fatigue in carbon-fibre composites. Philosophical 

Transactions Royal Society of London 1997;A355:1259-1294. 

[9] Adam, T., Gathercole. N., Reiter, H., Harris, B., Fatigue life prediction for carbon fibre composites, Advanced Composites Letter 

1992;1:23-26. 

[10] Gathercole, N., Reiter, H., Adam, T., Harris, B., Life prediction for fatigue of T800/5245 carbon-fibre composites: I. constant-amplitude 

loading, Fatigue 1994;16:523-532. 

[11] Beheshty, M.H., Harris, B., Adam, T., An empirical fatigue-life model for high-performance fibre composites with and without impact 

damage, Composites Part A 1999;30:971-987. 

[12] Kawai, M., A phenomenological model for off-axis fatigue behavior of unidirectional polymer matrix composites under different stress 

ratios, Composites Part A, Vol. 35, No. 7-8, pp. 955-963, 2004. 

[13] Kawai, M. and Suda, H., Effects of non-negative mean stress on the off-axis fatigue behavior of unidirectional carbon/epoxy composites at 

room temperature, J Compos Mater, 38 (10), (2004), 833-854. 

[14] Ramani, S.V. and Williams, D.P., Notched and unnotched fatigue behavior of angle-ply graphite/epoxy composites, in Reifsnider KL, 

Lauraitis KN, Fatigue of Filamentary Composite Materials, ASTM STP 636, (1977), 27-46. 

[15] Ansell, M.P., Bond, I.P., Bonfield, P.W., Constant life diagrams for wood composites and polymer matrix composites, In: Proc. 9th Int. 

National Conf. on Composite Materials (ICCM 9), Madrid, Vol. V, pp. 692-699, 1993. 

[16] Kawai, M. A method for identifying asymmetric dissimilar constant fatigue life diagrams of CFRP laminates. Key Engineering Materials, 

2007;334-335:61-64. 

[17] Kawai, M, Koizumi, M. Nonlinear constant fatigue life diagram for carbon/epoxy laminates at room temperature. Composites Part A 

2007;38:2342-2353. 

[18] Goodman, J., Mechanics applied to engineering, Longman, Harlow, UK (1899). 

[19] Zhou, J. and Lucas, J.P., Hygrothermal effects of epoxy resin. Part I: the nature of water in epoxy, Polymer, Vol. 40, 1999, pp. 5505-5512. 

[20] Zhou, J. and Lucas, J.P., Hygrothermal effects of epoxy resin. Part II: variations of glass transition temperature, Polymer, Vol. 40, 1999, 

pp. 5513-5522. 

[21] Kawai, M., Yajima, S., Hachinohe, A. and Takano, Y., Off-axis fatigue behavior of unidirectional carbon fiber-reinforced composites at 

room and high temperatures, J Compos Mater, 35(7), 2001, 545-576. 

[22] Kawai, M. and Sagawa, T., Temperature dependence of off-axis tensile creep rupture behavior of a unidirectional carbon/epoxy laminate, 

Compos Part A, 39, 2008, 523-539. 

[23] Kawai, M. and Taniguchi, T., Off-axis fatigue behavior of plain woven carbon/epoxy composites at room and high temperatures and its 

phenomenological modeling, Compos Part A, 37(2), 2006, 243-256. 

[24] Jen, M.R., Tseng, Y., Kung, H. and Hung, J.C., Fatigue response of APC-2 composite laminates at elevated temperatures, Composites Part 

B, Vol. 39, 2008, pp. 1142-1146. 

[25] Kriz, R.D. and Stinchcomb, W.W., Effects of moisture residual thermal curing stresses, and mechanical load on the damage development 

in quasi-isotropic laminates, In: Damage in Composite Materials, Ed. Reifsnider, K.L., ASTM STP 775, 1982, pp. 63-80, ASTM. 

[26] Shen, C. and Springer, G.S., Effects of moisture and temperature on the tensile strength of composite materials, Journal of Composite 

Materials, Vol. 11, No. 1, 1977, pp. 2-16. 

[27] Garg, A.C., Effect of moisture and temperature on fracture behavior of graphite-epoxy laminates, Engineering Fracture Mechanics, Vol. 29, 

No. 2, 1988, pp. 127-149. 

[28] Ray, B.C., Temperature effect during humid ageing in interfaces of glass and carbon fibers reinforced epoxy composites, Journal of 

Colloid and Interface Science, Vol. 298, 2006, pp. 111-117. 

[29] Patel, S.R. and Case, S.W., Durability of a graphite/epoxy woven composite under combined hygrothermal conditions, International 

Journal of Fatigue, Vol. 22, 2000, pp. 809-820. 

[30] JIS K7073. Testing method for tensile properties of carbon fiber-reinforced plastics. In: Japanese Industrial Standard, Japanese Standards 

Association, 1988. 

[31] JIS K7083. Testing method for constant-load amplitude tension-tension fatigue of carbon fiber-reinforced plastics. In: Japanese Industrial 

Standard, Japanese Standards Association, 1993 

[32] JIS K7076. Testing method for compressive properties of carbon fiber-reinforced plastics. In: Japanese Industrial Standard, Japanese 

Standards Association, 1991


[33] Haberle, J.G. and Matthews, F.L., An improved technique for compression testing of unidirectional fibre-reinforced plastics; development 

and results, Composites Part A, Vol. 25, No. 5, (1994), pp. 358-371. 

[34] Shen, C.H. and Springer, G.S., Moisture absorption and desorption of composite materials, Journal of Composite Materials, Vol. 10, No. 1, 

1976, pp. 2-20. 

[35] McKague, Jr EL, Reynolds, JD and Halkias, JE, Moisture diffusion in fiber reinforced plastics, ASME Journal of Engineering Materials 

and Technology, Vol. 98, 1976, pp. 92-95. 

[36] Silverman, E., Wiacek, C.R. and Griese, R.A., Characterization of IM7 graphite/thermoplastic polyetheretherketone (PEEK) for spacecraft 

structural applications. In: Composite Materials: Testing and Design (Tenth Volume), ASTM STP 1120, Ed. G.C. Grimes, ASTM, 1992, 

pp. 118-130. 

[37] Kawai, M., Shiratsuchi, T. and Yang, K., A spectrum fatigue life prediction method based on the nonlinear constant fatigue life diagram 

for CFRP laminates, Proc the 6th Asia-Australasian Conf Compos Mater (ACCM-6), Kumamoto, Kyushu, Japan, September 23-26, (2008), 

153-156. 

93

Influence of thermal and mechanical cycles on the damping 

behaviour of Mg based-nanocomposite 

Z Trojanová a, *, A Makowska-Mielczarek b,† , W Riehemann b , P Lukáč a 

a Department of Metal Physics, Charles University, Prague, Ke Karlovu 5, CZ-121 16 Praha 2, Czech Republic 

b Institute of Material Sciences and Engineering, Clausthal University of Technology, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany 

Abstract 

Magnesium matrix composites show improved wear resistance, enhanced strength and creep resistance in comparison 

with their monolithic counterparts, on the other hand keep low density and good machinability. Internal friction 

measurements are a suitable tool to detect changes in the microstructure of thermally or mechanically loaded composites. 

Samples from pure magnesium reinforced with zirconia nanoparticles were thermally cycled between room temperature 

and increasing upper temperature of thermal cycle. After thermal cycling amplitude dependence of damping measured in 

terms of the decrement was measured. Very high values of the logarithmic decrement are described to the poor binding 

between the matrix and ceramic nanoparticles. The influence of number of cyclic bending to fatigue on the damping 

behaviour of the same nanocomposite was determined at room temperature. The measured decrease of the resonant 

frequency indicates a loss of stiffness during cycling. Crack deflection along an interface is followed by the separation of 

the particle/matrix interface. 

Keywords: magnesium nanocomposite; internal friction; thermal cycling; cyclic bending; damage parameter 


New promising magnesium materials may be produced using nanosized ceramic particles as 

reinforcement. We may call these materials as nanocomposites. Mg based nanocomposites may be 

fabricated by mixing and comilling of microscaled metal powder with nanoscaled particles followed by 

hot consolidations [1,2] or by friction stir processing [3]. These methods offer a good route to 

incorporate ceramic particles into the magnesium (and Mg alloys) matrix in order to form bulk 

composites. These composites may be attractive in applications because of their high strength and 

low-density characteristics. In practice, materials with good mechanical properties and with good ability 

to suppress mechanical vibrations are needed. One way to reduce the vibrations is to use high-damping 

materials. Various methods can be used to determine the damping characteristics. In resonant 

experiments where the frequency is the resonant frequency of the vibrating sample, the decay of free 

vibrations of the system is measured after excitation. The logarithmic decrement δ which expresses the 

reduction in amplitude of vibration of a freely decaying system during one cycle is defined as 


E-mail addresses: ztrojan@met.mff.cuni.cz 

† Now: Volkswagen AG, Wolfsburg, Germany 

δ = ln (An/An+1) (1)

Z Trojanová, etc. / Influence of thermal and mechanical cycles on the damping behaviour of Mg based-nanocomposite 

where An and An+1 are the amplitudes of of the free decaying vibrations after n cycles and (n+1) cycles, 

respectively. Measurement of the logarithmic decrement at small strains (stresses) is a sensitive method 

determining the microstructure of the material. Damping as a function of temperature and/or frequency 

has been used to identify several cinetic processes in materials. 

The objective of the present paper is to estimate the influence of thermal and mechanical cycling on 

the damping behaviour of magnesium/ZrO2 nanocomposite. 

2. Experimental Procedure 

Experimental material for this study has been prepared using commercially available microcrystalline 

Mg powder with a particle diameter of about 20 m. ZrO2 nanoparticles with a characteristic size of 

14 nm were prepared by evaporation with the pulsed radiation of a 1000 W Nd:YAD laser. The zirconia 

nanopowder and Mg micropowder were mixed together in an asymmetrically moved mixer for 8 hours, 

than the mixture was milled together for 1 hour, then pre-compressed in a uniaxial press and 

subsequently hot-extruded at 450 o C with 650 MPa extruding pressure. During extruding he original 

more or less uniaxial grains changed into elongated grains with the long axis in the extrusion direction. 

ZrO2 nanoparticles, or their agglomerates are mainly located in the grain boundaries of the resultant 

material. 

Test specimens for internal friction measurements were machined as bending beams 85 mm long with 

a thickness of 3 mm and 10mm width. 

The specimens fixed at one end were excited into resonance by a permanent magnet fixed on the free 

side of the bending beam and a sinusoidal alternating magnetic field. The resonant frequency was about 

130-140 Hz. The damping was measured as the logarithmic decrement of the free decay of the 

vibrating beam. The strain amplitude dependencies of the logarithmic decrement, so called internal 

friction curves, were measured. The specimens were sequentially annealed at increasing temperatures 

up to 550 o C for 0.5 h and after every heat treatment quenched into water of ambient temperature. 

Annealing at higher temperatures was performed in an argon atmosphere to avoid oxidation. The 

internal friction measurements were carried out immediately after quenching at room temperature in 

vacuum (about 30 Pa). 

Cyclic bending of the samples to fatigue was realised by the controlled bending loading of the 

bending beam samples in the similar apparatus as used for the damping measurements automatically 

controlling the amplitude and number of vibrations. The amplitude was 1x10 -3 . From the time and 

frequency, the number of cycles was calculated. Immediately after cycling the strain amplitude 

dependence of the decrement was measured. Because of different apparatus settings in comparison with 

the previous case the resonant frequency of the system was about 60 Hz. The end of the fatigue life of 

the sample was manifested by the rapid decrease of the resonant frequency. The sample was cycled up 

to N=1.03x10 8 cycles where the sample broke. 

95

96 

3. Results 


Figure 1 shows an optical micrograph of the as prepared nanocomposite. The grain size estimated in 

the cross section was about 3 m and in the extrusion direction about 10 m. The distribution of the 

nanoparticles was not homogenous. The nanoparticles or their agglomerates were located mainly in the 

grain boundaries of the resultant material. Only several particles was found inside of grains. 

Fig. 1. The microstructure of as-extruded Mg/ZrO2 nanocomposite. 

Figure 2 shows the plots of the logarithmic decrement against the logarithm of the maximum strain 

amplitude before and after one thermal cycle between room temperature and increasing uppe r 

temperature of the thermal cycle. 

Decrement 

0.030 

0.025 

0.020 

0.015 

0.010 

0.005 

0.000 

as rec 

100°C 

200°C 

300°C 

400°C 

500°C 

10 -5 10 -4 10 -3 

Amplitude 

Fig. 2. Amplitude dependences of decrement measured at room temperature after thermal cycling at increasing upper temperature of the thermal 

cycle. 

For many metallic materials, the strain dependence of the damping capacity can be divided into a 

strain independent and a strain dependent component. In the case of the logarithmic decrement, the 

experimental finding results may be expressed as: 

= 0 + H () (2) 

0 is the amplitude independent component, found at low strain amplitudes. The component H depends 

on the strain amplitude and it is usually caused by dislocation depinning from weak pinning points in


the material. The critical strain cr at which the logarithmic decrement becomes amplitude dependent 

may be used to calculate the micro yield stress C according to the equation 

C = E cr (3) 

where E is the Young‟s modulus. From Figure 2 it can be seen that the applied thermal treatment 

influences previously the amplitude independent component 0, while the amplitude dependent 

component H varies with the upper temperature of the thermal cycle the only slightly. 

The logarithmic decrement plotted against number of cycles for two strain amplitudes is introduced 

in Figure 3. It can be seen that the decrement increases with increasing number of cycles for both 

amplitudes up to 2.4x10 6 cycles than slightly decreases, up to 2.9x10 7 cycles. Further cycling decreases 

the decrement until failure. 

() 

0.06 

0.05 

0.04 

0.03 

0.02 

5 x 10 -5 

1 x 10 -4 

-Mg+3%ZrO 2 

103 104 105 106 107 108 109 0.01 

number of cycles N 

Fig. 3. Logarithmic decrement depending on number of bending cycles at room temperature estimated for two strain amplitudes. 

4. Discussion 

4.1. Thermal cycling 

The amplitude independent material damping can be caused by different mechanisms (thermoelastic 

damping, grain boundary sliding, and point defects). The significant contribution to the damping in 

magnesium is dislocation damping. Temperature dependence of the amplitude independent component 

of the logarithmic decrement 0 is introduced in Fig. 4. It is obvious that the values of 0 are very high. 

Similar damping measurements were realised on a magnesium nanocomposite with alumina particles 

prepared with the same method [4]. The damping in the amplitude independent region estimated at the 

as received state is substantially lower 0(Mg+3n-Al2O3) = 0.00175 while 0(Mg+3n-ZrO2) = 0.0127. 

The high damping in the Mg+3n-ZrO2 nanocomposite is very probably due to weak bonding between 

zirconia nanoparticles in comparison with alumina nanoparticles where the bonding is nearly perfect. 

Very high damping in the composite with the zirconia nanoparticles is caused by an interfacial slip 

due to weak bonding between particles and matrix. In this case the frictional energy loss caused by 

sliding at the interfaces may become a primary source of damping. The damping component due to 

interfacial slip under the applied stress amplitude 0 can be expressed as [5-7] 

97

98 


2 

3 

( - 

) 

= Vp for 0 cr 

(4) 

2 

r 0 

2 

0 

EC 

cr 

where is the friction coefficient between both components of the composite, r the radial stress at the 

interface corresponding to stress amplitude 0 or strain amplitude 0. The critical interface strain cr 

corresponding to the critical interface shear stress cr is the strain at which the slip at the interfaces 

begins. EC is the elastic modulus of the matrix. Assuming that cr is much lower than 0 one obtains 

2 

3 

r = Vp 

(5) 

2 

The stress concentration factor k = r/0 has been reported to be 1.1-1.3 [7]. The model does not take 

into account possible effects of temperature or frequency on damping and therefore, the predictions of 

the model may be taken only as the first approximation. The effect of an additional damping due to the 

influence of particles can be clearly seen in Fig. 6. While the addition of alumina particles decreases the 

amplitude independent component, the addition of zirconia particles it expressively increases. The 

measured increase in 0 due to the addition of ZrO2 particles to Mg is about 0.008-0.009. Taking for the 

friction coefficient a typical value of 0.08, the relation (4) predicts a value for an additional damping 

owing to interfaces 0i = 0.04. The discrepancy between the predicted and measured value may be 

caused by a non-uniform strain state in specimens. They were subjected to bending and hence, strain 

reaches its critical value at which the interface sliding starts only in some sections of the specimen. High 

values of 0 obtained for Mg-zirconia nanocomposite is very probably caused also by the grain 

boundary sliding supported by diffusion processes. The dislocation contribution may be also not ruled 

out. 

Decrement 0 

0.014 

0.012 

0.010 

0.008 

0.006 

Temperature (°C) 

0 

0 100 200 300 400 500 600 

Fig. 4. Amplitude independent component depending on upper temperature of the thermal cycle. 

Decrease of the damping occurs after thermal cycling with the upper temperature higher then 250 o C 

is obvious from Fig. 4. This decrease indicates some changes in the interface between particles and the 

magnesium matrix. Nanoparticles were prepared by the evaporation with the pulsed radiation of a laser. 

The resulting powder was a mixture of crystalline and amorphous particles [8]. The observed decrease 

of damping is very probably due to partial phase transformation of ZrO2 nanoparticles and consequently 

better bonding at the interface.[9]. It restricts the interface sliding and energy dissipation. Thermal


cycling of the nanocomposite generates thermal stresses at the magnesium/zirconia interface due to a 

big difference between the thermal expansion coefficient (CTE) of the magnesium matrix and zirconia 

nanoparticles. These thermal stresses can achieve the yield stress in the matrix and then new 

dislocations are generated in the matrix. An increase in the dislocation density near reinforcement can 

be calculated as [10] 

B f T1 = 

b(1 - f ) rf 

where b is the magnitude of the Burgers vector of dislocations, B is a geometrical constant, the 

absolute value of CTE, f volume fraction of the reinforcing phase and rf its minimum size. Newly 

created dislocation may increase the amplitude dependent component of decrement. This increase of H 

= - 0 observed after thermal cycling at higher temperatures is obvious from Fig. 5 where the increase 

of damping is visible. 

- 0 

0.012 

0.010 

0.008 

0.006 

0.004 

0.002 

0.000 

-0.002 

400°C 

450°C 

500°C 

10 -5 10 -4 10 -3 

Amplitude 

Fig. 5. Amplitude dependent component measured after thermal cycling at temperatures 400-500 o C. 

decrement 0 x 10 3 

20 

15 

10 

5 

0 

0 200 400 600 

temperature (°C) 

Mg 

Mg+3n-ZrO 2 

Mg+3n-Al 2 O 3 

Fig. 6. The temperature dependence of the amplitude independent component 0 for microcrystalline Mg (Mg), Microcryslalline Mg with 3vol% 

of zirconia nanoparticles (Mg+3n-ZrO2) and microcrystalline Mg with 3% alumina nanoparticles (Mg+3n-Al2O3). 

To summarize the discussion to this point, the high damping of the Mg+3n-ZrO2 is due to the 

interface friction caused by weak bonding at the interface between magnesium matrix and zirconia 

99 

(6)

100 


nanoparticles. Observed decrease of the decrement after thermal cycling at temperatures higher then 250 

o C may be explained by the changes in the interface. The phase transformation in zirconia nanoparticles 

improves the bonding in the interface and restricts the interface sliding. Better bonding after thermal 

treatment at higher temperatures has a consequence in thermal stresses in the vicinity of the interface 

and newly created dislocations in plastified zones. 

4.2. Bending cycling 

The logarithmic decrement in the strain amplitude independent region at low frequencies yields in the 

Granato and Lücke theory [11-13] 

B 

 

36Gb 

d 4 

0 = (7) 

2 

where G is the unrelaxed shear modulus, b is the Burgers vector and Bd is the damping force per unit 

length of dislocation per unit velocity, is the dislocation density and length of the shorter dislocation 

segments pinned at weak pinning points, which may be foreign atoms or small clusters of the point 

defects. Observed increase of the decrement with the number of cycles NC (see Fig. 3) is caused by the 

increase of the dislocation density. Cycling in the region between 3 x 10 3 and 2.4 x 10 6 cycles leads to 

an increase of the decrement. The observed increase of the decrement indicates an increase of the 

dislocation density and also an increase in the distance between weak pinning points. Further cycling 

leads to the gentile decrease of the decrement up to 2.9 x 10 7 cycles. This decrease indicates a decrease 

of the dislocation density due to interactions between dislocations. Higher dislocation density restricted 

the slip length of vibrating dislocation segments. The decrement estimated for higher number of cycles 

then 2.9 x 10 7 decreases with increasing number of cycles. This decrease is very probably connected 

with the formation of crakes. This is in accordance with the development of the damage parameter with 

the number of cycles. The damage of the specimen after N cycles, D(N), can be defined as [14]: 

Damage D 

0.08 

0.06 

0.04 

0.02 

0.00 

( ) 

D N 

E f 

= 1- = 1- 

(8) 

E f 

2 

N N 

2 

o o 

103 104 105 106 107 108 109 -0.02 

Number of cycles N 

Fig. 7. Damage parameter plotted against number of cycles.


where EN is an effective Young‟s modulus of the specimen after N cycles and E0 is the Young‟s modulus 

for N = 0 and fN and f0 are the resonant frequencies of the specimen after N cycles and for N = 0, 

respectively. This definition is usual and reasonable [14] because DN = 0 for undamaged specimen, 

D(N) increases when cracks start propagating in the specimen and DN = 1 for a broken specimen. Fig. 7 

shows the damage D plotted against the cycle number N. A rapid increase of D occurred for N 2 x 10 7 . 

The measured decrease of the resonant frequency at the end of fatigue process indicates a stiffness loss 

due to the formation of cracks. Moreover it indicates that in this case of composite material cracks do 

not lead to recognisable damping contrary to others [15-17]. 


Thermal and mechanical cycling of the Mg/ZrO2 nanocomposite invoked irreversible changes in the 

microstructure. These changes are detectable using non destructive damping measurements. Internal 

friction measurements are the usefull tool for the study of fatigue of materials. 

Acknowledgments 

The authors thank the Grant Agency of the Czech Republic for financial support under grant 

106/07/1393. This work also received a support from the Ministry of Education, Youth and Sports of the 

Czech Republic by the project MSM 0021620834. 

References 

[1] J. Lan, Y. Yang, X.C. Li, Microstructure and microhardness of SiC nanoparticles reinforced magnesium composites fabricated by 

ultrasonic method, Mater. Sci. Eng. A, 386 (2004) 284–290. 

[2] H. Ferkel, B.L. Mordike, Magnesium strengthened by SiC nanoparticles, Mater. Sci. Eng. A 298 (2001) 193–199. 

[3] S.F. Hassan, M. Gupta, Development of high performance magnesium nano-composites using nano-Al2O3 as reinforcement Mater. Sci. 

Eng. A 392 (2005) 163–168. 

[4] Z. Trojanová, W. Riehemann, H. Ferkel, P. Lukáč. Internal friction in microcrystalline magnesium reinforced by alumina particles, J. 

Alloys Comp. 310 (2000) 396-399. 

[5] N.N. Kishore, A. Gosh, B.D. Agarwal, Damping characteristics of fiber composites with imperfect bonding, J. Reinforced Plastics and 

Composites 1 (1982) 40-64. 

[6] D.J. Nelson, J.W. Hanckok, Interfacial slip and damping in fibre reinforced composites, J. Mater. Sci. 13 (1978) 2429-2440. 

[7] J. Zhang, R.J. Perez, E.J. Lavernia, Effect of SiC and graphite particulates on the damping behavior of metal matrix composites, Acta 

Metall. Mater. 42 (1994) 395-409. 

[8] H. Ferkel, W. Riehemann, Laser-induced solid solution of the binary nanoparticle system Al2O3-ZrO2, Nanostructured Mater., 8 (1997) 

457-464. 

[9] I. Molodetsky, A. Navrotsky, M.J. Paskowitz, V.J. Leppert, S.H. Risbud, Energetics of X-ray-amorphous zirconia and the role of surface 

energy in its formation. J. Non-Crystalline Solids 262, 2000, 106-113. 

[10] R.J. Arsenault, N. Shi, Dislocations generation due to differences between the coefficients of thermal expansion, Mater. Sci. Eng., 81 

(1986) 151-187. 

[11] A.V. Granato, K. Lücke, Theory of mechanical damping due to dislocations, J. Appl. Phys. 27 (1956) 583-593. 

[12] A.V. Granato, K. Lücke, Applicaton of dislocation theory to internal friction phenomena at high frequencies, J. Appl. Phys. 27 (1956) 

789-805. 

[13] A.V. Granato, K. Lücke, Temperature dependence of amplitude-dependent dislocation damping, J. Appl. Phys. 52 (1981) 7136-7142. 

[14] J. Lemaitre, A Course on Damage Mechanics, Berlin, Springer, 1996. 

[15] J. Göken, W. Riehemann, Damping behaviour of AZ91 magnesium alloy with cracks, Mat. Sci. Eng. A 370 (2004) 417-421. 

101

102 


[16] A. Mielczarek, Z. Trojanová, W. Riehemann, P. Lukáč, Influence of mechanical cycling on damping behaviour of short fibrereinforced 

magnesium alloy QE22, Mat. Sci. Eng. A442 (2006) 484-487. 

[17] W. Riehemann, Z. Trojanova, A. Mielczarek, Fatigue in magnesium alloy AZ91 Alumina fiber composite studied by internal friction 

measurements, Procedia Engineering 2 (2010) 2151-2160.

Delamination during fatigue testing on carbon fiber fabrics 

reinforced PPS laminates 

Abstract 

J Bassery *, J Renard † 

Centre des matériaux P. M. Fourt, Mines-Paris Tech, CNRS UMR 7633, BP 87, F-91003 Evry, Cedex 

This paper discusses the static and fatigue behaviour and damage development in satin 5 carbon/pps woven fabric 

composite laminates. First, the orthotropic elastic stiffness matrix of 0 o -ply laminate has been determined by a global 

mechanical study in static (tensile, bending and compression tests). Then, an elastoviscoplastic model has been clearly 

identified to characterize the 45 o oriented sample behaviour during static tests (tensile, creep, torsion and 

tension-relaxation tests). Finally, fatigue tensile-tensile tests were performed and lead to in-situ observations of 

delamination, by using a high resolution camera. The experimental results show that the stiffness evolution follow two 

stages (onset then stabilization) for 0 o ply and angle-ply laminates too. This evolution is correlated with damage 

mechanism: transverse crack and delamination. But the maximum stiffness reduction is low and close to the experimental 

dispersion. Therefore, in a simplified approach, the onset delamination criterion has been identified on static tests. This 

criterion, based on Coulomb friction law, has been identified thanks to Arcan-Mines tests, and also comparison between 

2D ½ dimensional finite element model analyzis of tensile sample and experimental results. The home made 

Arcan-Mines device is an original experimental and initially used to qualify adhesive bonding assemblies. It has been 

modified to determine interface strength in carbon fiber fabric reinforced PPS laminates. The main interest of this testing 

device is to provide multiaxial state of stress as well as in tension than in shear or compression while always remaining a 

homogenous state of stress at the interface. The interface strengths (in tension or in shear) are directly used in the onset 

delamination criterion and give a good agreement between model predictions and experimental results. 

Keywords: carbon fiber fabric reinforced PPS laminate; onset delamination criterion; elastoviscoplastic model; Arcan-Mines test; static tests; 

fatigue tests 


The objective of this study is to predict initiation of delamination in polyphenylenesulfide (PPS) 

reinforced carbon fiber fabrics composites laminates during fatigue testing. In transportation 

engineering fields such as aeronautics or aerospace, composite materials have many applications 

because of their high strength/weight ratio. Thermosetting resin, even if they present interesting 

mechanical properties, are also characterized by undeniable drawbacks such as the necessity to be stored 

at low temperatures, some difficulties to control the reticulation process, a very long curing process and 

a handmade draping that generates most of the non reversible defects during the manufacturing process. 

In such a context, high-performance thermoplastic resins represent a promising alternative to solve 

thermosetting resins problems. Indeed, thermoplastic matrix offer a number of advantages compared to 

* E-mail address: josserand.bassery@ensmp.fr 

† E-mail address: jacques.renard@ensmp.fr

104 


conventional thermosetting resins such as epoxies. Thermoplastics exhibit good chemical resistance as 

well as an excellent damage and impact resistance and may be used over a wide range of temperatures. 

They have a very low level of moisture uptake which means their mechanical properties are less 

degraded under hot/wet conditions. Thermoplastic composite materials require different manufacturing 

and repair techniques. It is possible to get thermoplastic based laminates with complex shapes in few 

stages thanks to a thermoforming process. In addition, unlike thermosetting resins, thermoplastics may 

be re-melted after they are formed providing recycling possibilities. They can also be welded by heating 

and pressure process close to their melting point. However, thermoplastic composites are more difficult 

to repair than conventional thermosetting composites and high-performance thermpolastics are more 

expensive. A wide range of thermoplastics are available but in the area of high-performance 

thermoplastics, PPS composites are probably the most used. Because this material can exhibit a high 

crystallinity rate and high glass transition temperature. Crystallinity in high-performance polymers is 

important because it has a strong influence on chemical and mechanical properties: the crystalline phase 

tends to increase the stiffness and tensile strength while the amorphous phase is more effective in 

absorbing impact energy. Further a high glass transition temperature means that the mechanical 

properties remain stable under a wide range of temperature. Nevertheless, before making structural parts 

in thermoplastics composites, an accurate knowledge of the mechanical behaviour is needed as well in 

static [1] and in fatigue [2] and tensile tests have to be performed. When during fatigue testing 

delamination defined as the debonding between two adjacent layers occurs, very often that means a 

rapid and detrimental failure for the structure. Thus in order to establish a criterion able to predict 

delamination onset, fatigue tests at different stress levels and Arcan-Mines [3] tests have been 

performed. 

2. Delamination onset criterion 

Fig. 1. Illustration of the material used during this work. 

First, we suppose the homogeneity of the layers and their linear elastic behaviour. In the case of a flat 

smooth tension sample, the criterion is based on the following assumptions: 

-A normal negative strength (compression) delays the delamination onset in shear (modes II and III); 

-on the contrary, a positive normal stress accelerates the delamination onset. 

-finally a normal negative strength is shear equal zero, cannot provoke the delamination onset. 

These remarks are summarized by the law of Coulomb [4] describing the friction between two 

bodies. 

Therefore, the criterion rated c is written like this:

J Bassery, J Renard / Delamination during fatigue testing on carbon fiber fabrics reinforced PPS laminates 

+ - - 

( ) T ( ) ( ) 

2 2 2 

2 2 2 

3 / 1 1 3 / 1 2 2 3 / 2 

c = F Y + F + k F S + F + k F S 

(1) 

( 

- 

) ( 

- 

) 

( 

+ 

2 

) 2 

T ( 

2 

) 2 ( 

2 

) 2 

2 2 

2 2 

3 0 = 1 + 1 3 / 1 + 2 + 2 3 / 2 

If F therefore c F k F S F k F S 

If F 0 therefore c = F / Y + F / S + F / S 

3 3 1 1 2 2 

 

With F = n; F = n; F = n; n : normal strength 

1 13 2 23 3 33 

The scale mark of the study is: 1=warp, 2=weft and 3=thickness. 

The bending tests on three-points closed bearing show the shear mode II and the shear mode III are 

equivalent (see fig.8) so S1=S2=S and k1=k2=k. The parameters YT and S characterizing the interface 

strength between different layers have to be identified from literature [5]. In our case, such information 

is lacking concerning carbon fiber fabrics reinforced PPS laminates. We proposed an original 

experimental set-up, home made Arcan-Mines device, originally used to qualify adhesive bonding 

assemblies, and which has been modified to determine interface strength in carbon fibber fabrics 

reinforced PPS laminates. The parameter k characterizing the friction capacity between two layers has 

to be determined by comparison between observations make during tension tests and finite element 

analysis. In order to be independent from the mesh, the stresses needed for the criterion have to be 

calculated with a non-local method. 

Average method: it consists in averaging the stresses on a domain extending until a certain 

critical length rated a0.For each stresses used in the criterion; a critical length has to be known. 

But in the rest of this paper, only one critical length will be considered for the three out of plane 

stresses. 

a0 

( ) 1/ ( ) 

a = a d 

(3) 

ij 0 0 ij 

0 

Gradient method: this one consists in taking into account the first derivative of the out of 

plane stresses on a given area rated h. 

( y) = + y + h / 2 - y - h / 2 

(4) 

( ) ( ) 

ij ij ij ij 

Then, the two methods are combined in one. 

a0 

1 

( a ) = ( y) + ( y + h / 2 ) - ( y - h / 2)( 

y) dy 

(5) 

ij 0 

ij ij ij 

a0 

0 

Before the numerical simulations, the elastic static behaviour of the studied material has to be found. 

3. Static behaviour 

3.1 Orthotropic elastic stiffness matrix 

3.1.1 Definition 

The sudied material is a composite laminate with seven plies of harness satin five fabrics draped at 0 o . 

So the material exhibits three plans of symmetry, two by two orthogonal meaning that the elastic 

behaviour is orthotropic. This behaviour is described by the stiffness matrix C ij (with i, j = 1, 2, 3) or the 

105 

(2)

106 


compliance matrix Sij trough Hooke‟s law. Using Voigt notation, the Hooke‟s law of the matrix 

behaviour is described by: 

1 C11 C12 C13 0 0 0 1 1 

S11 S12 S13 

0 0 0 1 

 

 

 

2 

C21 C22 C23 0 0 0 

 

2 

2 

S21 S22 S23 

0 0 0 

 

2 

3 C31 C32 C33 

0 0 0 3 3 S31 S32 S33 

0 0 0 3 

= ou = 

4 0 0 0 C44 

0 0 4 4 0 0 0 S44 

0 0 4 

 

5 0 0 0 0 C55 

0 

5 

5 0 0 0 0 S55 

0 

5 

 

 

 

 

6 0 0 0 0 0 C 

66 

6 

 

 

 

6 0 0 0 0 0 S 

 

66 

6 

The engineering moduli (Young modulus, Poisson ration, shear modulus) are directly related to the 

compliance constants. Hence, the elastic matrix is: 

1 1/ E1 -12/ E1 -13/ 

E1 

0 0 0 1 

 

 

2 -21/ E2 1/ E2 -23/ 

E2 

0 0 0 

 

2 

3 -31/ E3 -32/ 

E3 1/ E3 

0 0 0 

3 

= 

4 0 0 0 1/ G23 

0 0 4 

0 0 0 0 1/ G 0 

 

5 13 

5 

 

 

 

 

 

 

 

6 0 0 0 0 0 1/ G 

12 

6 

By definition, compliance and rigidity matrix are symmetrical. 

That means that: S12=S21, S13=S31 and S23=S32 so an additional relation is obtained: 

The compliance elastic matrix becomes: 

/ E = / E ; / E ; / E = / E 

(8) 

21 2 12 1 31 3 23 2 32 3 

1 1/ E1 -12/ E1 -13/ 

E1 

0 0 0 1 

 

 

2 -12/ E1 1/ E2 -23/ 

E2 

0 0 0 

 

2 

3 -13/ E1 -23/ 

E2 1/ E3 

0 0 0 

3 

= 

4 0 0 0 1/ G23 

0 0 4 

0 0 0 0 1/ G 0 

 

5 13 

5 

 

 

 

 

 

 

 

6 0 0 0 0 0 1/ G 

12 

6 

In order to determine the Young moduli E1and E2, the Poisson ratio ν12 and the shear modulus G12, 

tension tests in the warp, weft and in 45 o directions were realized. The E3 modulus was obtained by 

making compression test on small disk in the thickness direction. Finally, three-point bending tests 

allowed estimating the shear modulus G13 and G23. The others Poisson ratios ν13 and ν23 are estimated 

with a simple rule of mixture and literature values. 

3.1.2 Experimental results 

3.1.2.1 Tensile tests 

According to standard NF EN 2561, tensile test were performed on 250mm*25mm samples cut in the 

warp, weft and 45 o directions. The samples of PPS matrix are reinforced with a carbon fiber fabric 

draped in 0 o of 7 plies in the thickness. On each end of the samples, 60mm tabs are made in glass epoxy, 

in order to observe failures outside the tensile machine jaws. Furthermore, these samples are dried at 

least one day before the test in an oven at 70 o C. The mechanical tests were realized with an Instron 

(6) 

(7) 

(9)


tensile testing machine equipped with a 100 KN load cell and two extensometer sensors which allow 

measuring the longitudinal and transverse displacements (fig.2). For warp and weft directions, the 

experimental curves are plotted with nominal strain εn and stress ζn, the definitions of which are: (10) 

F 

n = and 

S 

0 

l 

and Δl the current extension. 

n = where F is the current load, S0 the initial cross-section, l0 the initial gage length 

l0 

Fig.2. Experimental set-up for tensile tests [5]. 

Tensile test in the warp and weft directions 

In the warp and weft directions, the behaviour is elastic and not strain rate dependent (fig.3 a and b). 

It‟s due that in both cases; the behaviour of composite is controlled by the fibers. The Young moduli 

E1and E2 are the slopes of these curves. Their respectively mean values are about 60.59 GPa and 63.38 

GPa. The Poisson ration ν12 have been also calculated from these experiments and estimated at 0.048. 

The values of E1 and E2 are very close because of the fabric which is balanced. 

Stress (MPa) 

800 

700 

600 

500 

400 

300 

200 

100 

Tension test in warp direction 

ε'=1e-5/s 

ε'=1e-4/s 

ε'=1e-3/s 

0 

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0080 0.0090 0.0100 0.0110 0.0120 0.0130 0.0140 

Strain (-) 

Stress (MPa) 

800 

700 

600 

500 

400 

300 

200 

100 

Tension test in weft direction 

0 

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0080 0.0090 0.0100 0.0110 0.0120 0.0130 

(a) (b) 

Fig. 3. Tensile test curves in (a) the warp, (b) weft directions. 

Tensile in the 45o direction 

In the 45 o direction, a non-elastic and strain rate dependent behaviour can be observed (fig.4). 

Because it‟s the matrix composite this controls the behaviour of the composite beyond axis of the 

solicitation. Here, the plotted curve is obtained with true strain and stress which are respectively 

calculated from: 

l 

Strain (-) 

( 0 ) ( ( 0 ) 0 ) ( 0 ) ( ) 

= l / l = ln l / l = ln l + l / l = ln 1 + l / l = ln 1+ 

 

(10) 

true 

l 

n 

0 

ε'=1e-5/s 

ε'=1e-4/s 

ε'=1e-3/s 

107

108 


-1 

( ) ( ) ( ) ( ) 

= F / S = F S l / l = Fl / S l = F( l + l ) / S l = F / S 1 + l / l = (1 + ) (11) 

true 0 0 0 0 0 0 0 0 0 n n 

G12 is calculated from the slope of the previous curve and also with this formula: 

( ( ) ) 

G = F S - 

(12) 

12 / 2 0 xx yy 

Where F is the current load, S0 is the initial cross section and, εxx and εyy are the longitudinal and 

transverse strains. The mean value of G12 is about 3.99 GPa. 

Stress (MPa) 

250 

200 

150 

100 

50 

Tension test in 45° direction 

0 

0.0000 0.0250 0.0500 0.0750 0.1000 0.1250 0.1500 

Strain (-) 

Fig. 4. Tensile tests in the 45 o direction at different strain rates. 

3.1.2.2 Compression test on small disk in the thickness direction 

The compression samples are obtained by core-drilling under water and have a diameter equal to 18 

mm in order to be at least two times superior to the weave size (here 7 mm). All the samples are greased 

to limit friction strengths and placed between two compression plates. The displacement between both 

plates is measured by a linear variable differential transformer (LVDT). All the tries were made at 

ambient temperature, with a constant cross-beam speed (equal to 0.035mm/min) and below a maximum 

ε'=1e-5/s 

ε'=1e-4/s 

ε'=1e-3/s 

ε'=1e-2/s 

load of 50 KN to avoid any damage on the load cell. The results are the following: 

Stress (MPa) 

-20 

-40 

-60 

-80 

-100 

-120 

-140 

-160 

-180 

-200 

Compression test on small disk sample in the thickness direction 

0 

0.000 0.025 0.050 0.075 0.100 0.125 0.150 

Strain (-) 

Sample 1 

Sample 2 

Sample 3 

Sample 4 

Sample 5 

Sample 6 

Sample 9 

Sample 8 

Sample 10 

Fig. 5. Compression test on small disk sample in the thickness direction. 

The curves are obtained by using the following formulas: 

2 ( ) 

= 4 F / and = d / e 

(13) 

nc 0 nc 0 

Where F is the current load, 0 is the initial sample diameter, d is the plate displacement measured by 

the LVDT and e0 is the initial sample thickness. So here, only nominal stress and strain are considered.


The Young modulus E3 is the slope of the previous curve (fig.5). In order to stay in static stage, the 

imposed cross-beam speed corresponds to a strain rate of 10 -4 s -1 . Because of the setting up of 

compression plates and the friction strengths, the curves beginning are all biased. Therefore, the elastic 

constant will be determined only for stresses included between -40 and -180 MPa, that means where the 

behaviour is linear. Due to the difficulty to set perfectly the sample in the centre of compression plates, 

a substantial dispersion of the results is obtained. Anyway, the mean value, equal to 2.94 GPa, is close to 

the literature one [6]. Its value is small compare to E 1 and E2 but gets the same order of magnitude than 

the shear modulus G12. So for compression in the thickness direction, it‟s the resin which supports the 

load. In conclusion, by hypothesis the Young modulus E3 measured in compression will be equivalent to 

the tensile one. 

3.1.2.3 Three-point bending tests 

According to the standard EN 2563, bending test samples, the dimensions of which are 20*10mm 

were cut with diamond saw according to the warp and weft directions. The bending assembly used 

supports having all radiuses equal to 3mm and worked on tensile testing machine (fig.6). In order to 

observe an intralaminar shear failure, the distance between the fixed supports is 5 times the sample 

thickness. The deflection was measured by a LVDT setted in the middle of both fixed supports and the 

strength was recorded by a load cell of 25 KN. All the experiments were at room temperature and with a 

constant cross-beam speed (equal in 1mm / min). 

Fig. 6. Experimental set-up for three-point bending test. 

The experimental curves (strength versus deflection) are plotted below: 

Strength (N) 

Sample 1 

Sample 2 

Sample 3 

Sample 4 

Sample 5 

-0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 

0 

0.00 

Deflection (mm) 

Fixed supports 

1 750 

1 500 

1 250 

1 000 

750 

500 

250 

Strength (N) 

Sample 1 

Sample 2 

Sample 3 

Sample 4 

Sample 5 

Shifted support 

LDVT 

-0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 

0 

0.00 


(a) (b) 

Fig. 7. Three-point bending test curves in the (a) warp, (b) weft directions 

1 600 

1 400 

1 200 

1 000 

800 

600 

400 

200 

109

110 


In both cases, the bending behaviour is mainly linear (fig.7). The beginning of the try is a little bit 

biased because all the clearances of the experimental set-up have to be offset. Around 1.5 KN, a 

non-linearity appears. It‟s due to the outbreak of delamination cracks in the sample (fig.8). So for 

staying in the linear part, the slope of these curves will calculated from 0.2 and 1 KN. Also, the imposed 

cross-beam speed matches with a strain rate equal to 10 -3 s -1 . 

The experimental dispersion is not so much important. 

Fig. 8. Delamination observed by optical microscopy after a three-point closed bearing bending test (in red, the delamination cracks). 

The strength and deflection measured can be linked to the elastic moduli by this equation [7]: 

deflection 

( ) ( ) 

= + (14) 

3 

Fl / 48 EI0 Fl / 4GkS0 

Where θdeflection is the deflection in the middle of the sample, F the current load, I 0 the initial moment of 

inertia of the cross-section, k is a shear correction factor (equal to 5/6), S0 the initial cross-sectional area, 

and l the length between the two fixed supports. Besides E is the Young modulus and G the shear 

modulus. 

The geometrical constants are defined by: 

the initial width and the thickness of the sample. 

3 

0 = 0 0 /12 , S0 = b0h0 with b0 and h0 are in that order 

I b h 

The elastic moduli have to be separated from the experimental results, it means: 

( ) deflection 

( ) 

1/ E + 6 h / 5l G = 4 b h / Fl 

(15) 

2 2 3 3 

0 0 0 

The ratio θdeflection against F is the inverse of the slope of the curve introduced above. So in the warp 

direction, equation (15) becomes: 

And in the weft direction, equation (13) gives: 


( ) 

1/ E + 6 h / 5l G = 4 b h / Fl 

(16) 

2 2 3 3 

1 0 13 0 0 


( ) 

1/ E + 6 h / 5l G = 4 b h / Fl 

(17) 

2 2 3 3 

2 0 23 0 0 

Thanks to the tensile test, E1 and E2 are known. Hence, the mean values of G13 and G23 are 2.17 and 

2.12 GPa. Even in shear, the fabric of the study seems to be balanced. In the aim to check the accuracy 

of the correctional shear factor rated k, elastic finite element analyses have been performed. These 

results (fig.9 a and b) demonstrated that the mean values of G13 and G23 are pertinent.

Strength (N) 

Sample 1 

Sample 2 

Sample 3 

Sample 4 

Sample 5 


Simulation 

-0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 

0 

0.00 


1 800 

1 600 

1 400 

1 200 

1 000 

800 

600 

400 

200 

Strength (N) 

Sample 1 

Sample 2 

Sample 3 

Sample 4 

Sample 5 

Simulation 

-0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 

0 

0.00 


(a) (b) 

Fig. 9. Comparison between elastic simulations and results of three-points closed bearing bending tests in the (a) warp, (b) weft directions. 

3.1.2.4 Average orthotropic elastic stiffness matrix 

From the average different elastic moduli, the stiffness matrix (expressed in GPa) is equal to: 

61.113.431.06000 

 

3.43 63.92 1.07 0 0 0 

 

1.06 1.07 2.97 0 0 0 

R = 

0 0 0 3.99 0 0 

0 0 0 0 2.17 0 

 

 

 

0 0 0 0 0 2.16 

 

This stiffness matrix will be used for finite element analyses. 

3.2 Non-linear behaviour of the 45 o oriented samples 

3.2.1 Test on torsion bench on 45 o oriented samples 

The tensile tests in the 45 o direction put in evidence a non-linear behaviour. To determine the model 

of hardening (isotropic or kinematic), it is necessary to stress the material, outside its elastic domain, 

alternately in tension then in compression by way of zero. This experiment can be done on a tensile 

testing machine but it‟s a complex realization because of the risk of buckling of the sample. For this 

material, it is easiest to introduce a plane shear trough a torsional moment (fig.10a). Therefore, tests on 

a driven angle torsion bench (alternately positive then negative) have been accomplished (fig.10b). 

(a) (b) 

Fig. 10. (a) Angle driven torsion bench and (b) the setting of the sample. 

1 600 

1 400 

1 200 

1 000 

800 

600 

400 

200 

111

112 


From the current torque rated C, the nominal shear stress is given by this equation [8]: 

2 ( 0 0) 

= C / kb h 

(18) 

n 

Where k is a constant which depends on the ratio b0 against h0 (here, k=0.285), b0 and h0 are 

respectively the initial width and thickness of the sample. 

The result of a test at 2 o /s is shown below: 

Fig. 11. Torsion test results at 2 o /s. 

Beyond an angle of 30 o , the behaviour is non-linear as well as in tension than in compression. It 

corresponds in tension to a yield point equal to 60 MPa which is close to the one find during the tensile 

tests. At a shear stress of 69 MPa for reaching an angle of 50 o , the failure of the sample, provoked by 

delamination, is observed (fig.12). 

Fig. 12. Observation of the sample‟s edge after a torsion test by optical microscopy. 

This test demonstrates that the ratio between the yield point in tension and the one in compression 

remains constant along all the loading time (table 1). In conclusion, the hardening model will be an 

isotropic one. 

Table 1. Table of yield points after a torsion test

3.2.2 Creep/ recovery test 


The tensile tests in the 45 o direction show that the behaviour is sensitive to the strain rate. To specify 

the flow law which describes the viscosity, creep/recovery tests (fig.13) at different stress levels were 

realized. 

Fig. 13. Creep test machine and fastening of a sample with its strain gauge sensor. 

The tests have been made on Mayes creep testing machine equipped with a 20 KN load cell and one 

extensometer sensor, for measuring the longitudinal displacement, with an initial gage length equal to 

25 mm. The levels of load were corresponding to 20,30,40,50,60,70,80 and 90 % of the average tensile 

strength (fig.15 a). For every test, a stabilization of the evolution of the longitudinal strain was waited 

before switching to a recovery test. Thus, a complete description of the primary and secondary creep 

stages was made (Fig.14). After load removal, recovery test was stopped as soon as the evolution of the 

longitudinal strain was observed; in order to record relevant non reversible strains (fig.15 b). 

Above 30% of the tensile strength (50 MPa), irreversible strains are recorded and the evolution of 

longitudinal strain is non-linear. This limit is similar to the yield point obtained during the tensile test. 

So in first approach, the behaviour of the 45 o oriented sample will be an elastoviscoplatic model (below 

the yield point, the viscous part of the strain will be disregarded). The law of the flow describing the 

viscosity will be a Norton one. 

Fig. 14. Illustration of the different creep stages. 

113

114 


Creep stress (MPa) 

150 

130 

110 

90 

70 

50 

30 

10 

0.11; 65.91 

0.13; 50.05 

0.00; 32.86 

0.25; 81.98 

0.52; 99.32 

3.50; 115.25 

4.32; 131.17 

5.47; 143.42 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 

-10 

(a) (b) 

Non reversible strain (%) 

Fig. 15. (a) Results of creep/ recovery tests, (b) evolution of non-reversible strains on 45 o oriented samples. 

3.2.3 Elastoviscoplastic model for 45 o oriented samples 

The experimental study reveals that the mechanical response of 45 o oriented samples is non linear and 

strain rate dependent (figs.4, 11 and 15). Therefore, the chosen behaviour law is an isotropic hardening 

associated with a Norton flow rule (fig. 16). The law formulation comes from the thermodynamic theory 

of solids mechanics. In case of small strain, the total strain ε t can decomposed on a reversible part ε e 

(elastic) and a non reversible part ε in (inelastic). 

The elastic behaviour is modelled by the Hooke‟s law. 

t e in 

= + 

(19) 

e 1 

= - tr( ) I - 

 

E E 

(20) 

where E and ν are respectively the Young modulus and the Poisson ratio. 

The isotropic hardening is defined by the relation: 

0 

bp ( 1 ) 

R R Hp Q e - 

= + + - (21) 

where R is the hardening variable, p is the cumulated plastic strain, H is the linear constant, Q and b are 

the non linear constants. H, Q and b depend on the material. 

And p measures the strain path and its strain rate p 

is expressed as: 

and p 

is given by the Norton flow rule: 

in in 

 

p = 2 / 3 : 

 

( ) / 

where f(ζ) is the Yield function, K and n are the materials parameters. 

In this case, the Yield function is defined by the Von Mises criterion: 

 

n 

1/2 

(22) 

p = f K 

(23) 

( ) ( ) 

0 

where J depends on the second invariant of the stress tensor deviator: 

f = J - R 

(24) 

J ( ) = 3 / 2 s : s 

(25)


with s the stress tensor deviator. 

In conclusion, 6 materials parameters have to be identified. 

Fig. 16. Comparison between numerical simulation of elastoviscoplastic model and tensile test on 45 o oriented sample. 

3.2.4 Identification of the elastoviscoplastic model parameters for 45 o oriented samples 

In order to evaluate the ratio of viscosity in the material, tension-relaxation tensile tests have been 

also performed. These tests, which are driven in strain, consist in achieving a succession of strain levels 

from 0.1% to 15%. The experimental protocol is this one (fig.17a): 

a. Increase of the deformation, at a constant strain rate, until the wished level (here 1%), 

b. Maintaining the deformation until the complete stress relaxation, 

c. Unloading, at the same strain rate, until the stress reaches zero. 

A complete stress relaxation means a stabilisation of its value (Fig.17b). So, the higher strain will be, 

the more the time at a constant strain level will be long. The tests were realized on the tensile testing 

machine described above. Therefore, the viscosity should be erased. 

Strain (%) 

1.75 

1.5 

1.25 

1 

0.75 

0.5 

0.25 

0 

a 

b 

0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 

Temps (s) 

c 

110 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

1 500 2 000 2 500 3 000 3 500 

Time (s) 

4 000 4 500 5 000 5 500 

Fig. 17. (a) Experimental protocol of the tension-relaxation tests and (b) illustration of complete stress relaxation. 

3 tests are conducted with tensile test machine at constant strain rate of 10 -4 s -1 (Fig.18) on 45 o 

oriented samples. Above a strain of 0.6%, the behaviour is non-linear and then non reversible strains are 

measured. After a strain of 5%, the behaviour is more rigid. Indeed, the multiplication of the damages 

(Fig.19) allows the fibbers to be aligned in the straining direction. Around a strain of 15%, the sample 

breaks in the middle of its inside length. The non reversible strains values are close to the ones find in 

creep test. As the reproducibility of the experiment is correct, the use of the mean values, in order to 

identify the elastoviscoplastic model, is wise. The green curve represents the mean behaviour without 

Stress (MPa) 

115

116 


viscosity of 45 o oriented samples, so it will serve to identify the hardening parameters (R0, H, Q and b). 

The red curve represents the mean behaviour with viscosity of 45 o oriented samples, thus it will serve to 

identify the Norton flow rule parameter (K and n). The curves are plotted with true stress and true strain. 

Fig. 18. Experimental results of tension-relaxation tests. 

Fig. 19. In situ observations of the sample edge at strain of 5% during a tension-relaxation test on oriented sample at 45 o . 

The curves obtained are used as comparison with the stress/strain curve given by the finite element 

code Zebulon. By an iterative optimisation loop, all the elastoviscoplatic model parameters are found. 

The convergence criterion is the congruence of experimental and numerical curves by the least-squares 

method (Fig.202a). As a first approach, with the purpose of not including the damages in the chosen 

model, the numerical are stopped at a strain of 5%. In order to check the validity of the abovementioned 

material coefficients (their values are given in table 2), the complete simulation (Fig.20b) of the 

tension-relaxation test is run. The global envelope is well represented but the description of the 

unloading part is too much elastic. The model needs to be improved by adding a description of the 

damages. 

Table 2. Elastoviscoplatic model parameters for 45 o oriented samples


(a) (b) 

Fig. 20. Comparison between experimental and numerical stress/strain curves of tension-relaxation tests for 45 o oriented samples: (a) 

identification of the elastoviscoplastic model parameters, (b) validation of the found parameters. 

3.3 Arcan-Mines tests 

For composite material structures, delamination remains a harmful damage mode leading to a rapid 

ruin. This phenomenon is bound to the resistance between plies in mode I (tension), II (shear) and III 

(see paragraph 2). With the Arcan-Mines experimental set-up [9], the parameters YT and S, 

characterizing the interface strength between different layers respectively in mode I and mode II) are 

going to be identified. 

3.3.1 Experimental protocol 

The Arcan-Mines device is able to apply a multi-axial state of stress in tensile, compressive and shear 

loading (fig.21). This set-up is made of two half circular disks which are joined together thanks to the 

test specimen (fig.22a). Each test specimen is composed of a composite sample bonded between two 

metal substrates (here in steel) by an epoxy adhesive. So this test is able to analyze hybrid bonded 

assembly (fig.22b) behaviour (steel-epoxy-composite-epoxy-steel). 

(a) (b) 

Fig. 21. Arcan-Mines device supported by a tensile testing machine: (a) global set up, (b) the Arcan-Mines set up. 

117

118 


(a) (b) 

Fig. 22. Illustrations of Arcan-Mines experimental set-up for composite sample: (a) tension and shear configurations; (b) hybrid bonded sample. 

Such a test requires an appropriate surface preparation (grinding, sandblasting, chemical attack, and 

flame). Tested specimen required special treatment too. Samples have to be honed with a diamond saw 

in order to reduce the tested interface and to be sure to localize the breaking area (fig.25). Dimensions 

of the composite sample are 70*10mm. 

3.3.2 Experimental results 

Fig. 23. Composite sample geometry for Arcan-Mines test. 

The tests are realized on a tensile test machine at loading rate of 7N/s, equipped with a 5 KN load cell 

and high resolution extensometers (measurement base of 10 mm). To illustrate the reliability of this test, 

results on woven angle-ply laminate (0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o Mode I Arcan-Mines test on ) are shown (fig.24 and 25). 

0°/+45°/0°/+45°/0°/-45°/0° layer of c/pps 

Stress (MPa) 

12 

10 

8 

6 

4 

2 

0 

0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 

Longitudinal strain (%) 

(a) (b) 

Fig. 24. (a) Experimental curve, (b) failure surfaces of C/PPS composite (mode I, tension).

Stress (MPa) 

30 

25 

20 

15 

10 

5 

0 

J Bassery, J Renard / Delamination Mode II Arcan-Mines during fatigue test testing on on carbon fiber fabrics reinforced PPS laminates 

0°/+45°/0°/+45°/0°/-45°/0° layer of c/pps 

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 

Shear strain (%) 

(a) (b) 

Fig. 25. (a) Experimental curve, (b) failure surfaces of C/PPS composite (mode II, shear). 

In both case, a failure in the middle of the sample (so between the 0 o ply and 45 o ply) is observed 

(fig.24b and fig.25b). Moreover, one of the failure surfaces has a black colour that means there is no 

resin on it. This observation can be confirmed by a differential scanning calorimetry. Anyway, the 

fiber/matrix adhesion has been broken. Then, the Arcan-Mines test gives the intrinsic values of the 

resistance between plies for the studied carbon/pps laminate. The behaviour of the used epoxy has been 

characterized by previous Arcan-Mines tests. Thereby, the reduction of the tested interface has been 

sized, in order that in tension as well as in shear, the adhesive behaviour stays in its elastic domain. So 

by subtraction, the composite behaviour is obtained (fig.28). Also, the Young modulus of steel is higher 

than the adhesive one or the composite one (50 times as big), in consequence the hypothesis, that the 

extension due to the steel is negligible, is valid. 

(a) (b) 

Fig. 26. Analytic measurements for Arcan-Mines test in tension and in shear. 

119

120 


For tension (Fig.28a), the strain ε and stress ζ are given by these equations (30 and 31): 

With Δltotal is the extension measured by extensometer sensor. 

Or l 0 

So 

And 

steel 

ltotal = lcomposite + ladhesive + lsteel 

(26) 

ltotal = lcomposite + ladhesive 

(27) 

( ) 

l = 2 e F / E S 

(28) 

adhesive adhesive adhesive 

Where F is the current load, eadhesive the initial thickness of the adhesive, S1 the bonded surface and 

Eadhesive the adhesive‟s Young modulus. 

Therefore 

In conclusion, 

and 

( ) 

l = l - 2 e F / E S 

(29) 

composite total adhesive adhesive 

2 

1 

= F / S 

(30) 

composite 

( ( 1) 

) 

= l - 2 e F / E S / e 

(31) 

composite total adhesive adhesive composite 

S2 is the reduced section and ecomposite the initial thickness of the composite sample. 

For shear (fig.28b), the strain γ and stress η are given by the equations (36 and 37): 

l = l + l + l 

(32) 

total composite adhesive steel 

With δltotal is the extension measured by extensometer sensor. 

Or l 0 

So 

And 

steel 

l = l + l 

(33) 

total composite adhesive 

( ( 1) 

) 

l = 2e tan F / G S 

(34) 

adhesive adhesive adhesive 

Where F is the current load, eadhesive the initial thickness of the adhesive, S1 the bonded surface and 

Gadhesive the adhesive‟s shear modulus. 

Therefore 

In conclusion, 

And 

( ( 1) 

) 

l= l- 

2 e *tan F / G S 

(35) 

composite total adhesive adhesive 

= F / S 

(36) 

composite 

( ( ( 1) 

) ) 

2 

= l- 

2 e *tan F / G S / e 

(37) 

composite total adhesive adhesive composite 

S2 is the reduced section and ecomposite the initial thickness of the composite sample. 

In tension below a stress of 10 MPa and in shear below a stress of 24MPa, the behaviour is linear 

(fig.24a and fig.25a). Then in both case, till the failure, the composite has a non-linear behaviour. In


order to determine the origin of this non-linearity, acoustic emission instrumentation has been associated 

to the Arcan-Mines device. By comparison between tests on only adhesive and ones on composite, an 

amplitude threshold at 60dB has established that, in both case, this non-linearity is due to delamination. 

So the elastic limits obtained by Arcan-Mines tests will correspond to the parameters YT and S 

(respectively mode I and mode II) of the onset delamination criterion. From 7 tests (on the same 

material but on different laminates) for each case (tension or shear), the mean YT is equal to 12.74 MPa 

and the mean S is equal to 23.71 MPa. Compare to carbon/epoxy laminates, these values are low. It is, 

probably, due a weak fibber/matrix adhesion. In perspective, the Arcan-Mines device will be used to 

quantify the fatigue impact on interface strengths on carbon/pps composites. 

4. Fatigue study 

4.1 Experimental set-up 

Fatigue tension-tension tests were made on hydraulic testing system with a load control mode 

(fig.27a). Axial extensometer sensor is used to measure the longitudinal displacement. The test 

parameters (fig.27b) are: 

- the maximum applied stress ζmax from which woven 0 o -ply laminates have been performed at 

50%ζR, 70%ζR and 90%ζR, while woven angle-ply laminates (0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o and 

0 o /+20 o /-20 o /0 o /-20 o /+20 o /0 o ) have been performed at 30%ζR, 50%ζR and 70%ζR where ζR is the 

average ultimate tensile stress ; 

- the minimum to maximum stress ratio R, also called load ratio, in a cycle, was 0.1; 

- the frequency f was 1 Hz. 

All the tests were made at room temperature. Besides, during testing, a high resolution camera was 

used to observe in situ damage initiation on the edge of the specimen side and residual stiffness‟s were 

measured every N cycles (in general every 5 000 cycles). Therefore, the sample has to be polished 

before testing. 

(a) 

121

122 

4.2 Experimental results 

4.2.1 Delamination onset 


(b) 

Fig. 27. Fatigue experimental set-up [10]: (a) hydraulic machine; (b) fatigue loading procedure. 

In order to predict the onset of delamination under fatigue tension-tension loading, a relationship 

between the ratio of the maximum applied stress ζmax for onset delamination over pure tensile loading 

test ζonset, versus the number of cycles for delamination onset in mode I Nonset , has to be found (fig.28). 

σ max/σ onset 

1.20 

1.00 

0.80 

0.60 

0.40 

0.20 

obersavtions of delamination onset 

no obersavtion of delamination onset 

0.00 

0 100 000 200 000 300 000 400 000 500 000 600 000 700 000 800 000 900 000 1 000 000 1 100 000 1 200 000 

Number of cycles for delamination onset in mode I observations 

Woven 0°-ply laminate in warp direction 

Woven 0°-ply laminate in weft direcion 

Woven 0°/+45°/0°/+45°/0°/-45°/0° laminate 

Woven 0°/+20°/-20°/0°/-20°/+20°/0° laminate 

Fig. 28. Stress number of cycles curves for onset delamination (mode I, arrow means an infinite limit). 

For carbon/epoxy woven fabric composite laminates [4], the non-linear relation between ratio of ζmax 

to ζonset and Nonset can be expressed as: 

( K ) 

K2 

-( Nonset 

-1) 

max / onset 1 

 

where K1 and K2 are two constant parameters. 

= (38) 

These parameters are independent of the stacking sequence but only depend on the composite 

material. Due to the difficulty of precisely identify the delamination onset on satin 5 carbon/PPS woven 

fabric composite laminates, more experimental results would be needed for a more accurate fitting.

4.2.2 Damage mechanism 


4.2.2.1 0 o -ply laminates in weft direction 

50%ζR sample only develops ply cracking, also called transverse crack (fig.29 a). Contrary 70%ζR 

and 90%ζR levels (fig.29 b and c), which exhibit not only transverse cracks but also, respectively 

around 60 000 cycles and 200 000 cycles, intralaminar delamination. This damage is due to the bending 

forces created by the fabrics (here seven plies of harness satin five fabrics at 0 o ). 

Before testing 500 000 cycles 1 000 000 cycles 

(a) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=50%ζr (only transverse cracks) 

Before testing 10 000 cycles 60 000 cycles 

(b) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=70%ζr (transverse cracks and delamination) 


(c) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=90%ζr (transverse cracks and delamination) 

Fig. 29. In-situ optical observations during fatigue tests for different number of cycles (0 o laminates tested in weft direction). 

4.2.2.2 0 o laminates in weft direction 

In this loading direction, 50%ζR and 70%ζR levels show only transverse cracks (Fig.30.a and b), in 

123

124 


contrast to 90%ζR which displays also intralaminar delamination around 5 000 cycles (fig.30 c). Then, 

these delaminations growth with the number of cycles and propagate in the neighbouring yarns. 


(a) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=50%ζr (only transverse crack) 


(b) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=70%ζr (only transverse crack) 


(c) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=90%ζr (transverse crack and delamination) 

Fig. 30. In-situ optical observations during fatigue tests for different number of cycles (0 o laminates tested in the weft direction. 

4.2.2.3 0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o / laminates 

For this sequence, 50%ζR and 70%ζR levels show transverse crack and delamination in mode I, 

between 0 o -ply and 45 o ply, respectively around 300 000cycles and 5 000cycles (fig.31 b and c). For 

30%ζR, only transverse crack can be observed (fig.31 a).



(a) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=30%ζr (only transverse crack) 


(b) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=50%ζr (transverse crack and delamination) 



Fig. 31. In-situ optical observations during fatigue testing for different number of cycles (0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o laminates). 

4.2.2.4 0 o /+20 o /-20 o /0 o /-20 o /+20 o /0 o laminates 

For this sequence, 50%ζR and 70%ζR levels show transverse crack and delamination, between 0 o -ply 

and 20 o ply, respectively around 1 000 cycles and 50 cycles (fig.32 b and c). For 30%ζR, only transverse 

crack can be observed (fig.34 a) and test is still in progress. The delamination in mode II, between 

20 o -ply and -20 o -ply, is arduous to observe. A higher magnification is needed. 

125

126 



(a) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=30%ζr (only transverse cracks) 

Before testing 10 cycles 1 000 cycles 

(b) Observations made on sample tested in fatigue at f=1Hz, r=0.1 and ζmax=50%ζr (transverse crack and delamination) 

Before testing 10 cycles 50 cycles 


Fig. 32. In-situ optical observations during fatigue tests at different cycles (0 o /+20 o /-20 o /0 o /-20 o /0 o /-20 o /+20 o /0 o / laminates). 

In conclusion, the observations show that: 

- Damage mechanism evolution is first ply cracking then delamination ; 

- for different maximum applied stresses, the fatigue damage mechanisms are the same with a faster 

evolution with increasing maximum applied stress; 

- Further fatigue damage mechanisms are similar when compare to static tension tests. 

The results prove that in fatigue below a threshold there is no delamination in mode I (50%ζr for 

0 o -ply laminates and 30%ζr for 0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o and 0 o /+20 o /-20 o /0 o /-20 o /+20 o /0 o laminates). 

The 0 o /+20 o /-20 o /0 o /-20 o /+20 o /0 o laminates, in regard to the number of cycles needed to observe 

delamination, is less resistant.

4.2.3 Stiffness degradation 


Thanks to the fatigue test setting, the stiffness degradation can be investigated (fig.33). Two stages 

have been identified: onset and then stabilization. Form all carbon/PPS laminates, the highest stiffness 

reduction is around 5%, so close to the experimental dispersion, and its evolution is stabilized around 

100 000 cycles. Even though, transverse cracks and delaminations have been observed. In comparison 

with carbon/epoxy, the material of the study is less sensitive to fatigue. Therefore, the onset 

delamination criterion, in a simplified approach, can be only indentified on static tensile tests. 

E/E 0 

1.05 

1.00 

0.95 

5. Finite element analysis 

Woven 0°-ply laminate in warp 

direction 

Woven 0°-ply laminate in weft 

0.90 

0.85 

direction 

Woven 0°/+45°/0°/+45°/0°/-45°/0° 

laminate 

Woven 0°/+20°/-20°/0°/-20°/+20°/0° 

laminate 

0 100 000 200 000 300 000 400 000 500 000 600 000 700 000 800 000 900 000 1 000 000 

Number of cycles 

Fig. 33. Stiffness degradation during fatigue tests. 

To identify the parameter k for onset delamination criterion (characterizing the friction between two 

layers), a 2D ½ finite element simulation of the sample submitted to tension has been made. Due to the 

symmetries, only a quarter of the cross section has been modelled (fig.34). Experimentally, the 

delamination appears at free edges of the samples. Numerically, free edge interfaces exhibit stress 

singularities which are more and more accurate as the refinement of the mesh increase. The applied 

stress corresponds to the macroscopic applied test, for which in-situ observations of delamination in 

mode I have been noticed (equal to 70%ζr) on woven 0 o /+45 o / o /+45 o /0 o /-45 o /0 o laminate during static 

tensile tests. Each woven ply is considered as homogenous and orthotropic. Therefore, the elastic 

behaviour of one ply results from the orthotropic matrix identified in the paragraph III. 

Fig. 34. 2D ½ finite element model. 

127

128 


By a convergence study on the onset delamination criterion for a critical length a0 equal to one ply 

thickness in correspondence to experimental in-situ observations, the finest size of the mesh (equal to 

one ply thickness divided by 50) and the affected area h of the gradient method (h=one ply thickness 

divided by 10) have been fixed (see fig.35 a and b). 

Onset delamination criterion (-) 

1.80 

1.60 

1.40 

1.20 

1.00 

0.80 

0.60 

0.40 

0.20 

one ply thickness 

2 elements per ply mesh 






0.00 

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 

Critical length a0 (mm) 


2.25 

2.00 

1.75 

1.50 

1.25 

1.00 

0.75 

0.50 

0.25 

0.00 

one ply thickness 

h=1 ply 

h=1/5 ply 

h=1/10 ply 

h=1/50 ply 

h=1/100 ply 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 

Critical length a0 (mm) 

(a) (b) 

Fig. 35. (a) Evolution of the onset delamination for different mesh sizes; (b) Evolution of the onset delamination for different affected area h. 

Then, from the average stresses, which are obtained by combination of magnitude and gradient 

methods (see paragraph II), the k parameter is determined to have the onset delamination criterion equal 

to one at a critical length equivalent to one ply thickness (fig.36 a). Numerically, the interface 0 o /+45 o is 

the most solicited interface. Thus, the onset delamination criterion is applied on this interface. The 

obtained k parameter value is 0.425. Compare to carbon/epoxy laminates, this value is higher. 


1.10 

1.00 

0.90 

0.80 

0.70 

0.60 

0.50 

0.40 

0.30 

0.20 

0.10 

0.00 

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 

Critical length a 0 (mm) 

(a) (b) 

Fig. 36. (a) Onset delamination criterion evolution (0 o / 45 o plies interface with k=0.425, in red the critical length equal to the ply thickness); (b) 

In-situ observation of delamination for 0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o laminate during tensile test at 70% ζr. 

For 0 o /+45 o /0 o /+45 o /0 o /-45 o /0 o laminate, model prediction are in good agreement with experimental 

results (Fig.36 b). The validation of the parameter k, by comparison between numerical results and 

in-situ observations on 0 o /+20/-20 o /0 o /-20 o /+20 o /0 o laminate, is in progress. 

6. Discussion 

The Arcan-Mines device gives an estimation of stress and strain in the composite by deducting the 

displacements of the metal substrates and adhesives. This approach is based on approximations of


elastic properties and dimensions of the adhesive joint. At the end, the obtained interface strengths give 

a good prediction of the onset delamination. But in perspective, it will be pertinent to simulate the entire 

Arcan-Mines device in order to know precisely the stress distribution at the different interfaces of the 

composite [11]. 

7. Conclusion 

This study presents a procedure to evaluate the orthotropic elastic stiffness matrix of laminated 

composites in static through tensile, bending and compression tests. During tensile tests at different 

strain rate on 45 o oriented samples, a non-linear behaviour is observed. Thus, a method to identify the 

elastoviscoplastic model parameters is clearly described. This behaviour law should be coupled with 

damage. Consequently, the experimental set-up Arcan-Mines and monitoring procedure, to determine 

the onset delamination criterion interface strengths parameters, are described. Finally, a delamination 

initiation criterion and its validation for the considered materials are explained. Hence, a tension-tension 

fatigue tests campaign points out damage mechanism similar to the static case and a low stiffness 

reduction close to the experimental reduction. In a simplified approach, the onset delamination criterion 

in fatigue can be considered equal to the static one. Nevertheless, it will be accurate to investigate the 

fatigue impact on interface strengths. Only composite made of polyphenylenesulfide (pps) matrix 

reinforced with carbon fibre fabrics are tested. 


This work is a part of the project TOUPIE which aims at using high-performance thermoplastic 

composites for structural applications purposes. This project is supported by the DGE (Dotation Globale 

d‟Equipement) through the competitiveness cluster MOV‟EO in which several industrials and research 

laboratories are cooperating: Aircelle Company, AMPA Society, AXS Ingénierie Society, Université du 

Havre, ENSI Caen, INSA Rouen and Ecole des Mines de Paris. 

References 

[1] B. Vieille, J. Aucher, L. Taleb. Influence of temperature on the behavior of carbon fiber fabrics reinforced PPS laminates. Materials 

Science and Engineering: A Volume 517, Issues 1-2, 20 August 2009, Pages 51-60. 

[2] L.A.L. Franco, M.L.A. Grac, F.S. Silva. Fractography analysis and fatigue of thermoplastic composite laminates at different environmental 

conditions. Materials Science and Engineering A 488 (2008) 505–513. 

[3] S. Joannès, J. Renard, V. Gantchenko. The role of talc particles in a structural adhesive submitted to fatigue loadings. International Journal 

of Fatigue 32 (2010) 66–71. 

[4] P. Nimdum. «Dimensionnement en fatigue des structures ferroviaires en composites épais ». ENSMP phd thesis manuscript, Mars 2009. 

[5] B. Bonnet. «Comportement au choc de matériaux composites pour applications automobiles ». ENSMP phd thesis manuscript, April 2005. 

[6] C. Verdeau, A. R. Bunsell. « Effet des conditions d'élaboration sur le comportement mécanique, statique et dynamique de matériaux 

composites hautes performances a matrice thermoplastique semicristalline » Proceedings of:developments in the science and technology of 

composite materials,3rd european conference on composite materials,20-23 march 1989,bordeaux.-p.431-440. 

[7] J. Renard. « Elaboration, microstructure et comportement des matériaux composites à matrice polymère » Traité MIM – Mécanique et 

Ingénierie des Matériaux, série polymères, Editions Hermes, 2005. 

[8] S. Timoshenko. « Theory of elasticity »- McGraw-Hill Companies; Third edition, 1970 

[9] J.Y Cognard, P. Davies, L.Sohier, R.Créac‟hcadec. A study of the non-linear behaviour of adhesively-bonded composite assemblies. 

Composite Structures,76, 14 August 2006, 34-46 

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130 


[10] N. Revest, A. Thionnet, J. Renard, L. Boulay, P. Castaing. A continuum damage model for composite materials. Proceedings of fatigue 

design, november 2009, Senlis. 

[11] J.Y Cognard, P. Davies, B.Gineste, L.Sohier. Development of an improved adhesive test method for composite assembly design. 

Composites Science and Technology, 64, 11 November 2004, 359-368

Abstract 

A residual stiffness – residual strength coupled model for 

composite laminate under fatigue loading 

W Lian * 

Shanghai Aircraft Design and Research Institute, Commercial Aircraft Corporation of China, 5# Yunjin Road, Shanghai, China 

In this paper, the foregone stiffness degradation models and strength degradation models for composite under 

fatigue loading were reviewed simply. A new residual stiffness model was presented and a residual strength model 

coupled with it was established based on the basis that they are all determined by the damage evolvement and 

accumulation, then the residual strength can be accurately predicted by monitoring the residual stiffness. The coupled 

model was verified by experimental data, results show that the current models can describe the stiffness degradation rule 

and strength degradation rule of the composite multidirectional laminate fairly well and the coupled parameter was found 

to be a material constant. 

Nomenclature 

E(0) modulus of the virgin composite 

E(n) residual modulus at the nth cycle 

E(N) critical residual modulus when breaking 

fi 

frequency 

n cyclic number 

N fatigue life 

N* average fatigue life of some specimens 

r, ri 

Ri 

relative stress level to static strength 

stress ratio 

S(0) ultimate static strength 

S(n) residual strength at the nth cycle 

S(N) critical residual strength when breaking 

max peak stress 

DE 

DS 

damage parameter defined by the residual strength 

damage parameter defined by the residual stiffness 

u, v parameters in the stiffness degradation model 

w coupled model parameter 


E-mail address: lian.wei@163.com

132 



The composite has been widely used in aircraft's structure, especially in the main loading-bearing 

components recently. As a representative aircraft which applied great amount of composite material, 

B787, had made its maiden flight at the end of 2009 and will be delivered to customer at the end of this 

year. In B787, the composite was applied in wingbox, empennage and fuselage structure and the 

proportion of the composite weight to the total structure weight is near 50%, which had caused a 

revolution in composite material application, and it is much more so for Airbus A350XWB as a pursuer. 

Generally, in engineering field, people think that there is no fatigue problem for the composite, but 

this comment must be understood under the following conditions: 

(1) Low strain allowable: Considering safety and damage tolerance, the allowable strain for the 

advanced composite material in engineering is very low comparing to its ultimate fracture strain. 

(for example 4000 VS 15000 under tension and 3000 VS 10000 under compression) 

(2) Conception based on damage non-propagation: The damage in composite (due to impact or 

manufacture defects) structure is not allowed to propagate under serving load because the damage 

evolution or fatigue behavior in composite is not exactly mastered by people. 

Based on which, such low allowable strain would not induce fatigue damage in composite structure. 

From the fatigue-life diagram established by Talreja[1], we can find that the present common strain 

allowable value is under the fatigue limits for advanced composite. Surely, the advanced composite has 

perfect fatigue performance and the rate of the stress level for the fatigue limit to its ultimate strength 

reaches 60% generally. Totally, the low allowable strain and high fatigue performance result in the 

concept that the static mechanism performance covers up fatigue problem for the composite. 

However, the engineers have been applying themselves to enhance the allowable strain by any 

possible way, such as toughening, enhancing the damage tolerance or damage resistance. Boeing‟ 

engineers try to improve the composite‟s allowable strain from about 4000 presently to 

6000~8000 for the next generation civil transporter to reduce the structural weight and fuel 

consumption, then the fatigue problem would not be avoided any way at such high target strain. 

In reality, composite fatigue became a researching hotspot since 1970s due to the advance composite 

material‟s fast developing and increasing application. In the past forty years, researchers made great 

efforts on fatigue mechanism and behavior, rules of damage evolution and accumulation by various 

ways. Many models, damage parameters and life prediction methods were presented. However, there is 

still no recognized fatigue life prediction method for composite by far because the damage mechanism 

and fatigue behavior are really complex for the composite with multi-directional fiber and multi-phase 

micro structure. The most popular methods of characterizing the composite‟s fatigue properties and 

predicting life are phenomenological, such as those method and parameters based on residual stiffness, 

residual strength or fatigue life which don‟t treat of micro-mechanism of composite structure under 

cyclic loading, only adopt macro-parameters to characterize its fatigue properties straightforwardly.

W Lian / A residual stiffness – residual strength coupled model for composite laminate under fatigue loading 

2. Review of the residual stiffness and residual strength models 

The representational residual stiffness models presented by prevenient researchers are summarized 

simply in table 1, as following, 

Table 1. Collection of the residual stiffness models 

Presenter The residual stiffness model 

Yang [2] a 

E( n) = E(0)[1 - Qn ] 

E( n) = E(0)[1 - ( d + a B ) n ] 

Yang-2 [3] a3+ BS 

2 max 

Echtermeyer [4] E( n) = E(0) - log n 

Coats [5] 

* 

E( 

n) E 

A D 

= 1- 

 

E(0) E(0) A 

0 

E n E Da n N 

 

 

Plumtree [6] ( ) / (0) = 1- 1- ( 1 - / ) 

E n E K E n 

 

max 

Zhang [7] ( ) = (0) 1 - ( / (0) ) 

Whitworth [8] 

1 

m m 

E( n) = E( N)[ - hln( n + 1) + ( E(0) / E( N)) 

] 

E ( n) = E (0) - DC [ E(0) - / e )] n 

Whitworth-2 [9] a a a a 

max f 

Ye [10] 

En ( ) 

= 1 - [ NC( n + 1)] 

E(0) 

Hwang [11] c 1 

Bangyan [12] 

Philippidis [13] 

Vure [14] 

Shokrieh [15] 

d E( n) / dn 

Acn - 

=- 

 

1/( n+ 1) 2 n/( n+ 

1) 

max 

E( n) = E(0)[1 -( Kn ) (1 - q)] 

EN ( ) A c 

= 1 - K( ) N 

E(1) E 

0 

b 1/ B 

max 

En ( ) 

= [1 - ( c + 1) A n] 

E(0) 

c 1/( c+ 

1) 

max 

 

1/ 

log( n) 

- log(0.25) 

Eij ( n) = 1- Eij 

- + 

log( Nij 

) log(0.25) 

- f f 

 

Tserpes [16] Eij ( n) = 

A(1/ Nij ) + 1 

Eij 

(0) 

Mao [17] 

m1 m2 

E(0) - E( n) n n 

= q+ (1 - q) 

 

E(0) - E( N) N N 

Note: The other symbols are model parameters, please refer to the literature for details. 

It can be found that the upper residual stiffness models generally satisfy the boundary conditions, 

which are, 

E(n)=E(0), when n=0 

E(n)=Ecr(N), when n=N 

133

134 


Although the stiffness degrades irregularly when failure happens, a critical residual stiffness value could 

still be distinguished, which had been verified by experiments[4, 14], or an critical residual stiffness 

could be defined artificially based on the considering of structure safety or functional requirement. 

Totally, the upper residual stiffness models could be divided to two groups, one is to establish the 

relationship between the residual stiffness and the cycle number, such as the models presented by 

Yang [2] , Zhang [7] , Whitworth [9] , Hwang [11] , Philippidis [13] etc; the other is to establish the relationship 

between the residual stiffness and the life ratio, such as those presented by Plumtree [6] , Shokrieh [15] , 

Mao [2] etc. To the author‟s opinion, it is not robust to establish the relationship between the residual 

stiffness and the absolute cycle number because the fatigue life of the composite scatters seriously and 

one cycle loading induces different stiffness degradation in the different specimens or different fatigue 

stage for one specimen. Research and experiment results [16~19] had revealed that the curves of 

normalized residual stiffness (E(n)/E(0)) with life ratio (n/N) keep accordant with each other, which 

denotes the fatigue damage evolves according to similar rule for the composite with same layup 

sequence under similar fatigue loading spectrum, but their lives scatter seriously. 

For the residual strength, accordingly, many models had been established, as following in the table 2. 

Table 2. collection of the residual strength models 

Presenter The residual strength models 

Yang [20] c c c b 

S ( n) = S (0) - K n 

Yang-2 [21] 

Yang-3 [22] 

Adam [23] max 

max 

 

S (0) - 

max 

( ) = (0) - c c 

S (0) - 

max 

S n S K n 

c b 

max 

S (0) - 

S n S K n 

 

 

( ) = 

max c 

(0) - 

( c c 

( S (0) - 

max ) 

b 

max 

 

) 

x y 

Sn ( ) - log( n) 

- log(0.5) 

+ = 1 

S(0) - log( N) 

-log(0.5) 

 

( ) (0) [ (0) ] n 

S n = S - S - 

N 

Broutman [24] max 

n 

= - - 

logN Hashin [25] log 

[ S( n)] [ S(0)] [ S(0)] 

( ) 

n 

( ) (0) ( ) 

Charewicz [26] = + - 

S n max S max f 

N 

Schaff 27,28] S( n) S(0) S(0) 

= - - max 

Sendeckyj [29] ( ) 1 

s 

v 

n 

N 

 

S(0) = max S( n) / max+ 

( n -1) 

f 

 

Xiong [30] m 

n = C s - S S - S n 

3 

( (0)) (0) ( ) b 

Hahn [31] c c 

S ( n) = S (0) - cDn 

S ( n) = S (0) - A ( N - 1) 

Haplin [32] r r r 

A 

Whitworth [8] r r r r n 

S ( n) = S (0) - ( S (0) - 

max ) 

N 

s


Philippidis [33] S( n) = S(0) - ( S(0) - ) ( CNT/ p) 

Chou [34] 1 i 

i 1 

S ( n) S (0) S (0) max n 

 

- 

= - - 

 

Yao [35] 

max 

 

Tension: S( n) S(0) S(0) 

Caprino [36] max 

Revuelta [37] 

Reifsnider [38] 

Tserpes [16] 

= - - max 

m 

sin x cos( - 

) 

sin cos( x - 

) 

Compression: S( n) = S(0) -S (0) - ( n / N ) 

S( n) S(0) a (1 R)( n 1) 

 

= - - - 

1 1 1 

A A A A 

S ( n) = S (0) - B ( n - 1) 

max 

i-1 

max ( ) 

( ) = 1- 1 - * * d 

0 

n n n 

S n i 

S(0) 

N( n) 

N( n) 

 

 

2 

 

n n 

Sij ( n) = B+ C + 1 Sij 

(0) 

N 

ij N 

ij 

 

 

1/ 

log( n) 

- log(0.25) 

= - - + 

log( Nij 

) - log(0.25) 

 

 

Shokrieh [39] S ( n) 1 ( S (0) ) 

ij ij ij ij 

Note: The other symbols are model parameters, please refer to the literature for details. 

Similarly, the strength degradation models is the function of the cycle number, n or life ratio, n/N. 

And they satisfy the boundary conditions which are, 

S(n)=S(0), when n=0 

S( n)= Scr ( N)= max , when n =N 

Accordingly, the authors thought that it is not reasonable enough to establish the relationship between 

residual strength with absolute cycle number due to the scatter of the life and residual strength itself. 

Although the residual strength models in table 2 are more than those of residual stiffness, study on the 

strength degradation rule based on experiments is evidently less than that on the residual stiffness, 

because the strength degradation rule is not so inerratic as that of residual stiffness, it scatters more 

seriously. In addition, the experimental research on strength degradation is time and money consuming 

because only one residual strength value can be obtained for one specimen. However, the residual 

strength was an important mechanical parameter for the composite structure, because it has strong 

relationship with safety and reliability. What‟s more, failure must occur when the residual strength 

reaches to the peak stress of fatigue loading, so the residual strength has its natural criteria as a failure 

index. 

3. The residual stiffness-residual strength coupled model 

The foregone stiffness or strength degradation models were presented separately, however, the 

potential relationship between them has rarely been studied. To the best knowledge of the authors, only 

Whitworth[9] had established the relationship between a stiffness degradation model presented by 

himself(Eq. 1) with a modified Yang‟s strength degradation model (Eq. 2)by replacing their common 

v 

135

136 


parameters, life radio - n/N, as showing in formula (3), 

a a 

E( n) E( N) n 

= 1-H1- 

E(0) E(0) N S n = S - S - (2) 

N 

r r r r n 

( ) (0) ( (0) max ) 

a 

En ( ) 

1- 

 

r r 

Sn ( ) max E(0) 

= 1-1- 

a 

 

S(0) S(0) 

 

En ( ) 

H 1- 

 

 

 

E(0) 

 

where a、H and r are model parameters. But, there were no more efforts on such relationship research. 

In current research, the research on the potential relationship between the residual stiffness and 

residual strength was carried out presented on the basis of the following assumptions: 

(1) The damage evolves in the composite material under fatigue loading, which will induce the 

degradation of its stiffness and strength. 

(2) The damage accumulates irreversibly in the laminate during the loading acting continually, so the 

stiffness and strength degraded monotonously. 

(3) At the same time, the instantaneous residual stiffness and residual strength were determined by the 

same damage conditions in the laminate, there is inherent relationship between them. 

Firstly, due to the continuously nondestructive trackability of the residual stiffness, many researchers 

recommended it as a preferred damage parameter. In this paper, the following stiffness degradation 

model was presented and found to be versatile to describe the stiffness degradation rule in the whole 

range fatigue life for variable multidirectional laminates, 

u 

E( n) E( N) 1 - ( n / N) 

 

= 1- 1-1-v E(0) E(0) (1 - n/ N) 

 

where, u and v are experimental parameters which can be obtained by the stiffness degradation curve 

fitting, and they are determined by the laminate‟s stacking sequence and the load spectrum. 

As describing as part 2, the authors think that it is more reasonable to establish the relationship 

between the normalized residual stiffness (E(n)/E(0)) with the life ratio (n/N), experimental results [16-19] 

show that the normalized stiffness degradation curves accord with each other for the specimens with 

same layup sequence under the same loading in the dual-normalizing coordinate system, which would 

be confirmed again in Fig. 1~12 in part 4. Normalization eliminates the individual specimens‟ difference 

and life‟s scatter, then the disciplinarian emerges. 

Equation (4) is equivalent to the following formula, which is a kind of damage definition in reality, 

E(0) -E( n) 1 -( 

n / N) 

= 1- 

E(0) - E( N) (1 - n/ N) 

where, DE [0,1] . When n=0, DE=0, when n N , DE 1 . 

u 

v 

E 

(1) 

(3) 

(4) 

D 

(5) 

In the same format, another damage parameter based on the residual strength, DS, can be defined as 

equation (6)


S(0) - S( n) 

DS 

(6) 

S(0) - S( N) 

where, DS [0,1] . Theoretically, failure would not occur before the residual strength reaches to the peek 

stress of the loading spectrum, then S(N) should equal max . 

Then, considering the interval of DE & DS, the relationship between them was supposed to be the 

following equation simply, 

Then, we get equation (8). 

( ) w 

D = D 

(7) 

S E 

u 

S( n) max 1 - ( n / N) 

 

= 1- 1-1-v S(0) S(0) (1 - n/ N) 

 

So, the relationship between the residual stiffness and residual strength can be established as Eq. (9) 

S( n) E(0) - E( n) 

 

= 1-1- S(0) S(0) E(0) E( N) 

w 

w 

max 

 

- 

 

(9) 

where the parameter w can be easily obtained by residual strength experiment. 

4. verifying of the residual stiffness-residual strength coupled model 

Parameters u and v in Eq. (4) are very easy to obtain based on the recorded experimental data of once 

piece of specimen in a whole fatigue processing. In Eq. (8), u and v keep same value with those in Eq. 

(4) under the condition of same laminate and same loading spectrum, the single unknown parameter, w, 

can be obtained by even one residual strength experiment combined with the static strength. 

Lee&Jen[40] had researched the fatigue response of the thermoplastic matrix PEEK reinforced by 

carbon fiber AS4 composite laminates with three stacking sequence ([+45]4S, [0/90] 4S, [0/45/90/-45]4S) 

under dual stress level (ri), stress ratio (R1=0, R2=0.2) and frequency (f1=25Hz, f2=5Hz) experimentally, 

and enumerated the stiffness and residual strength degradation data in the figures. Those data was 

picked up by the authors and adopted to validate the adaptability of current residual stiffness - residual 

strength coupled model. 

From the experimental data, the critical residual stiffness ratio for three laminates was shown in table 

3. The critical residual strength ratio took the relative peak stress level to the static strength, 

r= / S(0) 

, which was shown in table 3 too. 

i 

max 

Table 3. The critical residual stiffness and residual strength for AS4/PEEK 

Laminate Loading case Critical residual stiffness ratio Critical residual strength ratio 

[+45]4S 

[0/90] 4S 

[0/45/90/-45] 4S 

r1=0.40 

0.40 

0.55 

r2=0.34 0.34 

r1=0.66 

0.66 

0.82 

r2=0.60 0.60 

r1=0.70 

0.70 

0.70 

r2=0.64 0.64 

Due to the sufficiency of the experimental data, u, v, w were determined by method of data fitting, 

their values were listed in table 4, the curves of the stiffness and strength degradation rule were shown 

137 

(8)

138 


Fig. 1~12, in which the invert experimental data was shown too. 

From table 4, three rules can bee found, 

(1) The value of u and v increases with the increasing fraction of ply 0 o for these laminates. 

(2) For same laminate, the value of u and v increases with the increasing of the stress level, ri. 

(3) Despite of the diverse value of u and v, the coupled parameter, w, does not almost change with 

laminate‟s layup sequence or loading case, and it is generally greater than 2.0. 

Table 4. The value of u, v and w for the laminates 

Laminate Loading case u v w 

[+45]4S 

[0/90] 4S 

[0/45/90/-45] 4S 

r1=0.40 0.50 0.51 2.04 

r2=0.34 0.56 0.61 2.01 

r1=0.66 0.83 0.72 2.23 

r2=0.60 0.96 0.68 2.14 

r1=0.70 0.75 0.51 2.09 

r2=0.64 0.82 0.62 2.17 

With the increasing faction of ply 0 o , the stiffness degradation rule tends to “sudden death”, under 

which the u and v will increasing due to the model‟s mathematical character. Similarly, with the 

increasing of the stress level, laminate‟s life will decrease and the damage may not evolve adequately 

and then the stiffness degradation rule tends to “sudden death” also. Based on the assumptions in part 3, 

the strength degradation rule has a inner relationship with stiffness degradation rule, the different 

damage evolvement processes for different laminates are imported to their corresponding residual 

strength model (Eq. (8) ) by the residual stiffness model, and the coupled parameter, w, might be a 

material constant. 

From fig. 1~12, it can be found that the residual stiffness model describes the stiffness degradation 

rule perfectly. And, the residual strength model describes the strength degradation rule fairly well. 

Residual stiffness ratio 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

r1= 0.4,R1= 0,f1=25 

r1= 0.4,R1= 0,f2= 5 

r1= 0.4,R2=0.2,f1=25 

r1= 0.4,R2=0.2,f2= 5 

Current model 

[ 45] 

4S 

0.0 0.2 0.4 0.6 0.8 1.0 

Life ratio (n/N ) 

Fig. 1. Stiffness degradation of laminate [+45]4S under stress level r1.


Residual strength ratio 



1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

r2=0.34,R1= 0,f1=25 

r2=0.34,R1= 0,f2= 5 

r2=0.34,R2=0.2,f1=25 

r2=0.34,R2=0.2,f2= 5 

Current model 

[ 45] 

4S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 2. Stiffness degradation of laminate [+45]4S under stress level r2. 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

r1= 0.4,R1= 0,f1=25 

r1= 0.4,R1= 0,f2= 5 

r1= 0.4,R2=0.2,f1=25 

r1= 0.4,R2=0.2,f2= 5 

Current model 

[ 45] 

4S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 3. Strength degradation of laminate [+45]4S under stress level r1. 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

r2=0.34,R1= 0,f1=25 

r2=0.34,R1= 0,f2= 5 

r2=0.34,R1=0.2,f1=25 

r2=0.34,R1=0.2,f2= 5 

Current model 

[ 45] 

4S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 4. Strength degradation of laminate [+45]4S under stress level r2. 

139

140 




1.0 

0.8 

0.6 

0.4 


r1=0.66,R1= 0,f1=25 

r1=0.66,R1= 0,f2= 5 

r1=0.66,R2=0.2,f1=25 

r1=0.66,R2=0.2,f2= 5 

Current model 

[0/90] 4S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 5. Stiffness degradation of laminate [0/90]4S under stress level r1. 

1.0 

0.8 

0.6 

0.4 

r2= 0.6,R1= 0,f1=25 

r2= 0.6,R1= 0,f2= 5 

r2= 0.6,R2=0.2,f1=25 

r2= 0.6,R2=0.2,f2= 5 

Current model 

[0/90] 4S 

0.0 0.2 0.4 0.6 0.8 1.0 

Life ratio(n/N ) 

Fig. 6. Stiffness degradation of laminate [0/90]4S under stress level r2 

1.0 

0.8 

0.6 

0.4 

r1=0.66,R1= 0,f1=25 

r1=0.66,R1= 0,f2= 5 

r1=0.66,R2=0.2,f1=25 

r1=0.66,R2=0.2,f2= 5 

Current model 

[0/90] 4S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 7. Strength degradation of laminate [0/90]4S under stress level r1.





1.0 

0.8 

0.6 

0.4 

r2= 0.6,R1= 0,f1=25 

r2= 0.6,R1= 0,f2= 5 

r2= 0.6,R2=0.2,f1=25 

r2= 0.6,R2=0.2,f2= 5 

Current model 

[0/90] 4S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 8. Strength degradation of laminate [0/90]4S under stress level r2. 

1.0 

0.8 

0.6 

0.4 

0.2 

r1= 0.7,R1= 0,f1=25 

r1= 0.7,R1= 0,f2= 5 

r1= 0.7,R2=0.2,f1=25 

r1= 0.7,R2=0.2,f2= 5 

Current model 

[0/ 45/90/-45] 2S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 9. Stiffness degradation of laminate [0/45/90/-45]2S under stress level r1. 

1.0 

0.8 

0.6 

0.4 

r2=0.64,R1= 0,f1=25 

r2=0.64,R1= 0,f2= 5 

r2=0.64,R2=0.2,f1=25 

r2=0.64,R2=0.2,f2= 5 

Current model 

[0/ 45/90/-45] 2S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 10. Stiffness degradation of laminate [0/45/90/-45]2S under stress level r2. 

141

142 


1.0 

0.8 

0.6 

0.4 

0.2 


r1= 0.7,R1= 0,f1=25 

r1= 0.7,R1= 0,f2= 5 

r1= 0.7,R1=0.2,f1=25 

r1= 0.7,R1=0.2,f2= 5 

Current model 

[0/ 45/90/-45] 2S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 11. Strength degradation of laminate [0/45/90/-45]2S under stress level r1. 

1.0 

0.8 

0.6 

0.4 

5. Evaluation of the coupled model 


r2=0.64,R1= 0,f1=25 

r2=0.64,R1= 0,f2= 5 

r2=0.64,R2=0.2,f1=25 

r2=0.64,R2=0.2,f2= 5 

Current model 

[0/ 45/90/-45] 2S 

0.0 0.2 0.4 0.6 0.8 1.0 


Fig. 12. Strength degradation of laminate [0/45/90/-45]2S under stress level r2. 

The main meaning of the coupled model is to establish the relationship between the residual strength 

and the residual stiffness because the residual strength, which is a key quantity for structure safety, can 

be more accurately predicted by monitoring the stiffness degradation for the composite structure in 

fatigue process. Although the residual stiffness is easy to measured continuously and nondestructively, it 

was still considered to be convenient to establish the relationship between residual strength with cycle 

number or life ratio when the safety is paid more attention according to traditional conception. However, 

in reality, it is insecure to establish such kind of relationship. Although, the cycle number or service time 

can be counted accurately, the actual life of a composite structure under fatigue loading can not be 

assured or predicted accurately before failure due to the greater scatter of the fatigue life, static strength 

and individual difference, which is the right reason why the residual strength obtained by traditional 

method scatters seriously. 

In anther words, one loading cycle induces different damage in different individual specimen or in the 

different life phase for the same specimen. On the other hand, as describing in part 3, the normalized


stiffness degradation curves accord with each other for the specimens with same layup sequence under 

the same loading in the dual-normalizing coordinate system, however, there is an important 

precondition which is the cycle number must be normalized by the real ultimate life of the specimen for 

the abscissa. Then, when we carry out residual strength experiment, we have no ideal of the actual life 

and the life ratio where the residual strength experiment should be carried out is ambiguous. 

In addition, the authors had carried out residual strength experiment on E-glass/Epoxy laminate 

specimen with a central hole, the material properties and the specimen‟s dimension can be found in 

literature[41] and the ratio of the hole diameter to the width of the specimen is 0.2. Although the 

residual strength does not reduce monotonously (increase then reduce) for the notched specimen at the 

beginning of the life range generally, however, the experimental results shows reasonable relationship 

between the residual strength the stiffness degradation ratio ( 1-E(n)/E(0)) instead of the anomalous 

relationship between the residual strength with the nominal life ratio, as shown in Fig 13~16, which 

approves the rationality of the discussion above. The experimental results confirm that the relationship 

between residual strength and life ratio is incredible, the data points show great scatter due to the 

complex fatigue mechanism and abnormal strength degradation rule of notched composite laminate. 

Residual strength (KN) 


20.0 

15.0 

10.0 

5.0 

6.0 

4.0 

2.0 

0.0 

stress peak 

(a) [0/90]2S with hole, r =0. 8 

0.0 0.2 0.4 0.6 0.8 1.0 

Life ratio (n/N* ) 

Stress peak 


20.0 

15.0 

10.0 

5.0 

stress peak 

Fig. 13. Strength degradation of laminate [0/90]2S with central hole. 

c 

(a) [+45]2S with hole, r =0.6 

0.0 0.2 0.4 0.6 0.8 1.0 



6.0 

4.0 

2.0 

0.0 

(b) [0/90]2S with hole, r =0.8 

0.0 0.1 0.2 0.3 0.4 0.5 

1-E (n )/E (0) 

Stress peak 

Fig. 14. Strength degradation of laminate [+45]2S with central hole. 

(b) [+45]2S with hole, r =0.6 

0.0 0.2 0.4 0.6 0.8 

1-E (n )/E (0) 

143

144 



25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

15.0 

10.0 

5.0 

0.0 

Stress peak 

0.0 0.2 0.4 0.6 0.8 1.0 


Stress peak 


(a) [45/0/0/-45]S with hole, r =0.7 


25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

Stress peak 

Fig. 15. Strength degradation of laminate [45/0/0/-45]S with central hole. 

(a) [45/90/-45/0]S with hole, 

0.0 0.2 0.4 0.6 0.8 1.0 



15.0 

10.0 

5.0 

0.0 

(b) [45/0/0/-45]S with hole, r =0.7 

0.0 0.1 0.2 0.3 0.4 0.5 

1-E (n )/E (0) 

Stress peak 

Fig. 16. Strength degradation of laminate [45/90/-45/0]S with central hole. 

(b) [45/90/-45/0]S with hole, r =0.6 

0.0 0.2 0.4 0.6 0.8 

1-E (n )/E (0) 

In all the figures above, figures (a) show the relationship between residual strength and nominal life 

ratio, the nominal life ratio is cycle number n divided by the average life (N*)of several (3~5) other 

specimens which are tested to failure and corresponding to the data point located on the stress peak 

( max ) line. Essentially, according to traditional method, we want to obtain the residual strength of the 

specimen under fatigue loading at the life ratio which is cycle number n normalized by the real life itself, 

however we hardly get it. However, if we test the residual strength at some stiffness degradation ratio, 

as shown in figures (b), the relationship between them becomes disciplinarian. 

6 Conclusion 

Based on the basis that the instantaneous residual strength and residual stiffness are determined by the 

damage condition in the material at the same time, a new residual stiffness model for laminate under 

fatigue loading was presented and a coupled model was set up to establish the relationship between the 

residual stiffness and residual strength. The experimental data of three kinds of AS4/PEEK laminates 

was adopted to verify the models, results show that the residual stiffness model was versatile to describe 

the stiffness degradation rule of the multidirectional laminates, the residual strength can be predicted 

precisely relatively by simple residual strength test according to the coupled model, the coupled model 

has two same parameters with the residual stiffness model and one more coupled model, so they are


easy for the engineering application. 

The coupled parameter, w, was considered to be a material parameter based on the validation results 

of three laminates with different stacking sequence (with different stiffness and strength degradation 

rule). For the material of AS4/PEEK, w is about 2.0 for the constant loading, and it needs additional 

experiment for the spectrum loading. There is no hypothesis about material and structure in the coupled 

model, so it can be extended to apply for other material and laminates theoretically. 

Due to the continue nondestructive trackability of the residual stiffness, it is more appropriate to use 

residual stiffness as the damage parameter, and the authors suggest that the residual strength can be 

tested under condition of some stiffness degradation ratio instead of life ratio. 

References 

[1] Talreja R.Fatigue of composite material.Lancaster,Technomic Publishing Company, 1987. 

[2] Yang J N, Jones D L, Yang S H, et al. A stiffness degradation model for graphite/epoxy laminates. Journal of Composite Materials, 1990, 

24: 753~769. 

[3] Lee L J, Fu K E, Yang J N. Prediction of fatigue damage and life for composite laminates under service loading spectra. Composites 

Science and Technology, 1996, 56: 635-648. 

[4] Echtermeyer A T, Engh B, Buene L. Lifetime and Young‟s modulus changes of glass/phenolic and glass/polyester composites under 

fatigue. Composites, 1995, 26(1): 10-16. 

[5] Coats T W, Harris C E. Experimental verification of a progressive damage model for IM7/5260 laminates subjected to tension-tension 

fatigue. Journal of Composite Materials, 1995, 29(3): 280-305. 

[6] Plumtree A, Shen G.. Prediction of fatigue damage development in unidirectional long fibre composites. Polymers and Polymer 

Composites, 1994, 2(2): 83-90. 

[7] Zhang D Q,Sandor B I. Damage evaluation in composite materials using thermographic stress analysis. Advances in Fatigue Lifetime 

Predictive Techniques, Philadelphia, ASTM, 1992: 341-353. 

[8] Whitworth H A. Evaluation of the residual strength degradation in composite laminates under fatigue loading. Composite Structures, 2000, 

48: 261-264. 

[9] Whitworth H A. Modeling stiffness reduction of graphite/epoxy composite laminates. Journal of Composite Materials, 1987, 21: 362-372. 

[10] Ye L. On fatigue damage accumulation and material degradation in composite materials. Composites Science and Technology, 1989, 36: 

339-350. 

[11] Hwang W, Han K S. Fatigue of composite, fatigue modulus concept and life prediction. Journal of Composite Materials, 1986, 20: 

155-165. 

[12] Bangyan L, Lessard L B. Fatigue and damage-tolerance analysis of composite laminates: Stiffness loss, damage-modeling and life 

prediction. Composites Science and Technology, 1994, 51: 43-51. 

[13] Philippidis T P, Vassilopoulos A P. Fatigue design allowables for GRP laminates based on stiffness degradation measurements. 

Composites science and technology, 2000, 60: 2819-2828. 

[14] Vure N R S, Kriz R D. Effect of cooling rate and stacking sequence on the fatigue behavior of notched quasi-isotropic AS4/PEEK 

Laminates. Journal of composites technology & Research, 1996, 18(2): 127-134. 

[15] Shokrieh M M, Lessard L B. Progressive fatigue damage modeling of composite materials: Part 1. Modeling. Journal of Composite 

Materials, 2000, 34(13): 1056-1080. 

[16] Tserpes K I, Papanikos P, Labeas G, et al. Fatigue damage accumulation and residual strength assessment of CFRP Laminates. Composite 

Structures, 2004, 63(2): 219-230. 

[17] Mao H, Mahadevan S. Fatigue damage modeling of composite materials. Composite Structures, 2002, 58: 405-410. 

[18] Rotem A. The fatigue behaviour of orthotropic laminates under tension-compression loading International Journal of Fatigue, 1991, 13(3): 

209-215. 

[19] Jessen S M, Plumtree A. Fatigue damage accumulation in pultruded glass/polyester rods. Composites, 1989, 20(6): 559-567. 

[20] Yang J N. Fatigue and residual strength degradation for graphite/epoxy composites under tension-compression cyclic loading. Journal of 

Composite Materials. 1978, 12: 19-38. 

[21] Yang J N, Jones D L. Load sequence effects on the fatigue of unnotched composite laminates. ASTM STP, 723, Philadelphia, American 

Society for Testing and Materials 1981: 213–232. 

145

146 


[22] Yang JN, Du S. An exploratory study into the fatigue of composites under spectrum loading. Journal of Composite Materials, 1983, 17: 

511–526. 

[23] Adam T, Dickson R F, Jones C J, et al. A power law fatigue damage model for fiber-reinforced plastic laminates. Proceedings of the 

Institution of Mechanical Engineers, Part C, 1986, 200(3): 155–166. 

[24] Broutman L J, Sahu S. A new theory to predict cumulative fatigue damage in fiberglass reinforced plastics. Composite Materials: Testing 

and Design, ASTM STP 497, 1972: 170-188. 

[25] Hashin Z. Cumulative damage theory for composite materials: Residual life and residual strength methods. Composites Science and 

Technology, 1985, 23(1): 1-19 

[26] Charewicz A, Daniel I M. Damage mechanisms and accumulation in graphite/epoxy laminates. Composite Materials. Fatigue and fracture, 

ASTM STP 907, Philadelphia, ASTM, 1986: 274-297. 

[27] Schaff J R,Davidson B D. Life prediction methodology for composite structures, Part I-Constant amplitude and two-stress level fatigue. 

Journal of Composite Materials, 1997, 31(2): 128-157. 

[28] Schaff, J R, Davidson B D. Life prediction methodology for composite structures. Part II- Spectrum fatigue. Journal of Composite 

Materials, 1997, 31(2): 158-181. 

[29] Sendeckyj G P. Life prediction for resin-matrix composite materials. Fatigue of composite materials, Amsterdam, Elsevier Science 

Publishers, 1990: 431-483. 

[30] Xiong J J, Li H Y, Zeng B Y. A strain-based residual strength model of carbon fibre/epoxy composites based on CAI and fatigue residual 

strength concepts. Composite Structures 2008, 85: 29-42. 

[31] Hahn H T, Kim R Y. Proof testing of composite materials. Journal of Composite materials. 1975, 9:297-311. 

[32] Haplin J C, Jerina K L, Johnson T A. Analysis of the test methods for high modules fibers and composites, ASTM STP 521, Philadelphia, 

American Society for Testing and Materials, 1973: 5-64. 

[33] Philippidis T P, Assimakopoulou T T. Using acoustic emission to assess shear strength degradation in FRP composites due to constant and 

variable amplitude fatigue loading. Composites Science and Technology, 2008, 68: 840-847. 

[34] Chou P C, Croman R. Residual strength in fatigue based on the strength-life equal rank assumption. Journal of Composite Materials, 1978, 

12: 177-194. 

[35] Yao W X, Himmel N.A new cumulative fatigue damage model for fiber-reinforced plastics.Composites Science and Technology, 2000, 

60: 59~64. 

[36] Caprino G. Predicting fatigue life of composite laminates subjected to tension-tension fatigue. Journal of Composite Materials, 2000, 

34(16): 1334-1355. 

[37] Revuelta D, Cuartero J, Miravete A, et al. A new approach to fatigue analysis in composites based on residual strength degradation, 

Composite Structures, 2000, 48: 183-186. 

[38] Reifsnider K L, Stinchcomb W W. A critical element model of the residual strength and life of Fatigue-loaded composite coupons. 

Composite Materials: Fatigue and Fracture, Hahn H T, ed. ASTM STP 907, Philadelphia, American Society for Testing and Materials, 

1986: 298-313. 

[39] Shokrieh M M, Lessard L B. Multiaxial fatigue behavior of unidirectional plies based on uniaxial fatigue experiments- I. Modelling. 

International Journal of Fatigue, 1997, 19(3): 201-207. 

[40] Lee C H, Jen M H. Fatigue response and modeling of variable stress amplitude and frequency in AS-4/PEEK composite laminates Part 1: 

experiments. Journal of Composite Materials, 2000, 34(11): 906-929. 

[41] Lian W, Yao W X. Fatigue life prediction of composite laminates by FEA simulation method. International Journal of fatigue, 2010, 

32(1):123-133.

An Energy-Based Fatigue Approach for Composites Combining 

Failure Mechanisms, Strength and Stiffness Degradation 

Abstract 

H Krüger *, R Rolfes, E Jansen 

Institute of Structural Analysis, Leibniz Universität Hannover, Appelstrasse 9a, 30167 Hanover, Germany 

In order to improve the fatigue analysis of large structures made of fibre-reinforced plastics a physically motivated 

fatigue assessment procedure is investigated. In contrast to the analysis procedure usually applied the novel model 

consists of a layer-wise continuum mechanics approach on macro scale and considers different failure modes. 

The approach subdivides into two analysis parts: discontinuous quasi-static degradation and continuous fatigue 

degradation. The discontinuous approach is based on a well-known failure mode theory. The continuous degradation 

approach makes use of an energy-based hypothesis, which combines strength and stiffness degradation. 

With the present approach stress redistributions and sequence effects can be investigated. 

Keywords: Fatigue modelling, reinforced composite, damage mechanics, layer-based approach, degradation, sequence effects 


For evaluating the fatigue behaviour of structures made of fibre-reinforced plastics (FRPs) it is 

common practice to use SN-curves on laminate scale in combination with the simple and linear damage 

accumulation rule according to Palmgren and Miner [2]. This is done even though this rule has been 

developed for metals, which are in contrast to FRPs isotropic and ductile and have only a single failure 

mode. Additionally stress redistributions between layers and within the structure can occur since the 

material properties of FRPs, stiffness and strength degrade depending on the loading and the 

development of tolerable cracks. This causes a non-linear damage accumulation and shows that 

Palmgren´s and Miner´s rule is not valid for FRPs. Finally, the whole procedure is not really suitable, it 

is purely empirical and does not represent the complex failure behaviour of FRPs. Furthermore, the 

procedure is also costly to apply, because due to this improper approach each laminate set-up and 

loading situation needs to be experimentally investigated. 

Due to these shortcomings there has been a lot of research activity in the field of modelling the 

fatigue behaviour of FRPs in the last decades. The models investigated can be classified in three groups: 

The first group is built by the so-called “fatigue life concepts” which are, similar to the Palmgren and 

Miner rule, linear and of purely empirical nature [3,4]. The second group comprises the 

phenomenological models [5,6,7], which are based on empirically determined evolution laws 

concerning the stiffness or the strength of laminates. Progressive damage models [8,9], the third group, 

* Corresponding author. Tel: +49 (0)511 762 2266; fax: +49 (0)511 762 2366 

E-mail address: H.Krueger@isd.uni-hannover.de

148 


describe the progressive development of cracks or delaminations. 

The present approach combines several advantages of different groups and avoids unwanted 

disadvantages. It is closest to the second type of models, since in principal it also bases on empirical 

evolution laws. But due to its energy-based methodology and combination with the fracture-mode 

dependent theory of Puck [1] it is more mechanically oriented and couples stiffness and strength 

degradation. In contrast to the progressive damage models it is applicable to arbitrary structures and 

allows for the consideration of large number of cycles, since it works on macro-mechanical scale and 

uses a block-wise loading approach. Due to the restriction to a 2D-approach efficient standard shell 

elements can be used and also the fatigue assessment of large structures (e.g. rotorblades of wind energy 

converters (WEC)) may be achievable. Since distinct stiffness and strength degradations occur during 

the lifetime of a structure made of FRPs it is required to investigate structures on a more global scale in 

order to cover the accompanying stress redistributions. Besides these global or macro-scale stress 

redistributions also local (meso-scale) stress redistributions between the layers of a laminate are 

accounted for, since the model is layer-based. 

The fatigue model is implemented in a material routine, which can be used in combination with the 

commercial FE-software Abaqus ® and its layered shell elements. Using this type of elements each layer 

can have its own material definition and, even more important, independent degradation factors. 

2. Overview and Framework of the New Fatigue Approach 

Within the present approach the standard structural analysis is extended by a fatigue assessment 

procedure (Figure 1). Therewith the analysis consists of two parts, the quasi-static and the cyclic part. 

First the structure will be evaluated against possible quasi-static failures as inter-fibre failures or fibre 

failures as described by Puck´s failure criterion [1]. If a tolerable failure occurs the material properties 

will be degraded as presented in chapter 3. Such a degradation is termed discontinuous because this 

happens only if a failure criterion is met. Fibre failures and inter-fibre failures with an inclined fracture 

surface are according to Puck intolerable due to their abrupt and explosive character and thus the 

analysis will be aborted in the case, that one of the corresponding criteria is met. However, during the 

fatigue life and also during the fatigue assessment some failures of filaments and single fibres occur, but 

these are regarded as uncritical since they are supposed to be very limited and release low-energy. 

If the quasi-static strength criterion is not met or is not met anymore after discontinuous degradation, 

it is changed over to the cyclic part of the analysis. Subject to the maximum stress, the number of cycles 

and the load ratio R, which is the ratio of the maximum stress to the minimum stress, the material is 

degraded by means of the new energy-based approach at each material point (chapter 4). This 

degradation is termed continuous, since each load cycle leads to a degradation until total degradation is 

reached. 

The analysis of the following loading step is conducted with degraded material properties and 

therewith stress redistributions on meso-scale (between layers) as well as on macro-scale can occur and 

the analysis can become non-linear.

An Energy-based Fatigue Approach for Composites Combining Failure Mechanisms, Strength and Stiffness Degradation 149 

Figure 1: Flowchart of the structural analysis including fatigue evaluation [13]. 

Since lightweight-structures are usually exposed to a large number of load cycles, which, 

depending on the application, may reach up to hundreds of millions, it is not desired to execute a 

cycle-by-cycle analysis. Therefore the approach provides the option to group the external loading to 

blocks of the same maximum loading and range as this is usually done with stresses, e.g. by means of 

the rainflow-count method, even if the correctness of the analysis may slightly decrease. Structures of 

mechanical engineering applications are often exposed to repetitive loading situations, then the analysis 

can be drastically shortened. 

The degradation factors are the same for the continuous and the discontinuous degradation. In order 

to sufficiently describe the stiffness and the strength degradation of a plane stress approach ten 

parameters are required. The degradation parameters of the material properties in normal direction need 

to be distinguished in tension and compression, since the effect of the cracks developed are different. 

This is not such pronounced for the parameters associated with shear. 

with: Ei j : stiffness 

Ri j : strength 

1 

1 

E E D E 

(1) 

j j j 

i 0, i E, i 0, i E, i 

R R D R 

(2) 

j j j j j 

i 0, i R, i 0, i R, i 

DE,i j : stiffness damage parameter (0: undamaged; 1: totally damaged) 

DR,i j : strength damage parameter (0: undamaged; 1: totally damaged) 

ηE,i j : stiffness degradation factor (1: undamaged; 0: totally damaged) 

ηR,i j : strength degradation factor (1: undamaged; 0: totally damaged) 

i: orientation 

j: direction (tension or compression) 

0: undamaged

152 


Fig. 3. Development of the degradation factors subject to the stress exposure fE,IFF and schematic illustration of multiple degradation. 

Indeed the effect of inter-fibre-failures on the shear stiffness depends on the direction of the normal 

stressing (tension or compression), but this difference is described to be not that drastic [11] and no 

quantitative data is available. Thus the shear degradation within a compressive or tensile regime is 

considered to be the same. 

This is not valid for the stiffness degradation perpendicular to the fibres. Straight cracks, as caused by 

IFF of mode A or B, open under tensile loading, but under compressive loading those simply close and 

the related stiffness remains unchanged. 

4. Continuous Degradation 

In contrast to the discontinuous degradation within the continuous degradation procedure each 

stressing leads to a certain degradation and also degradations due to compressive normal stresses and in 

fibre direction are considered. The evolution of damage bases mainly on the development of strains 

during the fatigue life process, whose free parameters need to be calibrated by means of fatigue tests or 

can be well estimated according to data given in the literature. This is shown exemplarily in figure 4 for 

the strain evolution perpendicular to the fibres. The static strain and the fatigue failure strain are known, 

the single free parameter combination (Δε2/Δn2) and allows for fitment to the material analysed. 

with 

 

2 n2 1 2 n2 

A , B 

n n 

fat 

1 

n 

f ,2 n 

2 0,2 1AB 1 11 N2 0,2 N2 

 

 

 

1 

2 2 2 2 

ε0: static strain 

εf fat : strain at fatigue failure 

n: number of cycles 

N2: number of cycles to failure in 2-direction 

(10)


Fig. 4. Evolution-curve of ε2-strains. 

The main constituent of the new continuous degradation method is an energy-based hypothesis, 

which was applied to concrete at first [10]. This hypothesis equals the dissipated energy during fatigue 

loading with that during quasi-static loading (fig. 5). This means that the damage state, in the sense of 

mechanical properties as stiffness and strength (in the same material orientation), only depends on the 

amount of energy dissipated, irrespective of how often and with which amplitude the structure has been 

loaded. Unlike the application to isotropic materials the orientation of stressing and the failure mode 

respectively need to be incorporated in case of anisotropic materials as FRPs, 

W ( D) W ( D, , n) 

(11) 

da, j fat, j fat 

i i 

Fig. 5. Development of energy dissipation and degradation caused by quasi-static (top line) or cyclic loading (bottom line), Wi da,j or Wi fat,j ; 

showing the example of tensile σ2-stresses (in-situ layer). 

Due to that approach the stiffness and the strength degradations are coupled together, so also a 

strength degradation of failures detected by the quasi-static strength analysis can be established. The 

residual strength is determined through the dissipated energy incorporated in a stress-strain-diagram. A 

degradation of the strength leads to a shrinkage of the fracture body, whose undamaged variant (ηR,i j = 

1.0) is described by Puck´s original failure criterion. The effects of the five independent strength 

degradation factors on the fracture body and therewith on the failure criterion is presented in figure 6. 

Different combinations of the strength degradation factors with ηR,i j = 1.0 or ηR,i j = 0.5 are shown.

154 


Fig. 6. Shrinkage of the fracture body with different combinations of the strength degradation factors (ηR,i j = 1.0 or ηR,i j = 0.5). 

5. Numerical Example 

In order to test the approach a numerical example is investigated. The example should show, that the 

degradation procedure reasonably works. It is checked, if stress redistribution and sequence effects due 

to stiffness degradations occur. 

5.1 Mechanical Model 

The developed approach is tested on an open-hole plate with a GFRP-[0/90/0] laminate lay-up, which 

is simply supported on the left edge (fig. 7). In order to reduce calculation costs and due to the 

symmetry of the structure and the loading only the upper half is modelled and only degradations caused 

by tensile stresses are considered. Standard shell elements with four nodes and a reduced integration 

scheme are used for the FE-model, Abaqus ® is chosen as the FE-solver. In-plane tension fatigue loading 

(R=0.1) is applied horizontally at the right-hand boundary. The effect of two different loading sequences 

are compared. They deviate only in their sequences, which are opponent to each other: The first load 

sequence is decreasing, so the largest amplitude is at first, and the second one is increasing and the 

largest amplitude is at last (fig. 7).


Fig. 7. Schematic diagram of the structure used for the numerical example and block diagram of two loading sequences. 

5.2 Material Model and Material Data 

The material data used for the numerical model can be found in table 1, the data is extracted from 

Knops [11]. The tensile stress-strain-curves implemented in the program can be found in Knops [11] and 

Maimi et al. [12] respectively and are illustrated in figure 8. 

Table 1. Material Data used for the numerical example. 

E∥ in MPa E⊥ in MPa G∥⊥ in MPa ν∥⊥ R∥ t in MPa 

45,600 16,200 5,830 0.278 1,140 

R⊥ t in MPa R∥ c in MPa R⊥ c in MPa R∥⊥ in MPa p⊥∥ t 

50 570 114 72 0.3 

p⊥∥ c p⊥⊥ t p⊥⊥ c Mag ηwm 

0.25 0.20 0.20 1.30 0.50 

ηws ηrE2 cE2 ξE2 ηrE21 

0.50 0.03 5.3 1.3 0.25 

cE21 ξE21 

0.70 1.5 

Unless appropriate SN-curves are available, in order to determine the number of cycles to failure N i 

caused by constant amplitude loading the formula according to [14] is used, which shows generally a 

good approximation to experimentally investigated SN-curves. Besides the strengths, the 

slope-parameters mi of the SN-curves allow for fitment to the material used, 

with mi: slope of the SN-curve (i: direction) 

SM: stress mean 

SA: stress amplitude 

i 

t c t c 

Ri Ri 2 

SM Ri R 

i 

Ni 

 

2 

S 

 

A 

. 

m 

(12)

156 

6. Results and Discussion 


Fig. 8. Tensile stress-stain-curves implemented in the calculation routine. 

Figure 9 presents the degradation of the tensile material stiffness perpendicular to the fibres of the 

inner 90°- and the outer 0°-layers after applying the different load sequences. If the applied load is high 

in the first stage of the loading sequence, the stresses close to the hole are much higher than in case of 

the increasing loading sequence. This leads consequently to a clearly higher degradation in that area. 

However the following loading steps do not cause a distinct further degradation. In case of the 

increasing loading sequence the area around the hole is already degraded before the structure is highly 

loaded. Due to that the total degradation in that area is comparably little. The stresses redistribute to the 

area between the edge and the hole of the structure, there on the contrary the degradation is higher. 

It can be stated that decreasing load sequences lead to a more local but higher degradation and 

increasing loading sequences to a more global and lower degradation. 

Fig. 9. ηE2 t -distribution after applying the two loading sequences (top: decreasing sequence, bottom: increasing sequence; left: 90°-layer, right: 

0°-layer).


7. Conclusions and Outlook 

The results show that it is possible to simulate degradations caused by fatigue loading and therewith 

sequence effects using the present approach, which seems to be promising. Due to the energy-based 

damage mechanics approach used it is possible to simulate stiffness degradation in combination with 

strength degradation of FRPs under a high number of cycles. By means of integrating Puck´s theory the 

present approach considers different failure modes and enables a relatively mechanical and precise 

fatigue assessment. Further steps are the improvement of the model with special attention to 

multiaxiality and interactions as well as the verification of the model. 

References 

[1] A. Puck, “Festigkeitsanalyse von Faser-Matrix-Laminaten – Modelle für die Praxis, Carl Hanser, München, 1996; also in: M. Knops, 

„Analysis of Failure in Fiber Polymer Laminates: The Theory of Alfred Puck“, Springer, Germany, 2008. 

[2] M.A. Miner, “Cumulative damage in fatigue”, Journal of Applied Mechanics (1945), 67, A159-A164. 

[3] Z. Hashin, A. Rotem, „A fatigue criterion for fibre reinforced composite materials“, Journal of Composite Materials, 7 (1973), p. 

448-464. 

[4] A. Plumtree, G.X. Cheng, „A fatigue damage parameter for off-axis unidirectional fibre-reinforced composites“, International Journal of 

Fatigue, 21(8) (1999), p. 849-856. 

[5] M.M. Shokrieh, L.B. Lessard, “Residual fatigue life simulation of laminated composites”, Proceedings of International Conference on 

Advanced Composites (ICAC 98), 15–18, December 1998, Hurghada, Egypt, p. 79–86. 

[6] J.N. Yang, D.L. Jones, S.H. Yang, A. Meskini, “A stiffness degradation model for graphite/epoxy laminates”, Journal of Composite 

Materials, 24 (1990), p. 753-769. 

[7] W.X. Yao, N. Himmel, “A new cumulative fatigue damage model for fibre-reinforced plastics”, Composites Science and Technology, 60 

(2000), p. 59-64. 

[8] X. Feng, M.D. Gilchrist, A.J. Kinloch, F.L. Matthews, „Development of a method for predicting the fatigue life of CFRP components”, 

in : Degallaix, S., Bathias, C. und Fougères, R. (Editor), International Conference on fatigue of Composites, Proceedings, 3- 5 June 

1997, Paris, France, La Société Française de Métallurgie et de Matériaux, p. 407-414. 

[9] M.M. Shokrieh, L.B. Lessard, “Progressive fatigue damage modeling of composite materials, Part I: Modeling”, Journal of Composite 

Materials, 34(13) (2000), p. 1056-1080. 

[10] D. Pfanner, “Zur Degradation von Stahlbetonbauteilen unter Ermüdungsbeanspruchung” („Degradation of Structures Made of Reinforced 

Concrete under Fatigue Loading“), PhD-Thesis, Ruhr-Universität Bochum, 2000. 

[11] M. Knops, „Analysis of Failure in Fiber Polymer Laminates: The Theory of Alfred Puck“, Springer, Germany, 2008. 

[12] P. Maimi, P. P. Camanho, J.A. Mayugo, C.G. Dávila: „A continuum damage model for composite laminates (Part I: Constitutive model; 

Part II: Computational implementation and validation), Mechanics of Materials, 39 (2007), S. 897-919. 

[13] H. Krüger, R. Rolfes: “A Physically Motivated and Layer-based Fatigue Concept for Fiber-Reinforced Plastics”, 14.-17. September 2010, 

CST conference, Valencia, Spain. 

[14] Germanischer Lloyd: “Richtlinie für die Zertifizierung von Windenergieanlagen“, engl.: „Certification Guideline for Wind-Energy 

Converters“, Germanischer Lloyd Wind Energie GmbH, Hamburg (2003).

Experimental characterization and analytical modeling of 

material non-linearity in fatigue analysis of polymer matrix 

composites 

Abstract 

M Magin, N Himmel * 

Institut für Verbundwerkstoffe GmbH – University Kaiserslautern, Erwin Schrödinger Str. Geb. 58 – 67663 Kaiserslautern, Germany 

Due to their high mechanical performance and advantageous cost and weight performance, fiber reinforced polymer 

matrix composites are widely used in aerospace and mechanical engineering. To asses the fatigue life of these composites 

in computational simulations, the underlying material models need to consider physical non-linearity under both static 

and cyclic loading. Non-linear material models of unidirectional composites with glass and carbon fiber reinforcement 

which are widely used in the wind energy and aircraft industry were determined experimentally and implemented into a 

fatigue life prediction program. Based on the experimental input, the influence of the physical non-linearity of the 

composite materials on the results of static and fatigue life analyses was investigated. While non-linear material models 

require significantly more experimental and analytical effort, their usage leads to more realistic fatigue life calculations, 

which could be shown in a comparison of experimental and analytical results using different linear and non-linear 

analytical models. 


To simulate the fatigue life of fiber reinforced polymer matrix composites, the underlying material 

models need to consider material non-linearity under both static and cyclic loading, such as stress-strain 

curves. In an on-going research project the physical non-linearity of polymer matrix composites with 

glass and carbon fiber reinforcement was investigated. The selected materials are representative for 

applications in the wind energy and aircraft industries. The non-linear material parameters of these 

composites were determined experimentally and implemented into a fatigue life prediction program. 

While non-linear material models require significantly more experimental and analytical effort, their 

usage leads to more realistic fatigue life calculations. 

2. Experimental characterization 

To investigate the inherent physical non-linearity of the selected composite materials experiments 

were carried on unidirectional laminates to determine tension and compression quasi-static strength 

parameters for [0], [90] and [±45] laminates prior to and after cyclic fatigue preloading with constant 

amplitude sinusoidal load under load control at stress ratios of R= -1, 0.1 and 10 for three different 

* E-mail address: norbert.himmel@ivw.uni-kl.de

Experimental characterization and analytical modeling of material non-linearity in fatigue analysis of polymer matrix composites 

stress levels. Also, stiffness degradation was continuously measured using the quotient of the stress and 

strain differences at the upper and lower reversal points of the hysteresis loop 

3. Modeling 

To model the fatigue life of fiber reinforced polymeric composites subjected to general in-service 

loading profiles a simulation tool based on the Critical Element Concept of Reifsnider and Stinchcomb 

[2] has been developed [1]. The available simulation uses non-linear S-N curves, Puck‟s inter-fiber 

failure criterion, and stiffness degradation models with an empirical delamination parameter [3]. The 

software was extended to incorporate non-linear material models for the stress-strain relationships of 

unidirectional composites for uniaxial fiber parallel, transverse, and shear loading, using a modified 

Ramberg-Osgood equation to predict the fatigue life more realistically. Furthermore, an optimized 

interface was generated for communication with a commercially available finite element program to 

allow the extension of the fatigue life analysis to geometrically more complex shaped structures and/or 

more heterogeneous load cases. 

4. Results 

Based on experimentally determined material properties, such as Fig. 1, the influence of the physical 

non-linearity on the fatigue life of polymer matrix composites was investigated. As a parameter study [4] 

showed the influence of the fiber-parallel stress-strain relationship is particularly strong as it influences 

directly the stress transfer during fatigue loading to the 0° plies and, therefore, the load parallel to the 

fiber direction carried by these plies. 

Fig. 1. R = +0.1 S - N diagram of unidirectional glass/epoxy composite perpendicular to fiber direction with linear and non-linear curve fits 

The comparison of experimental and simulation results of a carbon fiber reinforced 

vinylester-urethane hybrid resin toughened by liquid, epoxy-terminated butadiene-nitrile rubber 

(CF/VEUH:ETBN) subjected to miniTWIST variable amplitude loading (Fig. 2) shows that the best 

159

160 


correlations are obtained for a simulation mode combining non-linear stress-strain relations with 

inter-fiber failure and delamination induced stiffness reduction. A model assuming linear stress-strain 

behavior combined with the neglecting of stiffness degradation overestimates the fatigue life, while it is 

underestimated by combining linear stress-strain behavior and the full degradation of the 

multidirectional laminate to its 0° plies. 

Fig. 2. Test results and fatigue life predictions for [+45/0/-45/90]S CF/VEUH:ETBN under miniTWIST variable amplitude loading [3] 


The financial support of the German Research Foundation (DFG) within the research project 

'Lebensdaueranalyse dünnwandiger Faser-Kunststoff-Verbund-Strukturen unter Berücksichtigung 

werkstofflicher Nichtlinearitäten' (HI 700 / 11-2) to carry out the presented work is gratefully 

acknowledged. 

References 

[1] Himmel, N.: Fatigue Life prediction of Laminated Polymer Matrix Composites. International Journal of Fatigue, 24:2–4, 2002, p. 349 – 

360. 

[2] Reifsnider, K. L.; Stinchcomb, W. W.: A Critical-Elemental Model for the Residual Strength and Life of Fatigue-Loaded Composite 

Coupons; In: H. T. Hahn (ed.), Composite Materials: Fatigue and Fracture, ASTM STP 907, 1986, pp. 298 – 313. 

[3] Noll, T.; Magin, M.; Himmel, N.: Fatigue Life Simulation of Multi-axial CFRP Laminates Considering Non-linearity of Material. 4 th 

International Conference on Fatigue of Composites, Sept. 26-28, 2007, Kaiserslautern, Germany. 

[4] Magin, M; Himmel, N.: Effect of Physical Non-linearity on Cyclic Fatigue Life Prediction of Polymer Matrix Composites. 8th Intern. 

Conference on Durability of Composite Systems (Duracosys 2008), July 16–18, 2008, Porto, Portugal.

Abstract 

Calorimetric Analysis of dissipative Effects associated 

with the Fatigue of GFRP Composites 

H Sawadogo, S Panier *, S Hariri 

Polymers and Composites Technology & Mechanical Engineering Department, Ecole des 

Mines de Douai, 941 rue Charles Bourseul, 59508 Douai, France 

This paper deals with the calorimetric analysis of damage mechanisms of composite materials. Thermoelastic coupling 

source amplitude and the mean dissipation per cycle were derived from surface temperature field provided by an IR 

system. Cycling tests performed on glass/epoxy composites with initial defects underline that thermoelastic source 

distribution give a good localization of the defect. During fatigue tests, mean dissipation per cycle increase when the 

delamination growths and seems to be a good indicator of the damage evolution. 

Keywords: Mechanical dissipation; composite; fatigue; delamination; infrared thermography 


Infrared thermography methods are nowadays well known to evaluate the damage in composite 

materials. Theses methods are classified in two categories, passive and active. The passive methods 

consist to excite a structure by a thermal [1] or elastic wave [2] (vibrothermography) and to use infrared 

thermography to evaluate the temperature field. The second methods are based on the temperature 

variations due to the damage phenomena which occur when a mechanical load is applied to a specimen 

or a component. Some authors use directly the temperature changes to evaluate the damage [3, 4]. 

Various studies on metallic materials previously carried out by Chrysochoos and coworkers have shown 

that heat sources produced by the material itself were more relevant than temperature when analyzing 

various phenomena such as Luder's bands [5], fatigue [6] or strain localization [7]. The main reason is 

that the temperature field is influenced by conduction as well as heat exchanges with ambient air and 

grips, unlike local heat sources. In this study, the fatigue phenomena on GFRP composites were 

therefore studied using a calorimetric approach. The aim was to assess the heat source fields created 

during the fatigue test. The heat sources are derived from thermal images provided by an infrared 

camera using a local expression of the heat equation. A specific thermal image processing was 

developed to separately estimate the dissipated energy associated with the irreversible evolutions of the 

damage and the thermoelastic coupling sources induced by the reversible thermal expansion. 

2. Temperature: a good damage indicator? 

If we measure the surface temperature of a specimen during cycling test (self-heating test), we can 

* E-mail address: panier@ensm-douai.fr

162 


observe an increase of the surface average temperature and an oscillation around this average value 

(figure 1). These temperature variations are due to two different heat sources which are the 

thermoelastic coupling and the intrinsic dissipation. 

Fig. 1. Temperature variation during fatigue test [4]. 

The small amplitude oscillatory temperature variations is due to the reversible thermoelastic heating 

and cooling during each loading cycle. This coupling leads to an oscillation of the temperature at the 

same frequency as the load (Figure 1). The Thermoelastic Stress Analysis (TSA) method which is a 

standard technique of stress analysis used in industry is based on the theoretical treatment of the the 

thermoelastic effect due to Lord Kelvin who showed that the temperature change ∆T associated with 

adiabatic elastic deformation can be expressed in the form: 

3 

T = -K T 

(1) 

m ii 

i= 

1 

where Km is the thermoelastic constant, Δζii is the normal stress changes. 

The second type of heat source is the intrinsic dissipation associated with irreversible structural 

changes, cycle after cycle. This is characterized by a progressive increase in overall temperature of the 

specimen (Figure 1). In 1921, this phenomenon had been observed by Moore and Kommers [8]. But it is 

especially since the work of Luong [3] that the temperature stabilized after several cycles is used as an 

indicator of fatigue damage. By cycling a sample and determining the steady-state temperature for 

different stress levels, he observed that beyond a given limit, the steady-state temperature starts to 

increase significantly. This regime change corresponds to a situation where the fatigue limit is reached. 

This empirical method does not give good results for all materials. However, some models based on a 

physical basis (microplasticity) have been developped to describe this result [9, 10]. 

All these works concern only metallic materials. The applications of composite materials fatigue are 

rare even though they are historically one of the first materials studied. Indeed, Charles et al. have 

shown that it is possible to detect areas of stress concentration and location of cracking in glass/epoxy 

composite plates [11]. More recently, Toubal et al. showed that the surface temperature of a 

carbon/epoxy composite during a cyclic test have the same evolution than the damage typically

H Sawadogo, S Panier, S Hariri / Calorimetric Analysis of dissipative Effects associated with the Fatigue of GFRP Composites 

observed for composite materials [4]. The figure 2 showed the surface temperature variation measured 

by infrared thermography during a fatigue test [12]. The fatigue test was performed on woven 

glass/epoxy fabric [±45 o ] sample with a hole at a frequency of 5 Hz with a load ratio of 0.1 and a 

maximum stress corresponding to 45% of the UTS. 

Instead of working on the temperature (result) it was decided to identify the heat sources (origin) in 

the spirit of the works done by Chrysochoos et al. [5, 6]. 

3. Heat Diffusion Equation 

Fig. 2. Evolution of the surface temperature during a fatigue test [12]. 

The fatigue is considered as a dissipative, quasi-static thermomechanical process. The equilibrium 

state of each volume of material is then described by means of a set of n state variables. The chosen set 

of state variables is made of: the absolute temperature T, the linearised strain tensor ε and n-2 scalar 

components α1, α2, ... αn-2 of the vector a gathering the internal variables. Considering the first and second 

principles of thermodynamics and assuming that Fourier's law is used to model the heat conduction, the 

heat diffusion equation can be written as follow: 

where ρ is the mass density, C is the specific heat, k is the thermal conduction tensor, rext the external 

heat supply, the Cauchy stress tensor and the specific Helmhotz free energy. The right-hand 

side of equation (2) represents the heat sources produced by the material itself during the deformation 

process. It can be split into separate terms : the mechanical dissipation d1 which corresponds to the heat 

production due to various mechanical irreversibilities and the thermomechanical couplings sthe and sic. 

163 

(2)

164 


As the thermal informations given by the IR camera only concerns surface temperature field, the 

following assumptions are used to perform the heat source evaluation: 

the thermal conductivity is orthotopic and the thermal conductivity tensor have the following 

form : 

kxx 0 0 

k = 

 

0 kyy 

0 

 

 

0 0 k zz ( 

x, y, z) 

the density ρ and the specific heat C are independent of the internal state 

the convective terms included in the material time derivation are neglected hence 

the thermal gradients remain small throughout the thickness of the specimen 

T 

T = 

t 

the external heat supply rext is time-independent. Consequently, the equilibrium temperature 

( 0 ) 

field T0 verifies: ( ) 

- div k. grad T = rext 

the temperature variations induced by damage mechanisms remain too small to have any 

influence on the microstructural state hence sic = 0 

Under the previous assumptions and by integrating the equation (2) over the sample thickness, the 

following equation can be obtained: 

22 k 

xx kyy 

sthed1 + - - = + 

2D 2 2 

t C x C y 

C C 

where 1 h/2 

( x, y, t) = ( x, y, t ) dz 

h , s the ( x, y, t) 

, and 

-h 

/2 

d1 ( x, y, t ) are respectively the temperature 

variation = T- T0, 

thermoelastic source and intrinsic dissipation averaged through the thickness. 

is a time constant that characterizes the perpendicular heat exchanges between front and back specimen 

faces and the surroundings. Due to the small sample thickness and high thermal diffusivity, we can 

assume that the depth-wise averaged temperature field is close to the temperature distribution 

measured at the specimen surface. 

4. Computation of heat sources 

The purpose of the thermal data processing is to estimate the mean amplitude of the thermoelastic 

source sthe and the mean dissipation d 1 per cycle over a set of N loading cycles. The construction of 

the heat source distribution via equation (3) requires the evaluation of partial derivative operators 

applied to noisy digital signals. To improve the signal to noise ratio, it is then necessary to reduce the 

noise amplitude without modifying the spatial and temporal thermal gradients. Among several possible 

methods [6, 7], a special local least-squares fitting of the thermal signal is considered in this work. The 

local fitting function of the temperature charts is chosen as: 

(3) 

2D 

 

(4)


where the trigonometric time functions describe the periodic part of the thermoelastic effects while the 

linear time function takes transient effects due to heat losses, dissipative heating and possible drifts in 

the equilibrium temperature into account. Figure 3 gives an example of temperature field obtained after 

filtering. The quantities sthe and d 1 are evaluated separately by replacing in equation (3) 

respectively by the periodic and linear part of fit . 

5. Experimental Set-up 

Fig. 3. Unfiltered and filtered temperature field. 

The material studied is a glass fiber and epoxy resin composite. Three kinds of specimens were tested. 

Thin flat specimens were used 250 mm length, 25 mm width and 4 to 4.2 mm thickness with five plies. 

For the two first kinds of specimen (type 1 and 2), the middle ply is cutted before fabrication to initiate 

the damage (figure 4). Type 3 are specimens with a hole without initial damage except which generate 

by the hole drilling. The stacking of the specimens are type 1: [0]5 (UD specimens), type 2 and 

3:[0=90=0=90=0] (cross-ply specimens). 

The fatigue tests were conducted using a servo-hydraulic machine equipped with a 100 kN cell. The 

experimental setup included two focal plane array infrared cameras (IRFPA Cedip MW) to measure 

surface temperature on both sides of the specimen. The camera is a IR system with 320 x 256 detectors 

which provide high sensitivity of less than 20 mK at 30 o C. The use of two infrared systems allows the 

evaluation of the heat sources from the two faces of the specimen. To reduce the radiation of the 

surroundings and obtain better thermal measure, the testing machine is protected with paper and the 

working place around the cameras with a black tissue (figure 5). 

165

166 


Fig. 4. Specimen stacking with defect. 

Fig. 5. Fatigue testing machine. 

The fatigue tests are carried out by submitting series of loading blocks. Each block consisted of 2 000 

cycles performed at constant loading frequency fL = 3Hz, constant load ratio Rζ= 0.1, and constant 

stress range Δζ. At the end of each loading block, the thermal equilibrium has been awaited before the 

next block starts. Tensile tests were performed on each kind to evaluate the ultimate tensile strength 

(UTS). 

6. Results 

6.1 Thermoelastic coupling source 

The surface temperatures of the both sides of the specimen were recorded during fatigue tests. The 

average temperature over 50 cycles, in the case of UD specimen (type 1), is given in figure 6. Hot spot 

appears at the same place on the both sides. The assumptions that the measured surface thermal map is 

very close to the depthwise average temperature field, is then verified due to the small thickness of the 

specimen. The thermoelastic coupling source calculation permits to underline too the occurrence of one 

hot spot (figure 6). We can remark that the thermoelastic coupling map give a better localization of the 

hot spot.


Fig. 6. Distribution of the average variation of the surface temperature ( o C) and the 

6.2 Dissipation source 

ζmax=45%UTS 

s ( o C/s ) on the both sides of UD specimen at 

Different levels of loading have been applied to the type 1 specimens (20, 30, 40, 50 and 60% of the 

UTS). The plots of the thermoelastic coupling term are not given. Figure 7 shows the pattern of mean 

dissipation per cycle calculated at different stress ranges (20, 30 and 40%). For low level of loading 

(20%), no dissipation appears. For a load closed to 30% of UTS, localization of dissipation occurs. For 

higher load, final collapse of the specimen is characterized by a uniform dissipation along the initial 

defect (figure 7). This result shows that the dissipation source depends on the level of applied load. To 

be sure that the evaluated dissipation is linked with a damage process, the dissipation source was 

calculated during a delamination process. 

Fig. 7. Dissipation evaluated at different stress ranges ( o C/s). 

To study the delamination, cycling tests were performed on the cross ply specimens (type 2) with the 

same initial defect than the UD specimens (type 1). Pictures obtained with camera at different number 

of cycles show the the evolution of the delamination when a load of 40% UTS is applied (figure 8). 

Initially, the delamination is uniform (at 500 cycles) then the delamination growth is more important on 

the left of the specimen. The plot of the thermoelastic coupling source distribution after 1000 cycles and 

167

168 


4000 cycles gives an information on the stress concentration closed to the delamination zone (we can 

remark that the intensity is constant during the delamination propagation) (figure 9). From this plot, we 

can't conclude on the delamination growth. 

Fig. 8. Evolution of the delamination during fatigue test. 

Fig. 9. Distribution of s the ( o C/s ) at (a) 1000 cycles and (b) 4000 cycles. 

The evaluated dissipation source during the delamination process is given on figure 10. Initially, we 

have a uniform dissipation along the initial defect and after 1000 cycles, the dissipation increase on the 

left of the specimen where the delamination propagation is more important. The level of dissipation 

increase during the fatigue test and reach a maximum value of 0.15 C/s after 3 000 cycles. This value is 

constant during the delamination process. 

In figure 11, the trend of dissipation source along the specimen is pointed out during 4000 cycles. The 

shape of the profile is in a good agreement with the delamination propagation.


Fig. 10. Evolution of the mechanical dissipation during fatigue test ( o C/s). 

Fig. 11. Variations in dissipation profile during 4000 cycles. 

Fatigue tests were also performed on cross ply specimens without initial defect but with a hole (type 

3). The dissipation was calculated closed to the hole where the stress concentration is important. Figure 

12 shows the evolution of the dissipation source evaluated at different levels of loads with a new 

specimen for each test. For low stress ranges less than 30% of UTS, the intensity of dissipation source is 

small (less than 0.15 C/s) and constant. These specimens have reached a very high number of cycles 

169

170 


(100 000 cycles) without failure. At this level of stress, no damage or small damage was appeared. 

When the applied load increase, the dissipation increase too. For all the specimens, the calculation of the 

dissipation source was made 2000 cycles before the final failure of the specimen. In figure 13, the 

evaluated dissipation were reported for two fatigue tests performed on two specimens at different levels 

of load (50% and 60% of UTS). The obtained curves were similar for the two levels of loading. During 

the first 40% of life of the specimen, the level of dissipation was constant and small. Next, the 

dissipation increase until the failure of the specimens. 

7. Conclusion 

Fig. 12. Evolution of the calculated dissipation versus the applied load. 

Fig. 13. Evolution of the calculated dissipation for two levels of loading. 

This study is intented to show the relation between the dissipation of heat and the damage of the 

composites. Based on a local expression of the heat equation, an infrared image processing method is 

used to estimate the thermoelastic coupling source amplitude and the mean dissipation per cycle. This 

method had been used to study the damage of UD and cross ply glass/epoxy specimens with an initial 

defect. 

The localization of the defect is given by the thermoelastic source distribution due to the stress 

concentration near the defect. When an evolution of the damage is observed, the mean dissipation per 

cycle increase. Cycling tests performed on cross ply specimens underline the relation between the 

delamination growth and the mean dissipation per cycle distribution. The plot of the dissipation term 

during fatigue tests at two different levels of loading shows that the dissipation is low and constant at


the begin (until 40% of the life) and then increase until the final failure of the specimen. 

In terms of structure design, the mean dissipation per cycle mapping may be useful to evaluate the 

localization and the evolution of the damage. The next objectives are to underline the limits of this 

method. A fully coupled full field kinematic and thermal measurements with motion compensation must 

be performed to built up a coupled energy balance. 

References 

[1] X. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing, John Wiley & Sons, 2001. 

[2] N. Krohn, A. Dillenz, K. Nixdorf, R. Voit-Nitschmann, G. Busse, Ndt of shape adaptive structures, NDT & E International 34 (2001) 

269-276. 

[3] M. Luong, Infrared thermography of fatigue in metals, SPIE 1692 (1992) 222-233. 

[4] L. Toubal, M. Karama, B. Lorrain, Damage evolution and infrared thermography in woven composite laminates under fatigue loading, 

International Journal of Fatigue 28 (2006) 1867-1872. 

[5] A. Chrysochoos, H. Louche, Thermal and dissipative e_ects accompanying luders band propagation, Mat. Sci. Eng. A-struct. 307 (2001) 

15-22. 

[6] B. Berthel, B. Wattrisse, A. Chrysochoos, A. Galtier, Thermographic analysis of fatigue dissipation properties of steel sheets, Strain 43 

(2007) 273-279. 

[7] B. Wattrisse, A. Chrysochoos, J. Muracciole, M. Nemoz-Gaillard, Analysis of strain localization during tensile tests by digital image 

correlation, Experimental Mechanics 41 (2001) 29-39. 

[8] H. Moore, J. Kommers, Fatigue of metals under repeated stress, Chemical and metallurgical Engineering 25 (1921) 1141-1144. 

[9] C. Doudard, S. Calloch, F. Hild, P. Cugy, A. Galtier, Identi_cation of the scatter in high cycle fatigue from temperature measurements, C. 

R. Mecanique 332 (2004) 795-801. 

[10] E. Charkaluk, A. Constantinescu, Estimation of the mesoscopic thermoplastic dissipation in high-cycle fatigue, C. R. Mecanique 334 

(2006) 373-379. 

[11] J. Charles, F. Appl, J. Francis, Using the scanning infrared camera in experimental fatigue studies, Experimental Mechanics 15 (1975) 

133-138. 

[12] H. Sawadogo, Comportement en fatigue des composites monolithiques et sandwiches: d_etection et suivi de l'endommagement par 

techniques non destructives, Ph.D. thesis, Université de Lille 1 (2009). 

171

Fatigue-driven Residual Life Models Based on Controlling 

Fatigue Stress and Strain in Carbon Fibre/Epoxy Composites 

Abstract 

J J Xiong *, J B Bai, R A Shenoi 

Aircraft Department, Beihang University, Beijing, 100083, People’s Republic of China 

Two novel fatigue-driven models based on controlling fatigue stress and strain with four parameters are derived to 

evaluate fatigue residual life easily and expediently from the small sample test data for reliability-based design. The 

random model for fatigue-driven residual life is obtained by means of the randomized approach to a deterministic 

equation and the parameter determination formulae of models are respectively established to deal with the test data 

effectively and easily based on the maximum likelihood principle and the minimum residual sum of squares. In addition, 

the probability distributions for these two models are also given. Finally, the models are applied to two sets of 

experimental data, demonstrating the practical and effective use of the proposed models. It is shown from these examples 

that the models can logically characterize the physical characteristics and the phenomenological quantitative laws and the 

parameters of model can be estimated more easily and expediently, as well as fatigue-driven residual life can be obtained 

realistically according to the small sample test data using the new formulae. 

Key words: composites; fatigue; residual life; reliability; stress; strain 


Static and fatigue behaviour of high performance composites has been investigated extensively. 

Comprehensive reviews of the subject have been conducted by Reifsnider 

1 , Talreja 

2 and Shenoi 

The static tensile strength of composites is governed largely by the fibre strength but this cannot readily 

be expressed in a simple way because of the statistical nature of the fibre fracture and owing to the role 

of the matrix and/or interface during fracture. To cause overall composite failure it is generally accepted 

that there needs to be a critical cluster of fibre breaks adjacent to one another to trigger a catastrophic 

 

fracture 4 . The formation of such a cluster is dependent on the statistical distribution of the fibre 

strengths and the local stress transfer in the vicinity of a fibre break, which in turn is influenced by the 

fibre-matrix interface. The compression strength of the composite, on the other hand, is related to the 

ability of the matrix to support the fibre against buckling and the integrity of the fibre-matrix interface. 

 

Soutis et al 5 report compression strength data for high-strength and intermediate modulus fibres in 

epoxy resins of low to moderate toughness. 

During cyclic loading of notched laminates (below the static strength), the initial damage which 

develops at the notch is similar to that seen under quasistatic loading. This effectively leads to an 


E-mail address: jjxiong@buaa.edu.cn 

3 .

Fatigue-driven Residual Life Models Based on Controlling Fatigue Stress and Strain in Carbon Fibre/Epoxy Composites 

increase in residual strength with cycling, in particular under tension-tension loading. Under 

compression loading, the situation may be similar, with the residual strength generally increasing with 

cycling as a result of the damage growth and an associated reduction in stress concentration associated 

with the discontinuity. Situations in which fatigue failure of the notched laminates can occur are for the 

lay-ups where the progressive delamination growth in fatigue leads to a progressively greater instability 

of the load-carrying 

 

0 plies or ply blocks. This is most likely to be an issue under 

 

tension-compression loading. Wang et al. 6 studied notch fatigue strengthening under different cyclic 

 

stress levels and elapsed number of cycles in [0/90]4S AS4/PEEK laminates. Nuismer et al. 7 studied 

uniaxial failure of composite laminates containing stress concentrations. The relationships between the 

 

residual strength, fatigue cycles and stress concentration were given. Xiong, Shenoi et al. 8 have 

undertaken experimental investigations of the static and fatigue strength of T300/QY8911 carbon fibre 

reinforced composite laminates. It is observed that all tension-tension fatigue damage patterns of 

notched laminates are similar while the tension-tension fatigue properties vary with the laminate lay-up. 

The reduction of the stress concentration caused by the tension-tension fatigue damage leads to an 

improvement in the residual strength of the notched specimens in contrast to their static strength 

properties. The damage mechanics of notched laminates under compression-compression loading are 

more complex than those of tension-tension fatigue specimens; their damage patterns are influenced by 

the test clamping fixture, the layup, the size of specimens and the diameter of hole. The residual 

strengths are lower than those of the specimens without the fatigue damage. Fatigue strength of 

 

composites has been proved to be related to stress ratio (R). Harris et al 9 have studied the fatigue 

behaviour of a number of carbon-fibre-reinforced plastics (CFRP) laminates of HTA/913, HTA/982A, 

T800/5245 and T800/924. Replicate stress/life data were obtained at four stress ratios (R) of +0.1, -0.3, 

-1.5 and +10 on virgin samples and on damaged samples. The fatigue behaviour of a series of 

unidirectional hybrid composites has been established as a function of composition and of the stress 

ratio in repeated tension and tension/compression cycling. 

Under compression, as in the static case, fatigue behaviour is more dependent on the matrix and 

interfacial characteristics than the fibre strength. For [0/90/0] cross ply and [0/90/±45] quasi-isotropic 

laminates, damage is of four main types: matrix cracking, delamination in [0/90/±45] laminates, 

fibre/matrix debonding and 0 

fibre breakage 2 . Because of this variety of fatigue mechanisms 

closely related to anisotropy, including various mechanisms such as the interfacial debonding, matrix 

cracking, ply cracking, fiber breakage, and so on, it is difficult to define composite damage in a unique 

manner. Consequently, a variety of fatigue damage modelling techniques have been proposed that 

involve stiffness degradation, residual strength, crack density, crack length, etc, with the fatigue damage 

definition functions being dependent on the number of cycles and on material characteristic 

 

variables 10 . While the origins of the damage modelling trends were linear, many researches have 

proposed non-linear quadratic functions to account for the inherent complexities in composite behaviour. 

Based on the damage variables mentioned above, various theoretical, experimental and computational 

criteria have been proposed to estimate the overall life of a composite structure. Most of the damage 

173

174 


criteria are functions of the material characteristic variables; damage criteria based on the physical 

11 14 

characteristic of the materials have proved to be more promising - 

. It is specially emphasized that 

the damage criteria based on residual strength, stiffness and strain have been extensively developed and 

widely applied. Because of the simplicity and wide technological usage of the well-known 

Palmgren-Miner or Paris-Erdogan laws, very precise, experimentally-based, deterministic, linear 

residual strength or stiffness degradation models have been proposed to predict fatigue life of different 

laminates from the assumption that the matrix is the weak link of the system. 

In recent years, continuum damage mechanics has been applied to investigate the mechanics behavior 

of the anisotropic composites with multifarious failure modes. In the meso-scale, taking the softening 

effect of material into account, continuum damage mechanics introduces internal damage variables to 

denote the formation and growth of micro-cracks and micro-excavations which result in strength and 

stiffness degradation of material in macro-scale. Jessen and Plumtree 15 derived a damage evolution 

equation for glass fibre composites pultrusions and the damage S-N curve based on continuum damage 

 

principle. Shen et al. 16 

, Chow and Wang 17 

, Xiong and Shenoi 18 obtained the elastic damage 

constitutive relation for composite laminates by means of continuum damage mechanics. Phillips and 

 

Shenoi 19,20 applied damage mechanics to predict fatigue life of structural components such as tee 

connection and top hat stiffness. 

It is interesting in the above reviews to note that a large number of researches are grouped according 

to some important issues such as static tensile and compressive strength behaviour, tension-tension and 

compression-compression fatigue behaviour including the influence of the stress ratio on fatigue 

behaviour, damage mechanisms, and damage models. It is also clear that there is a need for a more 

practical and expedient model for structural applications, particularly in the aerospace field. In this 

paper an attempt is made to develop techniques for modelling the stress- and strain-based residual lives, 

to characterise long-term cyclic behaviour and to identify the governing parameters, all to be based on 

fundamental static and fatigue experimental data. 

2 Fatigue-driven residual life models based on controlling fatigue stress and strain 

 

A fatigue damage function is usually proposed as follows 1,2,21 : 

( , , , , 

, , ) 

D = D n r S T M (1) 

where D is the damage function, n is the number of cyclic loading, r is the stress ratio, S is the 

maximum cyclic stress, is the loading frequency, T is the current temperature and M is the 

moisture level. Since the temperature T and moisture level M of the specimen are constants or 

close to constants (by means of controlling the temperature and moisture rise) during the test. A 

degenerated form of Equation (1) is also sometimes represented as: 

( , , , ) 

D = D n r S 

(2) 

The level of damage can be characterized by residual strength of the specimen or structure, which 

represents the material strength, usually decreasing with increasing numbers of cycles. In a virgin state,


the residual strength equals the static strength; under fatigue loading conditions, the residual strength is 

equal to the maximum static stress to cause ultimate failure in the post fatigue condition. Thus, the 

change in residual strength can be regarded as the damage variable. Based on the assumption that the 

slope of the residual strength R ( n) 

is inversely proportional to some power b -1 

of the residual 

 

strength R ( n) 

itself, a rate equation was obtained as 11 : 

( ) ( , , ) 

b-1 

( ) 

dR n f r S 

=- (3) 

dn R n 

Here f ( r, S, ) is a function of r , S and . In case of without consideration of loading sequence 

effect and the change in local stress with damage evolution. Taking the integral of Equation (3) gives: 

( , , ) 

( ) 

n = f r S R -Rn 

175 

b 

0 

(4) 

where R 0 is the ultimate strength. Equation (4) describes the strength degradation of a sample 

subjected to constant amplitude, constant frequency cyclic loading. For the sake of simplicity, the 

loading frequency and the stress ratio r will be fixed, so f ( r, S, ) = f ( S) 

. Thus: 

( ) ( ) 

b 

0 

(5) 

n = f S R -Rn 

Equation (3) is a surface equation corresponding to residual strength R , fatigue stress S and 

 

number of fatigue stress cycle n . On the basis of the S-N curve equation 22 given as: 

( ) 

0 

m 

N = C S - S 

(6) 

where C is the material constant, m is the exponent constant of material, S is the fatigue strength 

and S0 is the fitting fatigue limit, or reference fatigue strength, one can obtain f ( S ) of Equation (6) 

as: 

Substituting Equation (7) into Equation (3) yields: 

( ) ( ) 

0 

m 

f S = C S - S 

(7) 

m 

( ) ( ) 

b 

n = C S - S0 R0 - R n 

(8) 

For a given failure state, namely fatigue residual strength R ( n) 

is given to be a certain of value 

R f , Equation (8) becomes S n 

b 

- curve as n = C ( S - S ) R- R = C ( S - S ) 

m m 

0 0 f 0 0 

consistent with 

S - N curve (6) used in fatigue. In the case of given loading stress S = s0, 

Equation (8) degenerates 

to the R - n curve as ( ) ( ) b 

m 

n C s - S R - R n = C R - R , which describes the 

( ) b 

= 0 0 0 

0 0 

phenomenological, monotonically quantitatively decreasing law of fatigue residual strength shown in 

the experiments. 

The ultimate strength R 0 and residual strength R ( n) 

are obtained respectively: 

R0= E0 f 

(9) 

R( n) = E( n) f 

(10)

176 

where f is the rupture strain, 0 


Substituting Equations (9) and (10) into Equation (8), one has: 

where 

b 

C0 C 

f 

E is the initial modulus and E ( n) 

is the residual modulus. 

m 

( ) ( ) 

b 

n = C0 S - S0 E0-En (11) 

= . Equation (11) describes the relationship between fatigue stress S , residual 

modulus E ( n) 

and cyclic loading number n . At a specific fatigue stress S , the relationship between 

residual modulus R ( n) 

and fatigue strain ( n) 

after n fatigue loading cycles becomes: 

S 

E( n) 

= (12) 

 

( n) 

Substituting Equation (12) into Equation (11), it is possible to have: 

m S 

n = C0 ( S - S0 ) E0- ( n) 

 

Equation (13) is the fatigue model based on controlling-strain to depict the relationship between fatigue 

stress S , fatigue strain ( n) 

and cyclic loading number n . 

3. Parameter determination of fatigue-driven residual life model 

 

From the randomized approach of deterministic equation 23 , a randomization of Equation (8) gives: 

m 

b 

( ) ( ) ( ) 

n = C S - S0 R0 - R n X n 

(14) 

where X ( n) 

usually is a log-Gauss stochastic process dependent on n , with 0 mean and constant 

standard deviation. The logarithmic form of Equation (14) is: 

where Y = lg n , a = lg C 

b 

(13) 

Y = a0 + a1x1 + a2x2 + U 

(15) 

0 , a 1 = m , a 2 = b , x1 = lg( 

S - S0) 

, x R - R( 

n) 

 

2 

U = lg X( 

n) 

. U is the random variable following a Gauss distribution 0, 

2 = lg 0 , 

N . From Equation 

(15), the random variable Y follows Gauss distribution N a + a x 

2 

+ a x , . 

According to the 

maximum likelihood principle, it can be shown that: 

where 

= 

0 

1 

1 

a0 = y -a0 -a1 x1 - a2x2 (16) 

L L - L L 

a1 

= 

L L - L L 

a 

l 

2 

12 20 22 10 

12 21 11 22 

L L - L L 

= 

L L - L L 

21 10 11 20 

12 21 11 22 

( ) 2 

yi - a0 - a1x1 i - a2x2 i 

i= 

1 

l 

2 

2 

(17) 

(18) 

(19)


L 

12 

L 

L 

10 

20 

L 

L 

= 

11 

22 

= 

= 

1 l 

y = yi 

l i= 

1 

1 l 

x = x 

1 1i 

l i= 

1 

1 l 

x = x 

= 

= 

l 

 

i= 

1 

l 

 

i= 

1 

l 

 

i= 

1 

2 2i 

l i= 

1 

l 

 

i= 

1 

l 

 

i= 

1 

( x - x ) 

1i 

1 

2 

( x - x ) 

2i 

( x - x )( x - x ) 

1i 

21 

1 

L = L 

12 

2 

2i 

( x - x )( y - y) 

1i 

1 

( x - x )( y - y) 

2i 

Eqns. (16) to (18) are functions of constants R 0 and S 0 . The constants R 0 and S 0 can be 

determined by means of the minimum value principle of the residual sum of squares (RSS) Q( R , S ) 

in Equation (15) in a four-stage process. 

(a) First, letting the residual sum of squares (RSS) as: 

l 

0 0 i 1 2 1i 3 2i 

i= 

1 

(b) Then, the value ranges of R 0 and S 0 are estimated as: 

2 

i 

i 

2 

2 

0 0 

( ) ( ) 2 

Q R , S = y - a - a x - a x 

(20) 

where R 

R0 ( Rmax 

, Rmax 

+ 

S0 0, 

S0 

min ) 

= maxR 

, R , , 

R , 

is a finite value, , ( i 1, 

2, 

, 

l) 

max 

residual strength, S S S S 

1 

2 

0min 1 2 

l 

R i 

177 

= is the test data of 

= min , , , l , and Si , ( i = 1,2, , l) 

is the fatigue stress. 

(c) Subsequently, for given initial values of R0 ˆ , S0 ˆ and calculation step lengths 1 , 2 , one can 

search and find out the value of ( , ) 

Q R0 S 0 by changing the values of R 0 and 0 

S during the 

above value ranges respectively,. Thus R 0 and S 0 pertaining to the minimum value of 

( , ) 

Q R S may be determined. 

0 0 

(d) Finally, the parameters a 0 , 1 a and 2 

a can be determined from Eqns. (16) to (18).

178 


C = 10 

L 

m = 

L 

12 

12 

( y-a 

x -a 

x ) 

L 

L 

20 

21 

1 1 

- L 

- L 

2 2 

22 

11 

L L - L L 

b = 

L L - L L 

21 10 11 20 

12 21 11 22 

By invoking the procedures of equations (16) to (20), one can obtain the undetermined constants E 0 , 

S 0 , C 0 , m , b and in Equation (13). 

4. Reliability prediction for fatigue-driven residual life 

In case there are a large number of test data of ultimate strength R 0 , the probability models of 

residual strength based on controlling-stress can be obtained from the PDF of ultimate strength R 0 . 

According to Equation (5), one can have: 

L 

L 

10 

22 

n 

R( n) = R0 

- 

f ( S) 

 

 

Generally, the ultimate strength R 0 follows the two-parameter Weibull distribution 11 and its 

distribution function is: 

( ) = = - -( 

) 

FR0 x P R0 x 1 exp 

 

x 

 

 

 

(22) 

Substituting for R 0 , the probability distribution function of residual fatigue strength R ( n) 

at a given 

fatigue stress S and fatigue stress cycles n is 

1 

 

b n 

FRn ( ) ( x) = P R( n) x P 

 

R0 x 

 

= 

 

- 

f ( S) 

 

 

 

 

1 

 

 

b 

1 

n 

x 

 

b n 

 

+ 

f ( S) 

 

 

F ( ) ( x) = P R0 x 

1 exp 

 

Rn + = - - 

f ( S) 

 

 

 

 

 

 

From Equation (24), it is clear that residual strength R ( n) 

follows a three-parameter Weibull 

distribution. Based on Equation (21), the residual strength Rp ( n) 

corresponding to a reliability level 

p is: 

1 

b 

n 

Rp( n) = R0 

p - 

f ( S) 

 

1 

b 

(21) 

(23) 

(24) 

(25)


Substituting Equation (7) into Eqns. (24) and (25) gives: 

1 

 

 

b 

n 

x+ m 

C( S - S0 

) 

F ( ) ( x) = P R( n) x = 1- exp - 

 

Rn 

 

 

 

 

 

n 

R n = R - 

( ) 

( - ) 

p 0 p m 

CSS0 Assuming fatigue failure occurs when the residual strength R ( n) 

equals the maximum cyclic stress 

S , or R ( n) 

= S , at the same time, n = N , then a transformation of Equation (8) gives: 

( )( ) 

0 

b 

1 

b 

179 

(26) 

(27) 

N = f S R - S 

(28) 

Since the ultimate strength R 0 is a variable and follows Equation (22), fatigue life N also is a 

variable and follows: 

N 

( ) ( )( ) 

F n = P N n = P fSR-Sn b 

0 (29) 

1 

1 1 

 

b 

b b 

n n+ S f ( S ) 

FN ( n) = P R0 + S = 1- exp - 1 

f ( S) 

 

 

b f ( S) 

 

 

Equation (30) shows that fatigue life N follows a three-parameter Weibull distribution. When 

( ) ( ) m 

S C S - S 

f 0 

= , Equation (30) becomes: 

5. Examples and discussion 

1 1 m 

b b 

( 0 ) b 

n+ C S S - S 

FN ( n) = P N n 

= 1- exp - 1 

m 

b C( S -S0) 

b 

 

Example 5.1 37 specimens was cut from ( 0, 90, 

45) 

s Graphite/Epoxy laminate panel. 12 

specimens were tested statically and their ultimate strengths are shown in Table 1 and Figure 1. 25 

specimens were subjected to fatigue loading at various maximum stress levels s and the results are 

tabulated in Table 2 and shown in Figure 1. One specimen did not fail at one million cycles and its 

residual strength was measured.. The fatigue tests were then stopped and the residual strengths were 

measured. All the fatigue tests were performed at a frequency of 20Hz with a stress ratio 0.1. 

 

 

(30) 

(31)

180 


 

Table 1. Ultimate strength of G/E [0,90,±45]S (unit: MPa) 11 

435.49 500.82 552.03 

457.28 517.53 560.80 

495.81 536.12 563.68 

498.73 540.05 580.31 

 

Table 2. Fatigue residual strength 11 data of G/E [0,90,±45]S 

S / MPa n / cycles R(n) / MPa S / MPa n / cycles R(n) / MPa 

441.90 1650 441.90 363.92 18790 363.92 

441.90 1950 441.90 363.92 3840 363.92 

441.90 1320 441.90 348.32 161000 348.32 

415.91 2050 415.91 348.32 110000 348.32 

389.92 50980 389.92 337.93 523500 337.93 

389.92 6480 389.92 337.93 863200 337.93 

363.92 155000 363.92 322.33 1346300 322.33 

363.92 228500 363.92 337.93 1007000 337.93 

363.92 88000 363.92 376.92 30000 376.92 

363.92 117580 363.92 376.92 30000 376.92 

363.92 228700 363.92 376.92 30000 376.92 

363.92 221200 363.92 376.92 30000 376.92 

363.92 310000 363.92 

Fig. 1. Fatigue residual life curves. 

From the test data shown in Tables 1 and 2, using the model in Equation (8) and its parameter 

estimation method presented above, the fatigue residual strength surface equation is determined as: 

65 -24.56 

n = 4.2110 S 519.89 - R n 

( ) 0.97 

 

(32)


From the data shown in Table 1, it can be shown that the percentile value pertinent to the probability of 

survival of 99.9% is 299.31 MPa. Based on Equation (27), fatigue residual strength surface equation 

with the probability of survival of 99.9% is: 

65 -24.56 

n = 4.2110 S 299.31- 

R n 

If S=363.92 MPa, Eqns. (32) and (33) became respectively as: 

( ) 0.97 

181 

 

(33) 

( ) 0.97 

n = 522.88 519.89-Rn (34) 

( ) 0.97 

n = 522.88 299.31-Rn (35) 

Using Equation (34), the mean value of the fatigue loading cycle at a residual strength, R = 363. 92 

MPa is 70102 cycles. From the experimental data shown in Table 2, the mean value of fatigue loading 

cycle at the residual strength of R = 363. 92 MPa is 152401 cycles. The relative deviation of 

prediction from the experimental result is: 

152401- 70102 

100% = 54% 

152401 

If S=337.93 MPa, Eqns. (32) and (33) became respectively as 

( ) 0.97 

n = 3228.11 519.89-Rn (36) 

( ) 0.97 

n = 3228.11 299.31-Rn (37) 

Using Equation (36), the mean value of fatigue loading cycle at the residual strength of R = 363. 92 

MPa is 502594 cycles. From the experimental data shown in Table 2, the mean value of fatigue loading 

cycle at the residual strength of R = 363. 92 MPa is 797900 cycles. The relative deviation of 

prediction from experimental result is 

797900 - 502594 

100% = 37% 

797900 

Equations (34) and (36) are shown in Figure 1. From Figure 1, it is seen that the calculated curves are 

consistent with the experimental data. From an accuracy check of the analysis results, the relative 

deviations of predicted results from experimental data at S=363.92 MPa and S=337.93 MPa are 54% 

and 37% respectively, with the acceptable scatter. One reason for the deviation of the model results from 

the experimental data is the small sample size of the test data. It is well known that fatigue lives of 

composite laminates are often very scattered. For this reason, generally, many sets of large sample 

experiments are conducted to obtain the population law and the analysis results with high reliability 

levels. In this case, reasonable constraints limited the experimental results that were feasible and 

permissible. If more specimens are used for fatigue tests at each stress level and more stress levels are 

considered, then more exact fatigue performance can be determined and more accurate calculated 

results can be obtained. An expression in the form of a power function product is adopted in Equation (8) 

to more easily and expediently estimate the parameters of this model, and there exist four parameters in 

this model to fit more adequately the experimental phenomenological quantitative laws. 

It is worth noting that Equation (8) can characterize fatigue residual strength properties; S and

182 


R ( n) 

in this model are expressed in the form of constant amplitude nominal stress, so the loading 

sequence effect and the change in local stress with damage evolution have not been taken into account. 

Example 5.2 A 20-ply T300/QY8911 plate was manufactured with a layup of 

 

- - and having a mean modulus E 0 of 54.34 GPa. Test-specimens 

45/ 0 2 / 45/ 90 2 / 45/ 0 / 45/ 90 s 

were cut from this plate for a scenes of static and fatigue tests. The geometry and dimensions of the 

specimens are shown in Figure 2. The four variables in the tension case are the dimensions of the central 

holes (10.00 mm), the thickness t (2.4mm), the width W (50mm) and the length L (300 mm). 

10 specimens were tested statically and the mean value of their fracture strains is 5286 . 11 

specimens were subjected to tension-tension fatigue loading at various maximum stress levels s and 

the results are tabulated in Table 3. The fatigue tests were performed in a frequency range of 10-15Hz 

with a stress ratio of 0.1. 

Nominal stress 

S / MPa 

285 

304 

320 

340 

Fig. 2. Notched specimen for static tension and tension-tension fatigue tests. 

Table 3. Strains at the hole-site of notched laminates under tension-tension fatigue loading (unit: με) 

Stress cycles n / cycles 

1 0.25×10 6 0.5×10 6 0.75×10 6 1.0×10 6 

4350 

4460 

4490 

4650 

4620 

4510 

4930 

4860 

4970 

5400 

5320 

4380 

4500 

4680 

4560 

5180 

4420 

4520 

4730 

4620 

5270 

5210 

n = 1×10 6 , ε = 5780; n = 2.2×10 6 , ε = 5960 

n = 1×10 6 , ε = 5630; n = 3.2×10 6 , ε = 6030 

4470 

4570 

4800 

4670 

5310 

4550 

4670 

4760 

4970 

4920 

4730 

5350 

5290 

5400 

From the test data shown in Table 3, by invoking Equations (16) to (20) and the procedures served from 

those, one can obtain the undetermined constants E 0 , S 0 , C 0 , m and b in Equation (13). The 

controlling-strain fatigue residual strength model is then determined as: 

- 

n= S - 

 

 

30 19.55 

8.75 10 54340.0 S 

From Equation (38), it is found that if S = 285MPa , then: 

n 

- 285.0 

 

 

18 

= 9.1210 54340.0 - 

6.20 

6.20 

(38) 

(39)


If S = 304MPa , then: 



n 

n 

n 

- 304.0 

 

 

18 

= 2.5810 54340.0 - 

- 320.0 

 

 

19 

= 9.4810 54340.0 - 

- 340.0 

 

 

19 

= 2.9010 54340.0 - 

Equations (38) to (42) are shown in Figures 3a to 3d. One can see that there is good agreement 

between the experimental data and the predicted curves; thus it is argued that the residual fatigue 

strength model of Equation (13) has adequately and logically characterized the physical characteristics 

and the phenomenological quantitative laws. 

(a) S = 285MPa 

(b) S = 304MPa 

6.20 

6.20 

6.20 

183 

(40) 

(41) 

(42)

184 



(c) S = 320MPa 

(d) S = 340MPa 

Fig. 3. Fatigue experimental data and the fitting strain-life curve for laminate [45/02/-45/902/-45/0/45/90]S of T300/QY8911. 

The focus of this paper has been to present two new practical models for predicting fatigue residual 

lives. The parameter estimation formulae of both of models are established. The applicability of the new 

models has been shown for two sets of experimental results for estimating fatigue residual lives. Close 

correlation is achieved between the predictions and the actual experimental results. 


This project was supported by the National Natural Science Foundation and Aeronautics Science 

Foundation of China 

References 

[1] Reifsnider K L. Fatigue of Composite Materials. Oxford: Elsevier, 1990 

[2] Talreja R. Fatigue of polymer matrix composites. In „Comprehensive composite materials (eds. Kelly A. and Zweben C.) (Volume 2): 

Polymer Matrix Composites‟, eds. Talreja R. and Manson J. E. Oxford: Elsevier, 2000


[3] Read PJCL, Shenoi RA. A review of fatigue damage modelling in context of marine FRP laminates. Marine Structures, 1995; 8(1): 

257-278 

[4] Bader M G. Composites. UK, Oxford: Butterworth Heinemann, 1991 

[5] Soutis C, Smith E C, Matthews F L. Predicting the compressive engineering performance of carbon fibre-reinforced plastics. Composites 

Part A, 2000; 31: 531-536 

[6] Wang CM, Shin CS. Residual properties of notched [0/90]45AS4/PEEK composite laminates after fatigue and re-consolidation. 

Composites Part B, 2002; 33: 67-76 

[7] Nuismer R. J. and Whitney J.M. Uniaxial failure of composites laminates containing stress concentrations. ASTM STP 593, 1975; 117-142 

[8] Xiong JJ, Shenoi RA, Wang SP, Wang WB. On Static and Fatigue Strength Determination of Carbon Fibre/Epoxy Composites. Part I: 

Experiments. Journal of Strain Analysis for Engineering Design, 2004; 39(5): 529-540 

[9] Beheshty M H, Harris B and Adam T. An empirical fatigue-life model for high-performance fibre composites with and without impact 

damage. Composites Part A: Applied Science and Manufacturing, 1993; 30(8): 971-987 

[10] Kaminski M. On probabilistic fatigue models for composite material. International Journal of Fatigue, 2002; 477-495 

[11] Yang JN and Liu MD. Residual strength degradation model and theory of periodic proof tests for Graphite/Epoxy laminates. Journal of 

Composite Materials, 1977; 11: 176-203 

[12] Xiong JJ, Shenoi RA. Two new practical models for estimating reliability-based fatigue strength of composites. Journal of Composite 

Materials, 2004; 38(14): 1187-1209 

[13] Xiong JJ, Shenoi RA, Wang SP, Wang WB. On Static and Fatigue Strength Determination of Carbon Fibre/Epoxy Composites. Part II: 

Theoretical Formulation. Journal of Strain Analysis for Engineering Design, 2004; 39(5): 541-548 

[14] Xiong JJ, Li YY, Zeng BY. A Strain-based Residual Strength Model of Carbon Fibre/Epoxy Composites Based on CAI and Fatigue 

Residual Strength Concepts. Composite Structures, 2008; 85: 29-42 

[15] Jessen, S.M. and Plumtree, A. Continuum Damage Mechanics Applied to Cyclic Behavior of Glass Fibre Composites Pultrusion. 

Composites, 1991; 22: 181-190 

[16] Shen, W. Peng, L. Yang, F. and Shen, Z. Generalized Elastic Damage Theory and its Application to Composite Plate. Engineering 

Fracture Mechanics, 1987; 28:403-412 

[17] Chow C. L. and Wang J. An Anisotropic Theory of Elasticity for Continuum Damage Mechanics. International Journal of Fracture, 1987; 

33: 3-16 

[18] Xiong JJ, Shenoi RA. A two-stage theory on fatigue damage and life prediction of composites. Composites Science and Technology, 2004; 

64(9): 1331-1343 

[19] Phillips H.J., Shenoi R.A. Damage Tolerance of Laminated Tee Joints in FRP Ship Structures. Composites, 1998; 29A: 465-478 

[20] Phillips H.J., Shenoi R.A. Damage Mechanics of Top-Hat Stiffeners Used in FRP Ship Construction. Marine Structures, 1999; 12: 1-19 

[21] Hwang W, Han KS. Cumulative damage models and multi-stress fatigue life prediction. Journal of Composite Material, 1986; 20: 125-153 

[22] Weibull W. Fatigue testing and analysis of results. New York: Macmillan Company, 1961 

[23] Xiong JJ, Shenoi RA. A practical randomization approach of deterministic equation to determine probabilistic fatigue and fracture 

behaviours based on small experimental data sets. International Journal of Fracture, 2007; 145: 273-283 

185

Prediction of transverse crack initiation of CFRP laminates 

under fatigue loading 

Abstract 

A Hosoi a, *, K Takamura b , N Sato c , H Kawada d 

a Department of Mechanical Science and Engineering, Nagoya University 

b Graduate School of Fundamental Science and Engineering, Waseda University 

c Composite Materials Research Laboratories, Toray Industries, Inc. 

d Depatment of Applied Mechanics and Aerospace Engineering, Waseda University 

The method to predict the initiation of a transverse crack in carbon fiber reinforced plastic (CFRP) laminates under 

cyclic loading was proposed by focusing on the periodicity of the transverse crack growth. The number of cycles to the 

initiation of the transverse crack was calculated by using the relationship between the transverse crack growth rate and 

the range of the energy release rate associated with transverse crack formation, the modified Paris law. The results 

obtained by the analysis showed good agreement with the experimental results. 

Keywords: transverse crack; fatigue; composite; prediction; reliability 


Carbon fiber reinforced plastics (CFRPs) are expected to be a primary structural material replacing 

lightweight metallic materials because they have excellent mechanical properties of specific strength 

and stiffness. On the other hand, the main accident cause of machinery and structures in metal materials 

is fatigue fracture. Therefore, it is necessary to evaluate properly the fatigue properties of CFRP 

laminates in order to establish their long-term durability and reliability. When CFRP laminates are 

subjected to cyclic loading, the damage, such as matrix cracks, delamination and fiber breakage, is 

mainly caused. Especially, the transverse cracks caused in 90 plies are generally first damage in CFRP 

laminates under cyclic loading, and they cause more critical damage of delamination and fiber breakage. 

Thus, it is very important to predict the initiation of the transverse crack under cyclic loading. 

Many experimental and analytical studies regarding the formation and propagation of transverse 

cracks under static and fatigue loadings have been conducted. Reifsnider and coauthors [1, 2] 

researched the cumulative behavior of transverse cracks. They showed experimentally that the number 

of the transverse cracks increased and the density of the transverse cracks was saturated finally as cyclic 

loading was applied. Nairn [3] derived the energy release rate associated with the transverse crack 

formation in cross-ply laminates on the basis of the stress analysis by a variational approach that Hashin 

[4] proposed, and evaluated quantitatively the behavior of the transverse crack growth under static 

tensile loading. Moreover, Liu and Nairn [5] applied the analysis to the evaluation of fatigue damage 

* Corresponding author. Address: Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan. Tel: +81-52-789-4674; fax: +81-52-789-3109. 

E-mail address: hosoi@mech.nagoya-u.ac.jp

A Hosoi, K Takamura, N Sato, H Kawada. / Prediction of transverse crack initiation of CFRP laminates under fatigue loading 

growth. Ogi et al. [6] evaluated the behavior of transverse crack growth under variable amplitude cyclic 

loading. On the other hand, Tong [7] and Yokozeki et al. [8] evaluated the behavior of the transverse 

crack propagating to the width direction in quasi-isotropic and cross-ply laminates under cyclic loading. 

Hosoi et al. [9-12] evaluated the behavior of transverse crack growth under very high-cycle fatigue 

loading over 10 8 cycles. 

The increase and propagation of transverse cracks have been widely evaluated by fracture mechanics 

methodology. Although the initiation of a transverse crack under static tensile loading was evaluated by 

the stress criterion [13], the energy criterion [3] or both [14], it is difficult to predict the initiation of a 

transverse crack under cyclic loading because the transverse crack initiates due to the accumulation of 

microscopic damage. Therefore, there are very few studies that the initiation of a transverse crack under 

cyclic loading was evaluated quantitatively. Takeda et al. [15] proposed that the initiation of transverse 

crack could be express by the Manson-Coffin equation. However, they evaluated the initiation of 

transverse crack by fitting of the experimental results. There is no study that the initiation of the 

transverse crack can be predicted accurately to my knowledge. In this study, the method to predict 

quantitatively the initiation of a transverse crack was proposed focusing on the periodicity of the 

transverse crack growth. 

2. Experiments 

2.1 Specimen 

CFRP laminates were made of T800H/3631 prepreg whose the fiber volume fraction is 57% and the 

cure temperature is 453 K using an autoclave. The stacking sequence of the laminates is cross-ply 

[0/902]s. Specimen dimensions were decided on the basis of ASTM D3039 as shown in Fig. 1. The 

thickness of the laminate was 0.864 mm. The mechanical properties of each specimen are shown in 

Table 1. In experiments of this study, the results in our previous research [11] were referred. 

Fig. 1. Specimen dimensions of cross-ply [0/902]s laminates. 

Table 1. Mechanical properties of cross-ply [0/902]s CFRP laminates 

Failure Strength 

b [MPa] 

Failure Strain 

b [%] 

Stiffness 

E [GPa] 

871 1.31 62.3 

187

188 


Table 2. Fatigue test conditions of cross-ply [0/902]s CFRP laminates 

Frequency f Hz 5 100 

Applied stress level (max/ti) * 0.60-0.90 0.40-0.50 

Stress ratio R 0.1 

* ti=871 MPa 

2.2 Fatigue test conditions 

Tensile fatigue tests were conducted at room temperature with a sine waveform under load-control 

conditions using a hydraulic-driven testing machine. Table 2 shows the fatigue test conditions. The 

applied stress level is defined as the maximum applied stress, max, per the stress of the transverse crack 

initiation under static tensile loading, ti. The fatigue test under a frequency of 100 Hz was conducted in 

the applied stress level of max/ti=0.40-0.50 in order to investigate the fatigue crack growth in high 

cycle. It was indicated that the influence of the frequency on the fatigue crack growth was small within 

the applied stress level of max/ti=0.40-0.50 in our previous research [9, 11]. The transverse crack 

growth was observed with a microscope and soft X-ray photography [11]. 

3. Analysis 

In this section, the method to predict the number of cycles to the transverse crack onset under cyclic 

loading is described. The transverse crack growth under fatigue loading could be evaluated with the 

relationship between the transverse crack growth rate and the range of the energy release rate associated 

with transverse crack formation as a following equation [5]. 

dD 

= A( ΔG) 

(1) 

dN 

where, D is the transverse crack density that is defined as the number of the transverse cracks per the 

gauge length, N is the number of cycles and G is the energy release rate range associated with 

transverse crack formation, G=Gmax-Gmin. A and are the constants obtained by experiments. 

Equation (2) shows the energy release rate associated with the formation of a new transverse crack 

between two existing transverse cracks in cross-ply laminates [3]. 

ET T 

 

G = 0 - C3t1Y ( D) 

ECC1 where ET and EC show the transverse modulus of the ply material and the modulus of the cross-ply 

laminate, respectively. 0 shows the tensile stress applied in the cross-ply laminate. is the difference 

between the transverse and longitudinal thermal expansion coefficients, =T-A. T is the difference 

between the specimen temperature and stress free temperature. C1 and C3 are the constants that depend 

on the material properties and the ply thickness. t1 is half thickness of 90 plies. Y(D) is a calibration 

function that depends on the crack density. 

In equation (2), it is defined that a new transverse crack is caused between two existing transverse 

cracks in the model. Therefore, equation (1) can be rewritten as equation (3) because the transverse 

2 

(2)


crack density becomes twice after the formation of new transverse crack. 

2D 

D 

N(2 D) N( D) 

A ΔG 

- 

- = (3) 

( ) 

Here, it is though that the transverse crack is formed in the sufficiently-long gauge length comparing the 

thickness of 90 plies. In the early stage of fatigue that the transverse crack density is low, it is assumed 

that the mechanism of the initiation of a transverse crack which was caused from an undamaged state is 

similar to the mechanism of the formation of a transverse crack which was caused between existing two 

transverse cracks. On the basis of the assumption, the relationship between the transverse crack density 

and the number of cycles is shown as Fig. 2. The number of cycles that the transverse crack initiates, Ni, 

in the gauge length, L, is equal to the number of cycles that the transverse crack density changes from 

1/L to 2/L. Therefore, the number of cycles to the transverse crack onset is expressed as 

1 

Ni N(2 / L) N(1/ L) 

LA ΔG 

= - = (4) 

( ) 

Fig. 2. The relationship between the transverse crack density and the number of cycles on the basis of the assumption that the mechanism of the 

initiation and increase of transverse crack is similar. 

4. Results 

4.1. Behavior of transverse crack growth 

Figure 3 shows the transverse crack density as a function of the number of cycles in cross-ply [0/902]s 

laminates under cyclic loading [11]. As the applied stress level becomes lower, the number of cycles for 

the transverse crack initiation increases and the saturation value of the transverse crack density becomes 

lower. 

4.2 Evaluation by modified Paris law 

In order to obtain the modified Paris law constants, A and , in equation (1), the relationship between 

the transverse crack growth rate and the energy release rate range was evaluated. It is important to 

evaluate accurately the transverse crack growth rate because the transverse crack growth rate changes 

depending on the transverse crack density. Figure 4 shows the relationship between the transverse crack 

189

190 


density and the energy release rate range, the solid line, and the relationship between the transverse 

crack density and the number of cycles, the open symbols, in the case of the applied stress level of 

max/ti=0.8. In the former case, the energy release rate range is constant when the transverse crack 

density is low. The energy release rate range gradually decreases as the transverse crack density is 

higher, because the stress sharing in the 90 plies decreases due to the increase of the transverse cracks. 

On the other hand, in the latter case, it was found that the transverse crack growth rate decreases as the 

energy release rate range decreased, and the transverse cracks are saturated finally. The behavior of 

transverse crack growth corresponds with the behavior of the energy release rate range. Figure 5 shows 

the behavior of the transverse crack growth within the area that the energy release rate range is constant 

in Fig. 4. From the result, it is shown that the increase of the transverse crack density is proportional to 

the number of cycles in the early stage of fatigue. The result indicates that the assumption is correct that 

the mechanism of the initiation and increase of the transverse crack is similar. The transverse crack 

density growth rate can be calculated from Fig. 5. Figure 6 shows the transverse crack density growth 

rate as a function of the energy release rate range, the modified Paris law. The modified Paris law 

constants are A=5.61e -38 and =11.3, respectively from Fig. 6. 

4.3 Prediction of transverse crack initiation 

The number of cycles to the initiation of transverse crack under cyclic loading was predicted by 

equation (4). In this study, the gauge length of L=120 mm and the modified Paris law constants of 

A=5.61e -38 and =11.3 were used. Figure 7 shows the results of the experiments and analysis for the 

prediction of transverse crack initiation under fatigue loading. In experimental results, the cycles of the 

first observation of the transverse crack by interrupting the fatigue test at the arbitrary cycles is regarded 

as the cycles to the transverse crack onset. The analytical result shows good agreement with the 

experimental results in Fig. 7. 

Transverse crack density mm -1 

max/ ti=0.90 f=5Hz 





1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

max/ ti=0.50 f=100Hz 

max/ ti=0.40 f=100Hz 

10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 

0 

Number of cycles n 

Fig. 3. Transverse crack density as a function of number of cycles in cross-ply [0/902]s laminates under each applied stress level [11].


Energy release rate range G J/m 2 

1000 

800 

600 

400 

200 

0 

0 0.5 1.0 

0 

1.5 

Transverse crack density D mm -1 

1.0 [10 5 ] 

Fig. 4. Transverse cracking fatigue date under the applied stress level of max/ti=0.8. The energy release rate range as a function of transverse 

crack density, the solid line, and transverse crack density as a function of number of cycles, the open symbols. 

Transverse crack density D mm -1 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.8 

0.6 

0.4 

0.2 

0 

0 1000 2000 3000 


Fig. 5. Transverse crack density as a function of number of cycles within the area of the constant energy release rate range in Fig. 4. 

Crack density growth rate mm -1 /cycle 

10 -9 

10 -8 

10 -7 

10 -6 

10 -5 

10 -4 

10 -3 

10 -2 

5Hz 

100Hz 

10 

100 500 1000 5000 

-11 

10 -10 

Energy release rate range G J/m 2 

Fig. 6. Transverse crack density growth rate as a function of energy release rate range. 


191

192 

5. Discussions 

Applied stress level max/ ti 

1.0 

0.8 

0.6 

0.4 

0.2 


Experiments 5Hz 

Experiments 100Hz 

Analysis 

10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 

0 


Fig. 7. Prediction of transverse crack initiation under fatigue loading. 

The reason that the analytical result showed good agreement with experimental results is discussed 

here. Generally, a fatigue crack grows partially due to the stress concentration at the crack tip under 

cyclic loadings once a microscopic defect initiates. When the transverse crack growth in CFRP 

laminates is considered, it is though that the transverse crack is not initiated after accumulation of 

damage in the matrix but the transverse crack is initiated partially due to the stress concentration at the 

microscopic defect, such as the interfacial debonding between a fiber and matrix. The transverse crack 

increases due to the repeat of the partial transverse crack growth by cyclic loading. Therefore, it is 

thought that the mechanism of the initiation and increase of transverse crack is similar in the early stage 

of the fatigue, and the growth of the transverse crack density was proportional to the number of cycles 

as shown in Fig. 5. 


In this study, the number of cycles to the transverse crack initiation under fatigue loading was 

predicted by focusing on the periodicity of the transverse crack growth. It is shown that the growth of 

the transverse crack density in the early stage of the fatigue is proportional to the number of cycles, and 

appropriateness of the proposed model was confirmed. In addition, the analytical results showed good 

agreement with experimental results for predicting the transverse crack initiation under fatigue loading. 

References 

[1] K. L. Reifsnider and A. Talug, Analysis of fatigue damage in composite laminates, Int. J. Fatigue 2 (1980) 3-11. 

[2] J. E. Masters and K. L. Reifsnider, An investigation of cumulative damaged development in quasi-isotropic graphite/epoxy laminates, 

ASTM STP 775 (1982) 40-61. 

[3] J. A. Nairn, The strain energy release rate of composite microcracking: A variational approach, J. Compos. Mater. 23 (1989) 1106-1129, 

(and errata: J. Compos. Mater. 24 (1990) 223-224). 

[4] Z. Hashin, Analysis of cracked laminates: A variational approach, Mech. Mater. 4 (1985) 121-136.


[5] S. Liu and J. A. Nairn, Fracture mechanics analysis of composite microcracking: Experimental results in fatigue, Proc. of the 5th Technical 

Conference on Composite Materials (1990) 287-295. 

[6] K. Ogi, S. Yashiro, K. Niimi, A probabilistic approach for transverse crack evolution in a composite laminate under variable amplitude 

cyclic loading, Compos. Part A-Appl. S. 41 (2010) 383-390. 

[7] J. Tong, Characteristics of fatigue crack growth in GFRP laminates, Int. J. Fatigue 24 (2002) 291-297. 

[8] T. Yokozeki, T. Aoki and T. Ishikawa, Fatigue growth of matrix cracks in the transverse direction of CFRP laminates, Compos. Sci. 

Technol. 62 (2002) 1223-1229. 

[9] A. Hosoi, Y. Arao, H. Karasawa and H. Kawada, High-cycle fatigue characteristics of quasi-isotropic CFRP laminates, Adv. Compos 

Mater. (2007) 16 151-166. 

[10] A. Hosoi, Y. Arao and H. Kawada, Transverse crack growth behavior considering free-edge effect in quasi-isotropic CFRP laminates 

under high-cycle fatigue loading, Compos. Sci. Technol. 69 (2009) 1388-1393. 

[11] A. Hosoi, J. Shi, N. Sato and H. Kawada, Variations of fatigue damage growth in cross-ply and quasi-isotropic laminates under high-cycle 

fatigue loading, J. Solid Mech. Mater. Eng. 3 (2009) 138-149. 

[12] A. Hosoi, N. Sato, Y. Kusumoto, K. Fujiwara and H. Kawada, High-cycle fatigue characteristics of quasi-isotropic CFRP laminates 

(Initiation and propagation of delamination considering the interaction with transverse cracks), Int. J. Fatigue (2010) 32 29-36. 

[13] J.W. Lee and I. M. Daniel, Progressive transverse cracking of cross-ply composites, J. Comp. Mater. 24 (1990) 1225-1243. 

[14] S. Ogihara, A. Kobayashi, N Takeda and S. Kobayashi, Damage mechanics analysis of transverse cracking behavior in composite 

laminates, Int. J. Damage Mech. 9 (2000) 113-129. 

[15] N. Takeda, S. Ogihara and A. Kobayashi, Microscopic fatigue damage progress in CFRP cross-ply laminates, Composites 26 (1995) 

859-867. 

193

Interfacial Fatigue Crack Propagation in Microscopic Model 

Composite using Bifiber Shear Specimen 

Abstract 

M Hojo a, *, Y Matsushita a , M Tanaka b , T Adachi c 

a Department of Mechanical Engineering and Science, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan 

b Department of Mechanical Engineering, Kanazawa Institute of Technology, Nonoichi, Ishikawa 921-8501, Japan 

c Institute for Frontier Medical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8507, Japan 

Interfacial fatigue crack growth behavior for GF/epoxy model composites was investigated using the bifiber shear 

(BFS) methods. This new type of the model composites was developed in our previous study for the in situ observation of 

the static crack growth behavior in a scanning electron microscope. The specimen is composed of two E-glass filaments 

of diameters of 23 and 40 m and bisphenol A type epoxy is impregnated between the filaments. The crack growth 

behavior under different stress ratios was investigated to clarify the fatigue crack growth mechanism. The frequency of 

the stress cycling was 30 Hz. The stress ratio, R, of the minimum to the maximum loads was kept constant under R = 0.1, 

0.3 and 0.5 during each test. Although the energy release rate gradually increases with the increment of the crack length, 

some specimens showed that the change in da/dN was not monotonous with the crack growth, suggesting the difference 

in the fatigue crack growth resistance along a single filament which was similar to that in the fracture toughness observed 

in our previous study. The fatigue crack growth resistance of the interface is much smaller than that of the composite 

laminates. The influence of the stress ratio became smaller when da/dN was correlated to Gmax than when da/dN was 

correlated to K or (G 1/2 ). Thus, the fatigue crack growth mechanism of the glass fiber/epoxy interface is completely 

different from that of the composite laminates where da/dN is often correlated to K under mode II loading and the 

contribution of resin is dominant. Fractographic observation showed rather brittle fracture morphology and less 

contribution of the resin fracture. This tendency also agrees with our former research on the static interface fracture 

criterion under different loading mode ratio. 


The maiden flight of B787 in 2009 and the project of A350XWB promise that carbon fiber reinforced 

plastics (CFRPs) become the common structural materials for the main wing and fuselage of 

commercial aircraft. Although composite materials have significantly greater resistance to fatigue 

loading than have any other class of materials, experimental evidences show that the damage in CFRP 

structures accumulates under fatigue loadings [1,2]. Stress - number of cycles to failure (S-N) diagrams 

usually show that the fatigue strength in fiber direction is lower than the static strength [3,4]. Loads for 

the onset of transverse cracks under fatigue loading are lower than those under static loading [5-7]. The 

energy release rate for the delamination fatigue crack growth threshold is below that for the fracture 

toughness [8-11]. 

Fracture of continuous fiber-reinforced composites in the fiber direction is caused by stochastic 

* Corresponding author. Tel.: +81-75-753-4836; fax: +81-75-771-7286. 

E-mail address: hojo_cm@me.kyoto-u.ac.jp

M Hojo, Y Matsushita, etc. / Interfacial Fatigue Crack Propagation in Microscopic Model Composite using Bifiber Shear Specimen 

damage accumulation based on inherent fiber strength distribution [12-18]. Here, interfacial strength 

plays an important role in this damage accumulation, and it is sure that the fatigue loading enhances the 

damage accumulation [19,20]. Fracture perpendicular to the fiber direction, transverse crack, governs 

the design limit of composite laminated structures. Experimental observations show that transverse 

cracks often occur at the interface, and these interfacial cracks coalesce into longer transverse cracks 

[21,22]. Since transverse cracks are usually the first damage observed in laminated structures and can 

cause delamination and fiber fracture in adjacent load bearing plies [23], it is quite important from the 

point of view of damage tolerant design. Moreover, these microscopic fracture mechanisms of 

continuous fiber-reinforced composite in fiber and transverse directions clearly indicate the importance 

of understanding interfacial fracture under fatigue loading. 

Although there are a number of experimental studies to evaluate interfacial strength in composite 

materials [24,25], little works have been reported on the fatigue behavior of the fiber/matrix interface. 

DiBenedetto et al. [26] briefly have dealt with the fatigue behavior of single carbon fiber/epoxy model 

composites. However, they only qualitatively characterized the increase of local yielding zone with an 

increase in applied fatigue cycles. Latour et al [27,28] carried out microdroplet tests under fatigue 

loading for carbon and Kevlar fibers with thermoplastic resin. They found S-N relations for interfacial 

strength under fatigue loading and also these relations were affected by saline environment. 

In our previous studies [29,30], the interfacial fracture mechanical properties for glass fiber and 

carbon fiber/epoxy interface were evaluated both under static and fatigue loadings using the 

microbundle pull-out test (the so-called microcomposite test). We found the almost horizontal S-N type 

relations for pull-out load. The effect of surface treatment on the glass fiber was minimal under fatigue 

loading although this treatment had some effect under static loading. We also carried out the fatigue 

tests under different stress ratios, and found that maximum pull-out load controlled the S-N diagrams 

for the interfacial fatigue fracture both for glass and carbon fibers. 

For fatigue loading, the evaluation of fatigue crack growth behavior with regard to the fracture 

mechanics parameter is quite important to understand its mechanism [31]. The drawback of the above 

mentioned microcomposite test method is the difficulties in the measurement of the crack length 

because the central pull-out fiber is surrounded by six fibers, and the exact crack propagation rate was 

not possible to be measured. Gradin et al. [32] reported the crack growth behavior of steel rod/epoxy 

interface using macroscopic model composites. Though they found the linear relationship between the 

crack growth rate and the energy release rate, the diameter of the steel rod was 10mm and far from the 

real microscopic fracture behavior in composite materials. 

We proposed new types of model composites, bifiber shear (BFS) and bifiber open (BFO) specimens 

for the in situ observation of crack growth behavior in a scanning electron microscope (SEM) [33]. The 

change of the static fracture toughness along the glass fiber (GF)/epoxy interface of a single filament 

was investigated under different loading mode. Both the opening and shear modes contribute in BFS 

specimens while the opening mode mainly contributes in BFO specimens. Though the general tendency 

showed that the fracture toughness increased with increasing crack length for both types of the 

specimens, the change of the fracture toughness along a single filament was observed. The initial 

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fracture toughness values for BFS and BFO specimens were rather insensitive to the loading mode. This 

result was completely different from that for bulk composite laminates [34-36], suggesting less 

contribution of resin fracture. 

In the present study, interfacial fracture behavior for GF/epoxy model composites was investigated 

under fatigue loading using the BFS methods. The interfacial crack growth behavior under different 

stress ratio was investigated to clarify the crack growth mechanism under fatigue loading. 

2. Experimental procedure 

2.1 Materials and specimen 

E-glass fibers of different diameters (df = 23 and 40 m, Nitto Boseki, without surface treatment) 

were used in this study. Bisphenol A type epoxy (Epikote 828) was used as matrix, and 

triethylenetetramine (10 wt%) was used as hardener [29,30,33]. Fig. 1 shows a schematic of bifiber 

shear (BFS) specimen developed in our previous paper [33]. Matrix resin was impregnated between two 

parallel filaments. The details of the specimen preparation processes were reported in our previous 

paper [33]. The specimens were cured at 50 o C for 80 min followed by 100 o C for 60 min. Then, the 

specimen was mounted on a paper frame. Special care was taken to keep the two fibers and the paper 

frame on the same plane for in-situ observation. 

Glass Fiber 

Epoxy Resin 

Load 

 

L 

Load 

Fig. 1. Schematic of bifiber shear specimen. 

The resin impregnation length, L, and fiber distance at the end of both resin impregnation, , were 

measured for all specimens using a digital microscope (VH-7000, Keyence) at a magnification of 375 

times. For specimens with df = 40 m, L was between 300 and 1300 m with an average of 740 m, 

and was between 30 and 60 m with an average of 37 m. For specimens with df = 23 m, L was 

between 200 and 1000 m with an average of 510 m, and was between 15 and 30 m with an 

average of 24 m. These values were almost identical to our former paper on the interfacial static


fracture toughness using the same specimen. Since the difference in at both end of resin impregnated 

region was less than 3% for each specimen, the averaged values were used for calculation. Though there 

were some differences in the thickness of the impregnated resin, the influence on the fracture 

mechanical parameters was small in our preparatory calculations. It was also confirmed that the 

diameter of fiber was almost the same for each specimen, and the change of the diameter within the 

specimen was negligible. Gold coating was carried out for all specimens before the following 

mechanical tests. 

2.2 Fatigue tests 

Fatigue tests were carried out with a special low-load-capacity fatigue testing machine of 10 N in 

capacity with an electromagnetic actuator (Shimadzu) which was installed in a scanning electron 

microscope (SEM, JEOL, JSM-5410LV) [33]. The paper frame was cut after griping the specimen with 

clip type grips. Then, specimens were loaded statically at the rate of 1.0x10 -6 m/s to introduce precracks 

of the length of about half of the fiber diameter. Here, the load corresponding to the onset of precrack, 

Ppre, was recorded. The following fatigue tests were carried out by keeping the maximum load, Pmax, 

constant at Ppre/2. The stress ratio of the minimum load to the maximum load was kept constant at 0.1, 

0.3 and 0.5. The speed of stress cycling was 30 Hz. The actual control mode of the testing machine was 

displacement control instead of load control owing to the stability of the tests. Here, the specimen 

compliance was calculated, and the displacement was controlled to keep the desired maximum load, 

Pmax, and the stress ratio, R, constant. Crack length was defined as the length from the bottom of the 

meniscus, and was measured using video recording of SEM during the tests. 

2.3 Fracture mechanics parameters at interface 

The calculation process to evaluate the energy release rate is summarized as follows. Three 

dimensional linear elastic stress analyses were carried out using a commercial finite element (FE) code, 

MSC MARC 2001, with a prepost processor, MENTAT 2001, to obtain the energy release rate. The 

energy release rate was calculated using crack closure method [39]. Taking the advantage of symmetry, 

the model consists of a half of the specimen. Fig. 2a shows the schematic and boundary conditions for 

the model. Whole length of the fibers was modeled to calculate the geometrical nonlinearity, and large 

displacement analysis was carried out. Fig. 2b shows the detailed model around the resin impregnated 

part. The minimum size of the mesh at the crack tip was taken as 1.3 m for fiber of df=40 m, and 0.72 

m for fiber of df=23 m. Material properties and the details of the actual calculation process to 

evaluate the energy release rate of each specimen were explained in our previous paper [33]. Fig. 3 

shows examples of the relationships between the energy release rate and the crack length. The energy 

release rate gradually increases with the crack growth when the applied stress is constant. 

The complex stress intensity factors of an interfacial crack, K1 and K2, were also evaluated for the 

specimen based on Erdogan‟s definition [40,41]. The mode ratio, K2/K1, increased sharply until the 

relative crack length, a/df, is about 1, and then the mode ratio leveled off at about 1.2 – 1.3 [33]. The 

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contribution of shear mode is slightly higher than that of opening mode for this specimen expect when 

the relative crack length is less than 1. 

a 

z 

x 

y 

Square root of energy release rate, G 1/2 (J/m 2 ) 1/2 

d f 

 

(a) 

x 

z 

Force direction 

y 

Fixed displacement 

d f : Fiber diameter 

L : Adhesion length 

: Fiber space 

a : Crack length 

Fig. 2. Boundary conditions and mesh for bifiber shear specimen. 

30 

25 

20 

15 

10 

5 

f =800MPa, d f =40m, =40m 

L=400m 

L=800m 

L=1200m 

0 

0 50 100 150 200 250 300 350 

Crack length, a(m) 

Fig. 3. Relation between square root of energy release rate, G 1/2 , and crack length, a, for bifiber shear specimen. 

(b)


3. Experimental results and discussion 

3.1 In situ observation of fatigue crack growth 

Figs. 4 and 5 indicate the snap shots of the fatigue crack propagation for tests with df = 40 m and 23 

m, respectively. The white arrows for the photos of N=0 indicate the precracks introduced before the 

fatigue tests. Fig. 6 and 7 show the relationship between the crack length and the number of cycles. For 

the case of Fig. 4, specimen S4062a, single fatigue crack started propagating from the left side meniscus. 

The propagation was stable until the final fracture at N=2.16x10 4 . For some specimens, cracks 

propagated from both sides of the meniscus. For the case of Fig. 5, specimen S2380a, the first crack 

started propagation from the left side meniscus. The second crack initiated from the right side meniscus 

at N=8.1x10 3 , and both cracks propagated at almost the same rate until final fracture at N=1.67x10 4 . Fig. 

8 compares the relationship for the crack length and number of cycles for two cracks in the same 

specimens. In this figure, the solid lines indicate the first cracks and the dashed lines indicate the second 

cracks. 

Fig. 4. Scanning electron micrographs of interfacial fatigue crack propagation from one end of meniscus (df=40m, S4062a). 

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Fig. 5. Scanning electron micrographs of interfacial fatigue crack propagation from both ends of meniscus (df=23m, S2380a). 

Crack length, a (m) 

700 

600 

500 

400 

300 

200 

100 

d f =40m, R=0.5 

0 

0 1 2 3 4 5 6 7 

Number of cycles, N (×10 4 ) 

Fig. 6. Relation between crack length, a, and number of cycles, N (df=40m, R=0.5). 

S4061d 

S4062a 

S4062b 

S4062e 

S4063d 

S4080e 

S4059a 

S4081e




350 

300 

250 

200 

150 

100 

50 

d f =23m, R=0.5 

S2369d 

S2370d 

S2383b 

S2383c 

S2380a 

S2384c 

0 

0 2 4 6 8 10 12 


Fig. 7. Relation between crack length, a, and number of cycles, N (df=23m, R=0.5). 

500 

400 

300 

200 

100 

S4081e, d f =40m, R=0.5 

S2380a, d f =23m, R=0.5 

0 

0 0.5 1 1.5 2 2.5 3 


Fig. 8. Relation between crack length, a, and number of cycles, N for specimens with two cracks propagated from both ends of meniscus. 

Since all the tests were carried out by keeping the maximum load constant during fatigue loading, the 

energy release rate gradually increases with the crack length. This brought the downwards convex 

tendency of the relationship between the crack length and the number of cycles as shown in Figs. 6 and 

7, where the crack growth rate gradually increased with the crack length owing to the power law 

relations. However, the crack growth behavior of each crack was far from monotonic increase of the 

crack growth rate. In some specimens, retardation of the crack growth was observed by the step like 

relationship in Figs. 6 and 7. In Fig. 8, two cracks in the same specimen showed different changes in 

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da/dN with number of stress cycles in the crack growth. This gives clear evidence that the possible 

slight fluctuation of the load control was not responsible for the change in the crack growth behavior. 

When the relative crack length, a/df, is smaller than 1, the difference in the mode ratio, K2/K1, may 

have influence on the crack growth behavior. However, the results of Figs. 6-8 show that this influence 

is minimal. 

3.2 Crack growth rate 

Figs. 9 and 10 show the relationship between the crack growth rate, da/dN, and the maximum energy 

release rate, Gmax, for the specimens with df=23 m under R=0.5. The corresponding relationship 

between the crack length and the number of cycles is shown in Fig. 7. The specimens shown in Fig. 9 

are categorized as type A where da/dN increased monotonically with the increase in Gmax. In this 

category, some specimens show that da/dN is expressed by a power law relationship, da/dN=AGmax n . 

However, other specimens showed that da/dN-Gmax relationship deviates to the lower values than those 

expected by the power law relation with the crack growth. The specimens shown in Fig. 10 are 

categorized as type B where the decrease in da/dN is observed, followed by the increase in da/dN during 

the propagation. 

In our previous study on the static fracture toughness using the same bifiber shear specimens, the 

change in the fracture toughness along single filament interface was observed [33]. Thus, the change in 

da/dN categorized as type B is due to the variation in the crack growth resistance along single filament 

interface. The difference of da/dN for two cracks in the same specimen as shown in Fig. 8 also supports 

this fact. 

Crack propagation rate, da/dN (m/cycle) 

10 -5 

10 -6 

10 -7 

10 -8 

10 -9 

10 -10 

10 -11 

d f =23m, R=0.5 

S2369d 

S2383b 

S2380a 

10 100 1000 

Maximum energy release rate, G (J/m 

max 2 4000 

) 

da/dN 

(a) Type A 

G Gmax max 

Fig. 9. Relation between crack propagation rate, da/dN, and maximum energy release rate, Gmax (df=23m, R=0.5, type A). 

In Fig. 11, the relationship between da/dN and Gmax 1/2 is compared with that between da/dN and G 1/2 

for all specimens in order to find out the controlling fracture mechanics parameter for interfacial fatigue


crack growth under different stress ratios. Here, the range of square root of the energy release rate, G 1/2 , 

is defined as Gmax 1/2 - Gmin 1/2 . Taking into account that the energy release rate, G, is proportional to the 

square of the stress intensity factor, K 2 (G=HK 2 where H is a parameter composed of elastic moduli 

[42]), G 1/2 is a parameter proportional to the stress intensity range, K, and Gmax 1/2 is a parameter 

proportional to the maximum stress intensity factor, Kmax. The definition of G 1/2 also fits the second 

definition of G by Matsubara et al.[43] where G=H(Kmax-Kmin) 2 . Then, da/dN – G 1/2 relation 

corresponds to da/dN – K relation, and da/dN – Gmax 1/2 relation corresponds to da/dN – Kmax relation, 

respectively [10,11,37]. In these figures, the test results under R=0.5 are shown with open symbols, and 

those under R=0.3 and 0.1 are shown with solid symbols. Triangle marks indicate the results with d f=40 

m, and square marks indicate the results with df=23 m. The da/dN-G 1/2 relationship indicates clear 

stress ratio dependency where the data points under R=0.3 and 0.1 are located right hand side of the data 

points under R=0.5. On the other hand, the da/dN-Gmax relationship indicates no clear stress ratio 

dependency although the data points are spread in a wide band. 


10 -5 

10 -6 

10 -7 

10 -8 

10 -9 

10 -10 

10 -11 

d f =23m, R=0.5 

S2370d 

S2383c 

S2384c 

10 100 1000 


max 2 4000 

) 

da/dN 

(b) Type B 

G Gmax max 

Fig. 10. Relation between crack propagation rate, da/dN, and maximum energy release rate, Gmax (df=23m, R=0.5, type B). 

For the case of unidirectional GF/epoxy laminates, the crack growth behavior under mode II loading 

was correlated to the stress intensity range, K without respect to the stress ratios [43] similar to the 

results of CFRP laminates [36,37]. Tests under mixed modes of I and II also showed that both K and 

Kmax contributed to the crack growth [44]. Thus, the controlling fracture mechanics parameter and the 

fatigue crack growth mechanism of the glass fiber/epoxy interface are completely different from those 

of GF/epoxy laminates. 

Fig.12 indicates the da/dN – Gmax relationship for the all specimens under different stress ratios. 

Large scatter was observed for the obtained data. However the da/dN – Gmax relationship for each 

specimen is within a narrow band when we apply a power law relation. The whole data can also be 

indicated by a wide band of a power law relationship as shown with the hatched area in this figure. The 

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204 


width of this scatter band is about three times in the energy release rate coordinate. It is interesting to 

note that the scatter band width under fatigue loading is quite similar to that for static R-curves where 

the plateau values range from 100 to 300 J/m 2 . 


10 -5 

10 -6 

10 -7 

10 -8 

10 -9 

10 -10 

10 -11 

da/dN-K max 

Gmax Kmax 

d f =40m R=0.5 

d f =23m R=0.5 

d f =40m R=0.3 

d f =40m R=0.1 

d f =23m R=0.1 

1 10 

60 

1/2 2 1/2 

Square root of maximum energy release rate, G (J/m ) 

max 


10 -5 

10 -6 

10 -7 

10 -8 

10 -9 

10 -10 

10 -11 

(a) 

(a) 

1 10 

d f =40m R=0.5 

d f =23m R=0.5 

d f =40m R=0.3 

d f =40m R=0.1 

d f =23m R=0.1 

Range of square root of energy release rate, G 1/2 (J/m 2 ) 1/2 

(b) 

(b) 

Fig. 11. Effect of stress ratio on crack growth behavior. 

The thick dashed line in Fig. 12 shows the result of unidirectional GF/epoxy laminates under mode II 

loadings under R=0.1 reported by Matsubara et al. [43]. The results under R=0.3 indicate slightly higher 

resistance in the da/dN-Gmax relation. Then the fatigue crack growth resistance of GF/epoxy laminates is 

about ten times higher than that of GF/epoxy interface. This difference also agrees with the difference of 

the fracture toughness between CF/epoxy laminates (about 2 -3 kJ/m 2 [43]) and GF/epoxy interface 

60


(about 100-300 J/m 2 in our previous research [33]). 

Crack Crack propagation propagation rate, rate, da/dN da/dN (m/cycle) (m/cycle) 

10 -5 

10 -5 

10 -6 

10 -6 

10 -7 

10 -7 

10 -8 

10 -8 

10 -9 

10 -9 

10 -10 

10 -10 

10 -11 

10 -11 

d =40m =40m R=0.5 

f 

d =23m =23m R=0.5 

f 

d =40m =40m R=0.3 

f 

d =40m =40m R=0.1 

f 

d =23m =23m R=0.1 

f 

Matsubara et al. 

R=0.1 

Scatter of G R at a=150m a=150m 

10 100 1000 


max 2 10 100 1000 4000 

Maximum energy release rate, G (J/m ) 

max 2 4000 

) 

Fig. 12. Relation between crack propagation rate and maximum energy release rate. 

3.3 Fractographic observation and mechanism consideration 

Figs. 13 and 14 show the fracture surfaces of the BFS specimens with df = 40 and 23 m, respectively. 

Both fiber side, (a), and resin side, (b), of the fracture surfaces were observed in these figures. For both 

figures, the point A indicates the onset point of fatigue cracks, and the point B indicates the onset point 

of final unstable fracture. Very smooth fiber surface was observed on the fracture surface of the fiber 

side without a trace of resin. Moreover, no significant difference was observed between the fracture 

surface of fatigue fracture and that of final unstable fracture. The morphology of the fracture surface 

indicates that the contribution of resin is minimal in the interfacial fracture of this model composite. It is 

also interesting to note that no significant difference was observed between the fracture surfaces of 

static and fatigue fracture [33]. 

For the case of composite laminates, the contribution of matrix resin is large, and this brings much 

higher fatigue crack growth resistance [45,46]. Moreover, shear plastic deformation is responsible for 

the fact that the stress range is the controlling fracture mechanics parameter for delamination fatigue 

[36,37]. Less contribution of resin for the interfacial fracture means that the fracture mechanism is 

rather brittle. This fact is probably responsible for that the interface fatigue crack growth under different 

stress ratios is controlled by the maximum energy release rate, and the fatigue crack growth resistance 

of interface is much lower than that of composite laminates [11,37]. 

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206 



Fig. 13. Scanning electron micrographs of fatigue fracture surfaces for S4081e. 

Fig. 14. Scanning electron micrographs of fatigue fracture surfaces for S2380a. 

Fatigue crack growth behavior of glass fiber/epoxy interface was investigated using a new type of 

model composites, bifiber shear (BFS) method. Tests under different stress ratios were carried out in a 

scanning electron microscope, and the in situ observation of the fatigue crack growth was successfully 

carried out. The contribution of the shear component is higher in this BFS specimen. 

Although the energy release rate gradually increases with the increment of the crack length, the


change in the fatigue crack growth rate, da/dN, was not monotonous with the crack growth. Thus, the 

fatigue crack growth resistance was not constant along a single filament. The fatigue crack growth 

resistance of the interface is about one order of magnitude smaller than that of the composite laminates. 

The controlling fracture mechanics parameter under different stress ratios was the maximum energy 

release rate, which was different from that of composite laminates. Fractographic observation confirmed 

that these differences were due to less contribution of resin fracture for the interface fatigue crack 

propagation. 


Authors would like to thank Mr. Y. Igarashi and R. Konishi of Graduate Student of Kyoto University 

for helpful discussion in experimental procedures. Authoers would also like to thank Dr. Y. Suzuki of 

Nitto Boseki for supplying glass fibers of special diameters. 

References 

[1] K. Reifsnider, editor. Fatigue of Composite Materials, Elsevier, Amsterdam, 1991. 

[2] R. Talreja, Fatigue of Composite Materials, Technomic, Lancaster, 1987. 

[3] L. Lorenzo, H.T. Hahn, Fatigue failure mechanisms in unidirectional composites. In: H.T. Hahn, editor. Composite Materials: Fatigue and 

Fracture, ASTM STP 907, ASTM, Philadelphia, 1986, pp.210-232. 

[4] H. Sembokuya, M. Hojo, C. Nagasawa, T. Aoki, K. Kemmochi, H. Maki, Effect of stress ratio on tension and delamination fatigue 

behavior in CF/epoxy laminates, Adv. Composite Mater., 1 (1991) 261-275. 

[5] N. Takeda, S. Ogihara, A. Kobayashi, Microscopic fatigue damage progress in CFRP cross-ply laminates, Composites, 25 (1995) 859-867. 

[6] N.T. Hoang, D. Gamby, M.-C. Lafarie-Frenot, Predincting fatigue transverse crack growth in cross-ply carbon-epoxy laminates from quasi 

static strength tests by using iso-damage curves, Intenational Journal of Fatigue, 32 (2010) 166-173. 

[7] S. Ogihara, N. Takeda, S. Kobayashi, A. Kobayashi, Effects of stacking sequence on microscopic fatigue damage development in 

quasi-isotropic CFRP laminates with interlaminar-toughened layers, Composites Science and Technology, 59 (1999) 1387-1398. 

[8] Wilkins DJ, Eisenmann JR, Camin RA, Margolis WS, Benson RA, Characterizing delamination growth in graphite-epoxy. In: Reifsnider 

K, editor. Damage in Composite Materials, ASTM STP 775, ASTM; 1982. p.168-183. 

[9] Bathias C, Laksimi A. Delamination threshold and loading effect in fiber glass epoxy composite. In: Johnson, editor. Delamination and 

Debonding of Materials, ASTM STP 876, ASTM; 1985. p.217-237. 

[10] Hojo M, Tanaka K, Gustafson C-G, Hayashi R. Effect of stress ratio on near-threshold propagation of delamination fatigue cracks in 

unidirectional CFRP. Compos Sci Technol 1987;29:273-292. 

[11] Hojo M, Ochiai S, Gustafson C-G, Tanaka K. Effect of matrix resin on delamination fatigue crack growth in CFRP laminates. Engineering 

Fracture Mechanics 1994;49:35-47. 

[12] Ochiai S, Osamura K. A computer-simulation of strength of metal matrix composites with a reaction layer at the interface. Metallurgical 

Transactions A 1987;18:673-679. 

[13] Ochiai S, Osamura K, Abe K. A study on tensile behavior of boron fiber-reinforced aluminum sheet in terms of computer-simulation. 

Zeitschrift fur Metallkunde; 1985:76:402-408. 

[14] Curtin WA. Stochastic damage evolution and failure in fiber-reinforced compocites. Advances in Applied Mechanics 1999;36:163-253. 

[15] Ochiai S, Hojo M, Inoue T, Shear-lag simulation of the progress of interfacial debonding in unidirectional composites. Compos Sci 

Technol 1999;59:77-88. 

[16] Okabe T, Takeda N, Kamoshida Y, Shimizu M, Curtin WA, A 3D shear-lag model considering micro-damage and statistical strength 

prediction of unidirectional fiber-reinforced composites. Compos Sci Technol 2001;61:1773-1787. 

[17] Okabe T, Sekine H, Ishii K, Nishikawa M, Takeda N, Numerical method for failure simulation of unidirectional fiber-reinforced 

composites with spring element model. Compos Sci Technol 2005;65: 921-933. 

[18] Okabe T, Takeda N. Elastoplastic shear-lag analysis of single-fiber composites and strength predinction of unidirectional multi-fiber 

composites. Composites Part A 2002;33:1327-1335. 

[19] Gamstedt EK, Berglund LA, Peijs T. Fatigue mechanisms in unidirectional glass-fibre-reinforced polypropylene. Compos Sci Technol 

1999;59:759-768. 

207

208 


[20] Nishikawa M, Okabe T. Microstructure-dependent fatigue damage process in short fiber reinforced plastics. International Journal of Solids 

and Structures 2010;47:398-406. 

[21] Hull D, Clyne TW. An Introduction to Composite Materials, 2nd Edition, Cambridge University Press; 1996. p.175. 

[22] Hobbiebrunken T, Hojo M, Adachi T, Jong CD, Fiedler B. Evaluation of Interfacial Strength in CF/Epoxies using FEM and In-situ 

Experiments. Composites Part A, 2006;37:2248–2256. 

[23] Schulte K, Stinchcomb WW. Damage Mechanisms-Including Edge Effects-in Carbon Fibre-reinforced Composite Materials. In: Friedrich 

K, editor. Application of Fracture Mechanics to Composite Materials, Elsevier, Amsterdam; 1989. p.273-325. 

[24] Kim J-K, Mai Y-W. Engineeried Interfaces in Fiber Reinforced Composites, Elsevier, Oxford, 1998. 

[25] Herrera-Franco PJ, Drzal LT. Comparison of methods for the measurement of fibre/matrix adhesion in composites. Composites 

1992;23:2-27. 

[26] DiBenedetto AT, Nicolais L, Ambrosio L, Groeger J. Stress transfer and fracture in single fiber/epoxy composites. In: Composite 

Interfaces, Proc. 1st International Conference on Composite Interfaces (ICCI-I), Ishida H, Koenig JL, editors, North-Holland, New York, 

1986. p.47-54. 

[27] Latour RAJr, Black J, Miller B. Fracture mechanisms of the fiber/matrix interfacial bond in fiber-reinforced polymer composites. Surface 

and Interface Analysis 1991;17:477-484. 

[28] Latour RAJr, Black J, Miller B. Fiber/matrix interfacial bond ultimate and fatigue strength characterization in a 37 o C dry environment. J 

Compos Mater 1992;26:256-273. 

[29] Hojo M, Terashima K, Igarashi Y, Shida M, Ochiai S, Inoue T, Sawada Y. Interfacial fracture in model composites under static and fatigue 

loadings -Mechanism consideration based on experimental and analytical approaches-. Materials Science Research International, STP-2, 

2001:189-196. 

[30] Hojo, M, Tanaka M, Hobbiebrunken T, Ochiai S, Inoue T, Sawada Y. Interfacial fracture of GF and CF/epoxy model composites under 

static and fatigue loadings. In: Fatigue 2002, Proceedings of the Eighth International Fatigue Congress, Vol. 1, EMAS, 2002, p.231-238. 

[31] Friedrich K, editor. Application of Fracture Mechanics to Composite Materials, Elsevier, Amsterdam; 1989. 

[32] Gradin PA, Backlund J. Fatigue debonding in fibrous composites. In: Advances in Composite Materials, Proc. 3rd International 

Conference on Composite Materials, Vol. 1, Pergamon Press, 1980, p.162-169. 

[33] Hojo M, Matsushita Y, Tanaka M, Adachi T, In-situ observation of interfacial crack propagation in GF/epoxy model composite using 

bifiber specimens in mode I and mode II loading. Compos Sci Technol 2008;68:2678-2689. 

[34] Bradley WL. Relationship of matrix toughness to interlaminar fracture toughness. In: Friedrich K, editor. Application of fracture 

mechanics to composite materials. Elsevier, 1989. p.159-187. 

[35] Benzeggagh ML, Kenane M. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with 

mixed mode bending apparatus. Composite Science and Technology, 1996;56:439-449. 

[36] Hojo M, Ando T, Tanaka M, Adachi T, Ochiai S, Endo, Y. Mode I and II interlaminar fracture toughness and fatigue delamination of 

CF/epoxy laminates with self-same epoxy interleaf. International Journal of Fatigue 2006;28:1154-1165. 

[37] Hojo M, Matsuda S, Ochiai S. Delamination Fatigue Crack Growth in CFRP Laminates under Mode I and II Loadings -Effect of 

Mesoscopic Structure on Fracture Mechanism-. In: Degallaix S, Bathias C, Fougeres R, editors. Proc. International Conference on Fatigue 

of Composites, SF2M, 1997. p.15-26. 

[38] Tanaka H, Tanaka K. Mixed-mode growth of interlaminar cracks in carbon/epoxy laminates under cyclic loading. In: Proc. ICCM-10, Vol. 

1, 1995, p.181-188. 

[39] Rybicki EF, Kanninen MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Engineering 

Fracture Mechanics 1977;9:931-938. 

[40] Erdogan F. Stress distribution in bonded dissimilar materials with cracks. Transactions of the ASME Series E, Journal of Applied 

Mechanics 1965;32:403-410. 

[41] Ikeda T, Miyazaki N. Mixed mode fracture criterion of interface crack between dissimilar materials. Engineering Fracture Mechanics, 

1998;59(6):725-735. 

[42] Sih GC, Paris PC, Irwin GR. On cracks in rectilinearly anisotropic bodies. Int J Fracture Mechanics 1965;1:189-203. 

[43] Matsubara G, Ono H, Tanaka K. Mode II fatigue crack growth from delamination in unidirectional tape and satin-woven fabric laminates 

of high strength GFRP. International Journal of Fatigue 2006;28:1177-1186. 

[44] Matsubara G, Nishikawa H, Nihei K, Tanaka K. Mode-Mixty Effect on Growth Behavior of Interlaminar Fatigue Cracks in High Strength 

GFRP. Trans. Japan Society for Mechanical Engineers, 2004;70A:1733-1740. 

[45] Bascom WD, Gweon SY. Fractograpy and failure mechanicms of carbon fiber-reinforced composite materials. In: Roulin-Moloney AC, 

editor. Fractography and failure mechanism of polymers and composites. Elsevier, 1988, pp.351-385. 

[46] Bradley WL. Relationship of matrix toughness to interlaminar fracture toughness. In: Friedrich K, editor. Application of fracture 

mechanics to composite materials. Elsevier, 1989. pp.159-187.

Experimental analysis and modelling of fatigue behaviour of 

thick woven laminated composites 

Abstract 

P Nimdum *, J Renard † 

Centre des matériaux P. M. Fourt, Mines-Paris Tech, CNRS UMR 7633, BP 87, F-91003 Evry, Cedex 

The objective of this work was to analyze the fatigue behaviour and the damage development in unidirectional and 

angle-ply 2/2 twill weave T800 carbon/epoxy woven fabric composite laminates. Fatigue tensile-tensile tests were 

performed and internal damage has been observed by using camera and optical microscope during testing. The 

experimental results show that the damage evolution can be characterized by two or three stages according to the 0 o ply 

and angle-ply laminates respectively. This evolution is correlated with damage mechanisms. Micromechanical 

three-dimensional finite element models of the twill weave woven fabric are proposed. Numerical simulations exhibit that 

the local bending of the thread induces local stress and strain gradients in the warp yarns in the vicinity of fill yarns 

curvature. Finally numerical results are correlated with experimental observation of damage mechanisms in 0 o ply 

laminate and experimental global stiffness reduction (20–25%) has been compared with numerical prediction. An original 

fatigue criterion for onset delamination during fatigue loading of angle-ply laminates has been proposed. This criterion is 

based on average values of the components of the stress field. Identification of the different parameters of this criterion 

has been made with experimental Edge Delamination Tests (EDT). Validation was made with tensile fatigue tests 

performed on angle-ply textile laminates with drilled circular hole. Further numerical predictions are in good agreement 

with experimental results. 

Keywords: delamination; woven composite; twill 2/2; thick composite; damage 


Composite materials have been widely used in high performance structures especially in automobile, 

wind turbine blades, marine industries, aircrafts, sports equipment, railway structure, etc. However, the 

application of unidirectional composites has several drawbacks such as impact resistance and tolerance 

in presence of a delamination. Therefore, the trend for composites applications is undergoing a 

transition towards the use of textile composite, also known as “woven fabric composites”. These 

materials present various attractive [1-3] since it provides improved impact resistance, better in 

out-of-plane mechanical properties and improved damage tolerant in the presence of the delamination 

due to the non-planar interply structure of woven fabric composites. Nevertheless, the stiffness and 

strength behaviour of woven fabric composites are dependent on many parameters such as the 

characteristics of fibers and matrix and weave architecture [4] (weave type, packing density of yarns, 

undulation angle etc.). 

* E-mail address: pongsak.nimdum@ensmp.fr 

† E-mail address: jacques.renard@ensmp.fr

210 


Thus, the woven carbon fabric/epoxy composite laminates present all their interest. The purpose of 

this work is to first present the damage mechanisms and to focus on the correlation between damage 

accumulation and mechanical property. Then, the finite element method (FEM) is applied for 

representing the failure mechanism and mechanical damage. Finally, we shall propose a criterion for 

onset of delamination under cyclic loading extended from a static criteria. 

2. Experimental procedure 

2.1 Material 

The composite material of this study was carried out on carbon (T800)/epoxy composite material. 

The carbon fiber density was 12.81 g/cm 3 . The diameter of carbon fiber is equal 7 m. This study 

focuses on woven fabrics composites which the interlacing of the fill and warp yarns was formed 

according to the 2/2 twill weave pattern as show in Fig. 1 with 0.65 mm for one ply thickness and the 

resulting fiber volume fraction V = 52. 

9% 

. The presence of weave structure induces very specific 

f 

physical phenomena. Therefore, first we study on woven 0 o -ply laminate i.e. each ply of laminate is 

similar orientation and then we study on woven angle-ply laminates ((0 o ,±20 o )s, (0 o ,±20 o 2)s, (0 o ,±30 o )s 

and (0 o , ±30 o 2)s). 

In case of woven 0 o -ply laminate, twill 2/2 weave has the same number of yarns in both directions 

such as fill ( x1 ) and warp ( x2 ) direction to provide balanced bi-directional properties in fabric plane. 

Fig. 2 shows the schema of woven fabrics. The unit cell is a square and composed of 4x4 yarns 

corresponding to about 9.2x9.2 mm. For this study, we perform on a thick composite consisting of 

several layers, this result that many different patterns were occurred in 0 o -ply laminates. In order to 

simplify in this study, we can classify in three significant cases such in-phase (IP), out-of-phase (OP) 

and intermediate phase (T90) (Fig. 2). 

In the case of angle-ply woven laminates, each ply is supposed to be a homogenous material. 

Fig. 1. (a) Scheme of the 2x2 twill weave architecture; (b) three elements of woven fabrics; (c) weave architecture – top view and (d) unit cells.

P Nimdum, J Renard. / Experimental analysis and modelling of fatigue behaviour of thick woven laminated composites 

Fig. 2. Different pattern possibilities in woven 0 o -ply laminates: (a) in-phase (IP); (b) out-of-phase (OP) and (c) T90. 

2.2 Experimental procedure 

Fatigue tension-tension loading was applied on hydraulic testing system (Fig. 3a). We chose to 

perform a load control mode. Axial extensometer is used to measure the longitudinal elongation. The 

changes in load and longitudinal displacement during fatigue tests are recorded. 

It is assumed that the material behaviour is linear to avoid strain rate effects consideration (or 

frequency effect). Fatigue tension-tension tests was performed with: (i) the difference of maximum 

applied stress ( max 

) from which woven 0 o -ply laminate will be performed at . 3 

R 

0 . 7 

R while woven angle-ply laminates will be performed at . 4 

R 

211 

0 , 0 . 5 

R and 

0 , 0 . 5 

R and 0 . 6 

R where R 

is the ultimate stress ; (ii) the ratio minimum to maximum stress (R), also called the load ratio, in a cycle 

was 0.1, (ii) the frequency (f) is 1 Hz, and (iii) all tests are performed at room temperature. 

(a) (b) 

Fig. 3. Experimental setup: (a) hydraulic machine; (b) profile of tensile-tensile fatigue tests. 

All specimens were cut from plates using the diamond wheel saw and were bonded with glass/epoxy 

or aluminium tabs onto each specimen end. During fatigue tests, the specimen surface (length 65 mm) is 

recorded at loading less than the maximum applied stress (Fig. 3b) with a digital CCD camera under 

white light illumination. 

3. Experimental analysis under fatigue loading 

3.1 Experimental analysis on 0 o -ply laminates 

3.1.1 Damage mechanism

212 


Fig. 4-6 shows that the main fatigue damage mechanisms are ply-cracking, also called transverse 

cracking, (see “a” in Fig. 4) and the intralaminar delamination (see “b” in Fig. 4). Generally, these 

delaminations are initiated at the edges of the specimen (“a” in Fig. 5). However, the observation of 

surface perpendicular to loading direction using ZEISS optical microscopy, show that intralaminar 

delamination does not only appear at free edges, but also inside of the specimens where the adjacent 

fills yarns bundles meet (see “c” in Fig. 6). These delaminations increase with the number of cycles (see 

“b” in Fig. 5 and 6). It should be noted that the delaminations propagate following a curved yarn and 

then interface between neighbouring yarns (warp/warp, warp/fill and fill/fill). This result corresponds 

with the final failure surface showing that most layers have been separated by intralaminar 

delaminations developed upon the interface of yarns without crossing them. 

Fig. 4. Types of damages during fatigue tests: (a) OP case at ζmax = 0.5ζR; 

(b) IP case at ζmax = 0.5ζR and (c) second form of IP case at ζmax = 0.7ζR. 

Fig. 5. Fatigue damage progression in woven 0 o -ply laminates. 

Fig. 6. Intralaminar delamination and its progression path on free-edge and inside surface of specimen.


With increasing of number of plies, intralaminar delamination will become more significant and 

earlier to occur (“a” for OP case and “b” for IP case in Fig. 7). On the other hand, transverse cracks are 

still locally in the surface layer of the specimen and their density remains relatively low. 

The observations show that for different maximum applied stress the fatigue damage mechanisms are 

identical with more rapidly damage evolution when the maximum applied stress increases. 

Fig. 7. Damage mechanisms in 4 layers . (Fatigue loading at ζmax = 0.7ζR) 

3.1.2 Damage evolution and stiffness degradation in 0 o -ply laminates 

If we consider the damage mechanism versus the number of cycles, we found that the damage 

evolution can be divided into two steps: (i) the initial damage with a threshold number of cycles depend 

on the pattern of neighbours layers (IP, OP and T90), the maximum applied stress and the number of 

plies (thickness effect) (ii) then, a rapid increase in density damages and then (iii) finally, saturation of 

damage density until ending of specimen fracture. 

If we now considered the stiffness reduction due to damage evolution as a function of number of 

cycles, we can identify three stages (Fig. 8) (i) a stage I in which a rapid stiffness reduction. This stage 

corresponds to the delaminations onsets, the multiplication of delaminations until their saturation 

density and then (ii) a slow decrease stiffness reduction to nearly stabilization. The results of 

experimental observation show that the regions of intersection of two fills yarn, also called out-of-phase 

regions, are a preferential position for intralaminar delamination onset. 

The fatigue tests in woven 0 o -ply laminates with 2, 4, 7 layers for different maximum applied stress 

show that the effect of the thickness for damage density can be neglected when the number of plies is 

greater than four (n > 4) (Fig. 9). The initiation and progression of damages are more rapidly for 

thin-plies. Nevertheless, all specimens give close to saturation level of damage density. Reasonably, 

with increasing maximum applied stress, the saturation density state is still similar but it is reached 

more quickly due to the initiation of damages and their progress are more rapidly. 

The reduction of rigidity is still related to the damage evolution. In stage II of quasi-stability state of 

stiffness reduction in which a stiffness reduction of 20-25% occurs whatever the thickness and the 

maximum applied stress. 

It can be seen that the correlation between transverse cracking density and intralaminar delamination 

density is given. The numerical results, more detail in next section (§4.3), allow to deduce that the onset 

of intralaminar delamination often leads to the transverse cracking. 

213

214 


Fig. 8. Normalised stiffness property and damage evolution of woven 0 o -ply laminates as a function of number of cycles. 

(a) (b) 

Fig. 9. Damage density as a function of number of cycles for different layer at ζmax = 0.7ζR: (a) transverse cracking density (df) and (b) 

intralaminar delamination density (dd). 

3.2 Experimental analysis on angle-ply laminates 

3.2.1 Damage mechanism 

We now consider the case of the woven angle-ply laminates, ( 0, 

20n 

) s and ( 0 

, 30n 

) s with n = 

1 and 2. In generally, due to edge effect lead to free-edge stress singularity at interface of adjacent layers 

and result in the onset of delamination, also called interlaminar delaminattion. First, the experimental 

results illustrate the onset delamination at interface + 20 n 

/ - 20n 

and + 30 n 

/ - 30n 

(Fig. 10). 

These delaminations are not straight (plan) but bended. They propagate to follow the interface of 

adjacent yarns and the crimp yarns. These delaminations are considered as shear mode (mode II and III). 

Then when the number of cycles increases, another mode of delamination appeared at the other 

interfaces under a mixed-mode of delamination. This result is also a good correlation with static tensile 

test [5]. It should be noted that this study is only interest in the delamination onset.


3.2.2 Stiffness degradation 

Fig. 10. Damage mechanism at ζmax = 0.6ζR versus number of cycles in (0 o ,±30)S laminate 

After the interlaminar delamination appeared, we investigate on stiffness degradation and find that 

the modulus decrease can be divided into three stages (Fig. 11): (i) initial region (stage I) with a slightly 

decrease stiffness reduction of about 2.5%. However, we note that the precision of stiffness reduction 

measurement related with the observation techniques and then, (ii) an intermediate region (stage II), in 

which an additional about 10% stiffness reduction occurs in an approximately linear fashion with 

respect to the number of cycles. Predominant damage mechanisms are the multiplication and 

development of interlaminar shear delaminations and (iii) the final region (stage III) with a rapid 

decrease of stiffness (about 40%), and then the stiffness reduction become unstable and lead to the final 

failure of specimen. Note that increasing of max only accelerates to the stiffness degradation (Fig. 

12). 

Fig. 11. Stiffness degradation as a function of number of cycles 

215

216 

3.2.3 Delamination onset 


(a) (b) 

Fig. 12. Stiffness degradation for different ζmax (to compare with ζR) as a function of number of cycles : 

(a) (0 o ,±20)S laminate and (b) (0 o ,±30)S laminate 

In order to propose the criterion for prediction the onset of delamination under fatigue loading, we 

need to determine the relationship among the maximum applied stress ( max ), onset of delamination 

stress under tensile loading test ( onset ) and the number of cycles to delamination onset ( N a ). Then, in 

this study we use four stacking sequences (two different families of laminates each family has two 

different thicknesses). By experimental results, the number of cycles to delamination onset as a function 

of the ratio of max to onset is illustrated in Fig. 13. If the ratio of max to onset is increase, the 

early delamination onset is observed. In order that compatible with static test, the ratio of max to 

onset is equal to 1, is taken into account. To determine by curve fitting to experimental results (Fig. 13), 

the nonlinear relation between ratio of max to onset and N a can then be expressed as 

 

 

max 

R 

= 

( K ) 

K 

-( 

N -1) 

2 

1 

where K 1 and K 2 are two constant parameters, these parameters are independent 

on i.e. the stacking sequence and number of plies (thickness) but depend on the composite material 

study. 

This expresion allow to propose the fatigue delamination onset criterion base on quasi-static 

delamination onset criterion in previous research [5]. 

Fig. 13. A number of cycles to delamination onset (Na) in different stacking sequences

4. FEM analysis 

4.1 Configuration 


In first part (§4.2), the 3D finite element model of the twill-weave unit cell consists of three-phases 

(Fig. 14): the matrix phase, the warp and fill yarns. This 3D-mesh taken into account the effects of yarns 

interlacing and orientation of adjacent layers, the geometry of yarns in woven structure is measured 

directly using optical microscopy observation (Table 1.). Note that due to the complicated structure of 

weave-fabric, in particularly for crimp region, hence many numbers of finite elements are required. 

Fig. 14. 3D finite element mesh. 

Table 1. Parameters characterizing the twill-weave geometry (variables are defined in Fig. 14 dimensions in mm) 

a=b c R 

9.2 0.65 4.15 

The mechanical response of a yarn is determined and validated by tensile tests. The yarn (straight 

region) was assumed transversely isotropic and linear elastic and is given in Table 2, while the property 

of the epoxy matrix is isotropic elastic with Young's modulus equal to 3.1 GPa and Poisson‟s ratio equal 

to 0.39. 

However, the second part (§4.3), the 3D finite element model of woven ply (heterogeneous periodic 

material) are took place by equivalent homogenous ply. Their material behavior determined by 

homogenization method, as detailed in section 4.2 and 4.3, is show in Table 3. The mesh near the 

interface corner of free-edge is refined in order to represent the stresses singularity due to the free-edge 

effect. 

Table 2. Mechanical properties of a fill and a warp yarn T800s where 1 refers to the fiber direction; 2 refer to transversal direction of fiber 

E11 (GPa) E22 = E33 (GPa) G23 (GPa) G12 = G13 (GPa) v23 v12 = v13 

210.00 9.250 3.7 4.7 0.25 0.33 

Table 3. Mechanical properties of an equivalent homogeneous ply of twill-woven fabrics 

E11= E22 (GPa) E33 (GPa) G23=G13 (GPa) G12 (GPa) v23 = v13 v12 

60.53 7.795 2.685 3.231 0.489 0,03 

4.2 Numerical analysis of damage mechanism 

In order to study the effect of curved shape of the reinforcing yarns (weaving structure effect) and 

adjacent layers, also called ply nesting effect, 3D finite elements model of two layers of twill woven 

36 

217

218 


0 o -ply laminate under tensile loading in the fill direction with periodic boundary condition (see in Eq.(1)) 

are applied. The computational results demonstrate that the weaving structure effect provoke the local 

bending due to the fill yarn bundles try to straighten. Moreover, the presence of neighboring layers 

affects to change the local bending direction along the x 3 

-axis. The deformed of local symmetrical 

bending occurred in case of out-of-phase, otherwise non-symmetrical occurred in case of in-phase and 

T90 (Fig. 15). These results are a good correlation with the experimental observations in previous 

section. 

(a) (b) (c) 

Fig. 15. Deformed mesh of 3D finite element model under unloading and loading: (a) in-phase; (b) out-of-phase and (c) T90. 

Moreover, the local bending provokes local stress (or strain) concentrations which depend on the ply 

nesting. The main purpose of this paper is to be interested by investigation of out-of-phase case since 

the damage mechanisms are earlier to occur and in consequence a rapid decrease of stiffness. Fig. 16 

shows that high strain 11 occurred in the matrix phase and warp yarns nearly the region of undulation 

of fill yarns, while, the shear strains 

23 and 31 remain relatively homogeneous. On the other hand, 

non homogeneous strain 33 distribution can be observed with this maximum strain nearly the region 

of adjacent fill yarns meet. Besides that increasing of maximum 33 can be induced with increasing of 

the number of plies. Nevertheless, if woven 0 o -ply laminate is more than four-layers ( n 4 ), the 

thickness effect can be neglected. 

Fig. 16. Stress-strain distribution on out-of-phase case.


4.3 Degradation in 0 o -ply laminates 

In this section we investigate each damage mechanism, considering at critical or saturation of damage 

density, affect on the macroscopic mechanical behaviour of the material. Fig. 6 was used to describe the 

geometry of damage to provide the determination of degradation of material due to intralaminar 

delamination by using 3D finite elements method which enable to simulate the delamination developed 

in the resin epoxy and at the interface of adjacent yarns (Fig. 17). The numerical homogenization 

procedure is used to determine the global mechanical properties and the periodic boundary conditions in 

 

x - x direction were applied. We assume small deformation assumption, therefore the volume 

1 

2 

variation is quietly small. The microscopic stress Σ ij 

~ and strain E ij 

~ tensors must be the averages of the 

microscopic corresponding quantities (see in Eq.(1)). In order to simplify the study, we are also assumed 

that the macroscopic behavior is isotropic in longitudinal and transverse ( x1 and x , 2 

 

respectively). 

Besides, this study neglects the friction contact problem when intralaminar delamination appeared. 

div 

= 0 

 

= c: 

on 

 

u = E 

. x + v with v x1-x2 periodic 

 

u = E 

. x or t = 

 

. n on in x3 

direction 

 

 

. 

n x1-x2 anti-periodic on 

 

 

 

= Σ or = E 

Fig. 18 shows the strains fields in unit cell before and after the intralaminar appeared. The good 

agreement of two approaches in term of experimental observation and numerical result for damage 

deformed (Fig. 6 and 18). It should to be underline that the redistribution of strains after delamination 

appeared can be observed (Fig. 18b and 18d). The concentration of strain on vicinity of yarns 

33 

crimping and nearly at interface of two fill yarns and in matrix on vicinity warp yarns inside 

11 

specimen are vanished, on the other hand, the concentration of on warp surface yarns is increased to 

11 

allow to understand why the transverse cracks appear immediately on surface warp yarns when the 

intralamina delamination onset and why their crack is never appeared inside the specimen. 

Consequently, a good agreement of two damages developed can be observed as an illustration in 

previous section. 

(a) (b) 

Fig. 17. (a) Intralaminar delamination embedded in matrix, fill and warp yarns and (b) mesh configuration of intralaminar delamination 

219 

(1)

220 


(a) (b) 

(c) (d) 

Fig. 18. Strains fields: ε11 before (a) and after (b) intralaminar delemination onset. ε33 before (c) and after (d) intralaminar delemination onset. 

The numerical results provide to determine the elastic coefficients of homogeneous ply equivalent 

with damaged and non-damaged state to be shown in Table 4. The stiffness reduction, both in tensile 

and shear modulus by the presence of intralaminar delamination are evident. The absence of constraint 

on local bending movement due to intralamina delamination onset allow the stretching of fill yarns 

bundle to become easy, in consequence, the stiffness is considerably reduced. The stiffness reduction of 

19.3% is close to experimental results. In order to obviously compare with experimental test, we also 

simulated the case of transverse cracking. The homogenized response shows that stiffness reduction is 

slightly and can be neglect. In summary, the intralaminar delamination is predominant on the stiffness 

reduction in woven 0 o -ply laminate. 

Macroscopic behavior in unit cell 

Table 4. Damages dominants in global stiffness reduction 

Non-damage 

(GPa) 

Damage 

(GPa) 

E11 60,53 48.854 19.3 

E22 60,53 48.854 19.3 

E33 7.795 1.487 80.93 

G23 2.685 1.068 60.3 

G13 2.685 1.068 60.3 

G12 3.231 3.14 2.08 

4.4 Prediction of delamination onset under fatigue loading 

4.4.1 Introduction 

Stiffness reduction 

(%) 

In order to predict the fatigue life and degradation in the composite material, the three categories in 

previous studies are proposed: (i) empirical approach, also so-called macroscopic failure theories [6-8], 

base on static strength criteria modified to account for cyclic loading; (ii) strength or stiffness 

degradation fatigue criteria [9,10] which strength or stiffness are evaluated as a function of number of 

cyclic loading; (ii) finally actual damage mechanics fatigue theory is base on the modelling of intrinsic 

defects in the composite material [11-14]. 

The first approach is presented in the empirical method and has found widespread use in fatigue


analysis although it does not account for plastic deformation during the cyclic loading. This approach is 

usually plotted in term of S/N diagram where S is the applied cyclic stress and N is the number of 

cycles. 

The second approach of fatigue life is defined by the modified static failure criteria [15] which take 

on a similar form to the Tsai-Hill criterion and can be written: 

= 

N 

1 1 

2 2 

2 12 

1 

N + N = 

212 N N 

where 1 , 2 and 12 are the in-plane normal, transverse and shear stress, respectively. 1 , 2 

N 

and 12 are the in-plane normal, transverse and shear fatigue strength as a function given in Eq. (3). 

R R 

Where 1 , 2 

respectively. 

and 

= f ( , R, N) 

N R 

1 1 1 max 

= f ( , R, N) 

N R 

2 2 2 max 

= f ( , R, N) 

N R 

12 12 12 max 

R 

12 represent the in-plane normal, transverse and shear static strength, 

Final approach describes the evolution of material behaviour throughout fatigue cyclic loading using 

damage progressive model. This approach based on damage mechanics is used to model both the 

quasi-static and fatigue loading by using the variation of the state function, also called free energy 

function. 

The main aim of this paper is to propose of delamination onset criterion under fatigue loading base on 

the second approach using the strength degradation, or residual strength. In order to simplify the 

problem, in this study, stiffness and strength reduction due to intralaminar delamination onset will be 

neglected and the equivalent homogenous ply is used with in-plan isotropic behaviour (Table 3) 

4.4.2 Delamination onset criterion under fatigue loading 

The edge effect generally leads to the stress singularities near free-edge interface which occur when 

we use the finite element analysis method. Consequently the use of local criterion, for delamination 

onset depends on the mesh size in the free-edge area. In order to avoid the mesh-dependent of finite 

element approximation, the delamination onset criterion should not only take account of point stress but 

also their distributions. As a result, many non-local stress criteria have been developed. We can classify 

them into two categories. 

The first category of criteria [16-19] is based on the average stress, often using an integral method, 

over an area or a line. In this study non-local stress criteria corresponding to the three anti-plane stresses 

which are defines as 

y0 

1 

( y ) = ( ) d 

(4) 

ij 0 

ij 

y0 

0 

221 

(2) 

(3)

222 


where and represent three local anti-plane stresses and average anti-plane stresses at interface, 

ij 

ij 

respectively. y is the critical length over which three average stresses are determined. 

0 

Then, the second categories of criterions represented the gradient of stress singularities using the 

weight function which allow to evaluate the weight changes in quantities [20,21]. In this study, we have 

been selected based on the average stress and their gradients in the vicinity of singular point. The 

gradient effect is taken into account by the first order derivative. The non-local stresses are then defined 

as: 

 

ij 

if y = 0 

 

ij = ij ij 

(5) 

ij 

 

ij + h ( + + ) if y 0 

x y z 

where h is characteristic length for taking into account the gradient effect. Note that h depends on the 

constituents, their geometries (lamina, woven-fabrics) of composites studied. 

However, due to the main aim of this paper, we will investigate the delamination onset at interface of 

adjacent layers. As a result, we can suppose that the gradient effects have been only evaluated along the 

interface. The Eq. (5) can then be rewritten as: 

ij if y = 0 

 

ij = 

ij 

(6) 

 

ij + hif y 0 

y 

To summarize that, the average non-local stresses ( ij 

~ ) which take into the effect of gradient on a 

neighborhood are determined upon the critical length. 

The criterion that we proposed to prediction the delamination onset under fatigue loading is based on 

an extension of delamination onset criteria under quasi-static loading [5]. Fatigue tests of woven-fabrics 

angle-ply laminates were performed in previous section. The interface of delamination onset and the 

number of cycles to delamination onset have been recorded. We assume that each ply remains 

undamaged until the onset of delamination and the interlaminar tensile and shear strength of the 

interface, which consist of three modes (I, II, III) and are determined by static tests, are damaged under 

fatigue loading. This degradation is related as a function of max , R , N and frequency (f) . The 

delamination onset criterion under fatigue loading is then introduced as: 

F3 + 

2 

F1 + k1 F3 - 

2 

F2 + k2 F3 

- 

2 

Fatigue 

T ( ,f , , max) Fatigue 

1 ( ,f , , max) Fatigue 

2 ( ,f , , max) 

 

+ + = 1 

Y N R S N R S N R 

 

In this study, R and f are constant at 0.1 and 1 Hz, respectively, to be able to simplify the equation 

above and to be rewritten as: 

where 


Y T , 


S1 and 

+ 

2 

- 

2 

- 

2 

3 1 + 1 3 2 + 2 3 

F F k F F k F 

+ + = 1 

Y f ( N, ) S f ( N, ) S f ( N, 

) 

T 1 max 1 2 max 2 3 max 


S 2 represent the intralaminar tensile (mode I) and shear (mode II and 

III) strengths under cyclic loading, respectively, while YT S and S de II and III) are the intralaminar 

1 

2 

(7) 

(8)


tensile (mode I) and shear (mode II and II) under quasi-static, respectively. f N, 

) , f N, 

) 

1( 

max 

2 ( max 

and f N, 

) are the degradation function of interlaminar strengths as mode I, II and III, 

3 ( max 

respectively. Assume that three modes are the same rate of degradation. In the same way as for static 

loading, two modes of interlaminar shear strength were assumed to be identical ( S ) 

can then be rewritten as: 

+ 

2 

- 

2 

- 

2 

3 1 + 1 3 2 + 2 3 

F F k F F k F 

+ + = 

Y S S 

T 

1 

( f( N, 

) ) 

max 

2 

223 

S = . The Eq. (8) 

In order to determine the degradation function, woven angle-ply laminate chosen are represented the 

predominant shear mode (III) to allow to neglect both mode I and mode II. Consequently, the criteria in 

the Eq. (9) can be simplified as: 

where 13 is the nonlocal stress, 

13 

 

 

S 

Non local 

= f( N, 

) 

max 

2 

(9) 

(10) 

13 and ~ 13 , at interface of delamination onset while S is the 

static interlaminar shear strength which are determined by non local method. Due to undamaged and 

in-plane isotropic behavior assumption until the delamination onset, it is useful to be able to determine 

the relation in Eq. (10) by the experimental results (macroscopic stress), (Fig. 13). The degradation 

function of interlaminar strength under fatigue loading is given as: 

 

S Non local 

max 

= = f N = 

onset Macroscopic 

( ) 1,032 N 

1 

-( -1) 

3 

By substituting Eq. (11) into Eq. (9), we obtain the criterion for free-edge specimens as: 

+ 

2 

- 

2 

- 

2 

1 

3 1 1 3 2 2 3 -( -1) 

3 

1,032 N 

F F + k F F + k F 

+ + = 

Y 

 

T 

S S 

 

In order to apply this criterion in Eq. (10) to circular-hole specimens, the interlaminar tensile and 

shear strengths in static case are modified. The transformation of coordinates as a function of angle of 

is used. is defined as illustrated in Fig. 19. The delamination onset criterion during fatigue 

loading applied to circular-hole specimens is therefore shown in Eq. (13). 

Fig. 19. Configuration of circular-hole specimens. 

2 

(11) 

(12)

224 


+ 

2 

- 

2 

- - 

( F3 ) ( F3 ) F F ( cos + sin ) F F ( cos -sin 

) 

+ + + 

Y S / (2 k ) S / (2 k) S / (2 k) 

2 3 1 3 

2 

T 

2 2 2 2 

( F ) ( F ) 

2 2 

1 

2 

2 

1 

2 

-( N -1) 

3 

1,032 

 

+ + = 

S S 

5. Prediction of delamination onset in circular-hole specimens 

2 

This section an overview of the experimental tests and numerical simulations in circular-hole 

specimens is in order to validate the delamination onset criterion which was identified in previous 

section under cyclic loading. 

5.1 Experimental procedure 

The specimen geometry for the open hole fatigue test had a hole diameter ( ) of 10 mm, a length ( L ) 

of 270 mm and a width ( l ) of 30 mm. The maximum applied stress at 0. 

6 

R 

0 , 30 

, at 0. 

65 

R 

and ( ) s 

max = for ( 2 ) s 

0 , 30 

and at 0. 

7 

R 

(13) 

0 , 20 

max = for ( ) s 

0 , 20 

were 

max = for ( 2) 

s 

preformed. The circular hole specimens polished prior to testing are observed at different number of 

cycles level i.e. 100, 500,1000, 5000, 1000, … etc. with the mirror which allow its to rotate around the 

axe (Fig. 20a, 20b). The angle observation ( ) is defined in Fig. 20c. The = 0 

is parallel to the 

applied load direction. 

5.2 Damage mechanism 

(a) (b) (c) 

Fig. 20. (a) Experimental setup; (b) Scheme of observation method; (c) Observation zone defined. 

The experimental observations of fatigue tests show that all specimens, whether the different 

thickness layers and stacking sequences, consist of three major damage (Fig. 21): intra-ply cracking 

(“a”), the intra-ply delamination (“b”) and finally inter-ply delamination (“c” and “d”). The effect of 

stacking sequence and thickness layer on the typical damages can then be neglected. Several intra-ply


cracks firstly occur in the surface yarns. Then, the interlaminar delaminations occur in both interfaces, 

and finally their developed will joined with the intralaminar delamination which generally occur to 

follow along the curved yarns in ply (lamina). 

It should be underline that typical damage mode of delaminage at the interfaces + 20 / 

-20 

and + 30 / 

-30 

is more difficult to observe due to interlaminar shear mode (mode III) representing the 

crack edges sliding without open mode. Consequently, the number of cycles to delamination onset 

determined in experimental testing remains uncertain. Thickness effect is no significant for delaminate 

onset location and the number of cycles to delamination onset, as shown in Table 5. On the other hand, 

we have found to affect significantly on the number of cycles to delamination onset with increasing the 

maximum stress level. 

Stacking sequence Interfaces 

(0,±20)S 

(0,±202)S 

(0,±30)S 

(0,±302)S 

Table 5. Experimental results during fatigue loading 

Position of delamination 

onset (α o ) 

0/+20 92 à 125 2000 – 3000 

±20 83 à 97 260 - 700 

0/+202 98 - 120 1660 - 3050 

±202 84 - 100 125 - 450 

0/+30 94 - 121 340 – 800 

±30 82 - 100 215 – 600 

02/+302 85 - 127 587 - 1250 

±302 85 -95 50 – 220 

Number of cycles to delamination 

onset (Nd) 

While, the interfaces 0 / + 20 

and 0 / + 30 

, the delamination occur as a mixed mode 

representing not only crack edge sliding but also crack edge opening. The open mode is generally easier 

to observe because delaminations propagation, after their initiation, are spontaneous and rapid to allow 

clearly visualize. 

(a) 

(b) 

Fig. 21. Damages mechanisms of fatigue loading for different stacking sequences: (a) (0 o ,±30 o ) at 3000 cycles and (b) (0 o ,±30 o 2)S at 2000 cycles 

225

226 


5.3 Delamination onset prediction: location and number of cycles 

In order to carry out an in-depth understanding of damage mechanisms at edge of circular hole, the 

finite element method has been use. A uniform tensile stress, also called the macroscopic stress 

simulated, was applied along the direction of x1 -axis (longitudinal axis) of circular test specimen. All 

specimens show that the same regions of stress/strain distributions are illustrated. Fig. 22, in case of 

, 20 

) s laminate, shows high concentrations of 11 and 11 

( 0 

can be observed at = 90 

around free-edge and nearly circular area (Fig. 22a). Then we can also observe the strong stress 

singularities of 33, 

23 and 13 at the interface between adjacent layers as shown in Fig. 22b, c 

and d, respectively. These stresses relate directly to the delamination onset as explained in previous 

section. 

(a) (b) 

(c) (d) 

Fig. 22. Distributions of stress-strain for (0 o ,±20 o )S laminates around a free-edge and nearly circular hole area (-90 o ≤α≤90 o ) (0 o ,±20 o )S: 

(a) ε11; (b) ζ33; (c) ζ23; and (d) ζ13. 

The numerical results of all stacking sequences of a laminate composite show the good accuracy of 

location predictions to delamination onset compared with the experimental results, as example illustrate 

in Fig. 23 for ( 0 , 30) 

s laminate case. The two approaches criterion, with and without gradients, 

predict to the same location of delamination onset. The numerical results show also a good correlation 

in term of damage mode (I, II and III) with experimental results. 

For the prediction of number of cycles to delamination onset, there is a good correlation between the 

numerical results and experimental observations. The close predictions obtained for 0 / 20 

and 

0 / 30 

interfaces while the slight prediction error of + 20 / 

-20 

and + 30 / 

-30 

interfaces can 

be found (Table 6). We suppose that the slight prediction error is caused by a typical mode III-type of 

delamination onset which is dominant in these interfaces. Consequently, this mode of delamination 

onset is more difficult to observe due to the closing mode. To overcome this problem, high accuracy 

observation techniques like acoustic emission are necessary.


Stacking sequence Interfaces 

(0,±20)S 

(0,±202)S 

(0,±30)S 

(0,±302)S 

Table 6. Numerical result for prediction of delamination onset under fatigue loading 

Numerical results of number of cycle to delamination onset 

h = 0,0 h = 0,01 h = 0,02 h = 0,03 

0/+20 3280 3800 10800 11500 

+20/-20 150 600 2100 2900 

0/+202 3200 3700 9010 9600 

+202/-202 0 18 350 560 

0/+30 250 450 2000 2400 

+30/-30 17 135 375 650 

02/+302 370 600 1950 2350 

+302/-302 0 0 2 15 

(a) 

(b) 

(c) 

Fig. 23. Delamination onset in (0 o ,±30 o )S laminate around a free-edge circular hole: (a) experimental observed; (b) and (c) numerical prediction 

at interface 0 o /30 o and +30 o /-30 o , respectively 


An experimental investigation and FEM in two families, unidirectional and angle-ply 2/2 twill weave 

227

228 


T800 carbon/epoxy woven fabric composites laminates, under fatigue loading have been presented in 

this paper. This study can be summarized as follow: 

(1) Unidirectional woven fabric composite laminates: 

Effect of thickness ( n 4 ) for variation of rigidities, the thresholds of damage in 0 o -ply 

laminate is neglect; 

Increasing the maximum applied stress accelerates the stiffness reduction and the damage 

evolution; 

The cracking in warp yarn and the intralaminar delamination are the major damage; 

The numerical simulation with FEM was used to investigate the woven effects on the 

out-of-phase case and show that the local bending provokes the local stress (or strain) 

concentrates which have a good correlation with the damage zone in experimental observation; 

The homogenization methods applied to the damaged material show that the stiffness reduction 

of 20% is caused by the delamination. This result is a good agreement with experimental 

testing. 

(2) Angle-ply woven fabric composite laminates: 

Due to the high interlaminar normal and interlaminar shear stress gradients at the free-edge 

region, the inter-ply delamination represent as the main damage to allow the stiffness reduction 

and final break. Increasing of number of plies (thickness effect) does not affect to the damage 

mechanism; 

The fatigue non-local criteria model (with and without gradient), which are identified the 

parameters by experimental Edge Delamination Tests (EDT), have been proposed to predict 

the delamination onset and to overcome the mesh-dependence problems; 

Validation criteria was applied on the circular-hole specimens and shown a good prediction the 

position of delamination onset. For the prediction of number of cycles to delamination onset, 

the close predictions obtained for 0 / 20 

and 0 / 30 

interfaces while the slight prediction 

error of + 20 / 

-20 

and + 30 / 

-30 

interfaces can be found due to precision error which 

occurs from the difficult observation of delamination onset in shear mode. 

We propose high accuracy observation techniques like the acoustic emission which allow more 

accurate monitoring and early detection of decohesion or slipping in shear mode within the material. 

Emission acoustic technique has many advantages such as in situ monitoring without removing the 

specimen and accuracy of damage detection. But the difficulty is to correlate between the acoustic 

signals and the typical damages. 


We gratefully acknowledge ADEME (Agence de l‟Environnement et de la Maîtrise de l‟Energie) for 

support from ARMINES Centre des Matériaux, in the project LICOS and ALSTOM.

References 


[1] Nicoletto, G. et Riva, E., “Failure mechanisms in twill-weave laminates: FEM predictions vs. experiments”, Composites: Part A, vol. 35, p. 

787-795, 2004. 

[2] Kelkar, A.D., Tate, J.S. et Bolick, R., “Structural integrity of aerospace textile composites under fatigue loading”, Material Science and 

Engineering B, vol. 132, p. 79-84, 2006. 

[3] Alif, N., Carlsson, L.A., et Boogh, L., “The effect of weave pattern and crack propagation direction on mode I delamination resistance of 

woven glass and carbon composites”, Composites:Part B, vol. 29B, p. 603-611, 1998. 

[4] Pandita, S. D., Huvsmans, G., Wevers, M., et Verpoest, I., “Tensile fatigue behaviour of glass plain-weave fabric composites in on- and 

off-axis directions”, Composites: Part A, vol. 32, p. 1533-1539, 2001. 

[5] Pongsak, N., “Dimensionnement en fatigue des structure ferroviaire en composites épais”, PhD thèse, Ecole des Mines de Paris, 2009. 

[6] Fawaz, Z et Ellyin, F., “Fatigue failure model for fibre-reinforced materials under general loading conditions”, Journal of Composite 

Materials, vol. 28(15), p. 1432-1451, 1994. 

[7] Demers, C.E., “Tension-tension axial fatigue of E-glasse fibre-reinforced polymeric composites : fatigue life diagram”, Construction and 

Building Materials, vol. 12, p. 303-310, 1998. 

[8] Bond, I.P., “Fatigue life prediction for GRP subjected to variable amplitude loading”, Composites: Part A, vol. 30, p. 961-970, 1999. 

[9] Philippidis, T.P. et Vassilopoulos, A.P., “Fatigue of composite laminates under off-axis loading”, International Journal of Fatigue, vol. 21, 

p. 253-262, 1999. 

[10] Broutman, L.J. et Sahu, S., “A new theory to predict cumulative fatigue damage in fiber glass reinforced plastics”, Composite materials: 

testing and design, (2nd conference). ASTM STP, 497, p. 170-188, 1972. 

[11] Talreja, R., “Fatigue of polymer matrix composites”. Comprehensive Composite Materials, Chapter 2.14, p. 529-552, 2003. 

[12] Thionnet, A. et Renard, J., “Laminated composites under fatigue loading : a dammage development law for transverse cracking”, 

Composite Science Technology, vol. 52, p. 173-181, 1994. 

[13] Thionnet, A. et Renard, J., “Modelling of the fatigue behaviour of laminated composite structures” In : Degallaix, S., Bathias, C. et 

Fougères, R. (eds.). International Conference on fatigue of composites. Proceedings, 3-5 June, Paris, Frace. La Société Français de 

Métallurgie et de Matériaux, pp. 363-369, 1997. 

[14] Caron, J.-F., “Modélisation de la cinétique de fissuration transverse en fatigue dans les stratifiés”, PhD thèse,Ecole Nationale des Ponts et 

Chaussées, 1993. 

[15] Hashin, Z. et Rotem, A., “A fatigue criterion for fibre reinforced composite materials”, Journal of Composite Material, vol. 7, p.448-464, 

1973. 

[16] Lorriot, Th., Marion, G., Harry, H., et Wargnier, H., “Onset of free-edge delamination in composite laminates under tensile loading”, 

Composites:Part B, vol. 34, p. 459-471, 2003. 

[17] Kim, R.Y., and Soni, S.R., “Experimental and Analytical Studies on the onset of delamination in laminated composites”, Journal of 

Composites Materials, vol. 18, p. 71-80, 1984. 

[18] Brewer, J.C. et Lagace, P.A., “Quadratic Stress Criterion for Initiation of delamination”, Journal of Composite Materials, vol. 22, p. 

1141-1155, 1988. 

[19] Joo, J.W., “A failure Criterion for laminates governed by free edge interlaminar shear stress”, Journal of Composite Materials, vol. 26(10), 

p. 1510-1522, 1992. 

[20] Bažant, Z.P. et Pijaudier-Cabot, G., “Nonlocal continuum damage, localization instability and convergence”, Journal of Applied 

Mechanics, vol. 55, p. 287-293, 1998. 

[21] Germain, N., Besson, J., Feyel, F. et Maire, J.F., “Méthodes de calcul non local appliquées au calcul de structures composites”, 

Compiègne JNC14, vol. 2, p. 633-640, 2005. 

229

Abstract 

Fatigue life assessment via ply-by-ply stress analysis under 

biaxial loading 

F Schmidt *, T J Adam, P Horst 

Institute of Aircraft Design and Lightweight Structures, Technische Universität Braunschweig, 

Hermann-Blenk Straße 35, 38108 Braunschweig, Germany 

A new modelling approach for calculating the stress redistributions due to matrix cracking within the fatigue life of a 

slightly non-symmetric composite is presented. Thereby, a ply-by-ply stiffness degradation model and an analytical 

engineering approach allowing the layer-wise calculation of lamina stresses are applied. The result is a single 

lamina-based S-N curve of the critically stressed layer (predominant fibre-parallel stresses) indicating the overall 

laminate failure under fatigue loading. Using experimentally fatigue loaded tube specimens under biaxial loading 

provides the fatigue damage information (crack densities depending on the biaxial stress ratio) adopted in the modelling 

approach. The application and a validation of the modelling approach are shown. 

Keywords: Polymer matrix composites; multiaxial fatigue; fatigue modelling; stress analysis 


It is well known that the number and variety of applications of fibre-reinforced materials are 

increasing steadily. At the same time the demand for safety and design rules is growing. Due to the lack 

of reliable life-prediction methods, resulting uncertainties in fatigue life make the sizing of structural 

components exposed to dynamic loads quite problematic. The reason is the complexity of the fatigue 

process which involves several individual and interacting damage mechanisms such as matrix cracking, 

delamination and fibre fracture. Moreover, the occurrence and accumulation of these damage 

mechanisms strongly depend on certain load parameters as e.g. the stress amplitude, the multiaxiality of 

stresses, the stress ratio and the frequency. Several authors divide the main fatigue behaviour (stiffness 

degradation) as well as damage development into three phases [1-4]. The fatigue damage and stiffness 

scenarios show the initiation and progression of transverse cracks with sharp tips and a steep decrease in 

stiffness (stage I), the development of local delaminations caused by transverse cracks and an almost 

linear decline in stiffness (stage II) and the concurrence of resulting local delamination surfaces with the 

final failure (stage III). These damage mechanisms and fatigue behaviours are used for fatigue models. 

Degrieck et al. [5] and Quaresimin et al. [6] review fatigue damage models and life assessment, where 

Quaresimin describes the fatigue behaviour under multiaxial loadings. Although most fatigue stress 

states in structural components possess a multiaxial nature, the fatigue behaviour under multiaxial 

* Corresponding author. Tel.: 0049-531-391-9921; fax: 0049-531-391-9904. 

E-mail addresses: frank.schmidt@tu-bs.de (F Schmidt), tj.adam@tu-bs.de (tj.adam@tu-bs.de), p.horst@tu-bs.de (P Horst)

F Schmidt, T J Adam, P Horst. / Fatigue life assessment via ply-by-ply stress analysis under biaxial loading 

conditions is far less investigated. That leads to further researches by Adden et al. [7] establishing a 

ply-by-ply stiffness degradation model. Concerning the major deterioration steps in composite fatigue 

depending on matrix cracking, delamination and fibre fracture, firstly the process of matrix cracking is 

taken into account. By adopting this model in the current work a theoretical bottom-up ply-by-ply 

approach for calculating the change of the internal stresses (assuming linear elasticity) of each layer 

caused by increasing crack densities is proposed. Using a lamina-based S-N curve of a critical stressed 

lamina – independent of the loading direction – leads to a prediction of the fatigue life of the overall 

laminate, whereas the local fibre-parallel stress in the layer serves as input parameter. Concerning the 

common denotation a lamina is defined to be a single unidirectional layer within the overall laminate. 

The required damage data for modelling validation is provided by fatigue experiments with NCF tube 

specimens and different biaxial and uniaxial load ratios. An important fact for the current modelling 

approach presented in this paper is, that NCFs can widely be treated like non-stitched laminates, when 

looking at their behaviour [8,9]. 

2. Material and testing procedure 

The specimens used in the experiments are tubes made of glass-fibre (roving OC111A from OWENS 

CORNING) non-crimped-fabrics. Each layer of the NCF provided by SAERTEX consists of four 

sub-layers, whose lay-up and relative mass fractions are shown in table 1. Two of these 

non-crimped-fabric layers form the investigated slightly antisymmetric lay-up 

[0 o ,-45 o ,90 o ,45 o ,-45 o ,90 o ,45 o ,0 o ]. The sub-layers are tied together with a tricot-type of stitching whereas 

the material of the stitching yarn is poly-ether-sulfone (PES). 

Table 1. lay-up of the used non-crimped-fabric 

Orientation ( o ) Mass per unit area (g/m 2 ) Relative mass fraction (%) 

0 638 49 

-45 301 23 

90 63 5 

45 301 23 

Using the common resin/hardener combination RIM135/RIMH137 from HEXION, which is for 

example used in the rotor blade manufacturing of wind-energy plants, the specimens with a diameter of 

46 mm and a length of 330 mm are manufactured by resin transfer moulding (RTM). Thereby, the tube 

specimens consist of two layers of the above mentioned NCF, which are wrapped around a mandrel with 

the inner and outer 0 o -angled plies of the NCF being parallel to the axial direction of the tube specimens. 

In further production steps, both ends of the tube specimens are reinforced by GFRP-doublers and 

bonded steel inserts of 70 mm length in order to prevent failure due to the fixing pressure of the testing 

machine. This type of specimens allows the investigation of biaxial loads with arbitrary load ratios and 

minimizes the so-called free-edge effect known from flat specimens. Moreover, the development of 

matrix cracks due to different fibre orientations in the NCF is expected (caused by the high intra- and 

interlaminar occurring stresses). As a consequence of the matrix crack development the overall material 

stiffness of the tube specimens decreases, which leads to interlaminar stress redistributions. 

231

232 


The mechanical tests are performed with a servo-hydraulic tension-torsion machine. By using 

different ratios of axial forces and torsional moments arbitrary multiaxial load ratios can be applied. All 

fatigue tests are performed in a force-controlled manner with R=-1 and a frequency of 2 to 5 Hz. In 

order to distinguish different load cases, the biaxiality ratio (parameter β) is introduced as follows: 

β = arctan 

( τ ) 

This is to say, the angle between the shear stress η and the tensile/compressive stress ζ indicates the 

different biaxial load cases. Hence, β=90 o means pure shear and β=0 o pure tension/compression loads. 

The other load cases are β=60 o (combination of tension/compression and torsion with a predominant 

shear part) and β=30 o (also a combination of tension/compression and torsion with the 

tension/compression part being dominant). For each load ratio fatigue testing is performed at different 

load amplitudes leading to low-cycle and high-cycle fatigue. 

σ 

Fig. 1. protocol of fatigue loading. 

In order to monitor the matrix crack development and to estimate the material stiffness, all fatigue 

tests are divided into three main steps (see Fig 1): the characterization step, the fatigue damage step and 

the discrete damage monitoring. The characterization steps are quasi-static tests conducted with 

force-controlled ramps (pure discrete tension/compression force and positive/negative torsion moments) 

in order to monitor the current material stiffness. These loads are chosen in a way that the loading is 

adequate for calculating the Young‟s and shear modulus, whereas it is considerably smaller than the 

applied cyclic load in the fatigue damage steps. Within the fatigue damage steps, cyclic loads (sinus 

wave form) with constant amplitudes and different biaxial load ratios are applied to introduce fatigue 

damages like matrix cracking, delaminations and fibre fracture. Matrix cracking indicated by the 

so-called crack density is the first occurring type of fatigue damage and is monitored stepwisely 

(discrete damage steps). Based on the nearly similar refraction indices of resin and glass fibre used for 

the tube specimens, the specimens are transparent and matrix cracks are observable via transmitted light 

method using an optical microscope (ZEISS Stemi 2000-C). Therefore, the fatigue tests are stopped


after several fatigue damage steps and the specimens are taken out of the tension-torsion testing 

machine. Up to 15 different areas of the specimens are monitored and the matrix cracks are counted 

using photographically documented cracking states. Differentiating the visible cracks by their 

orientation angle leads to the numbers of cracks of each single-layer direction (0 o , -45 o , 90 o and 45 o ). 

These numbers of cracks are referred to the size of the digital picture to calculate the crack densities of 

each layer direction. Then, all area- and layer-specific crack densities are averaged to obtain the overall 

layer-specific crack densities of each specimen. 

3. Modelling of stiffness degradation 

A finite-element-based analysis method to describe the stiffness degradation of a cracked 

unidirectional single-ply is developed by Adden et al. [7] and serves as a basis for further calculations of 

stress redistributions in composites under fatigue loading when linear-elastic behaviour is assumed. 

Using the technique of the representative volume element (RVE) leads to the computation of the 

stiffness degradation of one single-layer dependent on a parameter D. This so-called damage parameter 

D is a main result of the RVE approach and is equal to the product of crack density δ and ply thickness. 

It follows: 

D= t 

Concerning the set up of the model the RVE consists of two outer layers (0 o -orientation, no cracks) as 

supporting layers and one embedded single-ply (90 o -orientation) with two transverse cracks. Different 

crack densities δ are modelled by changing the RVE lengths while keeping all other dimensions and the 

number of cracks constant. By applying periodic boundary conditions by Garnich and Karami [10], 

energy-based homogenization methods and six different load cases (three normal stresses according to 

the ply axes and three corresponding shear stresses) the mechanical elasticity parameters of the inner 

cracked single-ply is calculated independently from the supporting layer. Furthermore, the relation 

between the damage parameter and the corresponding decline of stiffness is proposed to be expressed by 

the following degradation function: 

1 

1 c D = 

+ 

Here c and ξ are material parameters found by curve fitting. The application of this degradation 

function leads to the elasticity constants of a damaged unidirectional single-ply calculated for a given 

crack density. Adden et al. [7] show that transverse matrix cracks cause the degradation of five elastic 

parameters (E22, υ12, υ32, G23 and G12) of the cracked single-ply whereas the other components are not 

affected (see figure 2). This behaviour is transferred to other lay-ups in recent researches [11] and can 

be used for the specimen lay-up mentioned above. 

4. Laminate degradation modelling and ply-by-ply stress analysis 

As mentioned above, an analytical approach for calculating layer-wise average stresses in cracked 

laminates based on the single-ply stiffness degradation model by Adden et al. is presented. The basic 

idea consisting in modelling a multi-angle laminate by means of single-layer degradation and 

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experimentally observed crack densities is shown in figure 3. Subsequently, the global laminate 

behaviour is calculated using the single-layer degradation (described throughout the fatigue life) and a 

suitable laminate theory (comprising the single-layer orientations and thicknesses). In the current work 

the classical laminated plate theory (CLPT) is applied, whereas another research [11] shows the 

application of the described modelling approach for an extended three-dimensional laminated plate 

theory by Lin [12]. 

Fig. 2. degradation of elasticity parameters. 

Fig. 3. laminate degradation modelling approach. 

When dealing with fibre-reinforced multi-layered composites two different coordinate systems have 

to be distinguished. The first one is the global xy- or laminate coordinate system, where x denotes the 

length and y the width. The second coordinate system is the local or unidirectional 12-coordinate system. 

When describing the single-layer all properties are related to this local system. Thereby, 1 stands for the 

fibre-parallel direction and 2 for the in-plane fibre-normal direction. All properties follow a fixed 

notation rule, e.g. υ12 is a lateral contraction in direction 1 caused by a load along the 2-axis.


Modelling assumptions and main calculation strategy 

For calculating the mechanical behaviour of damaged composites with the analytical model, several 

assumptions have to be introduced. As mentioned above, the CLPT is applied in the current work and 

consequently only three elastic parameters (E22, υ12 and G12) of the modelling approach by Adden et al. 

[7] are considered for the calculation of the stiffness degradation and stress redistribution under fatigue 

loads. However, this simplification leads to sufficient results compared to the extended 

three-dimensional laminated plate theory [11]. Furthermore, it is assumed that linear elastic material 

behaviour is maintained throughout the fatigue life when considering discrete damage states. All 

discrete damage stages are characterized by the ply-specific damage parameter (calculated with the 

experimentally observed ply-specific crack density and the single-layer thickness) and a fixed loading 

which is equivalent to the maximum amplitude of the cyclic loading. Using the experimental stress ratio 

of R=-1 for all multiaxial fatigue tests leads to two different maximum amplitudes of the global stress 

states of the same biaxial stress ratio, one in tension and one in compression. Therefore, the local stress 

components of each single-ply are either tensional or compressive depending on the global loads and 

the lamina orientation angle. This determination affects the suggested model. As the single-layer elastic 

modulus E22 only degrades depending on the transverse crack opening under tensile stress, no loss of 

E22 is expected under compressive loads. Consequently, the transverse stresses ζ22,k of each lamina 

determine whether E22 has to be degraded or not. 

Furthermore, it is assumed that the stepwise damage state-based stress analysis of a continuously 

damaged material/load system reveals the processes of interlaminar stress redistributions. As a result of 

stress redistributions a so-called critical layer (layer with maximum fibre-parallel normal stress or shear 

stresses) forms causing the whole laminate to fail. For this reason it is particularly important to take the 

stress redistributions caused by the matrix cracking into account for calculating S-N curves (just 

considering the critical layer and lamina-based S-N curves) of composites under multiaxial fatigue 

loads. 

As schematized in figure 4 the main calculation strategy consists of four steps arranged on the meso 

(single-layer) and the macro (laminate) scale. The first step is the calculation of all undamaged and 

damaged single-layers with the rules of mixture (given in the German guideline VDI2014 [13]) as 

homogenization tool and so the full set of elastic moduli is obtained from the material properties (fibre 

and resin). By adopting the degradation model introduced in section 3 and by applying layer- and 

step-specific crack densities the elastic constants of the damaged single-layers (exponent D) are derived 

from the elastic constants of the undamaged single layers. Then the properties of the global laminate are 

calculated with the CLPT in step 2. Thereby, the multi-layer angle laminate is composed by coordinate 

transformation and homogenization leading to the laminate stiffness matrix ( ABD ). This overall 

stiffness matrix consists of the extensional stiffness matrix ( A ), the coupling stiffness matrix ( B ) and 

the bending stiffness matrix ( D ). Having the mechanical properties of the damaged laminate, the 

laminate and single-layer reactions along the global xy-coordinate system are determined in the third 

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step. Therefore an external load vector xy, L is designated and multiplied with the inverted laminate 

stiffness matrix 

D -1 

ABD to calculate the laminate strains xy, L . Due to the assumption of stress 

and displacement continuity at the interfaces of the laminas all layers have equal strains in the x- and 

y-direction. Thus, in a physical parallel connection the layer-wise strains xx, k are identical to the 

laminate strains xx, L . For the estimation of the single-layer stresses and the identification of critically 

stressed layers (step 4), the calculated strains xx, k 

have to be transformed for each lamina to OA, k 

(OA stands for local lamina coordinate system) using the transformation rule of the CLPT. Subsequently, 

the lamina-specific stress vector OA, k is calculated by multiplying the damaged lamina-specific 

stiffness matrix 

D 

S OA, 

k 

and the strain vector OA, k . With all lamina-specific stress states calculated for 

a discrete point of time (or more precisely for all lamina damage states belonging to a discrete number 

of load cycles) a maximum stressed lamina can be identified. 

Fig. 4. stepwise laminate degradation modelling and ply-by-ply stress analysis 

Furthermore, using experimentally obtained crack densities and repeating the complete operation for 

a series of discrete load cycles leads to the behaviour of moduli, strains and stresses throughout the 

fatigue life and over the number of cycles. Several conclusions on the processes of stress redistribution 

caused by fatigue damage and a critical layer formation can be shown by analyzing the results of the 

analytical modelling approach. Until now, fatigue life prediction approaches (stress-based S-N curves or 

strain-based fatigue life diagram) usually refer to the laminate behaviour, however, here the S-N method 

is proposed to be a universal lamina-based one just considering the critical layer. 

5. Experimental results 

As already mentioned, a ply-by-ply stress analysis for antisymmetric composite laminates under


multiaxial fatigue loading is conducted. Thereby, all investigations are based on crack data obtained by 

several experimental fatigue tests of biaxially loaded (biaxial stress ratios β = 30 o , 60 o and 90 o ) tube 

specimens made of non-crimped-fabrics. 

Varying the biaxial loads leads to different crack developments for all layer orientations and to 

individual and layer specific crack densities [7]. Under tension loads the matrix cracking in the 45 o , -45 o 

and 90 o -layers shows a quite usual behaviour, i.e. a very rapid increase of the crack densities to the 

highest absolute values in the most damaged layers within approximately the first 10-15 % of the 

lifespan. A significant amount of cracks in 0 o -directions is not visible. Regarding the monitored matrix 

cracking under biaxial loads (predominant shear part) it can be shown that the crack densities reach 

lower absolute values and that matrix cracking develops in the 0 o -directions, as well. This obviously 

results from the intralaminar loading of the 0 o -layes. Thus, according to the layer-specific crack 

densities the experimental degradations of Young‟s and shear moduli are dependant on the biaxiality 

ratio. 

Each layer in the laminate is degraded according to the monitored discrete damage steps in the fatigue 

life using the modelling approach presented in section 4 and the experimentally obtained crack densities. 

Then, homogenizing all lamina stiffnesses leads to the fatigue behaviour of the overall laminate for 

different load cases. The experimentally observed laminate behaviour can be calculated by a 

single-layer degradation quite well [7] and comparable results are obtained for the current researches. 

After the validation of the stiffness degradation behaviour the laminate reactions are computed in the 

next step. Thereby, applying the biaxial load cases leads to the overall laminate strains which are 

transferred to the single layers. By means of the degraded lamina stiffness established in the first 

modelling step, the intralaminar stress states are calculated for each single-ply. Due to the different 

degradation behaviours of the plies (dependent on the matrix cracking and the external biaxial load case) 

the initial lamina stress states change during the fatigue life and stress redistributions are expected. The 

ply-specific stress states and the changes in stresses (caused by the increasing matrix cracks in the layers) 

for a specimen subjected to a biaxial loading (β = 30 o ) are depicted exemplarily in figure 5. Here, a 

positive prefix marks tension and a negative prefix stands for compressive stresses. The initial stress 

state (ζ11, ζ22 and η12) of each ply is calculated for the undamaged laminate whereas the stress 

magnitudes depend on the external biaxial loads (here: a combination of tension and positive shear 

loads). Within the first 20-30 % of the life span matrix cracking increases rapidly and the highest rate of 

stress redistributions can be observed. Afterwards, the crack densities reach saturation and the change of 

lamina stresses decreases until final failure occurs. The highest fibre parallel tensional stresses ζ11 are 

obtained for the 45 o -layers, which increase about 19% during the first part of the fatigue life up to the 

final failure. Furthermore, the fibre parallel compressive stresses ζ 11 of the -45 o -layers (resulting from 

the transverse contraction of the laminate) increase by about 22 %, whereas the absolute value is 

significantly smaller than the value of the 45 o -layers. All other stress components of the 45 o - and 

-45 o -layers are small. Taking a closer look at the stress components of the 0 o -layers an increase of fibre 

parallel tensional stresses with progressive stiffness degradation is observed as well. In general, all fibre 

parallel lamina stress components ζ11, which are crucial for the final failure, increase due to the 

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decreasing lamina stiffness E22 and the resulting reduction of the transverse matrix stresses ζ22. Thus, 

the presented model approach allows to calculate the influence of matrix cracks on the stress 

development of each single-layer under fatigue loads. By means of the modelling approach the stress 

redistributions in any arbitrary composite with experimental crack densities can be analyzed. 

In figure 6 an explicit comparison of the initial stress state and the stress values at the end of the 

fatigue life is illustrated. Additionally, the differences of the single-layer stresses caused by external 

biaxial loads are shown. On the left hand side of figure 6 the change of stresses (caused by the matrix 

cracks) for a biaxially loaded specimen (β = 30 o ) is plotted. Due to the high tension part of this biaxial 

load ratio the 0 o -layers and the 45 o -layers reach the highest stress values. Considering the antisymmetric 

lay-up of the specimen the stress values of the single-layer depend on the relative position to the 

reference plane (see CLPT and the matrix of coupling stiffnesses). Thus, the stress values of the 

45 o -layers (and -45 o -layers) are different. In this example the highest fibre parallel stresses ζ11 are 

calculated for the inner 45 o -layer. As all shear stresses η12 are relatively small it can be assumed that the 

fibre parallel stresses ζ11 are crucial for the final failure of a single layer which leads to final failure of 

the overall laminate. Additionally, the 45 o -layers show the highest increase caused by observed matrix 

cracking and the inner 45 o -layer is clearly identified as the maximum stressed and critical layer in 

fatigue. As schematized on the right hand side of figure 6 the highest stress values are reached in the 

inner 45 o -layer for the biaxial load ratio of β = 60 o as well. 

a) stresses of one 0 o -layer b) stresses of one 45 o -layer 

c) stresses of one 90 o -layer d) stresses of one -45 o -layer 

Fig. 5. stress redistribution of single layers during fatigue life of one specimen (biaxial load ratio β = 30 o ).


a) biaxial load ratio β = 30 o b) biaxial load ratio β = 60 o 

Fig. 6. initial and end state stresses of specimens under different biaxial load ratios. 

Fig. 7. comparison of fibre-parallel stresses ζ11,45 o of the 45 o -layer for different biaxial load ratios. 

The presented ply-by-ply stress analysis and the calculation of the stress distribution are conducted 

for all specimens tested in the fatigue experiments. As an important result, all specimens show that the 

maximum fibre parallel stresses occur in the inner 45 o -layer. Consequently, the failure-critical layer is 

the same for all biaxiality ratios. Considering the assumption mentioned above (fibre-parallel stresses of 

the critical layer determine the final failure of the global laminate) the fibre parallel normal stresses are 

proposed to be used for further fatigue life prediction. All calculated final stresses ζ 11,45 o of the critical 

layer are referred to the appertaining number of accomplished load cycles and plotted in the 

lamina-based S-N diagram shown in figure 7. This S-N curve reveals a similar trend of the final 

maximum internal fibre parallel stresses for the different biaxial load ratios. Other S-N relationships in 

biaxial fatigue normally consist of several S-N curves each belonging to a discrete biaxiality ratio. 

Using the presented lamina-based S-N diagram leads to a single curve for all biaxial load configurations 

when employing calculated stress distributions and critical layer data. Moreover, the calculated final 

stress values of biaxially loaded laminates can be better compared to the stress values of unidirectional 

flat specimens for establishing a relationship which allows the fatigue life prediction of complexly 

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loaded laminates by means of simple unidirectional fatigue tests. By applying the CLPT and the 

degradation function shown in section 3 the calculation of the final stress states is realisable for arbitrary 

symmetric and antisymmetric lay-ups provided that the discrete damage states (crack densities) are 

known. With respect to further research work a damage accumulation law for the development of cracks 

is the next step. Afterwards, this law can be integrated in the exiting modelling approach with the result 

that experimental data is no longer required. 

6. Conclusion 

A modelling approach for a ply-by-ply stress analysis of a slightly non-symmetric composite 

subjected to multiaxial fatigue loads is explained. Thereby, applying a ply-by-ply stiffness degradation 

model and experimentally observed crack densities leads to analytical calculation for layer-wise stress 

distribution for multiple damage states in the fatigue life. In other words, the stress redistributions with 

increasing laminate degradation are calculated. Finally, the formation of a maximum stress loaded layer 

(critically stressed layer) is shown and used to set up a S-N diagram referring the maximum 

fibre-parallel normal stresses to the maximal number of cycles accomplished. All biaxially loaded 

specimens show a single lamina-based S-N curve not depending on the global ratio of biaxiality. 


The authors gratefully acknowledge the support by the German Science Foundation (DFG) within the 

project PAK267 (Effects of Defects). 

References 

[1] Schulte K. Baron C., Neubert N.: Damage development in carbon fibre epoxy laminates: cyclic loading, Composites, 1985, pp. 281-285 

[2] Nairn J.A., Hu S.: The initiation and growth of delaminations induced by matrix microcracks in laminated composites, International 

Journal of Fracture 57, 1992, pp. 1-24 

[3] Talreja R.: Damage and fatigue in composites – a personal account, Composites Science and Technology 68, 2008, pp. 2585-2591 

[4] Ladeveze P., Lubineau G., Marsal D.: Towards a bridge between the micro- and mesomechanics of delamination for laminated composites, 

Composites Science and Technology 66, 2006, pp. 698-712 

[5] Degrieck J., Paepegem W.V.: Fatigue damage modelling of fibre-reinforced composite materials: Review, Applied Mechanics Review 54 

No 4, 2001, pp. 279-300 

[6] Quaresimin M., Susmel L., Talreja R.: Fatigue behaviour and life assessment of composite laminates under multiaxial loadings, 

International Journal of Fatigue 32, pp. 2-16, 2010 

[7] Adden S., Horst P.: Stiffness degradation under fatigue in multiaxially loaded non-crimped-fabrics, International Journal of Fatigue 32, 

2010, pp. 108-122 

[8] Carvelli V., Corigliano A.: Transversal resistance of long-fibre composites: Influence of the fibre-matrix interface, Proceeding of the 11 

ECCM, Rhodes, Greece, 2004 

[9] Carvelli V., Chi T., Larosa M., Lomov S., Poggi C., Angulo D., Verpoest I., Experimental and numerical determination of the mechanical 

properties of multi-axial multe-ply composites, Proceeding of the 11 ECCM, Rhodes, Greece, 2004 

[10] Garnich, M. R., Karami, G., Finite Element Micromechanics for Stiffness and Strength of Wavy Fiber Composites, Journal of Composite 

Materials, Journal of Composite Materials 38, pp. 273 – 292, 2004 

[11] Schmidt F., Adam T. J., Horst P.: Fatigue modelling of a nominally defect-free GFRP composite under multi-axial loading, submitted to 

Composites Science and Technology, 2010 

[12] Lin, GF., Comparative Stress/Deflection Analyses of a Thick-Shell Composite Propeller Blade, ADA251080, David Taylor Research 

Center Bethesda MD Ship Hydromechanics DEPT, 1991 

[13] VDI 2014, Entwicklung von Bauteilen aus Faser-Kunststoff Verbunden – Blatt 1, published by VDI

Abstract 

Fatigue Damage initiation of a PA66/glass fibers composite 

material 

B Esmaeillou, P Fereirra, V Bellenger *, A Tcharkhtchi 

PIMM, Arts & Métiers ParisTech, 151, Boulevard de l’Hôpital, 75013 Paris, France 

Fatigue damage initiation of a PA66/glass fiber composite material is studied with broken tests carried out with an 

"alternative bending device" and a small applied strain. During the damage initiation period, no change of macroscopic 

properties, density, cristallinity ratio, glass transition temperature, flexural elastic modulus is observed. Polysequential 

tests are carried out with 3 rest times differing by their length. These rest times allow the relaxation of macromolecular 

chains in the region of the microdefects and increase the number of cycles at fracture. The most efficient break is the one 

just before the final fracture. The comparison of the fatigue behavior of the composite and its neat matrix shows that the 

microdefects relaxed during the break are identical to those which initiate damage and final fracture. 

Keywords: PA66/glass fiber composite; damage initiation; fatigue broken test; fatigue polysequential test 


The fatigue behavior of composite materials with short fibers is still a key problem despite the 

progress in material science. For many molded parts, the lifetime prediction is crucial. In the automotive 

industry, pressures and temperatures in engines are inclined to go up, which makes critical the fatigue 

properties of these parts. A fatigue curve displays the variation of the induced stress versus the number 

of cycles for a given strain and frequency. Generally, these curves display three parts: 1 o ) A fast decay of 

the induced stress due to the setting up of a thermal regime: an increasing temperature involves a 

decreasing elastic modulus; 2 o ) A long plateau (period 2) during which the induced stress decreases only 

slightly without any significant temperature change; 3 o ) A sudden stress reduction corresponding to the 

coalescence of microdefects followed by the sample fracture. For PA66/glass fibers, several research 

works [1-3] report that damage is initiated by the build-up of microdefects at fiber ends. Damage 

initiation occurs during the period 2 of stress stabilization. For unnotched samples of amorphous 

polymers, no significant change in macroscopic properties [4] (macroscopic compliance, cristallinity 

ratio, transition temperatures) is observed during this period. The aim of this work is to study damage 

initiation by the way of broken fatigue tests and polysequential fatigue tests. Broken fatigue tests are 

carried out and during every rest time, dogbone samples are analysed by Differential Scanning 

Calorimetry (melting temperature Tm, cristallinity ratio xc), density measurements, mechanical testing 

(Dynamic Mechanical Analysis, flexural modulus, ultimate stress). With polysequential fatigue tests, 

* Corresponding author. Tel.: +33 1 4424 6308; fax: +33 1 4424 6382. 

E-mail address: veronique.bellenger@paris.ensam.fr

242 


the effect of the rest time and break location on the fatigue lifetime is investigated. 

2. Material and methods 

The matrix is a thermoplastic Polyamide 66 reinforced by short glass fibres. The fraction 

crystallinity xc is determined by DSC experiments using the ratio 

value of melting enthalpy and 

c 

Hm 

H 

H 

m 

c 

m 

where Hm is the experimental 

the melting enthalpy of the 100% crystalline polymer. 

H = 

192 J/g [5]. Sample surface is observed in the most constrained part by optical microscopy with an 

Olympus BH2 or by scanning electron microscopy with a Hitachi S-4800 apparatus at an accelerating 

potential of 0.8 kV. Samples are not metallised before analysis. The loss modulus E” is measured by 

viscoelasticimetry on a NETZSCH DMA 242 apparatus. The test is performed in 3 points bending 

mode at a 10 Hz frequency, with a static force of 4 N and a dynamic force of 2N. The heating rate is 

5 o C/min. The initial mechanical properties are determined at 23 o C and 50% HR in bending mode with 

an INSTRON 4502. The strain rate is 2 mm/min and the bending length is 60 mm. 

The fatigue test [1] is performed in a flexural alternate bending device at a frequency of 10 Hz with a 

 

R= 

 

min 

max 

value equal to -1, at 23 o c and 50% RH. The applied strain is 0.013 for broken fatigue tests 

and 0.017 for polysequential fatigue tests. The most constrained part of the sample is determined by a 

linear elastic calculation [6], it is located at a distance of 18mm from the embedded part. The surface 

temperature in this area is measured during the test by a RAYTEK infrared camcorder. 

3. Results and discussions 

Broken fatigue tests are performed at 10 Hz with an applied strain of 0.013. The physico-chemical 

and mechanical properties, density, critallinity ratio, loss modulus, flexural modulus and ultimate stress 

are measured after 300 000 and 500 000 loading cycles. The values reported in Table 1 show that 

these properties are not modified during the damage initiation period. It does not mean that there is no 

defect build-up but their size/concentration is too small to induce a variation of the macroscopic 

properties. The loss modulus E" measured at 42 o C (the maximum value corresponding to T is 55 o C) 

seems to be constant except near the fracture (500 000 cycles) where it decreases when microdefects are 

generated. Before 500 000 cycles, the size of sub-micron defects, Fig 1, in the most constrained area is 

smaller than 0.2 µm. Between 0 and 500 000 cycles, flexural properties are unchanged taking into 

account the standard deviation. The last one reflects the heterogeneity of 500 000 loading cycle samples, 

heterogeneity which is also noticed for density and cristallinity ratio measurements. 

Polysequential fatigue tests are carried out at 10 Hz frequency and a strain = 0.017. The Fig 2 

displays the induced stress and the temperature versus the number of cycles. A first decrease of the 

induced stress from 85 MPa to 60 MPa is observed between 500 and 3000 cycles. It goes with an 

increasing temperature from 27 o C to 53 o C, then the temperature keeps on increasing but more slowly. 

This temperature increase induced by self-heating is smaller than the one reported before for another 

c 

m

B Esmaeillou, P Fereirra, V Bellenger, A Tcharkhtchi. / Fatigue Damage initiation of a PA66/glass fibers composite material 

PA66/glass fiber composite material [1]. The main difference between both composites is the sizing of 

glass fibers which is specific to PA66 whereas in the previous study, the sizing of glass fibers is 

unknown and probably much less efficient. The low mechanical resistance of the interface favors crack 

initiation and as a consequence an excess of self-heating temperature rise. This behavior can be 

explained by an increasing value of the loss modulus E" as shown by the viscoelastic spectrum, Fig 3, 

performed at the same frequency, 10 Hz. The dissipated heat at each mechanical cycle is equal to 

1 

= - ω E" where is the angular frequency, 0 the applied strain and E" the loss modulus. 

2 0 

Q ε 2 

For optical microscopy observation at the rest time, Surface sample is polished in the most constrained 

part before the test. After observation, the fatigue strain is again applied on the same sample. The time 

of break is at most 10 minutes. These successive breaks do increase the fatigue lifetime (65 000 cycles 

instead of 60 000 cycles at break). By optical microscopy, no damage is observed before 30 000 cycles, 

Fig 4(a). From this number of cycles, some pull out fibers appear near the surface but only in the most 

constrained part, Fig 4 (b,c) and just before the break Fig 4 (d), no microvoid/crack is visible. 

Fig. 1. SEM of the most constrained area of a specimen tested at 10 Hz and = 0.013 (broken test). 

Table 1. physico-chemical and mechanical properties of PA66/GF vs number of loading cycles 

Density (kg/m 3 ) xc (%) E‟‟42 o C (MPa) E (MPa) r (MPa) 

0 cycle loading 1409±13 35±4 343 6680 ± 200 190 ± 7 

300 000 cycle loading 1374±22 36±3 340 6860 ± 70 193 ± 8 

500 000 cycle loading 1404±8 38±5 290 6148 ± 612 204 ± 19 

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Fig. 2. Induced stress and temperature vs number of cycles of a fatigue test at 10 Hz and = 0.017 

Fig. 3. viscoelastic spectrum of PA66/glassfiber at 10 Hz, between -10 o C and 130 o C. 

Then the study is carried on with an unpolished sample by using scanning electron microscopy. After 

1000 cycles, some fiber ends are pulling out near the surface and initiate the skin fracture, Fig 5. This 

damage is nanoscale size that is why we call it nano cracks. It is very difficult to stop the fatigue test 

just before the sample break because the last phase of crack propagation is very fast. Cracks propagate 

first in zones where the fiber concentration is high, then in the matrix until the final fracture, Fig 6. 

This scenario recalls the work about the Essential Work of Fracture (EWF) of polyamide 66 filled with 

TiO2 nanoparticles [7]. Individual nanoparticles act as stress concentration points which promote tiny 

cavitations which coalesce into sub-micron ones, then rapidly grow into microvoids and initiate cracks 

due to the high level stress concentration.


(a) (b) 

(c) (d) 

Fig. 4. Optical microscopy observation of the most contrained part of a specimen tested at 10 Hz and = 0.017 (polysequential test) (a): initial, (b) 

30 000cycles, T=57 o C, (c) 45 000cycles, T=60 o C, (d) 60 000cycles, T=62 o C. 

(a) (b) 

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(c) (d) 

Fig. 5. SEM of the most constrained and polished area of a specimen tested at 10 Hz and = 0.017 (polysequential test) (a): initial, (b) 

1 000cycles, T=35 o C, (c) 5 000cycles, T=52 o C, (d) 10 000cycles, T=55 o C. 

Fig. 6. SEM of the most constrained and unpolished area of a specimen tested at 10 Hz, just before fracture (62 000 cycles). 

For polysequential fatigue tests, the first break occurs at 30 000 loading cycles and the rest time 

varies between 2 and 30 minutes. Then the same approach is done for a break at 45 000 loading cycles 

and for a break at 60 000 loading cycles close to the final sample fracture. For these test conditions, the 

number of cycles at fracture is 65000. The fatigue lifetime is the highest when the break occurs close to 

the final fracture, Fig 7, where the crack size is in a micron scale. It means that relaxation of defect 

build-up at the end of the damage initiation period is more efficient than the relaxation of defects 

build-up earlier. Fig 8 shows that an increasing rest time up to 20 minutes does increase the fatigue 

lifetime. Afterwards, between 20 minutes and 2 hours, the number of cycles at fracture remains constant, 

about equal to 110 000 cycles. That means that for an applied strain, 0 = 0.017, a rest time of 20 

minutes is enough for microdefects relaxation. When a rest time of 5 min is applied close to the final 

fracture, the mean stress induced is equal to 63 MPa, hence a 21 MPa gap with the initial induced stress. 

If the rest time is equal to 20 min, the mean stress induced (82 MPa) is practically equal to the initial 

induced stress (84 MPa). Now, the question is: what is the nature of the microdefects relaxed during the 

fatigue test break? Are they conformational changes in the amorphous phase? Robertson [8] considered 

for polystyrene and polymethyl methacrylate, a molecular model in which a shear stress field induced 

rotational conformations of backbone bonds, enough numerous to break up the rigidity and allow flow. 

The calculated properties agree reasonably well with experimental available results of cold drawing


experiments. Could they be packing density defects, for instance at the interphase crystalline/amorphous 

phases? An amorphous polymer can stand for a disorganized arrangement of structural units [9], each 

unit being located in a cage built up by the neighbor structural units. A "quasi punctual defect" is a spot 

made up by a structural unit and her first neighbors (the cage cited above) of which the free enthalpy 

level is higher than the mean value of the whole group of structural units. These "quasi punctual 

defects" correspond to local density fluctuations existing in the liquid state and which are frozen in the 

glassy state. Fatigue craze initiation was investigated in Polycarbonate [10]. The disentanglement of 

polymer chains plays an important role in void-like structures or "protocrazes" with a size of ~ 50nm. 

Could the same phenomenon occur in the amorphous phase of Polyamide 66? Are these defects, 

preplasticized domains again in the matrix? The pre-yield and yield behavior of amorphous polymers 

has been described with a metallurgical approach [11]. Some new mechanical data were analyzed in 

terms of dislocation-like defects involved by deformation in the macromolecular chain arrangement. 

The comparison of the fatigue behavior of the composite and its neat matrix gives interesting 

information. Fig 9 shows the evolution of the induced stress vs. the number of loading cycles for the 

composite and the neat matrix strained at 10 Hz frequency with an applied strain 0= 0.019. The induced 

stress is 3 times higher for the composite than for the neat matrix and of course the fatigue lifetime is 

much shorter. The first reason is the difference in elastic modulus value but the second one is the 

difference in self-heating. The surface temperature in the most constrained part of the specimen is 

recorded during the test, Fig 10. The temperature rise of the composite is higher and starts before the 

one of the neat matrix. Nano crack build-up at fiber ends, precursors of microcracks, induces an 

increasing damping and thus a higher temperature increase. The gap between the number of cycles 

corresponding to these two rises of temperature, means that the crack build-up at fiber ends play a key 

role in damage initiation. Are these defects relaxed during the break, identical to the microcracks which 

coalesce in zones where the fiber concentration is high? It is reasonable to answer positively because at 

the end of a rest time of 20 minutes just before the final fracture, the induced stress when the strain is 

again applied, is equal to the maximum and initial induced stress. The matrix is in a rubbery state and 

the temperature is high enough to induce the closing/deletion of microcracks. 

Fig. 7. Variation of the cycle number at fracture vs the number of loading cycles before the test break and for various rest times. 0 = 0.017, 90 

MPa, =10 Hz,RH = 50. 

247

248 


Fig. 8. Variation of the cycle number at fracture vs the rest time for 3 values of the number of loading cycles before the test break. 0 = 0.017, 

90 MPa, =10 Hz,RH = 50. 

Fig. 9. Induced stress of the neat matrix (——) and of the composite (------) versus the number of loading cycles, tested at a 10 Hz frequency, 0 = 

0.019 and ,RH = 50. 

Fig. 10. Surface temperature of the neat matrix (——) and of the composite (------) versus the number of loading cycles, tested at a 10 Hz 

frequency, 0 = 0.019 and ,RH = 50.



A fatigue curve displays 3 zones, of which the second one is very long, nearly 80% of the fatigue life, 

when the applied strain is low; during this period, damage initiation occurs but the size/concentration of 

microdefects build-up is too small to involve a change in macroscopic properties such as density, 

cristallinity, flexural elastic modulus… At the beginning of the third zone which is short compared to 

the second one, cracks propagation first occurs in zones where the fiber concentration is high, then in 

the matrix until the final fracture. The fatigue lifetime is higher during polysequential tests than during 

non-stop tests. The most efficient break is just before fracture. There is an optimum rest time for 

microdefects relaxation which is equal to 20 minutes for our material and testing conditions. The nature 

of these relaxed microdefects was investigated by comparing the fatigue behavior of the neat matrix and 

of the composite. For identical testing conditions, the self-heating of the composite is higher and 

occurs before the one of the neat matrix. It means that nano cracks build-up at fiber ends, precursors 

of microcracks, play the key role. The comparison of the initial induced stress and the induced stress 

after a rest time just before the specimen fracture seems to indicate that these micro-cracks are closed 

during the rest period. 


Many Thanks to Gilles Robert for helpful discussion and Rhodia Co for providing PA66/glass fiber 

compounds. 

References 

[1] Bellenger V., Tcharkhtchi A., Castaing Ph., Thermal and mechanical fatigue of a PA66/glass fibers composite materials. International 

Journal of Fatigue 2006; 28: 1348-52. 

[2] Noda K. Fatigue failure mechanism of short glass-fiber reinforced Nylon 66 based on non linear dynamic viscoelastic measurement. 

Polymer 2001; 42: 5803-11. 

[3] Horst J.J., Spoomaker J.L., Fatigue fracture mechanisms and fractography of short-glass fibre-reinforced polyamide6. J. Mater Sci 1997; 

32; 3641-51. 

[4] Baltenneck F., Trotignon J-P, Verdu J., Kinetics of fatigue failure of polystyrene. Polym Eng Sci 1997; 37 (10): 1740-47. 

[5] Mark J.E. Polymer data handbook, Oxford University press; 1999. p. 195. 

[6] Barbouchi S., Bellenger V., Tcharkhtchi A ., Castaing Ph, Jollivet T. Effect of water on the fatigue behavior of a PA66/glass fibers 

composite material. J Mater Sci 2007; 42; 2181-88. 

[7] Yang J., Zhang Z., Zhang H. The essential work of polyamide 66 filled with TiO2 nanoparticles. Comp. Sci. Technol. 2005; 65; 2374-79. 

[8] Robertson R.E. Theory for the plasticity of glassy polymers. J. Chem. Phys. 1966 ;44 ; 3950-56. 

[9] Perez J., Physique et mécanique des polymères amorphes. Technique et documentation Lavoisier; 1992. p. 34-35. 

[10] Hristov H.A., Yee A.F., Gidley D.W. Fatigue craze initiation in polycarbonate: study by transmission electron microscopy. Polymer, 1994; 

35; 3604-11. 

[11] Escaig B. A metallurgical approach to the preyield and yield behavior of glassy polymers. Polym. Eng. Sci. 1984; 24 (10); 737-49. 

249

Fatigue life prediction of off-axis unidirectional laminate 

F Q Wu *, W X Yao 

Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle, Nanjing University of Aeronautics 

and Astronautics Nanjing 210016, China 

Abstract 

The prediction method of fatigue life of unidirectional laminate with the special ply fatigue life is an important support 

to build the prediction model of fatigue life of any lay-up laminate based on the special ply fatigue life. In this paper, the 

fundamental mechanical hypothesis of the fatigue failure criterion of unidirectional laminate, which is developed from 

the static failure criterion of laminate, has been analyzed. Based on the investigation on the fatigue failure regularities of 

the different unidirectional laminates, a phenomenon has been found that the location of unidirectional laminate S-N 

curve is monotonously decreasing with the increasing of ply orientation angle in the same coordinate. Then, a function 

has been proposed to describe the phenomenon. To analyze the mathematical characteristic of the function deeply, a 

fatigue life prediction model, which the fatigue life of unidirectional laminate can be predicted with the fatigue lives of 

longitudinal and transverse laminates, has been proposed by means on a special material S-N curve function. Based on 

the model, the fatigue life of any unidirectional laminate can be predicted by the S-N curves of two arbitrary 

unidirectional laminates. Twelve sets of experimental data of five kinds of laminates were employed to verify the model, 

and the results show that predicted fatigue life is in agreement with the experiment ones. 

Keywords: composite; fatigue; off-axis unidirectional laminate; fatigue life prediction 


The laminate is the general composite material in engineering structure. To change the fiber volume 

fraction, ply orientation angle and ply stacking sequence of laminate, the different mechanical 

characteristic composite can be gotten easily, which satisfies the engineering necessity commendably. 

Because of the designability of material, the composite laminate has been used widely in aeronautics, 

astronautics, transportation, architecture and energy fields. The structural form of laminate decides the 

composite laminate is anisotropy material. The properties characteristic causes the mechanical analysis 

method of laminate is more complicated than the analysis method of isotropic material. The static 

mechanical theories of laminate are mature now, but the fatigue analysis method is imperfect, which 

need be developed. The usual method to get the fatigue S-N curve of laminate is by the fatigue 

experiment in engineering. The structure type is infinite about laminate with the same component 

material. If the fatigue lives of any type laminate with the same component material were gotten by the 

fatigue experiment, the cost and consumed time will be very high in engineering. Therefore, it is 

satisfied with the engineering requirement to build a fatigue life prediction model, which the fatigue life 

of laminate can be predicted by the fatigue lives of longitudinal and transverse laminates. Because the 

* E-mail address: stonewu@nuaa.edu.cn, Tel.: 86-25-84895717

F Q Wu, W X Yao. / Fatigue life prediction of off-axis unidirectional laminate 

ply is the basic element of laminate, the first step of the model is to solve the fatigue life prediction of 

ply with special laminate, like the analysis method of the static mechanics property of laminate. 

The unidirectional laminate is the orthotropic material and the ply orientation angle is the angle 

between fiber orientation and load orientation. Because of the simple structural form, the fatigue failure 

modes are simple in the unidirectional laminate. According to a great deal of the experimental 

investigations, the modes are matrix cracking, interfacial debonding and fiber breakage. The 

unidirectional laminate is the basic element of laminate. The fatigue life prediction model of 

unidirectional laminate is the foundation of the laminate fatigue life prediction method with special 

laminate fatigue life. To solve the fatigue life prediction of unidirectional laminate, many research 

investigations had been done. To develop the static failure criterion of laminate, Hashin [1] , Brogdon [2] , 

Awerbuch [3] and Jen [4] built the prediction model, which predicts the fatigue life of off-axis 

unidirectional laminate with the fatigue lives of longitudinal, transverse and shear laminates. But the 

calculated results are not good agreement with the experimental data. Kadi [5] , Plumtree [6,7] , Shokrieh [8] 

and A Varvani-Farahani [9] researched the relationship between the strain energy and the fatigue life of 

the unidirectional laminate under the fatigue loading and thought the relationship is linear function. 

According to the research, they built the prediction model, which predicts the fatigue life of the off-axis 

unidirectional laminate with the special laminate. Ellyin [10] analyzed the relationship of S-N curves of 

the different unidirectional laminates and proposed a prediction model by means on statistics, which 

predicts the fatigue life of the off-axis unidirectional laminate with a reference laminate. Kawai [11] 

thought the relationship between the fatigue strength and the fatigue life of the unidirectional laminate is 

satisfied with the exponential relationship. To fit the function by the experimental data, the fatigue life 

of the off-axis unidirectional laminate has been predicted. But the predicted result is not satisfactory. 

Many investigations to analyze the relationship of fatigue life among the different unidirectional 

laminates had been done by researchers. Many describing model has been proposed to predict the 

fatigue life of the off-axis unidirectional laminate with the special laminate. But there are bigger errors 

between calculated results and experimental data. In this paper, the fatigue failure mechanics of 

unidirectional laminate had been analyzed. Then, a prediction model had been proposed to predict the 

fatigue life of the off-axis unidirectional laminate with the fatigue lives of longitudinal and transverse 

laminates. 

2. Fatigue life prediction model 

2.1 Stress analysis 

When the off-axis unidirectional laminate is subjected to loading, the loading will be distributed on 

the on-axis of unidirectional laminate based on the balance principle of mechanics, as shown in Fig.1. 

There are quantitative relations among these stresses 

251

252 


2 

1 = xcos 

 

2 

 

2 = xsin 

 

12 = x sin cos 

 

Fig. 1. The stresses of unidirectional laminate. 

where the subscript 1 denotes the parallel fiber direction or the longitudinal direction, the subscript 2 

denotes the vertical fiber direction or the transverse direction, ζ1 is the longitudinal stress, ζ2 is the 

transverse stress, η12 is the in-plane shear stress, θ is the ply orientation angle, which is the angle 

between fiber direction and load direction. Based on the stresses in equation (1), there are many model 

had been proposed to describe the static failure of laminate. The Tsai-Hill criterion is used in 

engineering usual. To analyze the stresses of laminate under static loading, the Tsai-Hill function can be 

gotten. It is 

f 

2 2 2 

1 1 2 2 12 

x = - + + (2) 

2 2 2 2 

X X Y S 

( ) 

where the X is the static longitudinal strength, the Y is the static transverse strength, the S is the static 

in-plane shear strength and the ζX is the stress on loading direction. When the unidirectional laminate 

fractures under static loading, the f(ζX) is equal to 1 and the ζX is equal to ζθ,ult. Substituting Eq. (1) into 

Eq.(2) yields 

 

4 2 2 4 2 2 

cos - cos sin sin cos sin 

= 1 

+ + (3) 

X Y S 

,ult 2 2 2 

where ζθ,ult is the static strength of the off-axis unidirectional laminate on loading direction. 

Many laminate fatigue failure criterions were developed from the static failure criterion, as shown in 

the references [1-4] . In the developed criterions, a same mechanical hypothesis has been complied, which 

is the fatigue loading is processed as the quasi-static loading, the material properties degrade 

progressively and the laminate is identified with the new material at every cycle. Then, the static 

strength is substituted by the residual strength in the laminate static failure criterion. Based on the 

hypothesis, Brogdon [2] developed the laminate fatigue failure criterion from the Tsai-Hill model, as 

(1)


2 2 2 

1 1 2 2 12 

- + + = 1 

(4) 

2 2 2 2 

X N X N Y N S N 

( ) ( ) ( ) ( ) 

where N is the fatigue life. X(N), Y(N) and S(N) are the longitudinal fatigue strength, transverse fatigue 

strength and in-plane shear fatigue strength of laminate at fatigue life N, respectively. These values can 

be gotten from the correlated laminate S-N curves. For the θ angle off-axis unidirectional laminate, the 

fatigue strength is ζθ(N) at fatigue life N. Then, substituting Eq.(1) into Eq.(2) yields 

4 2 2 4 2 2 

 

cos - cos sin sin cos sin 2 

+ + 2 2 2 ( 

N ) = 1 

X ( N ) Y ( N ) S ( N ) 

 

Eq.(5) describes the relationship between the fatigue strength of θ angle off-axis unidirectional laminate 

and the fatigue strengths of longitudinal, transverse and in-plane shear laminates. When the S-N curves 

of longitudinal, transverse and in-plane shear laminates had been gotten, the S-N curve of θ angle 

off-axis unidirectional laminate can be calculated by Eq.(5). 

2.2 Failure analysis 

From longitudinal laminate to transverse laminate, the ply orientation angle of the off-axis 

unidirectional laminate increases and the laminate strength decreases, monotonously. When the angle is 

smaller, the fiber is the main load bearing structure and the corresponding failure mode is fiber breakage. 

When the angle is larger, the matrix is the main load bearing structure and the corresponding failure 

mode is matrix cracking. The arrangement order of off-axis unidirectional laminate S-N curves reflects 

the performance characteristics. The location of off-axis unidirectional laminate S-N curve is 

monotonously decreasing with the increasing of ply orientation angle in the same coordinate. The 

longitudinal laminate S-N curve is the upper limit and the transverse laminate S-N curve is the lower 

limit. A lot of fatigue experimental investigations [1,3,5,12,13] reflect the rule, as shown in Fig 2. 

Fig. 2. The S-N curves of unidirectional laminates. 

253 

(5)

254 


To analyze the fatigue length relationship between off-axis laminate and longitudinal and transverse 

laminate, a fatigue strength ratio has been defined, as 

( ) 

K N 

( N ) Y ( N ) 

( ) - ( ) 

- 

= 

X N Y N 

According to the mechanics significance of variables, the fatigue strength size order is Y(N) ≤ ζθ(N) ≤ 

X(N) in Eq.(6). Therefore, the value range of fatigue strength ratio is 0 ≤ K(N) ≤ 1. Substituting Eq.(5) to 

Eq.(6) yields 

( ) 

K N 

= 

4 2 2 4 2 2 

cos - cos sin sin cos sin 

1 + + - Y N 

( ) ( ) ( ) 

X ( N ) - Y ( N ) 

2 2 2 

X N Y N S N 

where the fatigue strengths X(N), Y(N) and S(N) are the functions about the fatigue life N. which are the 

S-N curve functions of the unidirectional laminates. The Eq.(7) shows that the fatigue strength ratio 

K(N) is the function about the fatigue life N and the ply orientation angle θ of off-axis unidirectional 

laminate. To analyze the mechanics meaning of K(N), the boundary conditions of Eq.(7) are gotten, as 

1) when the fatigue life N equals 1, the K(N) equals K0, 

2) when the θ equals 0°, the K(N) equals 1; 

3) when the θ equals 90°, the K(N) equals 0. 

2.3 prediction model 

K 

0 

,ult -Y 

= ; 

X -Y 

The S-N curves of the longitudinal and transverse laminates can be gotten by the fatigue experiment. 

But the cast is high and the accuracy is low to get the S-N curve of the in-plane shear laminate by 

experiment. To analyze mathematically, there are other functions describing or approximating the 

relationship between K(N) and N, θ, which the function form is different from the Eq.(7). The function 

is defined as 

( ) ( , 

) 

( ) 

K N = g N 

(8) 

The larger the fatigue loading is, the more the done work and the fatigue damage of laminate are, the 

less the fatigue life is. The fatigue strength of the off-axis unidirectional laminate is monotonously 

decreasing with the laminate fatigue life increasing, which is shown in many experiment results. Fig.3 

describes the mathematic characteristic of the change, as 

(6) 

(7)


Fig. 3. The fatigue strength ratio K(N). 

It is clear that the K(N) changes with the change fatigue life N in the Fig.3. But the quantitative relation 

between K(N) and lgN is unclear. The relation is considered a linear relationship based on the change 

trend of the laminate S-N curve in this paper. The unidirectional laminate strength is decreasing with the 

ply orientation angle increasing. The larger the fatigue strength is, the smaller the ply orientation angle 

at the same fatigue life N, as shown in Fig.2. So, the fatigue strength ratio K(N) is decreasing with the 

angle θ increasing, as shown in Fig.3. According to the function g(θ,N) meaning and purpose, the Eq.(8) 

should have the same change characteristics and boundary conditions with Eq.(7). Therefore, the 

function g(θ,N) has been proposed as 

( ) ( ) 

( ,ult -Y)( X -,ult) 

K N = g , N = K - 

lg N 

( X - Y) 

0 2 

where the parameter ζ is the proportional coefficient, which can be gotten by fitting experiment data. 

When the experiment data are lacked, ζ = YT/XT is commended, which XT is the static tensile strength of 

longitudinal laminate and YT is the static tensile strength of transverse laminate. Substituting Eq.(6) into 

Eq.(9) yields 

-Y X - 

 

 

 

X -Y X -Y 

,ult ,ult 

( N ) = Y ( N ) + 1- lg N ( X ( N ) -Y 

( N ) ) 

Eq.(10) describes the quantitative relationship between the fatigue strength of the off-axis unidirectional 

laminate and the fatigue strengths of the longitudinal and transverse laminates. When the S-N curves of 

the longitudinal and transverse laminates have been gotten, the S-N curve of the off-axis unidirectional 

laminate can be calculated by Eq.(10). To analyze the Eq.(10) deeply, it is found that the fatigue life of 

the off-axis unidirectional laminates can be calculated with any two known unidirectional laminate S-N 

curves. 

The S-N curve model is used to describe the unidirectional laminate S-N curve. The model has been 

chosen in this paper, which is proposed by reference [14] , as 

255 

(9) 

(10)

256 


( ) 

a 

N lg N 

= 1+ mexp 

--1 

ult 

b 

 

where ζ(N) is the material fatigue strength, ζult is the material static strength on the loading orientation, 

a, b and m are the experimental parameters. The model can describe all regions of the material S-N 

curve. 

3. Verification 

According to the experimental data of unidirectional laminate, the S-N curves of longitudinal and 

transverse laminates was gotten by the Eq.(11). To fit the experimental data, the parameters a, b and m 

were gotten by the least square method. Then, substituting the characteristic values of X, Y, S and θ of 

unidirectional laminate into Eq.(10) yields the S-N curve of the laminate. Based on Eq.(10), the fatigue 

life of the off-axis unidirectional laminate is predicted finally. The comprehensive experimental data 

published in Refs.[1,3,5,12,13] were used to validate the proposed fatigue life prediction model. 

According to the proposed algorithm, the fatigue life of the off-axis unidirectional laminate is calculated. 

The property values, S-N curve parameters and predicted results of laminates of this work are presented 

in Tables 1, 2 and Figures 4-15, respectively. 

Composite 

Table 1. Static mechanical properties of composite 

Longitudinal tensile 

strength X (MPa) 

Transverse tensile 

strength Y (MPa) 

Shear strength 

S (MPa) 

Glass/Epoxy [1] 1234.8 28.4 37.9 

Graphite/Epoxy [3] 1836 56.9 93 

E-Glass/Epoxy [5] 778.7 44.7 55 

T800H/2500 [12] 2472 48 60 

Carbon/PEEK [13] 2128 93 133 

Fig. 4. The predicted lives and experimental lives of Glass/Epoxy unidirectional laminates (R = 0.1). 

(11)

Composite 

Glass/Epoxy [1] 

Graphite/Epoxy [3] 

E-Glass/Epoxy [5] 

T800H/2500 [12] 

Carbon/PEEK [13] 


Table 2. The parameters of S-N curves of unidirectional laminates 

Unidirectional 

laminate 

Stress Ratio R a b m 

0° 0.1 2.6446 5.5829 0.7636 

60° 0.1 2.0031 8.1227 1.0 

[0]16 0.1 1.5021 7.1003 1.0 

[90]16 0.1 2.7437 4.3002 0.6001 

[0]10 

[90]20 

[0]16 

[90]16 

0.5 3.8535 4.271 0.3423 

0 3.4582 6.07 0.743 

-1 1.1282 6.858 1.0 

0.5 1.026 16.117 1.0 

0 1.3967 4.6964 0.865 

-1 2.7525 3.904 0.6735 

0.5 2.1484 5.2880 0.8001 

0.1 1.7504 3.2907 0.5590 

0.5 2.6767 2.4422 0.4201 

0.1 2.5921 3.4316 0.6246 

-1 2.1949 3.3457 0.7267 

[10]16 -1 1.7092 2.9149 0.6372 

[0]16 

[90]16 

0.2 1.8192 9.7871 1.0 

0 2.6042 4.8671 0.4551 

5 1.6166 8.8254 1.0 

-∞ 1.7204 8.1263 1.0 

0.2 1.6781 7.0601 1.0 

0 1.6251 5.0772 0.8102 

5 1.4771 6.5589 1.0 

-∞ 1.3349 6.2166 1.0 

257

258 


Fig. 5. The predicted lives and experimental lives of Graphite/Epoxy unidirectional laminates (R = 0.1). 

Fig. 6. The predicted lives and experimental lives of E-Glass/Epoxy unidirectional laminates (R = 0.5). 

Fig. 7. The predicted lives and experimental lives of E-Glass/Epoxy unidirectional laminates (R = 0).


Fig. 8. The predicted lives and experimental lives of E-Glass/Epoxy unidirectional laminates (R = -1). 

Fig. 9. The predicted lives and experimental lives of T800H/2500 unidirectional laminates (R = 0.5). 

Fig. 10. The predicted lives and experimental lives of T800H/2500 unidirectional laminates (R = 0.1). 

259

260 


Fig. 11. The predicted lives and experimental lives of T800H/2500 unidirectional laminates (R = -1). 

Fig. 12. The predicted lives and experimental lives of Carbon/PEEK unidirectional laminates (R = 0.2). 

Fig. 13. The predicted lives and experimental lives of Carbon/PEEK unidirectional laminates (R = 0).


Fig. 14. The predicted lives and experimental lives of Carbon/PEEK unidirectional laminates (R = 5). 

Fig. 15. The predicted lives and experimental lives of Carbon/PEEK unidirectional laminates (R = -∞). 

The results show that Eq.(10) predicts reasonably the fatigue life of the off-axis unidirectional 

laminate and the predicted results of large angle laminate are better than ones of small angle laminate. 

4. Discussion and Conclusions 

The laminate S-N curve is one of the important mechanics data in composite engineering structure 

design. To get the laminate S-N curve, the main engineering approach is fatigue experiment, now. But 

the laminate structure type with the same material is infinite because of its designability. It is 

unacceptable that every kind laminate S-N curve is gotten by the fatigue experiment. Therefore, the 

efficient analysis method should be built to obtain the laminate fatigue life, which has practical 

engineering value. Many investigations had been done and a promising ideal is developed, that is to 

build an analysis approach as the classical laminate theory, which the fatigue life of laminate can be 

predicted by the fatigue life of the special laminate. The first problem of the approach is how to predict 

261

262 


the fatigue life of the unidirectional laminate by the special laminate fatigue life. To resolve the problem, 

the internal relations among the laminates should be investigated. 

In this paper, the unidirectional laminate fatigue failure mechanics is analyzed and the mechanical 

hypothesis is accepted. Based on the hypothesis, the fatigue failure criterion is developed from the static 

failure criterion in laminate. To analyze the phenomenon, the location of the off-axis laminate S-N curve 

is monotonously decreasing with the increasing of ply orientation angle in the same coordinate. 

According to the mechanical investigation and the function mathematics analyzing, the fatigue life 

prediction model had been proposed, which predicts the off-axis unidirectional laminate S-N curve by 

the S-N curves of the longitudinal and transverse laminates or any two known unidirectional laminate. 

Twelve sets of experimental data of five kinds of laminates are employed to verify the model and the 

results show the model is reasonable. 

The proposed model function describes the relationship between the fatigue life and the fatigue 

strength of the off-axis unidirectional laminate. But the description is not perfect. The ζ is the important 

parameter to affect the fatigue life prediction accuracy in the proposed model. However, the value of ζ is 

the fitting value of the experimental data and lacks the mechanical theory basis. Maybe, it is the 

important reason of causing the error between the predicted values and the experimental data. 


The authors would like to acknowledge financial support from scientific research foundation 

(No.1001-909328) and research Innovation Foundation (No.1001-XCA10008) of Nanjing University of 

Aeronautics and Astronautics, National defense research foundation of China (No.1001-I110018). 

References 

[1] Z Hashin, A Rotem. A fatigue failure criterion for fiber-reinforced materials. Journal of Composite Materials, 1973, 7(4): 448~464. 

[2] D F Sims, V H Brogdon. Fatigue behavior of composites under different loading modes. K L Reifsnider, K N Lauraitis, editors. Fatigue of 

filamentary composite materials, ASTM STP 636. 1977, 185~205. 

[3] Awerbuch Jonathan, Hahn H T. Off-axis fatigue of graphite/epoxy composite. Fatigue of fibrous composite materials, ASTM STP 723. 

1981, 243~273. 

[4] M H R Jen, C H Lee. Strength and life in thermoplastic composite laminates under static and fatigue loads. Part II: formulation. 

International journal of fatigue.1998, 20(9): 617~629. 

[5] H E Kadi, F Ellyin. Effect of stress ratio on the fatigue of unidirectional glass fibre/epoxy composite laminae. Composites, 1994, 25(10): 

917~924. 

[6] A Plumtree, G X Cheng. A fatigue damage parameter for off-axis unidirectional fibre-reinforced composites. International journal of 

fatigue. 1999, 21(8): 849~856. 

[7] J Petermann, A Plumtree. A unified fatigue failure criterion for unidirectional laminates. Composites: Part A. 2001, 32(1): 107~118. 

[8] M Shokrieh Mahmood, F Taheri-Behrooz. A unified fatigue life model based on energy method. Composite Structures. 2006, 75(1-4): 

444~450. 

[9] A Varvani-Farahani, H Haftchenari, M Panbechi. A fatigue damage parameter for life assessment of off-axis unidirectional GRP 

composites. Journal of Composite Materials. 2006, 40(18): 1659~1670. 

[10] Z Fawaz, F Ellyin. Fatigue failure model for fibre-reinforced materials under general loading conditions. Journal of Composite Materials, 

1994, 28(15): 1432~1451. 

[11] M Kawai. A phenomenological model for off-axis fatigue behavior of unidirectional polymer matrix composites under different stress 

ratios. Composite Part A. 2004, 35(7-8): 955~963. 

[12] M Kawai, H Suda. Effects of non-negative mean stress on the off-axis fatigue behavior of unidirectional Carbon/Epoxy composites at 

room temperature. Journal of Composite Materials, 2004, 38(10): 833~854.


[13] M H R Jen, C H Lee. Strength and life in thermoplastic composite laminates under static and fatigue loads. Part I: experimental. 

International journal of fatigue.1998, 20(9): 605~615. 

[14] Wu Fuqiang, Yao Weixing. A new model of the fatigue life curve of materials. China Mechanical Engineering. 2008, 19(13): 1634~1637. 

263

Post-Impact Fatigue Damage Monitoring using Fiber Bragg 

Grating Sensors 

Abstract 

C S Shin *, S W Yang 

Department of Mechanical Engineering, National Taiwan University, No.1, Sec.4, Roosevelt Road, Taipei 10617, Republic of China 

Foreign object impact on composite may cause insidious damages that may grow to catastrophic failure under service 

loading. On using embedded fiber Bragg grating (FBG) to monitor these damage evolution in Graphite/Epoxy composites, 

we found the characteristic FBG spectrum gradually submerged against a rise of background intensity. By skipping the 

impact, directing the impact to positions away from the FBG and examining the extracted fibers, we concluded the above 

changes are due solely to damages in the composite initiated by the impact and aggravated by fatigue loading. Evolution 

of the grating spectrum reflects qualitatively the development of the incurred damages. 

Keywords: graphite epoxy composite; post-impact fatigue; structural health monitoring; fiber Bragg grating; damage evolution monitoring 


Composite structures such as aircraft wings or wind turbine blades are vulnerable to impact damage 

due to tool drop, bird-strike and hailstorm. The damages caused are often not evident on the surface and 

involved a number of different failure mechanisms such as delamination, debonding and matrix 

cracking [1] . However, on subsequent cyclic service loading, these microstructural defects may grow and 

eventually lead to catastrophic failures. Current non-destructive examination techniques are only 

sensitive to some of these failure mechanisms and are responsive only when the defect reaches a certain 

size. It is often impracticable to use these techniques for close monitoring of the development of these 

defects. Recently, there are general interests in the development of smart sensors integrated into 

structures to ensure continuous structural integrity monitoring. Fiber Bragg Grating (FBG) is one of 

such sensor element that finds increasing applications [2-6] . Optical fiber sensors have been shown to be 

able to monitor impact event occurrence [7, 8] and detect impact damages in composites [9, 10] . Optical 

fiber has a small diameter, long fatigue life and may be embedded inside a composite material and 

literally come into contact or at least into very close proximity of the internal defects. The output from 

an FBG is the shifting and changing shape of its characteristic reflected spectrum. There is no simple 

correlation between the spectrum changes and the damage mechanism involved. In the current work, we 

investigated the feasibility of employing fiber Bragg gratings (FBG) sensor to monitor the growth of 

post-impact fatigue defects. 

* Corresponding author. Tel.: 886-2-23622160 

E-mail address: csshin@ntu.edu.tw

2. Experimental procedures 

C S Shin, S W Yang. / Post-Impact Fatigue Damage Monitoring using Fiber Bragg Grating Sensors 

Quasi-isotropic laminates with T300/3501 Graphite/Epoxy prepreg stacked in the sequence 

[0/45/90/-45]s were cut into specimen coupons (200mm25.4mm1mm). FBG sensors were embedded 

in the two outer 0 o laminae along the axial loading direction as shown in Fig.1a. Each of the fibers was 

offset by 3mm from the centerline of the specimen. The fibers are led into the specimen coupon at one 

side and terminate inside the specimen at some distance short of the gripping position at the other side, 

as shown in Fig.1b. FBGs were fabricated in a Ge–B co-doped single mode fiber by side writing using a 

phase mask with a period of 1.05 m. The sensing length of the FBGs was about 10 mm. The 

reflectivity of the resulting FBG was about 99%, and the peak wavelengths were from 1550 and 

1551nm. The FWHM (full width half maximum) of the FBGs was about 0.175 nm. Impacts were 

made at one of the three locations designated A, B and C in Fig.1b, using a 260g aluminum falling 

weight from a height of 140cm with an apparatus that conforms to ASTM D5628. Positions A and C are 

respectively 30mm upstream and downstream of B as shown. The fiber on the side that faces the impact 

is designated L1 and the one on the back surface L4. After impact the coupons were subjected to cyclic 

loading from 0.5-5 kN at a frequency of 5Hz using an MTS servo-hydraulic test machine. The reflected 

spectra from the FBGs were interrogated periodically using an Anritsu optical spectrum analyzer 

(MS9710C OSA) under the load-free condition. Ultrasonic C-scan was also employed to examine the 

impact damage before and after the fatigue test. The above tests have also been repeated on specimens 

without undergoing any impact to serve as control. Fiber extraction was attempted in order to examine 

the integrity of the FBG after the impact and fatigue loading. 

Fig. 1. (a) Lay out of the prepreg stacking and the embedded optical fiber sensors; (b) positions of impact relative to the fiber sensor. 

3. Basic properties of fiber Bragg grating sensors 

When a broadband light is coupled into an optical fiber with a uniform Bragg grating, a single peak 

with wavelength satisfying the Bragg diffraction criterion will be reflected while the other 

wavelengths will be transmitted through: 

= 2neL (1) 

where ne is the effective refractive index and Λ is the periodicity of the grating. If the uniformity of the 

grating period is perturbed, the single peak reflected spectrum will broaden or chirped. When either or 

both of the ne and Λ change, the center wavelength of the reflected spectrum shifts. Λ will be changed if 

the FBG is subjected to a deformation. Such deformation may be caused by mechanical or thermal 

strains. ne will be affected by variation in temperature and the three-dimensional stress state acting on 

265

266 


the fiber. In general, the reflected wavelength will shift by ~1pm under a strain of 1 or a temperature 

change of 0.1 o C. If temperature variation is negligible, then the change in the spectrum basically reflects 

a change in the stress/strain status along the FBG. 


Impact at position B 

Fig.2 shows the FBG spectra just before and after impact for the fibers L1 and L4. Originally each of 

the FBG spectra has a single sharp peak. On embedding, curing and cutting into testing coupons, a shift 

in peak wavelength together with slight widening and splitting of the peak occurred as is evident in the 

solid lines in fig.2. This may be attributed to residual stresses that arose during the composite 

fabrication process. After the impact damage, the original peaks widened even more and split heavily 

into a number of distinct peaks (broken lines in fig.2). The above phenomena are more prominent in the 

spectrum from the L1 fiber. Such a change in the spectra suggests the strain distribution along the FBG 

has changed from roughly uniform to highly non-uniform. The latter is probably caused by the impact 

induced internal defects that have perturbed the residual stress field near the FBG. 

Fig.2. FBG spectra before and after impact damage. 

The impact damaged specimen was then subjected to cyclic loading. Fig.3 compares the impact 

damage visualized by ultrasonic C-scan before and after 200,000 fatigue cycles. Slight enlargement of 

the delaminated area can be seen. The extents of damage at a number of sections (1-1 through 4-4 in 

Fig.3) were examined under an optical microscope. Fig.4 shows typical observation at section 2-2. Note 

that the specimen in Fig.4a is different from that in Fig.4b as this examination is destructive. 

Delamination and matrix cracking occurred extensively in the lower half of the section. Marked 

aggravation of these damages is evident in Fig.4b during the cyclic loading. No significant damage is 

seen in the 1-1 and 4-4 sections.


Fig.3. Ultrasonic C-scan images of post impact damage at 0 cycle and 200000 cycles. 

Fig.4. Optical micrograph of the section 2-2 showing the positions of the fiber sensor and the extent of post-impact damage 

(a) just after impact; (b) after 200,000 cycles. 

The FBG spectra at various loading cycles are shown in Fig.5. On cycling, the peaks in the L1 

spectrum continued to widen gradually. The intensity of the background wavelengths tends to rise. At 

the end of 200,000cycles, the original peaks can still be recognized though they are not as distinct as 

before due to the rise in intensity of the background wavelengths. For the L4 spectrum, the intensity rise 

of the wavelengths surrounding the original peak occurred rapidly and at end of 200,000cycles, no peak 

is discernible in the spectrum. A possible cause of the gradual widening and submersion of the spectra 

peaks is the continuous development of the original impact damage in the composite that perturbs the 

strain field and caused steep strain gradient in the vicinity of the FBGs. If this is the case, then 

development of the FBG spectra may be employed to monitor the aggravation of the impact damage in 

a qualitative manner. However, the lost of reflection peak may also be caused by one or more of the 

following mechanisms: (1) fracture of the optical fiber, the flat smooth end of a nicely cleaved fiber may 

sometimes act as mirror which reflect lights without discrimination on the wavelength. If this fracture 

occurs somewhere within the FBG section, it may give spectra similar to that in Fig.5. (2) 

microcracking in the fiber causes stress concentration which alters the refractive index through the 

photoelastic effect, thus degrading the periodicity of the grating. The high temperature and pressure in 

the curing process, the impact loading and the soaking in water during C-scan examination may all be 

liable to induce defects that lead to microcracking in the optical fiber. The subsequent cyclic loading, 

alone or with the help from the former, may bring about fracture or microcracking. A number of 

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268 


experiments have therefore been designed to differentiate the responsible mechanisms. 

Impact at positions A or C 

Fig.5. Spectra changes from embedded FBGs in (a) L1 and (b) L4 with various fatigue cycles 

under a 140cm drop height and impact at position B. 

By keeping all aspects of the above experiment the same except the position of the impact damage, 

we may be able to test the micro-cracking and the fractured FBG hypotheses. By impacting at position 

A, any microcracks induced in this section of the optical fiber will not be able to affect the FBG 

downstream. If eventually fracture of the optical fiber occurred, the reflected spectra will either be 

extinguished or reflect all wavelength without discrimination. During the development of the fracture, 

severe weakening of the FBG peak will occur as the incident light is cut down. A gradual submersion of 

the FBG peak may also occur if part of light is reflected at the crack. If this occurs, we expect the 

process to develop quickly as the rise in the background intensity is complemented by a drop in the 

FBG peak intensity. Following the same line of reasoning, the above outcomes, except extinguishment 

of signal and weakening of the FBG peak, will also hold if impact is made at position C. 

For impact at either position, the resulting FBG spectra in the L1 fibers indeed maintained more or 

less the same Bragg reflection peak throughout the 200,000 fatigue loading cycles. However, that in the 

L4 showed the gradual peak submersion with the rise in intensity of the surrounding wavelengths 

(Fig.6). This renders the degradation of FBG periodicity by microcracks in the optical fiber hypothesis 

unlikely. A subtle difference between Figs 5 and 6 is that the submersion of the FBG peaks is delayed or 

occurring at a slower rate in the latter. For impact at position A, the FBG peak submersion occurred 

early but is still discernible after 200,000 cycles (Fig.6a). Since there is no significant reduction in the 

peak intensity, fiber fracture is unlikely the cause. For impact at position C, the FBG peak is maintained 

up to 160,000 cycles and submersion started to occur at 200,000 cycles (Fig.6b). The fiber fracture 

hypothesis cannot be conclusively ruled out here. 

A further possibility is the impact or the subsequent fatigue may have induced some matrix cracking 

at position B. Such cracking, if existed, will be rare as it is at a distance from the impact. This may 

explain the slower submersion of the FBG peaks in Fig.6. Moreover, if such cracking is induced by the 

original impact, it is unlikely to occur on the compressive side. This may explain the observation that


the FBG spectra in the L1 fibers remained more or less intact. 

Fatigue without impact 

Fig.6. Spectra from embedded FBGs in L4 with fatigue cycles for impact at positions (a) A and (b) C. 

Fig.7 shows the development of FBG spectra in a specimen that has undergone all the treatments as 

above except that no impact has been made. It can be seen that the curing process, the soaking into 

water for C-scan examination and the subsequent fatigue loading has not caused observable degradation 

of the FBG spectra during the 200,000 cycles of loading. The FBG peaks retained their shapes but 

drifted to longer wavelengths. This suggests that the current level of fatigue loading alone did not cause 

the defects that induce submersion of the FBG spectra as observed in Figs. 5 and 6. Such defects must 

have been initiated by the pre-fatigue impact and fatigue loading only aids their development and 

propagation. 

Fig.7. Spectra development from embedded FBGs in (a) L1 and (b) L4 with fatigue cycles in specimen without impact. 

Extracting and examining the FBG from the post-impact fatigued specimens 

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270 


Although the above tests have identified that the root cause of the FBG spectra changes during 

post-impact fatigue is the defects initiated by the impact, it is still inconclusive that whether such 

damages are induced in the composite or in the optical fiber or both. To clarify this, we soaked the 

post-impact fatigued specimens in acetone for 1 day, hoping to dissolve the resin and extract the optical 

fibers for examination. It was found that soaking has softened the resin to a great extent but did not 

dissolve it altogether. However, the Bragg spectrum has partially been restored after soaking. By 

carefully dissecting the softened specimens to draw out the optical fibers, we find that the fiber appeared 

intact and its characteristic FBG spectrum has been restored (Fig.8). 

Fig.8. Comparison of FBG spectra (i) before embedded in the composite specimen; (ii) after post impact fatigue for 200,000 cycles and (iii) after 

fiber extraction from the post impact fatigued composite specimen. 

Finally, to check whether there is any defect or microcracks induced in the optical fiber, the above 

extracted fiber was stuck on a thin spring steel strip. The later was bent to different curvatures while the 

FBG spectra were monitored. A strain gage stuck alongside the FBG recorded the strain at each 

curvature. Fig.9 shows the FBG spectra at different applied strain. It can be seen that the Bragg 

reflection peak shift to the right in proportion to the applied tensile strain. The shape of the peak 

maintained the same without any distortion or rising of the background intensity. This proves beyond 

doubt that the FBG sensor is defect-free and that the submersion of the reflection peaks in Fig.5 and 6 

can only be attributed to the steep strain gradient in the composite specimen in the vicinity of the FBGs. 

Such steep strain gradient has to be caused by the growing damages initiated by the impact and 

aggravated by the cyclic loading.


Fig. 9. Comparison of FBG spectra (i) before embedded in the composite specimen; (ii) after post impact fatigue for 200,000 cycles and (iii) after 

fiber extraction from the composite specimen. 

We may conclude that the fiber Bragg grating sensor successively survive a low velocity impact and 

the subsequent fatigue loading. The fading of the FBG peak in Fig.5 may be explained by the initial 

damage has developed to such an extent that it is approaching the FBG and has exerted steep strain 

gradients on the matrix surrounding the FBG, despite the fact that C-scan indicated otherwise. Thus, 

evolution of the grating spectrum reflects qualitatively the development in severity and proximity of the 

incurred damages. Quantitative correlation is deemed impracticable as the damages involved are 

complicated and may vary from case to case. Nevertheless, with suitably placed FBG (say on the back 

surface opposite an impact), one may be able to monitor status of structural health and give an alarm 

when the damage has grown beyond a certain size. The current tool will be especially helpful if one 

wants to monitor the effectiveness and long-term durability of a patch repair of the impact damage. 

More works are undertaken in these directions. 

5. Conclusion 

Embedded fiber Bragg gratings have been employed to monitor the post-impact fatigue damage 

development. It has been found that the fiber Bragg grating sensor can survive a low velocity impact 

and the subsequent fatigue loading. Evolution of the grating spectrum reflects qualitatively the 

development in severity and proximity of the damages incurred in the composite material. 


This work was carried out with support of the National Science Council projects 

(NSC96-2628-E-002-223-MY3). We are also indebted to Prof. S. K. Liaw of Department of Electronic 

Engineering of National Science and Technology University for some of the equipment support. 

271

272 

References 


[1] Ramesh Talreja. Fatigue of composite Materials. Technomic Publishing Co. Inc. Lancater. Penn. U.S.A.: 1987: 3-58. 

[2] Takeda, Nobuo; Mizutani, Tadahito; Hayashi, Kentaro; Okabe, Yoji. Application of fiber Bragg grating sensors to real-time strain 

measurement of cryogenic tanks. Proceedings of SPIE - The International Society for Optical Engineering 2003: 5056: 304-311 

[3] Skontorp, Arne. Structural integrity of quasi-isotropic composite laminates with embedded optical fibers. Journal of Reinforced 

Plastics and Composites 2000: 19(13):1056-1077 

[4] Hadzic, R.; John, S.; Herszberg, I. Structural integrity analysis of embedded optical fibres in composite structures. Composite Structures 

1999: 47( 1): 759-765 

[5] Hadzic, R.; John, S.; Herszberg, I. Structural integrity analysis of embedded optical fibres in composite structures. Composite Structures 

1999: 47( 1): 759-765 

[6] C.S. Shin and C.C. Chiang, ”Fatigue Damage Monitoring in Polymeric Composites using multiple Fibre Bragg Gratings,” International 

Journal of Fatigue.Vol.28, No.10, pp.1315-1321, (2006) 

[7] B. L. Chen, C. S. Shin, 2010, “Fiber Bragg Gratings Array for Structural Health Monitoring”, Special issue on Sensors, Actuators and 

Intelligent Processing, Materials and Manufacturing Process, 25:1-4, DOI:10.1080/10426910903426414. (2010) 

[8] C. S. Shin, B. L. Chen, J. R. Cheng and S. K. Liaw, 2010, “Impact response of a wind turbine blade measured by distributed FBG sensors”, 

Special issue on Sensors, Actuators and Intelligent Processing, Materials and Manufacturing Process, 25:1-4, 

DOI:10.1080/10426910903426448. (2010) 

[9] Chambers A.R., “Evaluating impact damage in CFRP using fibre optic sensors,” Composites Science and Technology 67, pp. 1235-1242, 

(2007) 

[10] Takeda S., “Delamination monitoring of laminated composites subjected to low-velocity impact using small-diameter FBG sensors,” 

Composites, Part A 36, pp. 903-908, (2005)

Delamination detection in CFRP laminates using A0 and S0 

Lamb wave modes 

N Hu a, *, Y L Liu a , H Fukunaga b,† , Y Li a 

a Department of Mechanical Engineering, Chiba University, Chiba 263-8522, Japan 

b Department of Aerospace Engineering, Tohoku University, Sendai 980-8579, Japan 

Keywords: Lamb wave; CFRP laminates; delamination; damage detection 


The structural monitoring techniques based on Lamb waves have been explored by many researchers 

in recent years, and the S0 and A0 Lamb wave modes have been widely employed for CFRP laminates 

with various damages, such as delamination [1,2] . However, there has been no comprehensive study on 

the different capabilities and features of the techniques based on these two modes for delamination 

detection. Moreover, when using the reflection from the delamination to detect it, it is unclear what kind 

of Lamb wave parameters, such as excitation frequency, is best for generating the strongest reflection 

from the delamination. The present work will focus on the above two key issues. From the present 

results, it can be found that the S0 Lamb mode is suitable for long-distance delamination detection due 

to its very small attenuation. However, it is difficult to detect small delamination. Furthermore, for the 

delamination located on or close to the mid-plane of laminates along the through-thickness direction, 

the S0 Lamb mode is not efficient. On the other hand, the A0 Lamb mode is suitable for various cases, 

no matter where the delamination is located or no matter what kind of stacking sequence of CFRP is 

used. Furthermore, the A0 Lamb mode is more efficient for detecting very short delamination, compared 

with that detecting long delamination. However, due to its high attenuation, its detection range is quite 

limited. Through extensive explorations, finally, it is found that the optimal excitation frequencies of 

actuator for obtaining strong reflections from delamination are close to the natural frequencies of the 

local delaminated portion, which implies that the strong reflections from delamination is caused by the 

resonance phenomenon of the local delaminated portion. 

2. Delamination detection using S0 Lamb wave mode 

First, the capability and characteristics of delamination monitoring technique based on the S0 Lamb 

wave mode is investigated. As shown in Fig 1, two CFRP laminated composite beams of stack 

sequences of [010/906/906/010] and [012/04/04/012] are used. The length, width and thickness of beam are 

1005mm, 10mm and 4.8mm, respectively. An artificial delamination is made at the interface between 

* E-mail address: huning@faculty.chiba-u.jp. Tel.: 81-43-2903204. 

† E-mail address: fukunaga@ssl.mech.tohoku.ac.jp. Tel.: 81-22-7956997.

274 


two plies by inserting a Teflon sheet of thickness of 25m. Four delamination cases are considered, 

which are [010//906/906/010], [010/906//906/010], [012//04/04/012] and [012/04//04/012], where the symbol “//” 

denotes the position of delamination along the through-thickness direction. The distance from the right 

end of the delamination to the right end of beam is 200 mm. In our experiments, three kinds of 

delamination lengths are employed, i.e., 30 mm, 20 mm and 10 mm, respectively. A circular PZT 

actuator (Fujiceramics, C6) is attached on the top surface of the left end of beam using a kind of very 

strong adhesive. In this case, the generated waves from the actuator merge into the reflected waves from 

the left end of beam directly, and the complex reflection pattern from both ends of the beam can be 

avoided. A same PZT sensor is attached on the top surface of the beam between the delamination and 

the actuator to pick up the reflected wave from the delamination. The diameter of PZT sensor and 

actuator is 10 mm and the thickness is 0.5 mm. Its material properties are: E11=62 GPa, E33=49 GPa, 

d33=472 pC/N, and d31=-210 pC/N. A PCI board of wave signal generation (National Instruments, NI 

PCI-5411) is used to generate the wave signal, which is amplified by an amplifier 

z 

Fig. 1. Schematic view of delaminated beam ([010//906/906/010]) with actuator and sensor (S0 mode). 

Table 1. Material properties of CFRP beams 

E [GPa] G [GPa] [kg/m 3 ] 

E11=115 

E22=E33=9 

G12=G23=G13=3 

12=13=0.3 

23=0.45 

(Krohn-Hite, Model-7500). After the signal is received by the sensor, it is amplified by a charge 

amplifier (FEMTO, DLPCA-200), and then sent into an oscilloscope (Tektronix, TDS3034B) for 

analysis. Finally, the obtained data from the oscilloscope are processed in a computer. By employing 

Hanning window, a signal of 5 cycles and 100 kHz is generated by applying 50 V voltage on the 

actuator as follows, 

Actuator アクチュエータ(PZT) (PZT) Sensor センサ(P (PZT) ZT) Delamination 擬似はく離(10/11層目) 

between 

10 th and 11 th plies 

x 

1005m m mmm 

455 

320 

1600 

0.5[1 

-cos(2 ft / N)]sin(2 ft), t N / f 

Pt () = 

 

0, t N / f 

4.8 

z 

where f is the central frequency in Hz and N is the number of sinusoidal cycles within a pulse. 

Here, the propagation speed of S0 Lamb mode is much higher than that of A0 Lamb mode, e.g., 

around 4 times higher in our case. For instance, in our experimental results, before the arrival of 

incident A0 Lamb mode at the sensor from the left to the right, the reflected S0 modes from the 

delamination and the right end of beam, which travel from the right to the left, already arrive at the 

30 

200 

10 

y 

(1)

N Hu, Y L Liu, H Fukunaga, Y Li. / Delamination detection in CFRP laminates using A0 and S0 Lamb wave modes 

sensor in advance. Therefore, in our sampling time domain for obtaining sensor signals, there is 

completely no A0 Lamb mode, and then it is easy to explain S0 modes only. Moreover, in this work, a 

large amount of the finite element method (FEM) simulations using a three-dimensional hybrid brick 

element proposed by the authors [3] combined with the explicit time integration algorithm have also 

been performed. The efforts for increasing the computational speed in our FEM code have been done. In 

computations, within one wavelength, at least ten elements are used. The material properties of PZT 

stated previously and material properties of CFRP in Table 1 are used. PZT actuator and sensor are 

modeled by a square shape of the edge length of 10 mm. In the delamination region, double nodes are 

set up at the top and bottom surfaces of delamination without consideration of contact effect at the 

interface for simplicity. To reduce the influence of sensor thickness on the wave propagation, which 

leads to the noise in the obtained computational wave signals, the small sensor thickness of 0.05 mm is 

continuously used in the following computations. 

For the case of [010//906/906/010], the comparisons of sensor signals obtained numerically and 

experimentally are shown in Fig 2. Both results are normalized by using the peak value of the incident 

wave. From Fig 2(a), it can be found that there is an obvious reflection from the delamination of 30 mm. 

The computational result agrees with the experimental one very well. For the case of 20 mm 

delamination, from Fig 2(b), the same reflection from the delamination can be identified. However, 

from the 10 mm delamination, in Fig 2(c), no clear reflection from the delamination in both results 

exists. Therefore, it means that for the cases of small delamination, the capability of S0 mode is 

questionable. It should be noted that there is completely no A0 mode in Fig 2 since it propagates too 

slowly and its incident wave from the actuator does not arrive at the sensor within 300 s as shown in 

Fig 2. Moreover, It is interesting to note that for other delamination cases defined previously, such as 

[010/906//906/010], [012//04/04/012] and [012/04//04/012], there is no obvious reflection from the 

delamination of various lengths. For the cases where the delamination is located on the mid-plane of 

laminates, the reason of detection incapability of S0 mode may be from the symmetric deformation 

mode of S0 mode along the through-thickness direction. For the case of [012//04/04/012], the delamination 

is still located near to the mid-plane of the laminates. The results of [012//04/04/012] of 30 mm 

delamination are shown in Fig 2(d) for reference. These results imply that the S0 mode cannot be used to 

detect the delamination which is located on or near the mid-plane of laminates. 

For the case of [010//906/906/010] of 20 mm and 30 mm lengths, to identify the delamination location, 

the wave propagation speed of S0 mode is needed in advance. As shown in Fig 3, an intact CFRP 

cross-ply laminated beam of [010/906/906/010] is used in experiment and FEM numerical computation. 

Two sensors are used to get the wave incident signals. The wave speed can be estimated from the 

distance (420 mm) and the arrival time difference of two sensors. The arrival times of incident wave on 

two sensors are collected by using the time point corresponding to the peak amplitude of incident 

waveform in the time domain directly. Although recently it is quite popular to use the wavelet 

transformation to identify the arrival time [4] , we have found that it is sufficiently accurate to simply and 

directly employ the information of wave signal in the time domain. At 100 kHz, the experimentally 

obtained wave speed of S0 mode is 6210 m/s and the numerically obtained one is 6260 m/s. Furthermore, 

275

276 


based on the transfer matrix method [5] and material properties in Table 1 for cross-ply laminated beams, 

the theoretically obtained wave propagation speed of S0 Lamb mode in this beam at 100 kHz is 6467 

m/s, which is also close to our experimental result. The corresponding theoretical propagation speed of 

A0 Lamb mode is 1506 m/s. Therefore, the wave propagation speed of S0 mode is around 4 times higher 

than that of A0 mode. 

Fig. 2. Waveforms for various delamination cases (S0 mode). 

Finally, by using the time difference between the arrival times of incident wave and reflected wave 

from the delamination, the position of delamination can be obtained easily with the help of the wave 

propagation speed. The identified delamination positions using both experimental and numerical 

techniques, which are marked by the symbol of “▼”, are shown in Fig 4. From this figure, we can find 

that the delamination position can be identified accurately, especially for the case of 30 mm 

delamination. For the case of 20 mm delamination, the error of identified positions is comparatively 

higher. As shown in Fig 2(b), the reason for this error is that the reflected signal from the delamination 

is partially overlapped with the reflection from the right end of beam, which causes the inaccuracy in 

the identification of arrival time of reflected wave from the delamination. Moreover, from the numerical 

simulations for the cases of very long delamination, we can clearly observe that the reflections occur at 

the two ends of delamination. We have found that the reflected S0 Lamb mode with a strong intensity,


which can be practically measured by the sensor with sufficient accuracy, actually starts from the right 

end of the delamination, but not from the left end of delamination. Therefore, in Fig 4, all identified 

delamination positions are located at the right region of the delamination. 

z 

アクチュエータ(PZT) 

Actuator (PZT) 

x 

z 

x 

センサ1(PZT) Sensor 1 

(PZT) 

205 420 

Fig. 3. An intact laminated beam ([010//906/906/010]) for measuring wave speed. 

(a) 剥離30mm 30 mm delamination 

(b) 剥離20mm 20 mm delamination 

Fig. 4. Identified delamination position ([010//906/906/010]). 

3. Delamination detection using A0 Lamb wave mode 

Sensor センサ2(PZT) 2 

(PZT) 

1005mm 10 

Num 解析実験 Exp. 

. 

4.8 

z 

y 

アクチュエータ(PZT) Actuator (PZT) センサ(PZT) Sensor (PZT) Delamination 

擬似剥離 

1005mm 10 

455 350 200 

In this section, we will investigate the characteristics of delamination monitoring technique based on 

the A0 Lamb wave mode. The various delamination cases stated previously are used. From our 

experimental results, it is verified that the A0 mode cannot propagate a long distance due to its higher 

attenuation. As shown in Fig 5, two actuators are located near the delamination. For the A0 mode, two 

actuators are attached on the top and bottom surfaces of the beam with applied out-of-phase voltages, as 

shown in Fig 5. Although this arrangement can generate relatively pure A0 mode, there are still 

reflections in S0 mode due to the mode change caused by the scattering between the Lamb waves and 

1mm 

7mm 

32mm 

51mm 

拡大 Enlarged 

Num 解析実験 Exp. 

. 

4.8 

z 

y 

277

278 


the delamination. To pick up the pure A0 mode, two PZT sensors are attached (Fig 5). The difference of 

signals between the two sensors can produce the pure A0 mode. Naturally, the summation of two signals 

can yield the pure S0 mode. The same signal as shown in equation 1 is used for the A0 mode, and the 

frequency of the signal, i.e., f, is 50 kHz. Other conditions are identical to those in the S0 mode. 

Furthermore, to confirm our experimental results, the same FEM simulations for the A0 mode are also 

performed. 

Actuator (PZT) Sensor (PZT) Delamination 

- 

+ 

(PZT) 

Fig. 5. Schematic view of delaminated beam with actuators and sensors (A0 mode). 

Fig. 6. Waveforms for various delamination cases (A0 mode).


アクチュエータ(PZT) 

Actuator (PZT) 

z 

x 

Fig. 7. Waveforms for various delamination cases (A0 mode). 

Sensor センサ1(PZT) 1 (PZT) 

センサ2(PZT) Sensor 2 (PZT) 

50 400 

Fig. 8. An intact laminated beam for measuring wave speed (A0 mode). 

First, to explore the capability of A0 mode for the cases where S0 mode fails, we have checked the 

case of [010/906//906/010] where the delamination is located on the mid-plane of laminates with three 

different lengths. As shown in Figs 6(a), 6(b) and 6(c), the clear reflection from the delamination can be 

identified for various delamination lengths when using A0 mode. Note that the results shown in these 

figures are the difference between the upper and lower sensors. It is also interesting to note that the 

reflection from the 10 mm delamination is the strongest one compared with those of 20 mm and 30 mm 

delamination cases, which may be caused by the overlapping of two reflections from the right and left 

ends of the delamination, when the delamination is short. Moreover, the A0 mode can be used for the 

delamination case of [010//906/906/010] where the S0 mode is capable for the 20 mm and 30 mm 

delamination. However, the A0 mode is more sensitive to the case of small delamination, e.g., 10 mm 

delamination where the S0 mode fails. For the stack sequence of [010/906/906/010], the influence of the 

delamination position along the through-thickness direction is small. For instance, the comparison of 

two waveforms of 10 mm delamination for the cases of [010//906/906/010] and [010/906//906/010] is shown 

in Fig 6(d). From this figure, we can find that there is no significant difference in the amplitudes of 

reflections from the delamination in the two waveforms. 

1005mm 10 

4.8 

z 

y 

For the cases of [012//04/04/012] and [012/04//04/012], the A0 mode is also very efficient. As shown in 

Figs 7(a) and 7(b), for 10 mm delamination and 20 mm delamination, we can clearly identify the 

reflections from the delamination in experimental results. Moreover, for short delamination, e.g., 10 mm 

delamination, similar to the results in Fig 6, the A0 mode is more efficient. Furthermore, from Figs 7(a) 

and 7(b), we can find that the influence of the delamination position along the through-thickness 

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280 


direction is insignificant. Again, the reflection from 10 mm delamination is stronger than that of 20 mm 

delamination. 

A 30 mm delamination 






Exp. Num. 

Num. 

Num. Exp. 

Num./Exp. 

Num. 

Fig. 9. Identified delamination position (A0 mode). 

To obtain the wave speed for the identification of delamination location, as shown in Fig 8, two intact 

CFRP laminated beams for the stack sequences of [010/906/906/010] and [012/04/04/012] are used in 

experiment and FEM numerical computation. Two sensor sets are used to receive the wave incident 

signals. The wave speed can be estimated from the distance (400 mm) and the arrival time difference of 

two sensor sets. At 50 kHz, for the A0 mode, experimental and numerical wave speeds for 

[010/906/906/010] are 1555 m/s and 1401 m/s, respectively. For [012/04/04/012], experimental and 

numerical wave speeds are 1723 m/s and 1406 m/s, respectively. It can be found that the difference of 

experimental wave speed and numerical one is higher in the case of [012/04/04/012]. This phenomenon 

may be caused by the comparatively lower material properties of CFRP in Table 1, which are used in 

Exp. 

Num. Exp. 

[010/906//906/010] 

[012/04//04/012]


FEM simulations. Especially, G23 and G13 may be lower than the practical ones. Finally, for various 

delamination cases, the delamination locations are identified experimentally and numerically. For 

[010/906//906/010] and [012/04//04/012], the identified delamination locations are shown in Figs 9(a) and 

9(b) as examples. 

4. Optimal excitation frequency of Lamb wave for delamination detection 

To improve the reliability of the damage detection techniques based on Lamb waves for CFRP 

composite laminates, we aims at excited wave signal features for obtaining the strongest reflected wave 

(or the weakest transmitted wave) from delamination in CFRP laminates. Especially, we focus on the 

effect of excitation frequency in Lamb wave signals. We only investigate the A0 mode here, however, as 

revealed later, the conclusion obtained in this research is a general one, which is also applicable to the 

case of S0 mode. 

Fig. 10. Computational model delamination detection using A0 mode. 

First, A0 mode propagation in CFRP delaminated beams, which is excited by two piezoelectric PZT 

actuators with out-of-phase applied voltages, is numerically simulated. The numerical method, based on 

a Chebyshev pseudospectral Mindlin plate element [6] proposed by present authors, is employed. The 

effectiveness of the numerical method for simulating the Lamb wave propagation in delaminated CFRP 

beams is verified by comparing the numerical results with experimental ones for the cases of 

[010/906//906/010] and [010//906/906/010] in advance. It is found that the present numerical method can 

yield highly accurate results with very low computational cost, generally from ten times to twenty times 

lower than those of some conventional FEM. 

Then, as shown in Fig 10, we investigate the excitation frequency of PZT which can lead to the 

strong reflection from the delamination for both cases of [010/906//906/010] and [010//906/906/010]. The 

reflection intensity is defined in Fig 11, i.e., H1/H0, which is the ratio between the amplitude of the 

reflected wave and that of the incident wave. 

For 30 mm delamination of [010/906//906/010], the normalized wave signals at the excitation 

frequencies of 4 different frequencies are shown in Fig 11. From this figure, it can be found that there is 

a very strong reflected wave from the delamination at the excitation frequency of 42 kHz, whereas the 

reflected wave from the delamination is the weakest one at 80 kHz, which implies that a higher 

excitation frequency of shorter wavelength may not be more powerful for detecting a delamination 

regardless of signal-to-noise ratio problem. Furthermore, the result also suggests that the common sense 

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that the waves of smaller wavelength are more sensitive to defects, may not be absolutely correct, at 

least in our defined frequency range. 

Fig. 11. Waveforms of various excitation frequencies ([010/906//906/010]). 

For 30 mm delamination of [010//906/906/010], the normalized original wave signals of the beam at the 

excitation frequencies of 45 kHz and 80 kHz are shown in Fig 12(a). It can be found that the signals are 

seemingly irregular since there is S0 mode generated due to mode change caused by interaction of the 

delamination and A0 mode when the delamination is not located on the mid-plane of beams. By 

calculating the difference between the signal of top sensor and that of bottom sensor, the pure A 0 mode 

can be collected. Figure 12(b) presents the wave signals of pure A0 mode at the excitation frequencies of 

45 kHz and 80 kHz. This figure demonstrates the same phenomenon as that in Fig 11, i.e., a higher 

excitation frequency generates a weaker reflection wave from the delamination. 

Finally, for various lengths of two cases of delamination, we investigate the reflection intensity 

H1/H0 corresponding to a wide frequency range, i.e., 15 kHz ~ 120 kHz. The results of [010//906/906/010] 

are plotted in Fig 13. From this figure, it is interesting to note that there are multiple peaks 

corresponding to the strong reflection. It means that there are multiple optimal excitation frequencies 

which can be used practically. High excitation frequency with smaller wavelength does not certainly 

lead to the strong reflection. 

To further explore the relationship between the delamination length and the excitation frequency, 

we pick up the multiple peaks corresponding to the optimal excitation frequencies in Fig 13 for the 

cases [010/906//906/010] and [010//906/906/010]. These results are plotted in Fig 14. From this figure, we 

can find that the optimal excitation frequencies of various orders decrease as the delamination length 

increases. 

To uncover the physical meaning of the above optimal excitation frequencies, we investigate the 

natural frequencies of the local delaminated regions in Fig 15 in detail. The models which only contain 

the upper or lower delaminated layers in beams as shown in Fig 16 are built up. In Fig. 16(a), 

for the case of [010/906//906/010], we only set up a half model along the through-thickness direction with


the lower delaminated layer since the delamination is located on the mid-plane of the beams. In Fig 

16(b), for the case [010//906/906/010], since the delamination is not located on the symmetrical plane, two 

models are built up. One is based on the upper delaminated layer, i.e., [010], and the other is based on the 

lower delaminated layer, i.e., [906/906/010]. In this vibration analysis, however, it is extremely difficult 

to model the true boundary conditions for the local delaminated region selected out. Only one point we 

can make sure is that the stiffness parameters of connection between the intact portion and the 

delaminated portions should be located between those provided by the fixed boundary condition and 

those provided by the pinned boundary condition. Therefore, the two common boundary conditions 

were used to estimate upper and lower limits of the natural frequencies of the local delaminated regions 

as shown in Fig. 16. 

Fig. 12. Waveform of various excitation frequencies ([010//906/906/010]). 

(a) delamination length: 10~20 mm 

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284 


(b) delamination length: 20~30 mm 

Fig. 13. Reflection intensity corresponding to various excitation frequencies ([010//906/906/010]). 

Optimal frequency [kHz] 

Optimal frequency [kHz] 

120 

110 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

60 

50 

40 

30 

20 

first peak 

second peak 

third peak 

fourth peak 

10 12 14 16 18 20 22 24 26 28 30 32 

Delamination length [mm] 

(a) [010/906//906/010] 

100 first peak 

second peak 

90 

third peak 

fourth peak 

80 

fifth peak 

sixth peak 

70 

10 

8 10 12 14 16 18 20 22 24 26 28 30 32 

Delamination Length [mm] 

(b) [010//906/906/010] 

Fig. 14. Optimal excitation frequency versus delamination length.


delamination delamination 

(a) [010/906//906/010] (b) [010//906/906/010] 

(a) 90/90 (b) 0/90 

Fig. 15. local delamination portion. 

fixed pinned 

upper part [0] 

lower part [90/90/0] 

(a) [010/906//906/010] (two boundary conditions) 

(b) [010//906/906/010] (two boundary conditions) 

Fig. 16. Model for natural vibration analysis. 

By using the delaminated models described above, we calculated their natural frequencies using an 

8-noded Mindlin plate element in ABAQUS. Surprisingly, it is found that the optimal excitation 

frequencies are located between the natural frequencies of models with the fixed boundary condition 

and ones of models with the pinned boundary condition. Taking 20 mm delamination ([010/906//906/010]) 

as an example, we discuss the relationship between the optimal excitation frequency and the natural 

frequency of the local delaminated regions in detail. In this case, there are three optimal excitation 

frequencies (17 kHz, 44 kHz and 105 kHz) in our investigated frequency range. Figure 17(a) shows that 

the smallest optimal excitation frequency is located between the first natural frequency of model 

([010/906//906/010]) with fixed boundary and that with pinned boundary; the second optimal one is 

located between the second natural frequencies of two boundary conditions; and the third optimal one is 

close to the seventh natural frequencies of two boundary conditions. The vibration modes corresponding 

to the first, second and seventh natural frequencies are all pure flexural, which are presented in Fig 17. 

Moreover, it is interesting to note that the vibration modes of the third, fourth, fifth and sixth natural 

frequencies are not pure flexural, which include some other displacement components, such as the 

unsymmetric bending mode along the width direction of the plate. Therefore, our research results show 

that the optimal excitation frequencies have inherent relationships with some natural frequencies of the 

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286 


local delaminated regions. Furthermore, those natural frequencies possess pure flexural vibration modes 

(A0 deformation mode). Therefore, when an excitation frequency of Lamb waves is close to these 

natural frequencies, resonance occurs which leads to a much higher reflection from the delamination. In 

this case, the excitation frequency becomes an optimal excitation frequency. Since there are many 

natural frequencies of the local delaminated region corresponding to pure flexural vibrations, there 

should be many optimal excitation frequencies correspondingly. The above finding is obviously 

inconsistent with the widely acknowledged common sense that the sensitivity of Lamb waves to 

damages increases as the frequency increases or the wavelength decreases, at least within the frequency 

range investigated here. This conclusion is also applicable to S0 mode where the resonant frequencies 

with the vibration modes corresponding to the deformation pattern of S0 mode, i.e., axial deformation, 

can be thought of as optimal excitation frequencies. 

The above finding is very helpful for designing a more appropriate wave signal when using Lamb 

waves in damage detections. For instance, a broad-band signal or a special designed signal pattern 

which is realized by emitting many individual narrow-band signals continuously one by one with a 

small frequency increment, should be used to guarantee the reliability of delamination detection. 

(a) Optimal excitation frequency 

Fig. 17. Optimal excitation frequency versus natural frequency (20 mm delamination [010/906//906/010]).

5. Conclusion 


In this report, we explore the characteristics of delamination monitoring techniques based S 0 and A0 

Lamb wave modes. It is found that the S0 mode can be used for the delamination detection in a wide 

region due to its small attenuation. However, it is insensitive to the small delamination or the cases 

where the delamination is located on or near the mid-plane of laminates. When using A0 Lamb wave 

mode, it is very powerful for various delamination cases although it can only detect the delamination 

which is near the actuator/sensor sets. Especially, the A0 mode is very suitable for small delamination, 

where very strong reflection can occur due to overlapping of two reflections from the two ends of 

delamination. Finally, we investigate the relationship between the actuator excitation frequency and 

reflection intensity from the delamination. It is found that there are multiple optimal excitation 

frequencies which can lead to the strong reflection. These multiple optimal excitation frequencies 

correspond to the natural frequencies of the local delaminated portion. It means that the strong reflection 

from the delamination is caused by the resonance of the local delaminated portion. The high excitation 

frequency with small wavelength does not certainly result in the strong reflection intensity or high 

detection sensitivity. 

References 

[1] Diamanti K, Soutis C, Hodgkinson J M. Lamb waves for the non-destructive inspection of monolithic and sandwich composite beams. 

Composites: Part-A, 2005, 36: 189-195. 

[2] Toyama N., Takatsubo J. Lamb wave method for quick inspection of impact-induced delamination in composite laminates. Composites 

Science & Technology, 2004, 64: 1293-1300. 

[3] Cao Y P, Hu N, Lu J, Fukunaga H, Yao Z H. A 3D brick element based on Hu-Washizu variational principle for mesh distorsion. 

International Journal of Numerical Methods in Engineering, 2002, 53: 2529-2548. 

[4] Jeong H, Jang Y S. Wavelet analysis of plate wave propagation in composite laminates. Composite Structures, 2000, 49: 443-50. 

[5] Nayfeh A H, Chimenti D E. Elastic wave propagation in fluid-loaded multi-axial anisotropic media. Journal of Acoustics Society of 

America, 1991, 89: 542-549. 

[6] Liu Y, Hu N, Yan C, Peng X, Yan B. 2009. Effects of integration schemes on accuracy of a Mindlin pseudospectral plate element. Finite 

Elements in Analysis and Design, 2009, 45: 538-546. 

287

Effect of Temperature on Fatigue behavior in nylon 6-clay 

hybrid nanocomposites 


S J Zhu a, *, M Kichise a , A Usuki b , M Kato b 

a Fukuoka Institute of Technology, Department of Intelligent Mechanical Engineering, 

3-30-1 Wajirohigashi, Higashi-ku, Fukuoka, 811-0295, Japan 

b Toyota Central R & D Labs, Inc., Nagoya, Japan 

The nylon 6-clay hybrid (NCH) nanocomposites were synthesized in Toyota Central R & D Labs in 

1987 [1]. Since the NCH nanocomposites showed high strength, elastic modulus, heat resistance and 

other properties, they have been used for automobiles, electronic industry and food package. It is 

expected that the applications of the nanocomposites will be extended to aerospace, energy, 

environment and biology industries if their time-dependent performances are evidenced. It was reported 

that the tensile strength of 5 wt% clay reinforced nylon 6 nanocomposite was higher than that of 2 wt% 

clay reinforced nylon 6 nanocomposite, but the fatigue life was opposite [2]. This means that cyclic 

deformation and fracture of NCH nanocomposites should be investigated to establish evaluation method 

for improving the nanocomposite and life prediction method. Moreover, mechanical properties of 

polymer are sensitive to temperature due to low glass transition temperature. In this research, tensile and 

fatigue behaviour at glass transition temperature was investigated and compared with that at room 

temperature. 

2. Materials and Experimental Procedures 

Three kinds of materials were used for monotonic tension and fatigue tests, which were nylon 6, 2 

wt% clay reinforced nylon and 5 wt% clay reinforced nylon nanocomposites. Both the tensile tests and 

fatigue tests were conducted at room temperature, 35 o C and 50 o C using a servo-hydraulic testing 

machine. The specimens for tests are 80 mm in gage length, 10 mm in width and 4 mm in thickness. 

The tensile tests with a displacement control were carried out at three strain rate of 10 -2 s -1 . The fatigue 

tests with a load control were performed at stress ratio of 0.1 and frequency of 0.1 Hz in sine wave form. 

The fracture surfaces were observed using scanning electronic microscope (SEM). 


It is shown that the 2 wt% clay reinforced nylon and 5 wt% clay reinforced nylon have similar 

strengths, which are increased by about 30% compared to those of nylon 6 at room temperature, as 

shown in Fig. 1. However, the tensile strength of 5 wt% clay reinforced nylon is higher than that of 2 

* E-mail address: zhu@fit.ac.jp

S J Zhu, M Kichise, A Usuki, M Kato. / Effect of Temperature on Fatigue behavior in nylon 6-clay hybrid nanocomposites 

wt% clay reinforced nylon at both 35 o C and 50 o Strain Rate : 10 

C. The early brittle fracture caused the 5 wt% clay 

reinforced nylon did not perform its ability in strength at room temperature. The increase in flowing 

ability at both 35 o C and 50 o C makes the 5 wt% clay reinforced nylon composite realize it 

strengthening ability. 

Tensile strength (MPa) 

-2 - 

s 

1 

110 

100 

90 

80 

70 

60 

50 

40 

Nylon6 

NCH-2 

NCH-5 

30 

15 20 25 30 35 40 45 50 55 

Temperature(℃) 

Fig. 1. Ultimate tensile strength versus testing temperature at a strain rate of 10 -2 s -1 . 

Maximum Stress (MPa) 

100 

90 

80 

70 

60 

50 

Nylon6 (20℃) Nylon6 (35℃) 

NCH-2 (20℃) 

NCH-5 (20℃) 

A 

40 

1 10 10 2 

10 3 

NCH-2 (35℃) 

NCH-5 (35℃) 

10 4 

Number of Cycles to Failure 

Fig. 2. Maximum stress versus number of cycles to failure at room temperature and 35 o C. 

The fatigue strength of 2 wt% clay reinforced nylon is also increased by about 30% compared to that 

of nylon 6, but the fatigue strength of 5 wt% clay reinforced nylon is slightly increased or similar to that 

of nylon 6 at room temperature, as shown in Fig. 2. The cyclic creep deformation is noted by examining 

using stress-strain hysteresis loops. The small cyclic deformation in 5 wt% clay reinforced nylon 

composite is attributed to the no increase in fatigue strength. The observation of fatigue fracture 

surfaces also shows brittle fracture features in 5 wt% composite, where crack initiated at small pores 

and a mirror zone can be seen. The fatigue fracture surfaces in 2 wt% composite show dimples and 

flowing morphology, implying a good compatibility of strength with ductility. 

Although the tensile strength and fatigue strength of NCH-2 are the highest at room temperature, the 

tensile strength and fatigue strength of NCH-5 became the highest at 35 o C. Fatigue fracture surfaces 

showed different patterns between at room temperature and 35 o C. 

A 

10 5 

289

290 

References 


[1] A. Usuki, Y. Kojima, M. Kawasumi, A. Okada, T. Kurauchi, O. Kamigaito, J. Mater. Res., 8 (1993) 1174. 

[2] S. Zhu, M. Okazaki, A. Usuki, M. Kato, J. Soc. Mater. Sci., Japan, 58(12) (2009) 969.

Fatigue Behavior of Unidirectional Jute Spun Yarn Reinforced 

PLA 

H Katogi a, *, Y Shimamura b , K Tohgo, T Fujii 

a Graduate Student of Science and Technology Educational Division, Department of Environment and Energy System, Shizuoka University, 

3-5-1 Johoku, Naka-ku, Hamamatsu, Shizuoka 432-8561, Japan 

b Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, Shizuoka 432-8561, Japan 

Abstract 

Natural fiber reinforced composites, which can be carbon neutral materials, have expected to be alternative materials 

of glass fiber reinforced plastics. Most of them use polylactic acid (PLA) as matrix because PLA is made out of plants 

and has biodegradability. They are often called „Green composites‟. Recently, unidirectional reinforcement techniques of 

natural fibers have been developed for improvements of modulus and strength. Fatigue property of the unidirectional 

reinforced composites should be investigated to assure the structural integrity. In this study, fatigue property of 

unidirectional jute yarn reinforced PLA was investigated and the fatigue mechanism was discussed. As a result, it was 

found that the S-N diagram had a steep slope like GFRP and the fatigue property of PLA dominated the fatigue life of the 

composite. 

Keywords: Green composite, Jute spun yarn, PLA, Fatigue property, Fatigue mechanism 


Natural fiber reinforced composites, which can be carbon neutral materials, have expected to be 

alternative materials of glass fiber reinforced plastics (GFRP). Many papers of natural fiber reinforced 

plastics (NFRP) have been published [1-7]. Most of them use polylactic acid (PLA) as matrix because 

PLA is made out of plants, i.e. renewable resource, and has biodegradability. They are often called 

„Green composites‟. Commercial products using green composites are available in market. Most 

products are processed with injection molding of short fibers.. 

Recently, unidirectional reinforcement techniques of natural fibers have been developed for 

improvements of modulus and strength [9, 10]. Fatigue property of the unidirectional reinforced 

composites should be investigated to assure the structural integrity. A few reports on fatigue property of 

natural fiber reinforced petroleum-based thermoset plastics have been reported [11, 12], but the fatigue 

behavior natural fiber reinforced biodegradable resin has never been reported. 

In this study, fatigue behavior of unidirectional jute yarn reinforced PLA was investigated and the 

fatigue mechanism was discussed. 

* Corresponding author. Tel&Fax: +81-53-478-1029. 

E-mail address: hkatogi@mechmat.eng.shizuoka.ac.jp

292 

2. Materials, specimen and testing methods 

2.1 Materials and Specimen 


Water-dispersible PLA resin (Miyoshi Oil and Fat Co., Ltd., PL-2000) was used as matrix. Jute spun 

yarn (BMS Co., Ltd., Asa no himo) was used as reinforcement. 

Alkaline treatment with NaOH5% of jute spun yarn for 3 hour at room temperature was conducted to 

make performs [13]. The alkaline treated fibers were washed by water, wound around a metallic plate, 

and dried in a furnace. Then the water-dispersible PLA resin was impregnated into the preform to make 

prepregs. The prepregs were unidirectionally laminated and hot-pressed at 140 o C for 20 min. The 

number of stacking is three, and five laminates were prepared. The volume fraction was measured using 

an optical microscope. The volume fraction of laminates was 27%, 28%, 31%, 43% and 44%. 

The specimen for quasi-static tensile tests and fatigue tests were shown in Fig.1. The specimen size 

was 10.0 mm wide, 140.0 mm long and 3.5 mm thick according to JIS K 7164. Aluminum tabs were 

glued. Figure 2 shows the cross section of the composite plate. It was found that PLA resin was well 

impregnated into yarns. 

2.2 Tensile Testing 

10.0 

140.0 

40.0 60.0 

Aluminium tab 

Fig. 1. Specimen. 

Fig. 2. Cross section of specimen. 

t: 2.7 

[unit :mm] 

Tensile tests are conducted to measure Young‟s modulus and ultimate strength based on JIS K 7164. 

Loading direction was the yarn direction. The cross-head speed was 1.0 mm/min. Both strain gauges 

and an extensometer were used for measuring strain. Seven specimens were prepared. The volume 

fractions of specimens were 27% and 44%.

2.3 Fatigue Testing 

H Katogi, Y Shimamura, K Tohgo, T Fujii. / Fatigue Behavior of Unidirectional Jute Spun Yarn Reinforced PLA 

Fatigue tests with sinusoidal wave were conducted using a hydraulic servo testing machine 

(Shimadzu Co., EM50kNT). The maximum stressmax was set to be 90% ~ 40% of ultimate strengthB 

and the stress ratio was set to be 0.1. During fatigue tests, cyclic stress-strain curves were recorded at 

10 3 , 10 4 , 10 5 and 10 6 cycles. The volume fractions of specimens were 27%, 28% and 31%. 

2.4 Residual Tensile Strength 

Residual tensile strength was measured after cyclic loading with max=0.8B. The conditions of cyclic 

loading were the same as those of fatigue testing. The volume fraction of specimens was 43%. 

2.5 Observation methods 

After cyclic loading, specimens were observed using an optical microscope and SEM in order to 

investigate damage propagation during fatigue testing. 

For damage observing during fatigue testing, fatigue tests of several specimens were interrupted. 

After the specimen surface was observed, matrix was hydrolyzed in water at 90 o C for 72 hr and damage 

of jute spun yarn was observed. 

Macroscopic and microscopic fracture modes of quasi-static and fatigue (max=0.8B and 0.5B) test 

specimens were also observed. 


3.1 Tensile Test 

Figure 3 shows a typical stress-strain curve. The stress-strain curve was almost linear. The average 

Young‟s modulus was 4.9 GPa ± 1.7 GPa and the average tensile strength was 59.5 MPa ± 3.7 MPa, 

where the error band is the standard deviation. 

Stress [MPa] 

60 

50 

40 

30 

20 

10 

0 

0 0.5 1 1.5 2 2.5 

Strain [%] 

Fig. 3. Stress - strain curve. 

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294 

3.2 S-N Diagram 


Figure 4 shows an S-N diagram. The S-N diagram had a steep slope. Fatigue limit was not observed. 

Fatigue life increased as increasing the volume fraction of reinforcement because higher volume 

fraction means lower stress in yarn and resin. The fatigue life at 10 6 cycles is around 55% of the 

ultimate strength; the fatigue property is similar to that of GFRP [14]. 

Residual strength [MPa] 

Stress amplitude [MPa] 

100 

80 

60 

40 

20 

30 

25 

20 

15 

10 

5 

Vf=27% 

Vf=28% 

Vf=31% 

10 

Number of cycles to failure Nf [cycle] 

0 101 102 103 104 105 106 107 0 

0.8ζB 

Fig. 4. S-N diagram. 

Fatigue life 

10 

Number of cycle [cycle] 

0 101 102 103 104 105 0 

Fig. 5. Residual tensile strength (ζmax=0.8ζB).


3.3 Residual Tensile Strength 

Residual tensile strength after cyclic loading (max=0.8B) is shown in Fig.5. In Fig.5, the vertical 

axis is residual tensile strength and the horizontal axis is the number of cycles when fatigue tests were 

interrupted. For reference, the maximum stress of cyclic loading and fatigue life with a factor of two 

scatter band are also shown. The residual tensile strength rapidly decreased just before final failure. This 

implies that fiber breakage of reinforced yarn occurs just before final failure. 

3.4 Damage Propagation 

3.4.1 Macroscopic and microscopic fracture observation 

Macroscopic fracture mode and facture surface of quasi-static tensile failure and fatigue failure for 

high (max=0.8B) and low (max=0.5B) stress amplitudes are shown in Figs.6 and 7. The macroscopic 

and microscopic fracture morphologies were similar regardless of loading condition and stress 

amplitude except for long delamination at low stress amplitude. 

3.4.2 Damage of composite during cyclic loading 

Figure 8 shows surface cracks just before fatigue failure (max=0.8B). It was found that many cracks 

initiated orthogonal to the loading direction in PLA resin during cyclic loading. It is noteworthy that 

breakage of jute filaments in front of large cracks in PLA resin was also found. 

(a) Quasi-static test. 

(b) Fatigue test (ζmax=0.8ζB). 

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296 


(c) Fatigue test (ζmax=0.5ζB). 

Fig. 6. Macroscopic fracture modes. 

(a) Quasi-static test. 

(b) Fatigue test (ζmax=0.8ζB). 

(c) Fatigue test (ζmax=0.5ζB). 

Fig. 7. SEM images of fracture portion of jute filament.


(a) Macroscopic image. 

(b) Non-crack surface (A area). 

(c) Resin cracks (B area). 

(d) Resin cracks and fiber breakage (C area). 

Fig. 8. Specimen surface after cyclic loading (ζmax=0.8ζB). 

3.4.3 Damage of jute spun yarn during cyclic loading 

From the results, we supposed that matrix cracking preceded the breakage of jute filaments. Thus, 

matrix was hydrolyzed for observation of damage in jute spun yarn. Figure 9 shows jute spun yarns 

297

298 


extracted from the specimen shown in Fig.8. In Fig.9, areas A, B and C correspond to those in Fig.8. 

The results showed that breakage of jute filaments occurred only when a matrix crack became larger 

enough to break jute filaments. 

3.5 Fatigue mechanism 

(a) Spun yarn underneath non-crack surface (A area) and small cracks (B area). 

(b) Fiber breakage at a tip of a large crack. 

Fig. 9. Jute spun yarn extracted from specimen after cyclic loading (ζmax=0.8ζB). 

The fracture mechanism of the unidirectional jute spun yarn reinforced PLA is probably as follows: 

fatigue cracks in PLA resin initiate and propagate from specimen surface until the cracks get to jute 

spun yarns; stress concentration at the crack tip leads to breakage of jute filaments; the accumulation of 

fiber breakage causes the final failure. Nonoyama et al. [15] reported that S-N diagrams of PLA with 

different crystallinity. The fatigue lives at any strain amplitude are equal or less than those of our results. 

This supports the proposed fatigue mechanism.


In the composite system we fabricated, the fatigue property of PLA probably dominates the fatigue 

life of the composite as a result of brittleness of PLA. In addition, the results indicated the fatigue 

property of jute is better than that of PLA. Therefore, usage of more ductile polymer such as PBS might 

enhance the fatigue life though the research work on the fatigue behavior of natural fibers is also 

needed. 

3.6 Cyclic stress-strain curve 

Typical cyclic stress-strain curves (max=0.5B) are shown in Fig.10. The cyclic stress-strain curve 

was almost linear regardless of the maximum stress amplitude. The changes of the strain range and 

average strain with the number of cycles are shown in Fig.11. The strain range, i.e. stiffness, remained 

unchanged during cyclic loading. On the other hand, the average strain continued to increase. The 

results indicate that creep deformation of PLA resin occurred during cyclic loading and thus caused the 

slight change of spun structure of yarn. 

Stress (MPa) 

60 

50 

40 

30 

20 

10 

Total strain range [%] 

0 

1000 cycle 

10000cycle 

100000cycle 

1000000cycle 

0 1 2 3 

Strain (%) 

4 5 6 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

Fig. 10. Cyclic stress-strain curves (ζmax=0.5ζB). 

10 

Number of cycle N 

3 104 105 106 0 

(a) Total strain range Δε 

max=60%,Vf=28% 

max=50%,Vf=28% 

max=40%,Vf=31% 

299

300 


Average strain (%) 


3 

2.5 

2 

1.5 

1 

0.5 

max=60%, Vf=28% 

max=50%, Vf=28% 

max=40%, Vf=31% 

10 

Number of cycle N 

3 104 105 106 0 

(b) Average strain range 

Fig. 11. Changes of total strain range and average strain. 

The fatigue behavior of unidirectional jute spun yarn reinforced PLA was investigated. The following 

conclusions were obtained. 

(1) The S-N diagram had a steep slope like GFRP and fatigue limit was not observed. 

(2) Fatigue cracks in PLA resin caused the breakage of jute filaments, and the accumulation of the 

fiber breakage led to the final failure. 

References 

[1] P. Wambua, J. Ivens and I. Verpoest, Natural fibres: can they replace glass in fiber reinforced plastics?, Compos. Sci. Technol., 63 (2003) 

1259-1264. 

[2] T. Nishino, K. Hirao, M. Kotera, K. Nakamae, H. Inagaki, Kenaf reinforced biodegradable composite, Compos. Sci. Technol, 63 (2003) 

1281-1286. 

[3] Y. Cao, K. Goda and S. Shibata, Development and mechanical properties of bagassa fiber reinforced composites, Adv. Compos. Mater., 16, 

4 (2007) 283-298. 

[4] H. Takagi, S. Kato, K. Kusano and A. Ousaka, Thermal conductivity of PLA-bamboo fiber composites, Adv. Compos. Mater., 16, 4 (2007) 

377-384. 

[5] K. Takemura and Y. Minekage, Effect of molding condition on tensile properties of hemp fiber reinforced composite, Adv. Compos. Mater., 

16, 4 (2007) 2385-394. 

[6] K. Okubo, T. Fujii and E. T. Thostenson, Multi-scale hybrid biocomposite: Processing and mechanical characterization of bamboo fiber 

reinforced PLA with microfibrillated cellulose, Compos. A, 40, 4 (2009) 469-475. 

[7] N. Graupner, A. S. Herrmann and Jörg Müssig, Natural and man-made cellulose fibre-reinforced poly(lactic acid) PLA composites: An 

overview about mechanical characteristics and application areas, Compos. A, 40 (2009) 810-821. 

[8] Khondker, U. S. Ishiakua A. Nakai and H. Hamada, A novel processing technique for thermoplastic manufacturing of unidirectional 

composites reinforced with jute yarns, Compos. A, 37, 12 (2006) 2274-2284. 

[9] G. Ben, Y. Kihara, K. Nakamori and Y. Aoki, Examination of heat resistant tensile properties and molding conditions of green composites 

composed of kenaf fibers and PLA resin, Adv. Compos. Mater., 16, 4 (2007) 361-376. 

[10] N. Towo and M. P. Anell, Fatigue sisal fibre reinforced composites: constant-life diagrams and hysteresis loop capture, Compos. Sci. 

Technol., 68 (2008) 915-924. 

[11] N. Towo and M. P. Anell, Fatigue evaluation and dynamic mechanical thermal analysis of sisal fibre-thermosetting resin composites,


Compos. Sci. Technol., 68 (2008) 925-932. 

[12] H. Kobayashi, M. Kubouchi, T. Sakai, T. Tumolva and K. Tsuda, Proc.10th Japan International SAMPE Symposium & Exhibition (2007) 

(CD-ROM). 

[13] P. K. Mallick, Fiber-reinforced composites, Marcel Dekker, (1993) 249-253. 

[14] Y. Nonoyama, M. Kawagoe and K. Sanada, Tensile properties and fatigue behavior of polylactic acid, Proc. 42th Hokuriku Shin‟etsu 

Branch Meeting of J. Soc. Mech. Eng., 047-1 (2005) 327-328. (in Japanese) 

301

Abstract 

An evaluation on thermal shock fatigue damage of SiC 

composite using nondestructive technique 

J K Lee a, *, S P Lee b,† , J H Byun c,‡ 

a Dept. Of Mechanical Engineering, Dongeui University, Busan 614-714, South Korea 

b Dept. Of Mechanical Engineering, Dongeui University, Busan 614-714, South Korea 

c Composite Materials Group, Korea Institute of Materials Science, Chanwon 641-831, South Korea 

The fabrication route of monolithic SiC materials by the complex compound of ultra-fine SiC particles and oxide 

additive materials have been investigated. SiC materials were fabricated by a liquid phase sintering process, using a SiC 

powder with an average size of about 30 nm. The ultrasonic technique, one of the nondestructive tests, was used to 

evaluate the optimum fabrication conditions of SiC materials by using the parameters of attenuation coefficient and 

velocity. In addition, a thermal shock test was conducted to evaluate the fatigue damage of the SiC material underwent 

thermal shock repetitively. 

Keywords: monolithic SiC material; attenuation coefficient; nondestructive test; ultrasonic wave; additive material 


Silicon carbide (SiC) is an useful material which be used under severe environmental conditions due 

to its high temperature resistance, mechanical property and aggressive chemicals.[1-2] However, the 

strength and the reliability of SiC materials are influenced by many parameters such as crystal structure, 

porosity, participation and defects despite of these advantages. Especially, the local stress distribution in 

the vicinity of the crystalline inclusions is affected by mismatches in the elastic properties, the 

coefficients of thermal expansion, and the values of the thermal conductivity of the crystalline and glass 

phases. Moreover, ceramics have often been used in the thermal structures such as automobile engines 

and turbines which generate thermal stress in material due to the temperature variety. Thermal shock 

fracture is a big problem in the practical use of ceramics, and it should be resolved for wide application 

of SiC materials. Lots of researchers have been focused on finding out the optimum fabrication route of 

monolithic SiC materials.[3-5] Mechanical properties of monolithic SiC materials count on the size of 

SiC particles besides the fabrication process. In present study, the fabrication route of monolithic SiC 

materials by the complex compound of ultra-fine SiC particles and oxide additive materials have been 

investigated. SiC materials were fabricated by a liquid phase sintering process, using a commercial SiC 

powder with an average size of about 30 nm. An Al2O3-Y2O3 powder mixture was used as a sintering 

additive. Especially, the effect of additive composition ratio on the characterization of monolithic SiC 

materials has been examined, in conjunction with the properties of ultrasonic wave. The ultrasonic 

* Corresponding author. E-mail address: leejink@deu.ac.kr. Tel.: 82-51-890-1663. 

† E-mail address: splee87@deu.ac.kr. Tel.: 82-51-890-1662. 

ffi E-mail address: bjh1673@kims.re.kr. Tel.: 82-55-280-3312.

J K Lee, S P Lee, J H Byun. / An evaluation on thermal shock fatigue damage of SiC composite using nondestructive technique 

technique, one of the nondestructive tests, is often used to evaluate the material property by damage 

caused external factors such as load, temperature and pressure. The attenuation and velocity of 

ultrasonic wave through materials are changed by the fabrication process of them, and the fabrication 

process is directly related with the mechanical properties of materials such as strength, density and 

Young‟s modulus. Therefore, the optimum fabrication condition for monolithic SiC material by additive 

composition ratio was derived by measuring the attenuation and velocity of ultrasonic wave. In addition, 

a thermal shock test was conducted to evaluate the fatigue damage of the SiC material underwent 

thermal shock repetitively.[6] Ultrasonic technique was also used to inspect the degree of thermal shock 

damage of the SiC material nondestructively. 

Mixed powder 

acetone 

zirconia ball Al2O3 zirconia ball Al2O3 zirconia ball Al2O3 Y Y2O 2O 2O 3 

SiC 

Rotation condition : 160rpm, 12hrs 

Hot-pressing 

pressure 

graphite 

mold 

High High High temperature 

temperature 

temperature 

argon 

atmosphere 

Sintering condition 

- temp. : 1820℃ - pressure : 20MPa 

- time : 1hr 

Fig. 1. Schematic diagram of fabrication process of SiC materials by the liquid phase sintering. 

Controller 

2. Materials and Experimental procedures 

Furnace 

Specimen 

Cycle 

Temp. 

Fig. 2. Schematic diagram of thermal shock test. 

The monolithic SiC materials were fabricated by a liquid phase sintering process, using a commercial 

SiC powder with an average size of about 30 nm and Al2O3-Y2O3 powder mixture as a sintering 

additive. The compositional ratio (Al2O3/Y2O3) varied with 0.4, 0.7, 1.5 and 2.3, respectively in order 

303

304 


to evaluate the effect of additive for the monolithic SiC material. The monolithic SiC materials were 

sintered at the temperature of 1820 ℃. The applied pressure and its holding time were 20 MPa and 2 hr, 

respectively. Fig. 1 shows the fabrication process of SiC material by the liquid phasing sintering. 

However, an ultrasonic technique was used to evaluate the mechanical properties of monolithic SiC 

materials fabricated by the change of additive composition ratio. The ultrasonic test has been conducted 

in the water to keep to a minimum the effect of couplant, because it exerts an enormous influence on the 

attenuation of waves. Frequency range of the used sensor was 10MHz. The same experimental device 

and sensor were used to clarify the degree of thermal shock fatigue damage of SiC material. In this 

study, a thermal shock tester was made for measuring the damage behavior and crack initiation of SiC 

material subjected to the cyclic thermal shock. Fig. 2 shows the schematic diagram of thermal shock test. 

The specimen was heated to 573K in the furnace for twenty minutes and then dropped into the water 

tank located under the furnace for cooling (295K). When the specimen underwent the repetitive thermal 

shock, many cracks were generated on the surface of the specimen, although the cracking was not 

observable by the naked eye. The microscope and SEM equipments were applied to evaluate the cracks‟ 

initiation and propagation on the surface of the specimen. 

3. Results and discussions 

Fig. 3 shows the variation of the attenuation and velocity of ultrasonic wave and flexural strength by 

the composition ratio of additive materials for the monolithic SiC material. As shown in Fig. 3 the 

flexural strength represented the highest at the composition ratio of additive materials 1.5 and the lowest 

at 2.3. The attenuation coefficients were wide range between 90dB/m and 700dB/m as the composition 

ratio of the additive materials increases. The attenuation coefficients were within the range from 

90dB/m to 300dB/m at the compositional ratio from 0.4 to 1.5. However, it was rapidly increased over 

600dB/m at the composition ratio of 2.3. Ultrasonic wave is a lot affected by sintering particles of SiC, 

voids in the specimen because the attenuation occurs due to the scattering and absorption by 

propagating of wave within materials. Therefore we can estimate the internal condition of material by 

analyzing the attenuation of ultrasonic wave. In case of the specimen of composition ratio of 2.3 the 

high attenuation coefficient is why the scattering of ultrasonic wave is increased by the particles of 

Y2O3 that don‟t sinter and many voids in the monolithic SiC material. In this work, many Y2O3 

particles from the microstructure inspection for the monolithic SiC material of additive material 2.3 

promoted the scattering of wave. However, the velocities were gradually increased with the amount of 

additive composition ratios. The velocities were ranged from 11500m/s to 11700m/s and proved the 

fastest velocity at the composition ratio of 2.3. From these results it is found the monolithic SiC material 

represents the highest flexural strength at the velocity of about 11650m/s and at the lowest attenuation 

coefficient. As shown in Fig. 3 the flexural strength and optimum fabrication conditions of the 

monolithic SiC material could be estimated by measuring the velocity and the attenuation in ultrasonic 

wave.


Flexural Strength(MPa) Velocity(m/s) 

11800 

11750 

11700 

11650 

11600 

11550 

11500 

700 

600 

500 

400 

300 

200 

100 

0 

Flexural strength 

Attenuation coefficient 

Velocity 

0.0 0.5 1.0 1.5 2.0 

0 

2.5 

Amount of addictive(Al 2 O 3 /Y 2 O 3 ) 

1000 

Fig. 3. Flexural strength, velocity and attenuation coefficient vs. amount of additive. 

Velocity(m/s) 

Attenuation Coefficient(dB/m) 

150 

145 

140 

135 

130 

125 

120 

115 

110 

12000 

11800 

11600 

11400 

11200 

11000 

Model: ExpDec2 

Equation: y = A1*exp(-x/t1) + A2*exp(-x/t2) + y0 

Weighting: No weighting 

Chi^2/DoF = 92.19536 

R^2 = 0.77851 y0 = 3605.06126 

A1 = -1746.30419 t1 = 810.11845 

A2 = -1746.30592 t2 = 806.42491 

800 

600 

400 

200 

ExpDec2 fit of Data1_A 

1 2 3 4 5 6 7 

Number of Cycle 

(a) Attenuation coefficient 

Model: ExpGro1 

Equation: y = A1*exp(x/t1) + y0 

Weighting: No weighting 

Chi^2/DoF = 177.23848 

R^2 = 0.48368 

y0 =-2907345.23786 

A1 = 2918989.10344 

t1 = 547135.83268 

ExpGro1 fit of Data1_D 

1 2 3 4 5 6 7 

Number of Cycle 

(b) Velocity 

Fig. 4. Attenuation coefficient (a), Velocity (b) vs. Number of cycles of thermal shock. 

Attenuation coefficient(dB/m) 

305

306 


SiC materials expect to be used as parts in the severe circumstances of low temperature and high 

temperature repetitively. Therefore it is essential that the thermal shock damage behavior of SiC 

materials by a rapid change in temperature should be clarified for high temperature applications. In this 

study, an ultrasonic test was used to evaluate the degree of thermal shock damage of SiC materials. Fig. 

4 (a) shows the change in the attenuation coefficient for the specimen fabricated at the compositional 

ratio 1.5 as the thermal shock cycle increases. The attenuation coefficient increased gradually until the 

third times of thermal shock and did not change at the fourth and fifth times. However, it was sharply 

increased at the sixth times of thermal shock. These decreases in attenuation coefficient are closely 

connected with the damage behavior of SiC material by thermal shock. That is, the ultrasonic wave after 

propagating the SiC material underwent thermal shock was scattered by a great number of micro cracks 

on the specimen, and the energy in ultrasonic wave was rapidly reduced. The received energy was 

gradually declined by the link-up of many micro cracks as thermal shock cycles were increased. The 

energy was sharply diminished due to the macro cracks caused the union between each micro crack at 

the six times of thermal shocks. Fig. 4(b) represents the change in velocity of ultrasonic wave as the 

thermal shock cycles increase. The velocity was from 11650 to 11700m/s with thermal shock cycles. 

The difference of 50m/s in velocity was in error by 0.4 percent and within the margin of error. Therefore 

the velocity did not change in spite of increase of cracks by the thermal shock cycles, and the 

characterization in tissue of material was not influenced by the thermal shock cycles under the 573K 

temperature. The considerable change in Young‟s modulus (E) of SiC material does not occur because 

the velocity of material has a closely connected with the Young‟ modulus. Fig. 5 shows the cracks on the 

surface of the SiC material using SEM as thermal shock cycles increase. Fig. 5(a) is the surface of the 

SiC material did not experience thermal shock at all. Fig. 5(b) is the specimen of 2 thermal shock cycles 

and Fig. 5(c) is the surface underwent the sixth times of thermal shock cycles. As shown in Fig. 4 there 

are many short and long cracks on the surface of the SiC material at only 2 thermal shock cycles. These 

cracks were linked up each other and became large cracks with increase of thermal shock cycles. An 

enormous amount of micro cracks and a few macro cracks were inspected at the 6 thermal shock cycles 

as shown in Fig. 5(c). Therefore it was found that a great deal of micro cracks generated at low thermal 

shock cycles and those were connected with each other to macro cracks as thermal shock increase 

repetitively. The SiC material was completely broken by these macro cracks with cyclic thermal shocks. 

(a) 0 cycle (b) 2 cycles (c) 6 cycles 

Fig. 5. Cracks on the specimen according to the thermal shock cycles.



(1) SiC material fabricated by liquid phase process and the flexural strength represented the highest at 

the composition ratio of additive materials 1.5 and the lowest at 2.3. 

(2) An ultrasonic test was one of useful means to estimate the flexural strength and optimum 

fabrication conditions of the monolithic SiC material nondestructively because the attenuation 

coefficient was the lowest of 90dB/m and 11650m/s in velocity at the composition ratio of additive 

materials 1.5. 

(3) The attenuation coefficient increased gradually as thermal shocks cycles increases, however the 

velocity did not change considerably. These decreases in attenuation coefficient are closely 

connected with the fatigue damage behavior of SiC material by thermal shock. 

(4) A great deal of micro cracks generated at low thermal shock cycles and those were connected with 

each other to macro cracks as thermal shock increase repetitively. The SiC material was completely 

broken by these macro cracks with cyclic thermal shocks fatigue damage. 


This work was performed as a part of basic research program supported by Korea Institute of 

Materials Science (KIMS) 

References 

[1] S. H. Lee, Y. I. Lee, Y. W. Kim, R. J. Xie, M. Mitomo and G. D. Zhan, Mechanical properties of hot-forged silicon carbide ceramics, 

Scripta materialia, 2005, 52: 153~156. 

[2] P. Norajitra, L. Buhler, U. Fischer, S. Gordeev, S. Malang, G. Reimann, Conceptual design of the dual-coolant blanket in the frame of the 

EU power plant conceptual study, Fus. Eng. Des., 2003, 69: 669~673. 

[3] L. Cheng, Y. Xu, L. Zhang and X. Yin, Oxidation behavior from room temperature to 1500℃ of 3D/SiC composites with different 

coatings, J. Am. Ceram. Soc., 2002, 85(4): 989~991. 

[4] E. Tani, K. Shobu, D. Kishi and S. Umebayashi, Two-dimensional woven carbon fiber reinforced silicon carbide/carbon matrix composites 

produced by reaction bonding, J. Am. Ceram. Soc., 1999, 82(5): 1355~1357. 

[5] G. Zheng, H. Sano, Y. Uchiyama, D. Kobayashi, K. Suzuki and H. Cheng, Preparation and fracture behavior of carbon fiber/SiC 

composites by multiple impregnation and pyrolysis of polycarbosilane, J. of the Ceramic Society of Japan, 1998, 106(12): 1155~1161. 

[6] MIK. Collin, DJ. Rowcliffe, Influence of thermal conductivity and fracture toughness on the thermal shock resistance of 

alumina-silicon-carbide-whisker composites, Journal of the American Ceramic Society, 2001, 84(6): 1334~1340. 

307

Fabrication of ti/apc-2 nanocomposite laminates and their 

fatigue response at elevated temperature 

M-H R Jen a, *, Y-C Sung a , C-K Chang a , F-C Hsu b 

a Dept. of Mechanical and Electro-Mechanical Engineering, National Sun Yat-Sen University, No. 70, Lienhai Rd., Kaohsiung 80424, Taiwan, 

ROC 

b Language Center, Fooyin University, No. 151, Chinhsueh Rd., Ta-liao, Kaohsiung 83102, Taiwan, ROC 

Abstract 

The Ti/APC-2 cross-ply nanocomposite laminates were successfully fabricated. The Ti thin sheets were surface treated 

by anodic oxidation of electroplating to achieve good bonding with APC-2 laminates. Nanoparticles SiO2 were dispersed 

uniformly on the interfaces of APC-2 with the optimal amount of wt 1%. The modified diaphragm curing process was 

adopted to manufacture the hybrid laminates for minimal impact of production. Basically, the tensile tests at elevated 

temperature were conducted to obtain the baseline data of mechanical properties, such as strength and stiffness. The 

results of longitudinal stiffness predicted by the rule of mixtures (ROM) were in good agreement with experimental data, 

whilst, those ultimate strength predicted by ROM were lower than the measured data. The superior mechanical properties 

of the hybrid laminates were demonstrated. Then, the tension-tension (T-T) constant stress amplitude cyclic tests were 

performed at elevated temperature to receive the S-N curves, fatigue strength and life. It is a surprise that almost no 

delaminations were observed in tensile and cyclic tests, even at elevated temperature and over a million cycles. 

Keywords: Nano; Composite Laminate; Hybrid; Fatigue; Elevated Temperature 


Until now, it is well-known that fiber-reinforced aluminum laminates (FRALL) have been 

successfully fabricated and comercialized [1]. The aramid fiber-reinforced aluminum laminates 

(ARALL) and glass fiber/aluminum (GLARE) were marketed by the Aluminum Company of America 

for wide applications, such as aircraft lower wing skin, fuselage and tail skins [2]. Moreover, carbon 

fiber-reinforced aluminum laminates (CARALL) show a superior crack propagation resistance under 

T-T fatigue loading [3]. Blohowiak et al. [4] fabricated Ti Gr composite laminates with the development 

of new thin adhesive systems at Boeing Co. However, the above mentioned FRALLs contain 

epoxy-resin polymer. The service temperature is not expected to exceed 373K. Hence, their applications 

are restricted at lower temperature. Based on the experience of successfully manufacturing the 

Mg/APC-2 nanocomposite laminates [5], high performance laminated hybrid composites were 

developed for the Ti alloys, using the grade 1 thin sheets sandwiched with the high strength cross-ply 

CF/PEEK prepregs. The PEEK polymer can sustain its mechanical properties up to 423K [6], thus it is 

postulated that the current Ti/CF/PEEK composite laminates might be utilized at higher temperatures. 

Anodic method is a commonly used surface treatment, especially in titanium alloys for structural and 

* Corresponding author. Tel.: +886-7-5252000 ext.4216; fax:+886-7-5254299. 

E-mail address: jmhr@mail.nsysu.edu.tw

M-H R Jen, Y-C Sung, etc. / Fabrication of ti/apc-2 nanocomposite laminates and their fatigue response at elevated temperature 

engineering applications. However, the bonding capability of polymer composites to titanium thin plates 

is still a problem. In order to improve their interfacial bonding capability, numerous surface treatments 

have been studied [7-8]. Previous research showed that bond durability and strength can be improved by 

surface treating [9]. Ramani et al. [10] found the chromic acid anodic method did excellent work. 

Chromic acid anodic oxidation produced an oxide layer of thickness 40~80 nm for the 5V and 10V 

treatments [11]. The anodic oxidation was a chromic acid solution with and without hydrofluoric acid 

(HF) addition. Zwilling, et al. [12] revealed that a thin oxide compact layer formed in chromic acid 

anodic oxidation and a duplex film composed of a compact layer surmounted by a porous layer grew 

from the fluorinated electrolyte. 

Nowadays, “lighter, thinner, stronger and cheaper” are the goals of materials science and engineering, 

especially in nanoscale age. Engineering materials at the atomic and molecular levels are creating a 

revolution in the fields of materials and processing. In recent years, inorganic nanoparticles filled 

polymer composites have attracted more and more attention because the filler/matrix interface in these 

composites might constitute a much greater area and hence influence the properties of composites to a 

much greater extent at rather low filler concentration [13]. Herein, our concern is focused on a small 

part of engineering application, i.e., adding SiO2 nanoparticles 1wt% optimally on the interfaces in 

APC-2 composite laminates to improve the mechanical properties due to static and cyclic loadings at 

elevated temperature [14]. Yao, et al. investigated the macro/microscopic fracture features of 

SiO2/Epoxy nanocomposites [15]. Mahrholz, et al. studied the reinforcement effect of silica 

nanoparticles in epoxy resins by liquid moulding processes [16]. Manjunatha, et al. studied the fatigue 

response of silica nanoparticles modified Glass/Epoxy composites [17]. The incorporation of inorganic 

particulate fillers into polymer matrix has been proved to be an effective way for improving the 

mechanical properties of the matrix. However, the dispersion state of nanoparticles in polymer matrix is 

of great importance for the mechanical properties of the composite. A homogeneous dispersion of 

nanoparticles is believed to contribute better to the property improvement [18]. 

From the bonding of Ti with APC-2 by the modified diaphragm curing process, Ti/APC-2 hybrid 

nanocomposite laminates were successfully fabricated. Also, the mechanical properties subjected to 

both tensile and cyclic tests at elevated temperatures were obtained. The failure mechanisms were 

observed. The response of mechanical behavior was highlighted. 

2. Fabrication 

The twelve-inch wide unidirectional AS-4/PEEK prepregs from Cytec Industries Inc. (USA) were cut 

and stacked into cross-ply [0/90]s laminates. The grade 1 (H: 0.015%, O: 0.18%, N: 0.03%, Fe: 0.2%, C: 

0.08% ) Ti sheets, supplied by KOBE STEEL LTD (Japan), were 0.5mm thick after rolled, heated and 

flattened with scratch brushing. The density of grade l Ti is 4.51 g/cm 3 , melting point temperature is 

1670 o C, ultimate tensile strength is 305MPa, and modulus of elasticity is 71GPa. 

Prior to lamination, the slimmed Ti sheets were subjected to pretreatment in order to create the tough 

bonding with the APC-2 prepregs. Naturally, Ti sheets possess high resistance to chemical etching. Thus, 

two different surface treatments of titanium sheets were chosen, one by mechanical polishing method 

309

310 


and another by chromic acid anodic method. The latter was found better as demonstrated by the results 

of tensile and cyclic tests even at elevated temperature. After anodic processing, the thickness of oxide 

coating film was about 40~80nm. The anodic oxide coating was observed uniform by SEM, and the 

composition of coating consisting of TiO2 by EDS. The nanoparticles SiO2 (Nanostructured & 

Amorphous Materials, Inc. USA) possess the average diameter 15±5nm, specific surface area 

160±20m 2 /g, spherical crystallographic and amorphous powder. The optimal amount of SiO2 was found 

1% by wt. of laminate [14]. 

The cross-ply APC-2 nanocomposite were sandwiched with the Ti sheets to produce Ti/CF/PEEK 

hybrid laminates, expressed as Ti/APC-2/Ti/APC-2/Ti totally 5 layers. The modified diaphragm curing 

process was shown in Fig. 1. The geometry and dimensions of a hybrid nanocomposite specimen were 

shown in Fig. 2. 

3. Experimental 

Fig. 1. Curing process for Ti/APC-2 hybrid nanocomposite laminates. 

(a) (b) 

Fig. 2. The (a) geometry and (b) dimensions of hybrid nanocomposites specimen. 

An MTS-810 servohydraulic computer-controlled dynamic material testing machine was used to 

conduct the tensile test and constant stress amplitude T-T cyclic test with stress ratio=0.1,


frequency=5Hz, sinusoidal wave form under load-controlled mode at elevated temperatures, such as 

25 o C(RT), 75, 100, 125, 150 o C (slightly above APC-2 Tg=143 o C). An MTS 651 environmental chamber 

was also installed to keep and control the corresponding temperature of a specimen for testings. A 

25mm MTS-634.11F-25 extensometer was used to monitor the strain continuously during the tests. 

4. Results 

The nanoscale structure of oxide layer which has been observed by SEM was shown in Fig. 3. A 

columnar and porous layer grown on titanium with fluorinated chromic acid electrolyte was found 

uniform. There exists a kink angle in stress-strain curves at all elevated temperatures. That results in the 

initial tangent modulus and secant modulus in longitudinal direction. The early yielding of Ti sheets is 

the main reason. Fig. 4 is an example of ζ-ε curve at RT. The mechanical properties, such as ultimate 

tensile strength and longitudinal stiffness, of Ti/APC-2 cross-ply nanocomposite laminates at elevated 

temperatures were listed in Table 1. 

Table 1. The averaged mechanical properties of Ti/APC-2 cross-ply nanocomposite laminates at various temperatures. 

Temperature ( o C) Ultimate Load (KN) ζult (MPa) εmax E11i (GPa) E11s (GPa) 

25(RT) 46.77±0.60 719.59± 9.22 0.015±0.0005 109.79±5.19 33.84±2.39 

75 44.39±1.09 682.87±16.79 0.014±0.0003 107.96±1.05 32.95±0.50 

100 41.48±1.33 638.15±20.39 0.013±0.0001 106.39±6.02 33.30±1.72 

125 40.26±0.56 619.38± 8.66 0.013±0.0001 104.83±8.38 33.16±0.64 

150 39.21±1.33 603.28±20.50 0.013±0.0001 101.71±0.53 33.71±1.71 

Kink angle is due to yielding of Ti sheets 

E11i (Initial Longitudinal Stiffness) E11s (Secant Modulus) 

25 o C: 0.001≤ε≤0.0022 0.0022≤ε≤0.006 

75 o C: 0.001≤ε≤0.0020 0.0020≤ε≤0.006 

100 o C: 0.001≤ε≤0.0019 0.0019≤ε≤0.006 

125 o C: 0.001≤ε≤0.0018 0.0018≤ε≤0.006 

150 o C: 0.001≤ε≤0.0017 0.0017≤ε≤0.006 

Fig. 3. Scanning electron microscopy image of oxide layer on the titanium surface by chromic acid anodic method. 

311

312 


Fig. 4. The stress-strain curve of Ti/APC-2 cross-ply nanocomposite laminate. 

After the constant stress T-T tests, the stress vs. cycles (S-N) curves for Ti/APC-2 cross-ply 

nanocomposite laminates at elevated temperature were received and shown in Fig. 5. It is reasonable to 

see the curves going downwards as the temperature rising. The normalized stress vs. cycles curves were 

shown in Fig. 6, in which the curves were almost mixed together. It needs be mentioned the normalized 

stress is the stress normalized by the ultimate strength at the corresponding temperature, not at RT. 

Some samples as shown in Figs. 5 and 6, did not fail even over a million of cycles at elevated 

temperatures. 

Fig. 5. The S-N curves of Ti/APC-2 cross-ply nanocomposite laminates at elevated temperatures.


5. Discussion 

Fig. 6. The normalized S-N curves of Ti/APC-2 cross-ply nanocomposite laminates at elevated temperatures. 

It is interesting to see a kink angle in stress-strain curves at various temperatures. The lower yielding 

stress of Ti sheets results in the feature. That was not obviously found in our previous tests of 

Mg/APC-2 and Al/APC-2 W/O nanoparticles, SiO2, composite laminates. The ultimate strength and 

initial tangent modulus of Ti/APC-2 laminates decrease as temperature rising; whilst the secant modulus 

almost remains unchanged. Almost no delaminations were observed during the tensile tests until the 

sample failed. That can be demonstrated in Fig. 3, an uniform oxide layer on Ti sheets improves the 

bonding capability and strength with PEEK matrix. 

Until now, there has been no widely accepted rules to predict the mechanical properties of hybrid 

nanocomposite laminates. Then, based on the constant stress assumption and neglecting Hill‟s 

concentration factors the simplified ROM, Eqs.(1) and (2), are adopted for a hybrid nanocomposite 

laminate consisting of four phases, such as Ti sheet, fiber, matrix and nanoparticle [19]. 

E = E + E + E 

(1) 

11i Ti Ti APC-2 APC-2 SiO2 SiO2 

= + + 

(2) 

ult Ti Ti APC-2 APC-2 SiO2 SiO2 

where E11i is the initial tangent modulus, ζult is the ultimate strength, the subscripts Ti, APC-2, and SiO2 

are Titanium sheet, APC-2 composite laminate and SiO2 nanoparticle. The efficiency coefficient η 

would decrease as reinforcement aspect ratio decreasing. From previous literature review [20], the SiO2 

nanoparticles with an aspect ratio of ≈1 the η is assumed to be ≈0.1 for short fiber reinforced 

composites. 

The mechanical properties of PEEK have been enhanced obviously by adding 15nm SiO2 

nanoparticles into PEEK polymer with a small weight percentage [20]. Meanwhile, the theoretical 

ultimate strength predictions were 8~15% less than the experimental data. In this study the ultimate 

strengths at varied temperature, predicted by ROM listed in Table 2, are also found 3~11.11% less than 

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the experimental data. It can be explained that the micro-scale reinforcements are similar in size to 

critical cracks causing early failure [21-22], while the nano-scale reinforcements are an order of 

magnitude smaller. That can prevent early failure and enhance toughness [23]. Moreover, in nano-scale, 

the interfacial area creates a significant improvement of polymer matrix with the reinforcements. Hence, 

the reinforcing efficiency of traditional ROM may not be suitable for nanocomposite laminates. From 

Table 2, it also demonstrates that the anodic method of surface treatment on Ti sheets works well and 

provides good bonding with APC-2. Nevertheless, the experimental data for longitudinal stiffness, E11i, 

listed in Table 3, are close to the predictions by ROM. 

Table 2. The measured ultimate strength of Ti/APC-2 cross-ply laminates in comparison with the results predicted by ROM. 

Table 3. The measured longitudinal stiffness of Ti/APC-2 cross-ply laminates in comparison with the results predicted by ROM. 

For nanocomposites, the properties and structure of interfacial region are not yet known quantitatively, 

presenting a challenge to predict the properties of polymer nanocomposites [24]. Until now, it has been 

still a popular issue to predict the properties of two-phase polymer nanocomposites with nano-scale 

reinforcement. In this case, the four-phase nanocomposite laminates were successfully fabricated. Also, 

it is a very complicated problem to predict the mechanical properties at varied temperatures. Although it 

looks good for longitudinal stiffness with small errors, it is interesting to see that the data of strength 

were greater than those predicated by ROM. That is contrary to our expectation, since the received data 

of strength should be less than those predictive values because of the imperfection of constituent 

material and the defects caused by fabricating. Maybe, the simplified ROM is not appropriate for the 

prediction of strength, whilst, it is suitable for the stiffness predation. From the opposite point of view,


the obtained mechanical properties and the fabrication process are much better than those ever existed. 

The S-N curves generally go downwards as temperature increasing. Importantly, the trend of S-N 

curves is monotonically non-increasing less than 10 2 cycles, because they are flat, and becoming sharply 

dropped afterwards. Almost all samples treated by anodic method can resist cyclic loading nearly 10 6 

cycles, and some even over 10 6 cycles without failure. Also, little delamination was found during the 

cyclic tests. The superior bonding capability of surface-treated Ti Sheets will matrix PEEK is verified. 

6. Conclusion 

The Ti/APC-2 hybrid cross-ply nanocomposite laminates were fabricated. The concluding remarks 

were summarized as follows. 

• Ti/APC-2 hybrid laminates were successfully fabricated. 

• It was obvious that the chromic acid anodic method of surface treatment works very well. 

• The ROM originally for short-fiber reinforced composites can provide a rough prediction for the hybrid 

nanocomposites. The predicted values of ultimate strength are lower than the measured data, and those 

of longitudinal stiffness are close to the measured data. 

• In fatigue tests, almost no delaminations were found at 10 6 cycles. 

• Ultimate tensile strength, longitudinal stiffness E11i, and S-N curves go downwards as temperature 

rising, especially at 150 o C. The secant modulus was kept unchanged at various temperatures. 


The authors would like to gratefully acknowledge the sponsorship from National Science Council 

under the project no. NSC 96-2221-E-110-072 

References 

[1] L. B. Vogelsang and J. W. Gunnink, ARALL: A materials challenge for the next generation of aircraft, Material and Design, 7 (6), pp. 

287-300, 1986. 

[2] T. Lin, P. W. Kao and F. S. Yang, Fatigue behaviour of carbon fibre-reinforced aluminium laminates, Composites, 22, No. 2, pp. 135-142. 

1991. 

[3] T. Lin and P. W. Kao, Effect of fiber bridging on the fatigue crack propagation in carbon fiber-reinforced aluminum laminates, Material 

Science and Engineering, A190, pp.65-73, 1995. 

[4] K. Y. Blohowiak, R. A. Anderson, W. B. H. Grace, J. W. Grob and D. H. Fry, “TiGr”Laminates: Development of New Thin Adhesive 

Systems and Associated Test Methods, SAMPE Journal, 45, No. 3, pp. 30-36, 2009. 

[5] M.-H. R. Jen, Y.-C. Tseng and P.-Y. Li, Fatigue response of hybrid magnesium/carbon-fiber/PEEK nanocomposite laminates at elevated 

temperature, Journal of JSEM, 7, Special Issue, pp. 56-60, 2007. 

[6] T. E. Attwood, P. C. Dawson, L. J. Freeman, L. R. J. Hoy, J. B. Rose and P. A. Staniland, Synthesis and properties of polyaryletherketones, 

Polymer, 22, pp. 1096-1103, 1981. 

[7] G. W. Critchlow and D. M. Brewis, Review of surface pretreatments for titanium alloys, Int. J. Adhesion and Adhesives, 15, pp.161-172, 

1995. 

[8] P. Molitor, V. Barron and T. Young, Surface treatment of titanium for adhesive bonding to polymer composites: a review, Int. J. Adhesion 

and Adhesives, 21, pp. 129-136, 2001. 

[9] A. J. Kinloch (Editor), Durability of structural adhesives, Springer Publishers, pp. 255-262, 1983. 

[10] K. Ramani, W. J. Weidner and G. Kumari, Silicon sputtering as a surface treatment to titanium alloy for bonding with PEKEKK, Int. J. 

Adhesion and Adhesives, 18, pp. 401-412, 1998. 

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316 


[11] B. M. Ditchek, K. R. Breen, T. S. Sun and J. D. Venables, Morphology and composition of titanium adherends prepared for adhesive 

bonding, In: Proc. 25th Nat. SAMPE Symp., pp.13-24, 1980. 

[12] V. Zwilling , M. Aucouturier, E. Darque-Ceretti, Anodic oxidation of titanium and TA6V alloy in chromic media. An electrochemical 

approach, Electrochimica Acta, 45, pp.921-929, 1999. 

[13] C. L. Wu, M. Q. Zhang, M. Z. Rong, K. Friedrich, Silica nanoparticles filled polypropylene: effects of particle surface treatment matrix 

ductility and particle species on mechanical performance of the composites, Composites Science and Technology, 65, pp. 635-645, 2005. 

[14] M.-H. R. Jen, Y.-C. Tseng, C.-H. Wu, Manufacturing and mechanical response of nanocomposite laminates, Composites Science and 

Technology, 65, pp. 775-779, 2005. 

[15] X. F. Yao, D. Zhou, H. Y. Yeh, Macro/micro fracture characterization of SiO2/epoxy nanocomposites, Aerospace Science and Technology, 

12, pp. 223-230, 2008. 

[16] T. Mahrholz, J. Stängle, M. Sinapius, Quantitation of the reinforcement effect of silica nanoparticles in epoxy resins used in liquid 

composite moulding processes, COMPOSITES: Part A, 40, pp. 235-243, 2009. 

[17] C. M. Manjunatha, A. C. Taylor, A. J. Kinloch, S. Sprenger, The tensile fatigue behaviour of a silica nanoparticle-modified glass fibre 

reinforced epoxy composite, Composites Science and Technology, 70, pp. 193-199, 2010. 

[18] G. Zhang, A. K. Schlarb, S. Tria, O. Elkedim, Tensile and tribological behaviors of PEEK/nano-SiO2 composites compounded using a ball 

milling technical, Composites Science and Technology, 68, pp. 3073-3080, 2008. 

[19] C. T. Herakovich, Mechanics of Fibrous Composites, John Wiley & Sons, Inc., 1998. 

[20] M.C. Kuo, C.M. Tsai, J.C. Huang, M. Chen, PEEK composites reinforced by nano-sized SiO2 and Al2O3 particulates, Materials 

Chemistry and Physics, 90, pp.185-195, 2005. 

[21] T. Liu, I. Y. Phang, L. Shen, S. Y. Chow, and W.-D. Zhang, Morphology and Mechanical Properties of Multiwalled Carbon Nanotubes 

Reinforced Nylon-6 Composites, Macromolecules, 37 (19), pp. 7214-7222, 2004. 

[22] Z.H. Xia, W. A. Curtin, and B. W. Sheldon, A New Method to Evaluate the Fracture Toughness of Thin Films, Acta Materialia, 52, pp. 

3507-3517, 2004. 

[23] W. Naous , X.-Y. Yu , Q.-X. Zhang, K. Naito, Y. Kagawa, Morphology, tensile properties, and fracture toughness of epoxy/Al2O3 

nanocomposites, Journal of Polymer Science Part B: Polymer Physics, 44(10), pp. 1466-1473, 2006. 

[24] L.S. Schadler, L.C. Brinson, and W.G. Sawyer, Polymer Nanocomposites: A Small Part of the Story, Journal of Materials,59, pp. 

53-70 ,2007 

[25] W.D. Callister Jr, Materials Science and Engineering: An Introduction, 6th ed., Wiley, New York, USA, 2003.

Fatigue and Fracture of Elastomeric Matrix Nanocomposites 

Abstract 

C Bathias *, S Y Dong 

LEME, University Paris 10, 50 rue de Sévres, Ville d’Avray 92410 (Fr) 

This paper is a review of what was done in our laboratory by several PHD students (Lu Chuming, K. Legorju, S. Dong) 

in order to have a better understanding and prediction of the mechanical behaviour and of the damage of elastomeric 

matrix used for rubber composites. Both, monotonic and cyclic loadings are of interest. 

Keywords: NR; SBR; fatigue; fracture; cavitations 


Elastomeric matrix composites are usually reinforced by mineral particles such as carbon black and 

sometime by long metallic or organic fibbers. In absence of fibber, rubbers can be considered as 

nanocomposites. 

As soon as rubber is subjected to a cyclic strain, its temperature increases, especially within the 

material. This temperature increase results in a modification of the properties and possibly to damage. 

Within natural rubber and within some other synthetic rubbers, the amorphous micro-structure tends to 

partly crystallize when the deformation is significant. In addition, under cyclic pressure, it seems that 

rubber can be subjected to a chemical damage along with a solid-liquid phase change, and maybe with an 

influence of the ambient air. In other words, under natural loading conditions, rubber fatigue cracking is 

a function of the combination of three damaging types: mechanical, thermal and chemical. 

Experience shows that under cyclic loading, rubbers get damaged until the formation of one or 

several main cracks which propagate. Like in metals, crack initiation and then crack propagation are 

usually studied separately. Since 1953, Rivlin and Thomas [1], then Lake [2] and Lindley [3] in the 1960s, 

and finally Gent and Stevenson in the 1980s [4,5] applied Griffith criterion (G) to the tearing of 

elastomers. In this case, the dissipated energy rate G is replaced, by the authors cited above, by the 

notion of tearing energy T whose physical definition is similar to G. 

However, the elasticity of elastomers is not linear and in addition, cracks subjected to high 

deformations do not remain sharp as Griffith model suggests. Nevertheless, there is not energy 

dissipation due to plasticity and the failure mechanisms of rubbers are of the “fragile” type. When the 

fracture mechanics is applied to fatigue cracking, the cyclic damaging of rubbers depends on the 

mechanical stress (frequency, ratio R) but also on the temperature and on thermal dissipation, and 

finally on the environment and obviously on the combination of all these parameters. Air oxygen is 


E-mail address: claude@bathias.com

318 


known to significantly influence the fatigue of rubbers. In what follows, we will try to propose a 

comprehensive approach of the fatigue cracking of natural rubbers by defining the main mechanical 

parameters and the influence of the damaging mechanisms related to the micro-structural aspect of 

rubbers, in order to understand crack propagation. 

2. Fatigue life of natural rubbers 

Natural rubbers reinforced with carbon black are amorphous at ambient temperature. Stretched by a 

traction loading, these rubbers partly crystallize. As the mechanical properties are clearly different 

before and after crystallization, a strong influence of the mean stress on the fatigue life time, is 

expected. 

In Figure2, the effect of the mean stress on the life time is illustrated by some results obtained on a 

natural rubber subjected to an alternate stress of 1 MPa and then of 1.5 MPa. Specimens are axi-symmetrical 

with a hour glass shape of de 26 mm diameter (Figure1). 

Fig. 1. Endurance specimen. 

The initiation of the crack can be predicted using an SN curve. In natural rubber, for mean stress 

lower than the alternate stress value, corresponding to a traction-compression mode, fatigue life 

decreases when the stress increases. 

Fig. 2. Effect of the mean strain on the life time of rubbers 

(NR natural rubber ; CF polychloroprene ; SBR polybutadiene) 

However, under a tension-tension mode, the mechanism gets suddenly reversed: the natural rubber 

gets reinforced and leads to a better behavior under increasing mean straess. This reinforcement is due 

to the formation of crystallite which prevents any crack initiation and progression to occur.

C Bathias, S Y Dong. / Fatigue and Fracture of Elastomeric Matrix Nanocomposites 

2.1 SN curve regarding crystallisable rubbers 

To characterize the behavior of materials under fatigue conditions, Wöhler‟s representation is 

defined by this equation: 

Log Nf = a - b (1) 

In this representation, a and b are two constants; is usually the amplitude of the applied stress. This 

equation can be represented by a line with - Log Nf coordinates. 

As the compression strain distroyed the crystallites which got formed under traction. It would be 

more suitable to give Wöhler‟s equation with the maximum strain instead of the strain amplitude. The 

equation can then be written as: 

Log Nf = a - b max (2) 

In order to apply the Wöhler equation, a stress term cris which comes from the crystallization effect 

is introduced. The equation becomes then: 

2.2 Crack propagation within natural rubber 

Log Nf = a - b max - cris (3) 

cris = 0 lorsque min >0 et cris >0 lorsque min < 0 (4) 

In order to apply traction or compression, a thick cantilever specimen with a lateral notch is used. 

As we would like to avoid geometry issues, a large specimen (see Figure 3) with a length of 150 mm, 

is used. The fatigue crack gets initiated from a mechanical notch cut with a razor blade and with a 

length of 20 mm. Crack propagation is studied as a function of the dissipated energy rate, given by the 

following equation: 

1 

T dU 

= (5) 

b dA 

where “U” is the elastic energy for a crack with a surface of “A”. Thickness “b” is corrected by the 

lateral deformation at the crack tip when “T” is determined thanks to the compliance method. Crack 

length “a” is measured with a video camera recorder. According to Griffith criterion, the dissipated 

energy level is calculated in the case of a crack extension given when failure occurs. The growth of the 

crack comes then to: 

T = Tmax - Tmin 

Fig. 3. Cracking specimen to be used for rubbers. 

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320 

2.3 Crack growth curve – Influence of ratio R 


Cracking experiments confirm the existence of a sigmoid relationship between da/dN and T which 

can be written as: 

da n 

= C. T 

(6) 

dN 

For the low values of T, a non-cracking threshold Ts) can be defined (see Figure 4). The 

threshold significantly increases when ratio R increases which is different from what is observed in 

metals. We should point out that when ratio R reaches 0.5, the crack does not propagate anymore under 

fatigue conditions whatever the maximum force applied. 

Fig. 4. Cracking curve as a function of ratio R. 

However, when ratio R reaches -1, under symmetrical traction-compression conditions, threshold 

Ts is almost inexistent. As a consequence, the fatigue crack does not propagate, even for the lowest 

stress when R =- 1. 

When we have a traction-compression stress, a chemical decomposition of the rubber can be observed 

at the crack tip where black drops come out. The cyclic damaging under compression is likely to lead to 

an oxidation, a chemical reaction, which comes after mechanical damaging. 

In the reverse case where ratio R is equal to 0.5, the elongation at the crack tip is of several hundreds 

percents, which leads to a local crystallization of the natural rubber, which goes against crack 

propagation. This crystallization effect does not occur anymore when R = -1 as the reversibility of 

crystallization appears during the compression phase. 

We can seriously conclude that propagation strength of fatigue cracks within natural rubber is much 

better when the statistical stress of the cycle is high but also when the minimum stress of the cycle 

under compression is very damaging. 

2.4 Influence of the test temperature 

As we can expect, the cracking rate increases when the temperature increases (see Figure 5). For a 

same ratio R = 0.2, the cracking threshold drops from 10 to 3 kN/m between 25 o C and 80 o C, as the


tests were carried out in air. This weakening of the strength with temperature is related to the increase of 

the mechanical damage, of the chemical damage as well as of the decrease of crystallization. 

2.5 Influence of the environment and crossed environment-temperature effects 

The environment does obviously influences chemical damaging. Some tests carried out in air, in water 

and under dry nitrogen at 25 o C clearly show the effect of gaseous oxygen (see Figures 5and6). In water, 

the cracking threshold is higher than in air as the dry nitrogen environment gives the highest threshold 

(respectively 10, 20 and 50 kN/m when R = 0.2). To make sure that the effect of water is not related to 

thermal dissipation, some tests run in water and in air at 50 o C were compared. They show that the 

cracking threshold at 50 o C is still higher in water than in air. Thus, the environment effect occurs in the 

same way at 25 o C and at 50 o C. 

Fig. 5. Influence of the temperature on the NR cracking. 

This study shows that gaseous oxygen accelerates fatigue cracking at room temperature and also at 

higher temperatures when ratio R is positive, which means as soon as crystallization occurs when the 

crack tip gets opened. 

Nevertheless, when crystallization does only occur when R = -1, it seems that fatigue cracking is not 

the same in air than in water. To get a cracking threshold when R = -1, any trace of oxygen must be 

removed in under pure nitrogen. The threshold reaches then 10 kN/m (Figure5). 

We can then conclude from this experiment that the influence of the environment is more significant 

than the amorphous-crystalline transformation inhibited by compression at the crack tip. Under 

traction-compression conditions, just some oxygen traces can keep the chemical damaging going at the 

crack tip as it only disappears under nitrogen. 

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322 


Fig. 6. Influence of the environment on NR cracking. 

Fig. 7. Combined influence of the temperature and of the environment 3- Propagation mechanisms of cracks within natural rubber. 

By fractography, different cracking mechanisms due to fatigue were observed. The evolution of the 

micro-structure is important depending on the propagation rates. When the cracking rates are low (at the 

cracking threshold), the mechanisms become fragile. Secondary micro-cracks get multiplied. For faster 

rates, we can observe more facets and a rougher relief. The existence of fatigue striations can be 

observed for high cracking rates (10 -3 mm/cycle) (see Figure 8). 

Fracture mechanisms obtained when R = -1 present some small transformed zone, due to the high 

compression levels obtained, leading to a significant chemical deterioration. 

The more we increase ratio R, the more wrenching we can observe. Nevertheless, their distribution is 

more homogeneous. We can also notice the presence of many cupules of about 1 µm.


Fig. 8. Streaks on the fracture of a natural rubber. 

Whatever the loading ratio, at high magnification, a typical structure of the failure of rubber: some 

micro-tongues, which underwent an irreversible deformation. Their size is of a few microns and they 

can be found on the entire specimen (see Figure 9). 

Finally, whatever ratio R studied, the reinforcement phenomenon due to crystallization of stretched 

chains does not directly influence the micro-structure of the fracture mechanisms. When the temperature 

increases, more tongues are formed and their shape gets better. But we cannot find any tongue in water 

or under nitrogen, mediums where there is no gaseous oxygen. As a consequence, these tongues are 

typical of chemical damaging due to gaseous oxygen of the amorphous rubber, with a possible more 

pronounced deterioration due to the increase of the temperature. 

Fig. 9. Typical tongue formation. 

The study of the damaging mechanisms of the cracking of natural rubber leads to the following 

conclusions: 

– a pre-strain under traction conditions improves the behavior under fatigue thanks to the 

crystallization of the stretched chains. However, switching to compression damages much more the 

material; 

– in addition to mechanical damaging, we have to consider a significant chemical damaging due to the 

oxygen in air and moreover, when the temperature increases, the oxidation reaction gets accelerated. It is 

then worth working under an inert atmosphere, like nitrogen, for any temperature. A non-cracking 

threshold when R = -1 did not exist in water and in air; 

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324 


– finally, if the fractographic study does not allow us to totally link the micro-structure to the 

cracking mechanisms of this rubber, it still allows us to qualitatively observe the influence of the 

various factors related to damaging. We should note that the microscopic formation mechanism of 

the tongues strongly depends on the gaseous oxygen and on the amorphous property of natural 

rubber. 

The natural rubber clearly shows the interdependence of the mechanisms of fatigue damaging of polymers: 

the mechanical stress, the chemical activity, the effect of the temperature and the architecture of the 

macro-molecules. 

3. Multi-axial fatigue of rubbers 

It is needless to say that the loading, usually occurring within pieces and structures made of 

elastomers, is multi-directional. In the case of metals subjected to multi-axial fatigue, the stress tensor 

deviator is a convenient parameter to predict the fatigue life as the damaging of metals is mainly due to 

plastic deformation. The plasticity of metals depends on the dislocations sliding and this sliding depends 

on the shear stress due to the stress tensor deviator. This is why the equivalent Von Mises stress is 

successfully used to define the multi-axial fatigue life. Can we apply this approach to elastomers? The 

answer to this question is no as there is no plasticity in elastomers according to Friedel‟s dislocations 

theory. 

Fig. 10. Equipment allowing the study of the bi-axial fatigue of elastomers 

The fatigue damage mechanisms of rubbers are different from those within metals. Bathias and Le 

Gorju [5] previously showed that, within rubber, shear leads to quasi-cleavages which is obviously not 

the case in metals. They also showed that the stresses get more bi-axial and thus make ductility stronger, 

leading to some formation mechanisms of pseudo-dimples. Finally, they showed that due to a given 

hydrostatic tension, cavitations are formed on rubber. All these mechanisms operate under bi-axial 

fatigue. They are obviously different from the mechanisms we can observe within metals. In these 

conditions, Von Mises stress cannot correctly define the fatigue of rubbers. For the same reasons, we do 

not see why the prediction of multi-axial fatigue of rubbers could be established based on a single 

parameter. 

Nevertheless, it seems that the maximum principal stress usually rules damaging under bi-axial

fatigue conditions. 


This is why, some recent publications do not focus on these fundamental data regarding the fatigue of 

elastomers which cannot be presented by a single digital approach, and it‟s not enough. 

Figure 11 gives an example of a prediction of the life time of a natural rubber as a function of the 

principal stress for some traction-compression-torsion tests. 

4. Cavitation of rubbers 

Fig. 11. SN curve of a natural rubber under traction-traction conditions. 

Cavitation is a peculiar damaging phenomenon and specific to rubbers. When a cylindrical and 

axi-symmetrical specimen (planar deformation) is streched, some vacuoles get formed in its core, which 

grow and multiply with the elongation or with the number of cycles and progressively lead to the failure 

of the material. These cavities are not holes or bubbles. They are due to the formation of a strong 

tri-axial stress field within the material which leads to some spherical conformations of the 

macro-molecules, when the hydrostatic stress (average of the principal stresses) reaches a certain critical 

value. 

Contrainte principale max 

(MPa) 

The cavitation property cannot be given according to a critical elongation. However, a numerical 

calculation linked to a non-destructive control by tomography allowed us to show that the cavitation of 

natural rubbers occurs around a hydrostatic pressure of 2 MPa for any loading. Within the SBR rubber, 

cavitation appears for a hydrostatic pressure of 7 to 8 MPa. 

Figure 11 presents the cavitation phenomenon. 

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326 

5. Conclusion 


Fig. 12. Fatigue cavitation due to the hydrostatic pressure observed by SEM and by tomography. 

Rubber composites, which have now been materials used in the mechanical industry for just fifty 

years, are much less known than metals due to fatigue damaging. They do not react in the same way to 

stresses. Increasing the average stress of a cyclic loading applied to a natural rubber comes to increasing 

its fatigue life. This is at the opposite of what occurs in a metal! This paper intended to show that neither 

the Von Mises stress, nor Griffith dissipated energy bring any satisfying solutions to entirely predict the 

initiation and propagation of fatigue cracks within these rubber nanocomposites. 

References 

[1] R.S. Rivlin, A.G. Thomas, “Rupture of Rubber”, J. Polymer Sci. 10, 291, 1953 

[2] C.J. Lake, “Aspects of Fatigue and Fracture of Rubbers”, Prog. Rubber Technol 45, 89, 1983 

[3] M.J. Lindley, “Energy for Crack Growth in Model Rubber Components”, Strain Anal 7, 132, 1972 

[4] A.N. Gent, Engineering with Rubber, Hanser Publishers, New York, 1992 

[5] A. Stevenson, “Fatigue Crack Growth in High Load Capacity Laminates”, Int. J. Fracture 23, 47, 1983 

[6] C. Bathias, K. Le Gorju, “Fatigue Initiation and Propagation in Natural and Synthetic Rubbers”, International Journal of Fatigue 24, 85-92, 

2002

Correlation between crack propagation rate and cure process of 

epoxy resins 

Abstract 

V Trappe *, S Günzel 

Federal Institute for Materials Research and Testing, BAM-V.64, Unter den Eichen 87, D-12205 Berlin, Germany 

Fracture mechanics approaches are increasingly applied for the characterization of epoxy resins‟ and adhesives‟ 

mechanical properties. Therefore, the fracture toughness and crack resistance under static load [1] often is regarded as 

state of the art to figure out material improvements. However, experimental investigations on the fatigue behaviour, thus 

the crack propagation according to [2], seem to be much more sensitive to characterize the materials for in service 

loading conditions. At first an efficient testing concept was developed at BAM V.64. Therefore the geometry for a 

modified single edge notched tensile specimen (SENT) was developed in order to assure an appropriate resolution in 

measuring the crack length via a CCD-camera [3]. In the next step the influence of the cure temperature on the 

fracture-mechanical properties was investigated. 

Keywords: Fracture toughness; crack resistance; fracture mechanics; plastics; crack propagation 


Fibre reinforced plastics are increasingly used for lightweight constructions such as aircrafts and 

wind energy applications. The requirement is to manufacture the resins within a wide temperature range 

(20-200°C) and to impregnate fabrics and inlays in different manufacturing methods (prepreg, resin 

injection, hand lay-up). Furthermore, the health tolerance, thus the industrial safety, gains more 

importance. This requires an advancement of resin systems in a continuous manner, while 

simultaneously keeping a high standard of mechanical behaviour in composites. Within the framework 

of different research series at BAM, working group V.64, it could be determined that an optimization of 

the fracture toughness and crack resistance does not necessarily lead to an improved fatigue resistance. 

In general, the specimens developed for crack propagation investigation of metals are insufficient for 

epoxy resins and adhesives. However, with a modified SENT-specimen, which was developed at BAM, 

it is possible to efficiently perform crack growth and to characterize plastics‟ fatigue behaviour with 

cohesive fracture. The methods and the results will be discussed in the presentation. 


Some plastics, especially epoxy resins are very brittle compared to metallic materials. This results in 

a 10 to 100 times smaller fracture toughness. Additionally, the crack growth rate at the threshold value 

* Corresponding author. tel.: ++49 30 8104 3386 

E-mail address: volker.trappe@bam.de

328 


of crack propagation could be small at about 10E-6 mm/cycle. Furthermore the Paris-line increases 

strongly and hence it is very difficult to measure the range of stable crack propagation for this class of 

materials. A reasonable number of specimens for crack propagation measurements for metallic materials 

are well known (Fig 1). However, in [2] only the compact tension (CT) and single edge notched bending 

(SENB) specimen are recommended in this standard. In Fig. 1 the normalized geometry calibration 

factors for several common types of specimens are compared. Hence, for a brittle epoxy resin the range 

of stable crack propagation is only 30% more than the stress intensity of the pre crack length. 

Comparatively, for a metallic material the stress intensity could be enhanced over a range of 

approximately 250% until instable crack propagation occurs. Thus according to [2], under cyclic 

loading with a constant load amplitude, the recordable crack growth of a SENB specimen is only 7% of 

the width W in an epoxy resin compared to 20% of W for a double edge notched specimen (DEN) and 

hence 3 times higher. For metallic materials, even for the SENB specimen, the recordable crack length 

is more than 20% and consequently, it is not problematic to measure the crack propagation with an 

appropriate resolution. A modified short SET specimen in a fixed clamping set up was chosen (Fig 1) 

because the recordable crack growth length is nearly the same and the preparation of only one pre crack 

with a razor blade is much easier. At constant load amplitude and a load ratio of R=0, 1 da/dN over ΔK 

experiments were performed in a servohydraulic tensile testing machine INSTRON 8800. Each 1000 

cycles the crack length was measured automatically by a CCD-camera with a resolution of at least 

W/2000 hence 25μm at the modified SET-specimen (thickness 6mm). 

3. Results 

Fig. 1. geometry calibration factors of different specimens. 

A pure epoxy resin was cured at the two different temperatures 50°C and 60°C over 15 hours and the 

crack propagation was measured in these two states. Beside the measured values, the range of stable 

crack growth according to Paris [5]

V Trappe, S Günzel / Correlation between crack propagation rate and cure process of epoxy resins 

( ) m 

da = C K 

(1) 

dN 

C and m are material constants, is plotted as a straight line. The values of fracture toughness are stated 

in Fig. 2 according to [1]. Even when the fracture toughness of the two different curing states is nearly 

the same, the crack propagation rate of the higher cured material is 10 times lower than the other one as 

shown in Fig. 2 and hence the number of load cycles to failure is 10 times higher. 

4. Conclusion 

Fig. 2. crack propagation rate and cure process 

Focussing on the in service life of plastics and adhesives regarding the cohesive failure, crack 

propagation measurements are much more sensitive for evaluation of materials improvements than 

fracture toughness tests. However, performing crack propagation experiments at brittle epoxy resins 

with constant load amplitudes according to [2] is very difficult, hence the recordable crack growth is 

very small. Therefore, a modified single edge notched tensile specimen has been developed, which 

enables a 3 times higher stable crack length under cyclic loading. Hence, the crack growth could be 

recorded with good resolution online, automatically implemented in the fatigue test simply by a 

CCD-camera. A strong correlation between crack-growth rate in the pure matrix material and the fatigue 

behaviour of a glass-fibre and carbon-fibre composite are assumed. First tests seem to be promising. 

Reference 

[1] ISO 13586:2000: Plastics – Determination of fracture toughness – Linear elastic fracture mechanics approach 

[2] ISO 15850:2002: Plastics – Determination of tension-tension fatigue crack propagation - Linear elastic fracture mechanics approach 

[3] Günzel, S., Trappe, V.: Ermittlung bruchmechanischer Kennwerte an Epoxid-Harzen, Werkstoffprüfung - Berlin 2008, DVM report 642, p. 

295-300, ISBN 978-3-00-026399-6 

[4] ASTM E647-00: Standard Test Method for Measurement of Fatigue Crack Growth Rates 

[5] Gross D.: Bruchmechanik – Mit einer Einführung in die Mikromechanik; Berlin [u.a.], Springer-Verlag, 2007 

329

330 


[6] Heckel K.: Einführung in die technische Anwendung der Bruchmechanik; München, Wien; Hanser Verlag, 1983 

[7] Haibach E.: Betriebsfestigkeit – Verfahren und Daten zur Bauteilberechnung; Berlin [u.a.], Springer Verlag, 2006

Thermal fatigue of AX41 magnesium alloy based composite 

studied using thermal expansivity measurements 

Abstract 

Z Drozd *, Z Trojanová, P Lukáč 

Faculty of Mathematics and Physics, Charles University, Prague, Ke Karlovu 5, CZ-121 16 Praha 2, Czech Republic 

Magnesium alloy AX41 (Mg-4Al-1Ca in wt. %) reinforced with 15 vol% of short Saffil fibres was used in this study. 

Thermal expansion was measured over a wide temperature range from 25 up to 400 o C in four runs. The thermal 

expansion coefficient was estimated during heating and cooling. The Young‟s modulus of the composite was estimated by 

the measurements of the resonant frequency of the free vibrations of the sample. Samples for these measurements were 

thermally cycled between room temperature and an increasing upper temperature of the thermal cycle. The modulus 

defect estimated from the difference between the resonant frequency before the thermal cycling and after cycling was 

compared with the relative change of the thermal expansion coefficient. Similar course of the temperature dependence of 

both quantities indicates that the deviation from the linearity has the common reason: thermal stresses and increased 

dislocation density. 


Light alloys reinforced with short fibres or particles have unique and desirable thermal and 

mechanical properties [1]. When compared with monolithic metals and alloys, metal matrix composites 

(MMCs) have higher strength, Young‟s modulus, wear resistance, fatigue resistance, and lower thermal 

expansion [2]. Investigations of mechanical and physical properties of light metals composites (among 

them magnesium alloys based composites) are important not only for applications but also for better 

understanding of the processes responsible for their behaviour. An attractive attribute of MMCs is the 

ability to tailor the thermal conductivity and the coefficient of thermal expansion (CTE). This can be 

achieved by careful control of the low expansion: reinforcement volume percent, particle size, and 

particle packing characteristics [3-5]. 

It is known that in composites, there is a large difference in the coefficients of thermal expansion 

between the matrix and the ceramic reinforcement. When a metal matrix composite is cooled from a 

higher temperature to room temperature, misfit strains occur because of different thermal contraction at 

the interfaces. These strains induce thermal stresses that may be higher than the yield stress of the 

matrix. Therefore, the thermal stresses may be sufficient to generate new dislocations at the interfaces 

between the matrix and the reinforcement. Accordingly, after cooling the composite, the dislocation 

density in the matrix is higher than in unreinforced matrix. An increase in the density of newly created 

dislocations near reinforcement fibres has been calculated as [6, 7] 

* Corresponding author. Tel.: +221912410; Fax: 221 912 406. 

E-mail address: drozd@mff.cuni.cz

332 


B f cT = 

b(1 - f ) t 

where f is the volume fraction of the reinforcement, t is its minimum size, b is the magnitude of the 

Burgers vector of dislocations, B is a geometrical constant, Δαc = αf – αm is the difference in the CTEs of 

the reinforcement and the matrix, and ΔT is the temperature change. 

The yield stress of MMC decreases with increasing temperature. At a certain temperature, the values 

of thermal stresses at the interfaces may exceed the yield stress of the matrix, and plastic flow can occur. 

A permanent elongation as well as contraction of the sample length during thermal exposition was 

observed by several authors [8-11]. The sample exhibited a residual contraction (or elongation) upon 

cooling to room temperature, while the temperature dependence of the thermal expansion coefficient 

was measured. The value of the observed permanent (residual) change of the sample length after the 

measurement of thermal expansion depends on the matrix, volume fraction of reinforcement, and the 

maximum temperature of the thermal cycle. The thermal expansion behaviour may be characterised by 

the temperature dependence of the thermal strain parameter (L/L0)th defined by the following equation 

[12]: 

L L L 

 

= - 

L L L 

0 th 0 exp 0 rm 

where (L/L0)exp is the measured strain of the composite sample, (L/L0)rm is the strain the composite 

sample calculated by the rule of mixtures and L0 is the original length of the sample. The rule of 

mixtures is a function of the volume fraction of the reinforcement and the strain of the matrix and the 

reinforcement. Parameter (L/L0)th represents the departure of the composite behaviour from the case 

where no thermal stresses are present. It should be note that (L/L0)exp is determined by dilatometer in 

the axial direction of the sample. 


A commercial magnesium alloy AX41 (4wt%Al, 1wt%Ca, balance Mg) was used as the matrix. The 

alloy was reinforced with -Al2O3 short fibres (Saffil ® ). The composite was prepared by squeeze casting. 

The preform consisting of Al2O3 short fibres showing a planar isotropic fibre distribution and a binder 

system (containing Al2O3 and starch) was preheated to a temperature higher than the melt temperature 

of the alloy and then inserted into a preheated die. The two-stage application of the pressure resulted in 

MMCs with a fibre volume fraction of approximately 15 vol.% . The mean diameter of fibres was 3 μm 

and their length 78 μm (measured after squeeze casting). 

Cylindrical samples for the thermal expansion measurements had a length of 50 mm and a diameter 

of 6 mm. The planes of planar randomly distribute fibres were parallel to the longitudinal axis of the 

samples. Figure 1 shows the microstructure (light micrograph) of as prepared composite taken from the 

fibres plane. The linear thermal expansion of the composite samples was measured in an argon 

atmosphere, using the Netzsch 410 dilatometer, over a temperature range from room temperature to 400 

o C for heating and cooling rates of 2 K/min. The accuracy of the apparatus was controlled by measuring 

(1) 

(2)

Z Drozd, etc. / Thermal fatigue of AX41 magnesium alloy based composite studied using thermal expansivity measurements 

of the coefficient of thermal expansion of pure Mg and comparing it with the literature data. The 

agreement between measured and tabled data was in the range ±1%. The thermal expansion curves of 

composites were measured with four thermal (heating and cooling) cycles (runs). The results obtained in 

the third and fourth thermal cycles were practically the same as those in the second cycle. The relative 

changes in the thermal expansion coefficient /=((T)-(25 o C)/(25 o C) were calculated. 

Fig. 1. Microstructure of the sample of the investigated material. 

The Young‟s modulus E was estimated after each thermal cycle by measurement of the resonant 

frequency of free vibration of the sample at ambient temperature [13]. Thermal cycles between room 

temperature and an increasing upper temperature were performed step by step up to 430 o C. The 

temperature step was 20 o C and duration of the sample at each temperature 15 minutes. The modulus 

defect E/E =(E-E0)/E0 (where E0 is the modulus value without thermal treatment) was estimated. 

3. Results 

Figure 2 shows the temperature dependences of the thermal strain obtained during the four thermal 

cycles. From the figure it is seen that the curves obtained in the second, third and fours rune are 

practically the same. Also the estimated difference between the heating and cooling part of the 

dependence is in the second and following cycles smaller. The temperature dependences of the CTE for 

heating, measured for four thermal cycles, are shown in Fig. 3. The addition of Saffil fibres decreases 

the CTE from 25x10 -6 K -1 estimated for the alloy to 20x10 -6 K -1 for the composite at room temperature. 

Further thermal cycling led to the additional decrease of the CTE to approximately value of 16x10 -6 K -1 . 

The dilatation characteristics are also influenced by the residual strain, which is connected with a 

permanent change of the sample length. The temperature dependence of the residual strain was obtained 

by subtracting the relative elongation obtained in the first run and the relative elongation in the second 

thermal cycle. It is introduced in Fig. 4. The permanent changes in the sample length (residual 

contraction) measured after individual thermal cycles are shown in Fig. 5. 

333

334 

relative elongation (10 -4 ) 

100 

80 

60 

40 

20 

-20 


0 

runs 2 - 4 

0 100 200 300 400 500 

T (°C ) 

run 1 

Fig. 2. Temperature dependence of the thermal strain for the first and second run. 

CTE (10 -6 K -1 ) 

30 

25 

20 

15 

10 

5 

0 

runs 2-4 

run 1 

0 100 200 300 400 500 


Fig. 3. Temperature dependence of the CTE of the composite under heating. 

residual strain (10 -4 ) 

2 

0 

-2 

-4 

-6 

-8 

-10 

-12 

0 100 200 300 400 500 


Fig. 4. Temperature dependence of the residual strain of the investigated composite.

4. Discussion 


residual elongation (m) 

0 

-20 

-40 

-60 

1 2 3 4 

number of thermal cycles 

Fig. 5. Residual elongations after individual thermal cycles. 

Using the Grüneisen theory of thermal expansivity [14], it follows (Cp – Cv) = ( 2 TV0)/K, and from 

isotropic elasticity, K = 3(1 - 2)/E. Hence, the following relationship between the thermal expansion 

coefficient and the Young‟s modulus can be written: 

( Cp -Cv) 3( 1-2) 2 

= (3) 

TV E 

here Cp and Cv are the specific heats at constant pressure and volume, V 0 the molar volume, K the 

compressibility modulus and the Poisson ratio. Considering that the term (Cp – Cv) 3 (1.-.2)/V0) is at 

a certain temperature T constant, the relationship between the modulus defect and relative change of the 

thermal expansion coefficient: 

0 

1E =- (4) 

2 E 

The modulus defect E/E (=(E-E0)/E0, where E0 is the modulus value without thermal treatment, is 

given by the following equation 

2 

- E / E= 

 

 

(5) 

where is a constant, is the dislocation density and the length of dislocation segments between weak 

pinning points (solute atoms, point defects). 

The temperature dependences of the / and the modulus defect E/E are given in Fig. 6. Note, that 

the modulus defect is plotted against the upper temperature of the thermal cycle. It can be seen that both 

dependences exhibit a maximum at a temperature of 310 o C. 

Temperature changes during the thermal cycle invoke thermal stresses in the matrix which may reach 

its yield stress and generate new dislocations in plastic zones. The radius of the plastic zone is given by 

the following approximate relationship [15] 

335

336 


4 

E 

M 

rplz = rf . T 

(5-4 ) y 

where EM is Young's modulus of the matrix, is Poisson constant, y the yield stress in the matrix and rf 

is the radius of fibres. Similarly, it is possible to express the volume fraction of the plastically deformed 

matrix [16] 

/ 

0.12 

0.08 

0.04 

0.00 

-0.04 

4E 

fplz = f M 

 

 

( 5- 4) 

 

E/E 

/ 

y 


1/2 

 

. T 

-1 

 

run 1 

0 100 200 300 400 500 

Fig. 6. Temperature dependencies of the relative changes of the thermal expansion coefficient and the E-modulus defect. 

where f is volume fraction of the reinforcing phase. Fresh dislocations in plastic zones, produced by 

different expansion behaviour of the matrix and the reinforcements due to temperature changes, are only 

slightly pinned and contribute substantially to modulus defect [15]. Plastification of the matrix is due to 

newly created dislocations. An increase in the dislocation density near reinforcement can be calculated 

according the equation (1). Considering that the number of pinning points is constant, the effective 

length of dislocation segments increases with increasing dislocation density. The similar situation can be 

considered in the sample thermally cycled in the dilatometer. Although the thermal expansion 

coefficient was determined on the specimen heated in the dilatometer, the increase of the dislocations 

density may be considered due to thermal stresses generated in the matrix. It is suggested that, in 

addition to the regular lattice temperature expansion, the extension of mobile dislocation loops, which 

are a result of the accommodation of the thermal stresses, causes localized increases in volume and an 

increase in the apparent expansion coefficient. An increasing tendency of the modulus and CTE defects 

stopped at a temperature of 310 o C. Thermal loading up to higher temperatures decreases the both 

defects. The radius of the plastic zones in the vicinity of fibres was estimated according to relationship 

(5) to be about 11 m. The volume fraction of plastic zones exhibits after thermal treatment at 310 o C 

about 82% of the matrix volume (substituting into relationship (6) for =20x10 -6 K -1 , rf=3 m, EM=45 

GPa, =0.35, y=45 MPa [17]). The plastic zones in the matrix may overlap and dislocations may 

annihilate. Thermal stresses in the AX41 alloy matrix which are originally tensile convert to 

compression ones [11]. Dislocations moving under arising compression stresses in the inverse direction 

-2E/E 

(6) 

(7)


interact with dislocations of opposite sign and may annihilate. Relatively high maximum strain 

amplitude renders possible movement of free dislocation segments in the slip plane. Solute atoms and 

their small clusters are obstacles for the dislocation motion. After loading at higher temperatures, 

increasing concentration of vacancies interacts with dislocations producing jogs on the dislocation lines. 

Thermally activated motion of dislocation segments is restricted and the both defects decrease. A 

deviation from the temperature dependence of the CTE is observed. Values of the CTE decrease with 

temperature above about 310 o C (Fig. 3). The yield stress of the matrix decreases with increasing 

temperature. The internal stress state in the matrix is tensile. It is decreasing during heating and the state 

becomes compressive at some temperature. At a certain temperature plastic deformation in the matrix 

occurs. This deformation induces changes in the internal stress, which modify the elastic properties in 

the matrix. The specimen length is reduced under compression stresses. This leads to a decrease in the 

CTE, which is observed. Thus, decreasing dislocation density reduces the additional thermal expansion 

coefficient. 

5. Conclusion 

Magnesium alloy AX41 reinforced with short Saffil fibres was prepared by the squeeze casting 

technology using a perform. The thermal expansion was measured over a wide temperature range from 

ambient temperature up to 400 o C in four runs. The addition of Saffil fibres decreases the thermal 

expansion coefficient. This decrease is the maximum in the first run; in the second and other runs the 

value of the CTE is practically the same. The permanent contraction of the sample was observed after 

each thermal cycle. Observed value of this contraction decreases with increasing number of thermal 

cycles. The composite was thermally cycled between room temperature and increasing upper 

temperature of the thermal cycle up to 430 o C. After each thermal cycle the resonant frequency of the 

free vibrations of the sample was measured. The modulus defect E/E (calculated from the resonant 

frequency) and the relative change of the CTE / exhibit the similar temperature dependence with a 

local maximum at 310 o C. Considering formation of plastic zones as a consequence of thermal stresses 

invoked in the matrix, newly created dislocations are the reason for the observed changes. Thermal 

loading at temperatures higher than 310 o C yields a new situation: Thermal internal stresses generated at 

temperatures higher than 310 o C are high enough to invoke motion of new dislocations. Thermal cycling 

at temperatures higher than 310 o C causes movement and annihilation of new dislocations in the matrix, 

under appearing compressive internal stresses, which leads to a decrease of the / and the absolute 

value of the modulus defect. 


This work is a part of the research plan MSM 1M2560471601 "Eco-center for Applied Research of 

Non-ferrous Metals" that is financed by the Ministry of Education, Youth and Sports of the Czech 

Republic. This work was also supported by the Grant Agency of the Academy of Sciences of the Czech 

Republic under Grant IAA201120902. 

337

338 

References 


[1] N. Chawla, K.K. Chawla, Metal Matrix Composites, Springer, New York, 2006. 

[2] K. Weinert, M. Lange, M. Schoer, Magnesium Alloys and Their Applications. (Ed. K.U. Kainer), DGM, Willey-VCH, Weinheim (2000) 

412. 

[3] N. Chawla, X. Deng, D.R.M. Schnell: Mater. Sci. Eng. A 426 (2006) 314–322. 

[4] A. Rudajevová, P. Lukáč, The influence of interfacial chemical reactions on the residual and thermal strain in reinforced magnesium alloys 

Kovove Mater. 46 (2008) 145-150. 

[5] Y.D. Huang, N. Hort, H. Dieringa, K.U. Kainer, Analysis of instantaneous thermal expansion coefficient curve during thermal cycling in 

short fiber reinforced AlSi12CuMgNi composites, Compos. Sci. Technol. 65 (2005) 137–147. 

[6] R.J. Arsenault, N. Shi, Dislocations generation due to differences between the coefficients of thermal expansion, Mater. Sci. Eng., 81 

(1986) 151-187. 

[7] D.C. Dunand, A. Mortensen, On plastic relaxation of thermal stresses in reinforced metals Acta Metall. Mater. 39 (1991) 127-139. 

[8] R. U. Vadyia, K.K. Chawla, Thermal expansion of metal-matrix composites, Comp. Sci. Technol. 50 (1994) 13-22. 

[9] Z. Trojanová, P. Lukáč, F. Chmelík, W. Riehemann, Microstructural changes in ZE41 composite estimated by acoustic measurements. J. 

Alloys Compd. 355 (2003) 113-119. 

[10] Z. Trojanová, F. Chmelík, P. Lukáč, A. Rudajevová, Changes in the microstructure of QE22 composites estimated by non-destructive 

methods, J. Alloys Comp. 339 (2002) 327-334. 

[11] P. Lukáč, Z. Trojanová, F. Chmelík, A. Rudajevová, Changes in the microstructure of magnesium composites estimated by 

non-destructive methods. Int. J. Mater. Product Techn. 18 (2003) 57-69. 

[12] A. Rudajevová, J. Balík, P. Lukáč, Thermal expansion behaviour of Mg–Saffil fibre composites, Mater. Sci. Eng. A 387-389 (2004) 

892-895. 

[13] J. Göken, W. Riehemann, Dependence of internal friction of fibre-reinforced and unreinforced AZ91 on heat treatment, Mater. Sci. Eng. A 

324 (2002) 127-133. 

[14] M. J. Hordon,: B. S. Lementy, B. L. Averbach, Influence of plastic deformation on expansivity anelastic modulus of aluminium, Acta 

Metall. 6 (1958) 446-458. 

[15] E. Carreño-Morelli, Interface stress relaxation in metal matrix composites, in Mechanical Spectroscopy Q-1 2001, R. Schaller, G. Fantozzi 

and G. Gremaud, Eds., Materials Science Forum, vol. 366-368 (2001) 570-580. 

[16] E. Carreño-Morelli, S.E. Urreta, R. Schaller, Mechanical spectroscopy of thermal stress relaxation at metal–ceramic interfaces in 

Aluminium-based composites, Acta Mater. 48 (2000) 4725-4733. 

[17] Z. Trojanová, P. Lukáč, Physical aspects of plastic deformation in Mg-Al alloys with Sr and Ca, Inter. J. of Mater. Research 100 (2009) 

270-276.

Abstract 

Fatigue behaviour of woven composite joint 

J Y Zhang a, *, Y Fu a , L B Zhao b , X Z Liang c , H Huang b , B J Fei a 

a Institute of Solid Mechanics, Beihang University (BUAA), Beijing 100191, PR China 

b Schools of Astronautics, Beihang University (BUAA), Beijing, 100191, PR China 

c Beijing Aeronautical Manufacturing Technology Research Institute, Beijing, 100024, PR China 

Fatigue behaviour of a particular woven composite adhesive bonded joint subjected to tensile-tensile cycle loading is 

researched. Tests were conducted under fatigue and monotonic loadings in order to research the durability of such bonded 

joints. A careful observation of cracking mechanisms during fatigue life showed that filler and tip zone is the potential 

weakness in the joints. The experimental outcomes expatiated that the endurance limit loading, lower than the initial 

damage loading, is about half of the ultimate static strength. The results also showed that fatigue lifetime of composite 

joint comprised of two stages: initiation stage, which is less than 25% of the fatigue lifetime, and the propagation stage 

for the rest up to failure. Four stiffness degradation modes, named stable slight reduction mode, abruptly decreasing mode, 

step decrease mode and constant stiffness mode, exhibited in fatigue test. 

Keywords: Composite structures; Adhesive joints; High cycle fatigue; S-N curves; Tensile loading 


Weight and production cost reductions are important goals for aircraft structural researchers and 

engineers. Integrated composite structure design concept, which enable reduction in fastener and part 

counts and lead to remarkable decrease of assemble cost and structural weight, provide an available way 

to realize these goals[1]. An all-composite π joint, presented in CAI projects of NASA [1, 2], is an 

effective structural connector to realize integrated composite structures and thus a key technique [1, 2]. 

However, π joints belong to the category of out-of-plane joints, which are potential weakness to transmit 

tensile, bending and shear load between different parts of the airplane [3]. Obviously, a deeply 

understanding on fatigue behaviour of composite π joints is significant for the safety of integrated 

composite structures. 

Nowadays there are relative little literatures concerning on the fatigue behaviour of out-of-plane 

joints. Based on the research work on static behaviour of tee joint [3-5], Shenoi et al. [6-10] took the 

lead in exploring fatigue behaviour of tee joint and top hat joint at the end of 20th century. Firstly Read 

and Shenoi [6] briefly reviewed investigations on fatigue behaviour of FRP laminates and summarized 

various theories to model damage accumulation. Then Phillips et al. [7, 8] applied damage mechanics to 

predict fatigue life of structural components such as tee connection and top hat stiffener. Shenoi and 

Read [9, 10] provided deep understanding on the high cycle fatigue behaviour of a particular single skin 


E-mail address: jyzhang@buaa.edu.cn

340 


tee joint made of FRP. Stiffness degradation, residual strength and energy dissipation characteristics 

obtained from a comprehensive series of tests, covering joints with varying material and geometry 

configurations are detailed discussed. Furthermore, a design methodology encompassing fatigue 

considerations is proposed. Recently, a composite adhesive tee joint was tested under fatigue and 

monotonic loadings by Marcadon [11] in order to study its durability. Careful observations on cracking 

propagation during fatigue life showed that fatigue mechanisms were strongly dependant on the joint 

structural geometry. Moreover, the fatigue lifetime of such joints is separated into two stages, the 

initiation stage, which is about a third of the fatigue lifetime, and the propagation stage for the rest up to 

failure. 

However, until very recently, relative little work concerning fatigue behaviour of composite π joint 

was published in the open literature. To provide more understanding on this subject, high cycle fatigue 

behaviour of a woven composite adhesive bonded joint subjected to tensile-tensile cycle loading was 

investigated in this paper. 

2. Geometry and material parameters of woven composite joint 

A woven composite joint with detailed configuration and geometric parameters is shown in Fig. 1. 

A shaped overlaminate co-bonded with a precured skin and then secondary-bonded with web plates at 

90 o direction. The shaped overlaminate is constructed from two plies of L prepreg, one ply of U 

prepreg and base prepreg, which are made of carbon/bismaleimide woven composite (CBWC). Some 

adhesive are added between the prepregs. The stacking sequences of L, U and Base prepreg and the 

location of adhesive are shown in Fig.1 too. The connections between the L, U and Base prepreg are 

achieved from unidirectional carbon/bismaleimide (UDCB) prepreg with 0º fibre direction, which are 

extruded by the L, U and base prepreg to form two prism-like fillers. The skin is manufactured by a 

glass fibre composite core covered with eight plies of same UDCB prepregs on both sides, in which the 

stacking sequence of the eight plies is [45 o /90 o /-45 o /0 o ]s. Whereas the web is fabricated by a Kevlar 

honeycomb and glass fibre reinforcement composite which covered with eight plies of UDCB prepregs 

on both sides with the stacking sequence [90 o /90 o /-45 o /45 o ]s. The material parameters are listed in Table 

1. 

Elastic parameters 

E1 

(GPa) 

Table 1. Elastic parameters and strength allowable values of CBWC and UDCB 

E2 

(GPa) 

E3 

(GPa) 

v12 v13 v23 

G12 

(GPa) 

G13 

(GPa) 

CBWC 60 60 7.46 0.035 0.31 0.31 5.18 5.18 5.18 

UDCB 121 7.46 7.46 0.31 0.31 0.44 5.18 5.18 2.59 

Strength allowable 

values 

S1t 

(MPa) 

S1c 

(MPa) 

S2t 

(MPa) 

S2c 

(MPa) 

S3t 

(MPa) 

S3c 

(Mpa) 

S12 

(MPa) 

S13 

(MPa) 

CBWC 601.2 581 563.9 578.2 51 209 112.1 87.9 87.9 

UDCB 2326 1236 51 209 51 209 87.9 87.9 99.2 

G23 

(GPa) 

S23 

(MPa)

J Y Zhang, Y Fu, L B Zhao, X Z Liang, H Huang, B J Fei. / Fatigue behaviour of woven composite joint 

3. Behaviour under static tensile load 

3.1 Static test programme 

Fig. 1. Geometry of π joint sample. 

Static tests were operated to identify the ultimate static strength (USS), which is the maximum force 

applied to the π joint and also the value of peak force for the fatigue test. The specimen and 

experimental apparatus for the static tensile test of composite joint is illustrated in Figure 2. The test 

was implemented in a servo hydraulic testing machine (Instron 8803). The skin was perpendicularly to 

the force axis, and the load was applied on the top end of the web plate. A rigid bracket jig was fixed at 

the base of the test machine to hold the π joint specimens. Both ends of skin plate were clamped by two 

eye rigid plates bolted to the rigid bracket. The rigid plates were at 80mm away from the centerline of 

joint. 

Fig. 2. Specimen and experimental set-up for static tensile test. 

For composite materials, the USS can vary with the load rate applied to the materials. The 

recommended practice is for the USS to be established by static testing at a rate approximating the load 

rate in the fatigue test in ASTM D-3039 [12]. Refer to relative researches [13, 14]; the static loading of 

341

342 


π joints was undertaken at a constant speed 1-2mm/min, which is very low to clearly identify the 

various failure mechanisms and the sequence in which they occurred. 

Three samples referred to the aforementioned woven composite π joint were tested. The displacement 

of the crosshead was recorded as load against displacement curve. Typical damage and failure events in 

tests were recorded by video and photographs. For the geometry complexity of the joint, an inner 

damage is difficult to be observed in experiment. Thus, initial damage was characterized by noise 

emitted during loading and a notable drop-off in load vis-a-vis the load-displacement curve. Final 

failure was observed and illuminated by the maximum load on the load-displacement curve. 

3.2 Static test results 

For sample 1 and 3, the observable damage firstly appeared in the tip zone as shown in Fig.3(a). 

However, for sample 2, the observable damage appeared at the interface between the filler and L 

prepreg as shown in Fig. 3(b). Then new damage occurred in the tip zone quickly. For all the samples, 

with the increased load, the crack in the tip zone propagated towards the centerline of joint along the 

interface between the base prepreg and skin. Fig.3(c) gives the final failure pattern in the experiment. 

The joint was pulled apart on the upper ply of base prepreg, when the ultimate failure occurred. 

(a) Crack in the tip zone (b) Crack in the filler zone 

(c) Final failure 

Fig. 3. Failure patterns under static loading. 

The initial and final failure strengths of three samples in experiment are listed in Table 2. It can be


seen that the ultimate strength of woven composite π joint is 1.274kN, which is necessary for the fatigue 

test. 

Table 2. Initial/ultimate static strength in static tensile test 

Results Test 1 Test 2 Test 3 Average of tests 

Initial failure load /kN 0.753 0.700 0.750 0.734 

Final failure load /kN 1.240 1.244 1.339 1.274 

3.3 Numerical strength distribution 

The numerical analysis work in this programme has two main reasons. The first aspect was with 

respect to the difficulties in inspecting the test specimens for their complex geometry and small size. 

Secondly, the finite element model allowed for load paths and stress/strain/strength patterns to be 

assessed effectively, which was an inability for the experimental work. In this part of the paper, the 

stress/strength analysis is used to explain the trends seen in the experimental results and to understand 

the location of failure in the joint. A three dimensional finite element model is established by the 

generalized software ABAQUS ® , as shown in Fig. 4. In this model eight-noded solid elements C3D8 

were adopted in most area and six-noded solid elements C3D6 were used to fit the complex and 

irregular boundary. There are 160230 elements and 174608 nodes in total. The element size was reduced 

at the filler zone and tip zone, which were sensitive to the stress concentration. The finite element model 

was restrained at the two ends of skin to represent the clamping arrangement used during 

experimentation. A tensile load 0.637N was applied on the top of the web. 

Fig. 4. Finite element model. 

A traditional maximum stress failure criterion was chosen to assess the failure of plies in the joint. 

However, a modified maximum stress failure criterion [15] was used to assess the filler‟s failure for its 

block configuration characteristics. Assessed by the corresponding failure criteria, the strength 

distribution contour of composite π joint is shown in Fig.5, which provides more information about the 

static mechanical behaviour of woven composite π joint. It can be seen that a high stress level appears in 

the filler zone and tip zone. These two parts have weak load carrying capability and thus will be 

potential damage onset under service load. 

343

344 

4. Behaviour under fatigue load 

4.1 Fatigue test programme 


Fig. 5. Strength distribution in the filler zone and tip zone at tensile load 0.637kN. 

The clamps used in fatigue test were the same as the static tensile test. A tensile-tensile load was 

applied to the web of each π joint specimen while the two ends of skin were fully clamped. Fig.6 

illustrated the set-up for the π joint experimental programme under fatigue loading. A servo hydraulic 

testing machine (MTS 880) was used to implement the fatigue test at a constant amplitude sinusoidal 

loading with the load ratio R=Fmin/Fmax=0.1. The frequency of the tests is 5Hz. 

Fig. 6. Set-up for composite π joint experimental programme. 

The specimens were cycled at a series of constant maximum load values up to rupture. The maximum 

loads chosen were 80%, 70%, 60% and 50% of the ultimate static strength of joint. This allowed a 

complete knowledge of the fatigue life behaviour of woven composite π joints. 

For each cycles a measurement was taken of the maximum load and deflection value by the control 

computer. A microscope with precision 0.01mm was also undertaken at intervals during test to provide a 

visual observation at the front surface of each specimen. Thus, a record was made of any observed 

damage, including initiation, growth, and localization; leading to ultimate failure of joint. At the same 

time, the cycles corresponding to these typical events were also recorded during the experiment.


4.2 Fatigue life of composite π joint 

The cycles with respect to the crack onset and final failure under various loads level are listed in 

Table 3. An amount of scatters of fatigue life was immediately obvious for these specimens. The reasons 

were twofold. The first was due to complex structural configuration and multiple material components 

of joint. Secondly, it could be argued that the scatter was related to consistency of specimen 

manufacture. 

A further observation that can be made concerning the fatigue lifetime in Table 3 was a very short 

fatigue crack initiation life N ini , which was less than 22% of total fatigue lifetime N. Indeed, at a very 

limited number of cycles, initial crack could be observed on the front surface of all the specimens, 

which underwent load lever from 50% to 80% USS with R=0.1. Unlike composite laminates, where 

fatigue limit is about 60-80% USS, the fatigue endurance limit of composite π joint is far lower than 

50% USS if the fatigue failure is assessed by the fatigue crack initiation. Moreover, to some extent, the 

crack growth experienced a long time and was predominant to the total fatigue lifetime. 

Table 3. Fatigue life of joints under tensile loading 

Specimen No. Fmax Nini Ncg N lgFmax lgN lg N Fmax/USS 

1 1019.0 398 186564 186962 3.00 5.27 4.32 0.8 

2 1008 29381 30389 4.48 

3 672 2398 3070 3.49 

4 1 11254 11255 4.05 

5 892.0 5566 94434 100000 2.95 5.00 4.94 0.7 

6 800 50974 51774 4.71 

7 1 126116 126117 5.10 

8 764.4 11868 511536 523404 2.88 5.72 5.26 0.6 

9 1793 39162 40955 4.61 

10 19697 266848 286545 5.46 

11 637.0 501 >10 6 

>10 6 

2.80 >6.00 6.00 0.5 

Results from the experimental average value in terms of applied load and number of cycles to failure 

were plotted to produce S-N curve in dual-logarithm coordinates system, as shown in Fig.7. Under the 

experimental load level, the curve exhibits a well linear characteristic when the joint are fatigued. As the 

load increased, the number of cycles tended to decrease. Thus, the variation law of fatigue life with the 

load level could be expressed by two-parameter function, as written below 

lg F = 3.552 - 0.1249lg N 

(1) 

max 

4.3 Fatigue failure location and failure process 

Visual observation results depicted by the photographs could provide insight into the failure 

mechanisms of joint under fatigue load. A summary of experimental observation results is listed in Table 

4. The column of left-filler or right-filler denotes the load cycles when first crack could be observed at 

left filler or right filler. The column left-tip or right-tip gives the load cycles with respect to first crack 

occurrence in left or right tip zone, due to debonding of the horizontal leg of L prepreg with skin. For 

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different specimens, summary of crack onset location, final failure location, growth life of main crack 

and corresponding figure, which illustrated failure patterns of each specimen, is listed in the following 

columns, respectively. 

Fig. 7. S-N curve of the joint. 

Table 4. Fatigue failure location and failure process of specimens 

No. Left-Filler Right- Filler Left-tip Right-tip Crack onset location Final failure location Figure No. 

1 2824 893 398 ----- Left-tip Left-tip Fig.8(a) 

2 ----- 1 1008 ----- Left-Filler Left-tip Fig.8(b) 

3 1942 1 2072 672 Right- Filler Right-tip Fig.8(c) 

4 ----- 1 7112 1 Right- Filler Right-tip Right-tip Fig.8(d) 

5 3213 2209 5566 33200 Right- Filler Left-tip Fig.9(a) 

6 ----- 2100 3189 800 Right-tip Right-tip Fig.9(b) 

7 ----- 1485 1723 1 Right-tip Right-tip Fig.9(c) 

8 ----- 418 11868 978 Right- Filler Left-tip Fig.10(a) 

9 ----- 988 4128 1793 Right- Filler Right-tip Fig.10(b) 

10 95523 1 ----- 19697 Right- Filler Right-tip Fig.10(c) 

11 ----- ----- ----- 501 Right-tip ----- Fig.11 

The fatigue failure process of specimens 1 loaded at 80% USS is shown in Fig.8(a). At a very limited 

number of cycles 398, the left horizontal leg of L prepreg was peeled from the skin and an obvious 

crack could be observed. As the cycles increased, new cracks was noticed, located at the fillers of joint. 

The new crack occurred at the right filler with 893 cycles and then at the left filler with 2824 cycles. 

With the number of cycles increased, the delamination crack at the left tip zone propagated stably; the 

crack at the right filler grew slowly while no obvious propagation could be observed in the left filler. Up 

to final fatigue failure, no crack could be examined at the right tip zone. Because of the stable crack 

propagation started at left tip zone, the joint was eventually peeled off along the interface of π 

overlaminate with the skin.


(a) Specimen 1 (b) Specimen 2 

(c) Specimen 3 (d) Specimen 4 

Fig. 8. Failure patterns with Fmax=80%USS. 

Fig.8(b) illustrates the failure patterns of specimen 2 loaded at 80% USS. At the first load cycle, an 

obvious crack along the interface between the right filler and L prepreg could be observed. After 1008 

cycles, a delamination crack occurred at the left tip zone. With the increased cycles, the cracks grew 

stably both at left tip zone and right filler. No visual crack was apparent at the left filler and right tip 

zone for this specimen. At last, the crack at left tip zone ran through the connection of joint and resulted 

in final rupture. 

Fig.8(c) showed the failure patterns of specimen 3 at different cycles. The specimen was also loaded 

at 80% of the ultimate strength of the joint. For this specimen, a crack could be observed at the right 

filler in the first load cycle, just like specimen 2. When the number of cycles arrived at 672, 1942 and 

2072, new cracks could be found at the right tip zone, left filler and left tip zone respectively. As the 

number of cycles increased, the crack at the right tip zone grew quickly while those in others place 

propagated slowly. Therefore, the crack at right tip zone propagated along the interface between the U 

prepreg and skin, and led to final collapse. 

The failure of the fourth specimen loaded at 80% USS was depicted in Fig.8(d). Two cracks occurred 

in the first load cycle, at right filler and right tip zone respectively. The two events were instantaneous 

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and therefore observing their sequence with the naked eye was impossible. As the number of cycles 

arrived at 7112, a new crack could be observed at the left tip zone. With continued cycles, the crack at 

the right tip zone propagated quickly and led to ultimate peeling of the π overlaminate from skin. 

(a) Specimen 5 (b) Specimen 6 

(c) Specimen 7 


Overall, for specimens loaded at 80% USS, two fatigue damage forms were exhibited. The crack 

onset occurred in the filler during the first load cycle. From then on, delamination crack occurred in the 

tip zone. As the cycles increased, the crack in the filler grew slowly whilst that in the tip zone 

propagated quickly. Thus, the final fatigue failure is predominated by the crack growth located at the tip 

zone. 

Fig. 9(a) described the failure process of specimen 5 under 70% USS. Initial crack occurred on the 

surface of right filler when the number of cycles arrived at 2209. From then on, new cracks appeared at 

the left filler, left tip zone and right tip zone when the number of cycles arrived at 3213, 5566 and 33200. 

The cracks at the left and right tip zone grew quickly whilst that at the filler propagated slowly up to 

final failure. The crack at left tip zone passed through the connection area and converged with the crack 

propagated from right tip zone, causing complete loss of joint strength. 

For specimen 7, the failure could be expressed by Fig.9(b). Initial delamination crack took place at


right tip zone at the number of cycles 800. New crack appeared at right filler and left tip zone with 

reference to the number of cycles 2100 and 3189 respectively. The crack at right tip zone propagated 

stably and quickly. When the number of cycles arrived at 41480, the crack abruptly grew 15mm and 

arrived at the underside of U prepreg. Subsequently, the crack continued stably and joined with the 

crack propagated from left tip zone, which led to the peeling of the overlaminate and skin. 

Failure patterns of the last specimen loaded at 70% USS was shown in Fig.9(c). During the first load 

cycle, visual crack could be found at the right tip zone. Subsequently, when the number of cycles 

arrived at 1485 and 1723, new cracks appeared at right filler and left tip zone respectively. With the 

increasing load cycles, the cracks at left and right tip zone grew symmetrically and stably. At the same 

time, the crack at the right filler propagated slowly. It is worth noting that the crack at the right filler 

stopped to grow when the crack started from right tip zone arrived at the underside of right filler. 

Eventually, the cracks from the left and right tip zone joined and the final rupture occurred. 

According to the Fig.9 with reference to specimens loaded at 70% USS, several physical phenomena 

could be summarized. Compared to those specimens load at 80% USS, only one specimen produced 

initial crack during the first load cycle. At the load level of 70% USS, generally, crack onset occurred at 

tip zone and subsequently new cracks took place at the filler. As the cycles increased, the cracks at the 

filler grew slowly. However, the crack at tip zone grew quickly and eventually resulted in the final 

collapse. During this process, two propagation forms could be observed. The first was a stable 

propagation up to rupture, which was dependant on the symmetrical growth of the cracks from two tip 

zone. Secondly, an abruptly instant failure could be observed if one side of the cracks grew quickly. 

Fig.10(a) gives the failure patterns of specimen 8 loaded at 60% USS. Crack onset appeared at right 

filler with the number of cycles 418. New cracks occurred at right and left tip zone at the number of 

cycles 978 and 11868 respectively. As the load cycles increased, the cracks at left tip zone and right 

filler grew quickly. However, the crack at right tip zone stopped due to lack of drive force, caused by the 

propagation of crack at right filler. At last, the crack from left tip zone passed through the underside of 

U prepreg and converged with the crack from right filler, leading to final failure. 

Fig.10(b) described the failure process of specimen 9 under 60% USS. Initial crack occurred on the 

surface of right filler when the number of cycles arrived at 988. From then on, new cracks appeared at 

the right and left tip zone when the number of cycles arrived at 1793 and 4128 respectively. With the 

increasing load cycles, cracks at left and right tip zone grew symmetrically and stably. At the same time, 

the crack at the right filler propagated slowly. The right tip zone crack grew to the underside of right 

filler rapidly when the number of cycles arrived at 25324. Then the right tip zone crack grew stably 

through the connection area and converged with the crack propagated from left tip zone, causing 

complete loss of joint strength. 

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350 


(a) Specimen 8 

(b) Specimen 9 (c) Specimen 10 


Fig.10(c) showed the failure patterns of specimen 10 at different cycles. The specimen was also 

loaded at 60% of the ultimate strength of the joint. For this specimen, a crack could be observed at the 

right filler in the first load cycle, just like specimen 2, 3 and 4. When the number of cycles arrived at 

19697 and 95523, new cracks could be found at the right tip zone and left filler respectively. As the 

number of cycles increased, the crack at the right tip zone grew quickly while the other cracks 

propagated slowly. Therefore, the crack at right tip zone propagated along the interface between the U 

prepreg and skin, and led to final collapse. 

Fig.10 illustrated failure patterns of specimens loaded at 60% USS. Compared to those specimens 

load at 80% and 70% USS, only one specimen produced initial crack during the first load cycle. At the 

load level of 60% USS, generally, crack onset occurred at tip zone. As the cycles increased, the crack at 

tip zone grew quickly and led to final rupture. The same propagation forms, a stable propagation and an 

abrupt failure, as those specimens loaded at 70% could be found. However, the fatigue initiation life and 

growth life for these specimens loaded at 60% increased due to the reduction of load level. 

Fig.11 described failure process of specimen 11 loaded at 50% USS. After 501 load cycles, 

delamination crack appeared at right tip zone. However, the crack grew slowly and not reached the


underside of right filler until the test was stopped at the number of cycles10 6 . During this process, no 

visual crack could be observed at the filler zone and left tip zone. 

Fig. 11. Failure patterns of specimen 11 with Fmax=50%USS. 

Above all, the failure mode under fatigue tensile-tensile load was found to be extremely similar to the 

mode observed during static loading. The crack onset location was random but limited to the filler zone 

and tip zone at a very limited number of cycles. If the crack onset occurred initially at fillers then the 

next failure event was the delamination crack in the tip zone. Final failure was consistent, due to the 

delamination crack took place at tip zone. Further, it is worth noting that the number of cycles to cause 

crack onset was loosely dependant on the applied load. To some extent, the fatigue life of composite π 

joint is dependent on the crack propagation form. 

4.4 Stiffness degradation 

A large amount of studies related to stiffness reduction, as a fatigue measure, are based on 

experimental observations. They consider stiffness degradation as a result of various micromechanical 

parameters such as crack initiation, delamination, and fibre matrix debonding and fibre breakage under 

cyclic loading [16]. Present research is aimed to depict stiffness degradation throughout the life of each 

joint specimen. 

For each cycle, the deflection δ of web and applied load P were obtained from continued 

measurements during experimentation. With these parameters, generalized stiffness of each cycle could 

be defined as the ratio of the applied load to the deflection of the web: 

k = P / 

(2) 

i max i max i 

Where ki, as a fatigue measure, denotes an ability to resist tensile deformation for composite π joint. 

Assume the generalized stiffness examined at the initial loading stage to be k 0 , which denotes the 

initial value of stiffness degradation for specimens under fatigue load. Then the normalized generalized 

stiffness could be expressed as: 

The normalized fatigue life could be written as: 

k = k / k 

(3) 

i 

0 

351

352 

where N is the total fatigue life. 


n = n / N 

(4) 

From the continued measurements of the load and deflection during experimentation, the change in 

the slope of the load-deflection curve could be obtained, and thus any global stiffness degradation could 

be identified. The slope of the load-deflection versus the fatigue life of the specimen normalized with 

respect to the number of cycles to failure is shown in Fig. 12. 

(a) Fmax=80%USS (b) Fmax=70%USS 

(c) Fmax=60%USS (d) Fmax=50%USS 

Fig. 12. Stiffness degradation curves. 

Fig.12(a) is reference to the specimens loaded at 80% USS. A slight increasing of the generalized 

stiffness could be observed in initial stage of fatigue load. Then the generalized stiffness descended 

stably from crack generation, further propagation, up to final failure. The total amount of descent is no 

more than 15%. An exception is for specimen 1, whose generalized stiffness decreased obviously at first 

and then remained unchanged. The failure of major area of right filler resulted in loss of load carrying 

ability in fatigue test. 

Fig.12(b) is associated with specimens loaded at 70% USS. Similar to the specimens loaded at 80% 

USS, the generalized stiffness also increased a little at first. However, an abrupt stiffness degradation 

could be found for specimen 5 and 6, due to a rapidly crack growth in the fatigue test. From then on, the 

stiffness degraded slowly until final rupture, which corresponded to the stable crack growth stage. 

Moreover, due to no remarkable failure at filler zone and symmetric stable crack propagation at tip zone,


the stiffness of specimen 7 waved from 0.95 to 1.15 during the fatigue test without obvious descent. 

Fig.12(c) is reference to the specimens loaded at 60% USS. Three specimens give different stiffness 

degradation process in this figure. Generalized stiffness decreased obviously at first and then decreased 

slowly in Specimen 8. This is because of the failure of major area of right filler at the beginning of 

fatigue test. Generalized stiffness of specimen 9 decreased faster than the others, and a small abrupt 

stiffness degradation could be found, due to a rapidly crack growth in the fatigue test. A slight 

increasing of the generalized stiffness of specimen 10 could be observed in initial stage of fatigue load. 

Then the generalized stiffness descended stably from crack generation, further propagation, up to final 

failure. 

Fig.12(d) showed the experimental stiffness degradation curve under 50% USS. As the crack at tip 

zone slowly developed and grew in joint 11, the stiffness of the joint are reduced slightly. 

In a summary, four stiffness degradation modes for composite π joints exhibited in fatigue test due to 

their complex structural configuration and a variety of failure mode. (1) Stable slight reduction mode, 

corresponding to specimens that the crack only occurred at tip zone and continued to grow stably in 

fatigue test, such as specimen 2, 3, 4, 10 and 11. (2) Abruptly decreasing mode, with respect to 

specimens that crack took place at filler zone and major region of filler failed, such as specimen 1 and 8. 

(3) Step decrease mode, associated with specimens that crack at one side of tip zone propagated rapidly 

to the underside of U prepreg, such as specimen 5, 6 and 9. (4) Constant stiffness mode, with reference 

to the specimens that cracks at left and right tip zone had a stably symmetric propagation, such as 

specimen 7. 


Static and fatigue tests have been conducted on composite π joints under tensile loading. A detailed 

analysis of damage evolution has been proposed so on to understand the fatigue behaviour of the sample. 

From this study, the following concluding remarks can be made: 

The endurance limit loading is lower than the initial damage load and about half of the ultimate 

static strength. 

The fatigue lifetime of composite joint comprised of two stages: initiation stage, which is less 

than 25% of the fatigue lifetime, and the rest is devoted to the crack propagation stage. 

The sample in fatigue tensile test has similar damage onset and propagation patterns with that in 

static tensile test. The filler zones and tip zones are the potential weakness in the joints. There are 

high stress concentrate on the tip of horizontal leg of L prepreg, resulting in the ultimate collapse 

occurred on the upper ply of base prepreg. 

Because of the complex structure and a variety of failure mode, different stiffness degradation 

modes for composite π joints are detected in fatigue test. 


The research work is supported by the National Science Foundation of China (10902004) and the 

Fundamental Research Funds for the Central Universities (YWF-10-02-090). 

353

354 

References 


[1] Taylor RM, Owens SD. Correlation of an analysis tool for 3-D reinforced bonded joints on the F-35 joint strike fighter. AIAA-2004-1562. 

[2] Butler B. Composites affordability initiative. AIAA-2000-1379. 

[3] Shenoi RA, Hawkins GL. Influence of material and geometry variations on the behaviour of bonded tee connections in FRP ships. 

Composites 1992;23(5):335-345. 

[4] Hawkins GL, Holness JW, Dodkins AR, Shenoi RA. The strength of bonded tee joints in FRP ships. Plasti, Rubber, Compos Process 

Applic 1993;19:279-284. 

[5] Blake JIR, Shenoi RA, House J, Turton T. Progressive damage analysis of tee-joints with viscoelastic inserts. Composites Part A 

2001;32:641-653. 

[6] Shenoi RA, Read PJCL. A review of fatigue damage modelling in the context of marine FRP laminates. Marine Structures 

1995;8:257-278. 

[7] Phillips HJ, Shenoi RA. Damage tolerance of laminated tee joints in FRP ship structures. Composites Part A 1998;29A:465–78. 

[8] Phillips HJ, Shenoi RA, Moss CE. Damage mechanics of top-hat stiffeners used in FRP ship construction. Marine Structures 

1999;12:1-19. 

[9] Shenoi RA, Read PJCL, Hawkins GL. Fatigue failure mechanisms in fibre-reinforced plastic laminated tee joints. Int J Fatigue 

1995;17(6):415-426. 

[10] Read PJCL, Shenoi RA. Fatigue behaviour of single skin FRP tee joints. Int J Fatigue 1999; 21:281–296. 

[11] Marcadona V, Nadot Y, Roy A, Gacougnolle JL. Fatigue behaviour of T-joints for marine applications. Int J Adhesion & Adhesives 2006; 

26:481–489. 

[12] ASTM D3039/D 3039M-00. Standard test method for tensile properties of polymer matrix composite materials. 2002. 

[13] Feih S, Shercliff HR. Adhesive and composite failure prediction of single-L joint structures under tensile loading, Int J Adhesion & 

Adhesives, 2005;25:47-59. 

[14] Pei JH, Shenoi RA. Examination of key aspects defining the performance characteristics of out-of-plane joints in FRP marine structures. 

Composites Part A 1996;27A:89-103. 

[15] Qin TL. Strength Prediction Method and Failure Mechanism of π Joint in FRP Structures. Master Degree Dissertation, Beihang University. 

2010;17-35. 

[16] Taheri-Behrooz F, Shokrieh MM, Lessard LB. Residual stiffness in cross-ply laminates subjected to cyclic loading. Composite structures, 

2008;85:205-212.

Damage in thermoplastic composite structures: application to 

high pressure hydrogen storage vessels 

Abstract: 

C Thomas a , F Nony a, *, S Villalonga a , J Renard b,† 

1: CEA, DAM, Le Ripault-F-37260 MONTS, France 

2: Centre des Matériaux, P.M.Fourt UMR CNRS 7633 BP 87, 91003 EVRY, France 

The design of reinforced laminated composites for type IV high pressure vessels application takes into account the 

initial mechanical properties of the material including safety coefficients but without any consideration with durability 

and damage resistance. 

This study focuses on the different damages occurring in carbon fibres / polyamide matrix composite structures with 

the objective to understand their influence on the mechanical properties and then the conception and manufacturing 

process of composite structures. The first part is dedicated to the characterization of the material and particularly its 

initial thermal and mechanical properties. Then, considering the different orientations of the filamentary wounded 

structure, damage processes are investigated (matrix cracking, delamination). In addition, first results of a dedicated 

filamentary winding process are presented. The influence of the key parameters is assessed. 

Keywords: damage; composite; thermoplastic; high pressure vessels; hydrogen 


Among the different storage strategies, compressed gaseous hydrogen storage (CGH2) seems to be 

the maturest solution. To be efficient, this storage must be done at high pressure (above 35 MPa and up 

to 70 MPa for on-board applications). For several years, CEA has been involved in the development of 

type IV high pressure vessels and has obtained promising achievements [1]. This type of vessels 

presents a polymeric liner, which exhibits high hydrogen tightness and which is reinforced by a 

structural composite layer. This structural layer allows the vessels to withstand high mechanical stresses 

and its design takes into account the burst pressure (140 MPa) and the number of cycles of 20 to 875 

bars (5 000 to 15 000 for vehicles applications and more than 100 000 for others applications). This 

design is done, considering the initial mechanical properties. The material durability and damages, 

particularly, for thick shells, are not well known and at present not directly taken into account. 

Damages are induced by the synergetic effect of environmental stresses or loading and the structure 

heterogeneity or existing defects. These defects can be due to critical material or inappropriate process 

parameters. 

This study focuses on the damages of carbon fibres / polyamide matrix composites structures. 

Thermoplastic matrix composites can be considered as relevant candidates since they present many 

* E-mail address: fabien.nony@cea.fr. Tel.: 0033 2 47 34 40 00. 

† E-mail address: jacques.renard@ensmp.fr. Tel.: 0033 1 60 76 30 31.

356 


advantages. They exhibit numerous potential interests in terms of impact resistance, durability and 

recyclability. The manufacturing process is also attractive because it offers potential reducing composite 

manufacturing costs and time (e.g. no need of thermal curing) [2]. In the case of high pressure vessels, 

the composite layer is manufactured by filament winding. The main limit of the process is the required 

heating system, which is used to soften and melt the matrix. In addition to that, a pressure must be 

applied during laying up to ensure sufficient material consolidation. On going R & D activities are 

focused on winding process optimization. 

The initial mechanical and thermal properties of the material are determined. Two different damage 

processes, delaminating and matrix cracking are studied. It aims at understanding damages occurring 

during the qualification tests of vessels like hydraulic pressure cycling or burst. In parallel, the 

thermoplastic pre-impregnated tape winding process is being developed and the influence of 

manufacturing parameters on material structure and properties is also being studied. 

Major expected outcomes are improvement of the modeling and the manufacturing thanks to the 

knowledge of material behaviour and durability. 

2. Material and methods 

2.1 Materials 

The studied materials, Carbostamp TM PA 6 and Carbostamp TM PA 12, are polyamide matrix 

(polyamide 6 or 12) reinforced with T 700 Carbon Fibres from Toray SOFICAR. The fibre volume 

fraction, determined by pyrolysis at 500 o C, is about 50 %. The matrix is semi crystalline and presents a 

melting point at 175 o C for the polyamide 12 and at 215 o C for polyamide 6. Testing samples consist in 2 

mm thick specimens for tensile test on unidirectional (45 o , 90 o ) or cross-plied ([02.902]s or [± 45 o ]s) 

laminates and in 1 mm thick specimens for longitudinal (0 o ) tensile test. The density is about 1.41 g/cm 3 

for Carbostamp TM PA 12 and about 1.47 g/cm 3 for Carbostamp TM PA 6. 

2.2 Sample manufacturing 

Laminates and wound samples (rings and pipes) are manufactured using UD fully pre impregnated 

tapes (Carbostamp TM ). Flat samples are dedicated to the determination of mechanical properties and the 

study of damage processes, whereas wound samples are dedicated to the study of the filament winding 

process parameters influence. 

UD flat specimens and cross-plied laminates are manufactured by hot compression moulding. The 

mould and the materials are heated to reach 210 o C for polyamide 12 and 230 o C for polyamide 6. Then a 

pressure is applied. Finally the pressurized mould is cooled to a temperature below 60 o C at 5 o C/min and 

the consolidated specimen is extracted [3]. 

Rings and pipes are manufactured by filament winding, which is commonly used for high pressure 

vessels application. The most important difficulty is the high flexural rigidity of the tape. Pre heating of 

the tape is required to soften the tape for a better motion and further thermal boost is required to melt 

the matrix. The heating temperature must be high enough to reach a low viscosity value, which makes

C Thomas, F Nony, etc. / Damage in thermoplastic composite structures: application to high pressure hydrogen storage vessels 

the matrix inter layer diffusion easier but must not trigger oxidation. Other parameters can have an 

influence on the material structure and properties [4-6]. After placement a sufficient pressure must be 

applied to ensure satisfying consolidation and minimize void content. The tape is also subjected to a 

roving tension to keep the fibre orientation. However, this tension must be appropriate to avoid broken 

filaments. The velocity of the mandrel also plays a key role. It must be compatible with the melting of 

the matrix and the consolidation of the structure. 

The process developed in this study presents a preheater (infrared), which raises the temperature just 

below the melting point, and a heater (infrared), which raises it above the melting point near the 

mandrel (Figure 1). The consolidation is ensured by a compaction roller. An adjustable tension is 

magnetically applied to PA/FC tape spools. 

2.3 Material properties and damage investigation 

Fig. 1. Development of thermoplastic composite filament winding process. 

Tensile tests have been conducted, using a 250 kN machine Zwick Roel Z 250, according to the 

standard ISO 527-5 [7], on unidirectional specimen with three different orientations 0, 90 and 45 o 

(orientations of fibres compared to the tensile load direction). Scanning electron microscopy (SEM) has 

been used to characterize the failure surface of the specimens. 

Fig. 2. Schematic view of crack density measurement by optical microscopy and example of cracking for [02,904,02] sequence. 

Damage by intralaminar cracking is also studied. This type of damages mainly occurs with 

cross-plied laminates (stacking sequences 02/90n/02), that are submitted to tensile loading [8]. The 

loading is applied by 50 MPa steps, cracks are observed by optical microscopy and a camera is focused 

on polished specimen side edges to determine crack density as a function of load (Figure 2). 

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358 


Loading / unloading tests have been performed on [± 45]s laminates not only to show the 

visco-plastic behaviour of the matrix but also the delaminating process. The loading is applied by 10 

MPa steps. The influence of the loading rate (0.1, 1 and 5 MPa/s) and of the relaxation duration (2, 15 

and 30 minutes) is assessed. Damage development is also characterized by microscopic observation. 

Tests have also been performed on samples with embedded fiber Bragg grating (FBG) sensors for 

damage detection ((transverse cracks and delaminating) or stress / strain gradients measurements. 

2.4 Study of filament winding influence 

Rings are manufactured with different processing parameters (pressure of consolidation, heating 

temperature and roving tension) and are intended to undergo tensile tests (according to ASTM D 2290 

standard [9]) to assess respective influence. 


3.1 Material properties-Quasi static tensile tests 

Quasi static tensile tests with a constant crosshead speed of 1 or 2 mm/min have been performed on 

[458], [908], [± 45]s and [04] multi-layers samples. Applied stresses have been calculated as the ratio of 

applied loads to composite cross-section area. Strains are measured by a numerical extensometer. 

The table 1 sums up the values obtained for Carbostamp TM PA 6 and Carbostamp TM PA 12. 

Matrix 

ζ11 

(MPa) 

Table 1. Mechanical properties of Carbostamp TM PA 6 and PA 12 (hot compression molded samples) 

E11 

(GPa) 

ε11 (%) 

ζ22 

(MPa) 

ε22 (%) 

E22 

(GPa) 

ζ45 o 

(MPa) 

G12 

(GPa) 

PA 12 1860 105 1.25 25 0.7 3.7 33 6.30 0.32 87 

PA6 1485 112 1.16 22 0.38 5.95 26 6.81 - 93 

μ12 

ζ±45 o 

(MPa) 

Scanning electron microscopy (SEM) pictures, carried out to characterize the failure surfaces (Figure 

3) show that the fibre/matrix adhesion seems to be efficient even in the case of transverse tensile test 

which is believed to be one of the most sensitive tests for assessing the relative interfacial adhesion 

strength in composites. Consistently with Evstatiev and al [10], that can be explained by the presence of 

reinforcing matrix transcrystalline phase on the fiber surface, which presents high nucleation ability. 

A difference can be noticed between the respective breaking stress of unidirectional 45 o sample and 

[± 45 o ]s laminate. Indeed, it is multiplied by two or three for the cross-plied sample. For the first one, 

breakage occurs when the first crack appears, whereas for the second one, the development of multiple 

cracks and delaminating can be observed (Figure 4). 

3.2 Study of damage by intralaminar cracking 

Basically, tensile tests on UD specimens produced no cracking and failure occurring with no prior 

macroscopic warning. Cross-plied laminates such as stacking sequences of [02, 904, 02] exhibit matrix 

cracking when they were submitted to tensile loading. The cracks appear parallel to the fibres in plies 

oriented off the loading direction (plies at 90 o in this case) (Figure 6). The loading is applied by 50 MPa


steps until break. The number of cracks is evaluated at the end of every loading/unloading cycle. The 

evolution of the density of cracks (i.e. the number of cracks per observed length expressed in mm) as a 

function of applied load show the kinetic of damage by intralaminar cracking. As it can be seen, the 

material presents a Kaiser effect, since the damage density of the cycle n+1 increases if the loading 

stress is up to the cycle n one. For both materials no crack was observed for an applied stress below 200 

MPa (Figure 5). Above this level, the level of crack density increased until a limit which seems to be 

reached before failure, at around 600 MPa. For an applied load up to 700 MPa, longitudinal cracks 

and delaminating appear until break (figure 7 and 8). 

[04] specimen [908] specimen [458] specimen 

Fig. 3. Failure surface of specimen after tensile test, SEM records. 

Fig. 4. Cracks observed on [± 45 o ] samples. 

Fig. 5. Crack density d (number of cracks in 90 o ply/mm) during loading for 02/904/02 sequences of Carbostamp TM PA 6 and Carbostamp TM PA 12. 

359

360 


Fig. 6. Transverse cracks (loading between 200 and 600 MPa). 

Fig. 7. Longitudinal cracks (loading up to 700 MPa). 

Fig. 8. Delaminating (loading up to 700 MPa) 

The Carbostamp TM PA 6 limit of crack density is lower than Carbostamp TM PA 12 one. That can be 

explained by the strength of the matrix, which is lower for PA 12 (ζ break (PA 12) = 55 MPa < ζ break (PA 

6) = 80 MPa). It can also be explained by a lower shear resistance for Carbostamp TM PA 6 than for 

Carbostamp TM PA 12. Existing defects have also an influence on process of damages. Regions with low 

matrix content and porosity can initiate cracks (Figure 9 and 10). 

Cracking has also an influence on the rigidity of the material. As noticed, the rigidity represented by 

the ratio between the modulus at a given load over the initial modulus decreases when the applied load 

increases, i.e. when the crack density increases (Figure 11). This decrease begins when the first cracks 

appears. 

3.3 Study of damage by delaminating 

Loading / unloading cycles performed on [±45]s laminates show different aspects of the material 

.


behaviour. First of all, the behaviour can be considered as non linear. Then, for an applied stress up to 

25-30 MPa, the formation of a hysteresis loop can be noticed. This loop is wider and wider with the 

increasing stress. In addition to that, the material presents a residual plastic strain (Figure 12). 

Fig. 9. Example of crack initiated by porosity. 

Fig. 10. Example of crack initiated by matrix poor region. 

Fig. 11. Evolution of the longitudinal modulus E as a function of the applied load for Carbostamp TM PA 6 [02, 904, 02]. 

361

362 


Fig. 12. Visco-plastic behaviour of the matrix-loading/unloading tests on [±45]s laminates (Carbostamp TM PA 12, stress rate: 1 MPa/s, relaxation 

time: 15 minutes). 

These two phenomenons are directly linked to the visco-plastic behaviour of the matrix. The two 

matrixes, polyamide 12 and polyamide 6, exhibit similar behaviour. Closed to the breaking stress, the 

residual strain can be associated not only with the visco-plastic behaviour of the matrix, but also with 

damage by delamination. The damage process begins by the formation of ply cracking which propagate 

to the neighbouring interface by delaminating. 

These damages influence the shear rigidity of the material. This influence can be revealed through 

the evolution of shear modulus, G12, as a function of applied load. The shear modulus decreases while 

the applied load increases. The influence of two parameters on this evolution has been assessed. Three 

different loading rates (0.1, 1 and 5 MPa/s) and three different relaxation times (2, 15 and 30 minutes) 

have been tested. One can see in Figure 13 and 14 that these two parameters have no influence on the 

evolution of shear modulus and thus on the damage process. 

Fig. 13. Influence of the loading rate on the evolution of the shear modulus: (a) Carbostamp TM PA 12 (b) Carbostamp TM PA 6. 

However, these two parameters have an influence on the residual strain. Indeed, the residual strain 

increases when the loading rate decreases, since the creep phenomenon is more important. Besides, this 

residual strain decreases when the relaxation time increases. One can see this observation for 

Carbostamp TM PA 6 on Figure 15.


Fig. 14. Influence of the relaxation time on the evolution of the shear modulus: (a) Carbostamp TM PA 12 (b) Carbostamp TM PA 6. 

Fig. 15. Influence of the loading rate (a) and the relaxation time (b) on the residual strain during loading/ unloading tests performed on [±45]s 

Carbosatmp PA 6 laminates. 

3.4 Detection of damages with embedded fiber Bragg grating sensors 

Same tests as before have been performed on samples with embedded FBG sensors. Such sensors 

have already been used to detect microscopic damages in composite laminates, like transverse cracks 

and delaminating [11]. Indeed, these defects trigger changes in the reflection spectra that can be 

investigated at various tensile stresses. 

For [02, 904, 02] laminates, the FBG sensors were embedded at the 0 o /90 o interface in the 0 o ply 

parallel to the fiber. Thus, the embedment does not deteriorate the mechanical properties of the 

composite, since the maximum elongation of the FBG sensor is much larger than that of the reinforcing 

carbon fibers. The sensor is sensitive to transverse cracks that run through the thickness and width of 

the 90 o ply. When there is no crack (applied load below 200 MPa), the reflection spectra keep its shape 

and the wavelength is shifted corresponding to the strain. Then, when the loading stress increases, 

cracks appear. The form of the reflection spectra is distorted. The highest peak becomes small and other 

peaks appear (Figure 16). This distortion is more pronounced when the crack density increases. After 

unloading, spectra recovered their height but not their shape because of the strain distribution caused by 

transverse cracking. For high stresses, the signal is lost because of transverse compression load under 

tabs which induced high optical attenuation. 

363

364 


Fig. 16. Detection of transverse cracks with an embedded FBG sensors-Investigation of the reflection spectrum 

for an applied load up to 200 MPa. 

All these observation are consistent with those done by Okabe et al. on CFRP laminates [12]. 

For [[±45s]]2 laminates, the FBG sensors were embedded between two plies oriented at 45 o . Before 

delaminating, the spectrum keeps its shape and the center wavelength shifts corresponding to the strain. 

When delamination appears (loading up to 60 MPa), the spectrum becomes Larger. Other peaks appear 

too because of a non-uniform axial strain distribution along the sensor (Figure 17). This deformation is 

irreversible. The delamination propagates until breaking. Breaking of the samples and the sensors are 

simultaneous. 

Fig. 17. Detection of delaminating with an embedded FBG sensors. 

These observations are consistent with bibliography on CFRP laminates [13, 14]. 

3.5 Influence of the filament winding parameters 

As mentioned before, filament winding process involves different key parameters that influence the 

architecture of the material, its mechanical properties and then the damage evolution. 

To analyze the influence of the parameters of the process, tensile tests were performed on rings. 

These tests performed on rings allowed a simple mechanical characterization avoiding to test flat 

wounded specimens the purpose of which should be as closer as possible to the process. This testing 

method is easy to conduct but the stress distribution is inhomogeneous along the perimeter of the ring. 

The stress concentration is particularly high in the area of the gap. As the consequence, the modulus can


not be determined and the measured strength is expected to be lower than those obtained with flat 

samples (1530 MPa). 

Figure 18 shows the influence of the roving tension. We can see that the maximum stress decreases 

when the roving tension is increased. A high tension may trigger fibers damages like breaks. 

4. Conclusions and prospects 

Fig. 18. Influence of roving tension on maximum stress obtained during NOL tests. 

Transverse cracking and delamination have been studied on two different carbon fibers reinforced 

polyamide matrix (PA 12 and PA 6) composites, taking into account the initial thermal and mechanical 

properties. The two materials exhibit similar behaviour regarding these two damages process. 

Concerning transverse cracking, for both materials, cracks appear for a load up to 200 MPa, and the 

crack density increases until a limit. After that, longitudinal cracks and delaminating appear until the 

specimen failure. PA 6/ carbon fibers composite present a crack density limit lower than PA 12 / carbon 

fibers composite, because of the high strength of the matrix. 

Shear behaviours is also close and damage by delamination does not seem to be influenced by 

loading rates and relaxation time. 

Further, embedded FBG sensors have shown an interesting way for damage detection, since the 

occurring damage as ply cracking or delamination trigger a distortion of the spectrum shape and a shift 

of the wavelength. 

In addition, the thermoplastic pre-impregnated tape winding process has been developed and the 

influences of the manufacturing parameters on the structural fabricated material and its properties have 

been investigated. 

This preliminary study may contribute to improve the understanding of results registered (acoustic 

events) during qualification tests of vessels as cyclic hydraulic pressure tests or burst. 

The results obtained in this study would be compared with those obtained with thermoset matrix / 

carbon fibres composites in order to quantify the respective advantages / weaknesses of thermoplastic 

matrix composite structures in terms of mechanical properties and durability. 

365

366 



This work has been supported by the French National Research Agency through Plan d‟Action sur 

l‟Hydrogène et les Piles à Combustible programme (Projet HYPE, N o ANR-07-PANH-006). 

References 

[1] Nony.F., Mazabraud P., Villalonga S. et al. Type IV 700 bar-vessel for Compressed Gaseous Hydrogen Storage; Material Research and 

Performance Achievements. 17th World Hydrogen Energy Conference, Brisbane, Australia, 15-19 June 2008. 

[2] Tomlimson W.J., Holland J.R. « Advantages of Pultruding Thermoplastics». Reinforced Plastics, Vol. 37, Issue 10 (1993), pp. 46-49 

[3] MC Donnell P., Mc Garvey K.P. Processing and mechanical properties evaluation of a commingled carbon-fibre/PA 12 composite. 

Composites: Part A, Vol. 32 (2001), pp. 925-932 

[4] Henninger F., Friedrich K. Thermoplastic filament winding with online impregnation. Part A: process technology and operating efficiency. 

Composites: Part A, Vol. 33 (2002), pp. 1479-1486 

[5] Henninger F., Friedrich K. Thermoplastic filament winding with online impregnation. Part B: Experimental study of processing parameters. 

Composites: Part A, Vol. 33 (2002), 1677-1688 

[6] Lauke B., Schöne A., Friedrich K. High performance thermoplastic composites fabricated by filament winding in Proceedings of 

International Conference of Advanced Composites, Wollongong, Australia 1999 

[7] NF EN ISO 527-5, Détermination des propriétés en traction, conditions d‟essai pour les composites plastiques renforcés de fibres 

unidirectionnelles, juillet 1997 

[8] Renard J, Favre J.P., Jeggy Th. Influence of transverse cracking o, ply behaviour: introduction of a characteristic damage variable. 

Composite Science and Technology, Vol. 46 (1993), pp. 29-37 

[9] Standard ASTM D 2290, Standard Test Method for Apparent Hoop Tensile Strength of Plastic or Reinforced Plastic Pipe by Split Disk 

Method, January 2004 

[10] Evstatiev M., Friedrich K., Fakirov S. Crystallinity Effect on Fracture Rings made of Thermoplastic Powder impregnated Carbon or Glass 

Fiber. Composites International Journal of Polymeric Material, Vol. 21 (1993), pp 177-187 

[11] Takeda N., Okabe Y., Mizutani T. Damage detection in composite using optical fibre sensors. Proc. IMechE Part G: Aerospace 

Engineering, Vol. 221 (2007), pp. 497-507 

[12] Okabe Y., Mizutani T., Yashiro S., Takeda N. Detection of Microscopic damages in composite laminates with embedded small-diameter 

fiber Bragg grating sensors. Composites Science and Technology, Vol. 62 (2002), pp. 951-958 

[13] Takeda N., Okabe Y. KuwaharaJ., Kojima S., Ogisu T. Development of smart composite structures with small-diameter fiber Bragg 

grating sensors for damage detection: Quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing. 

Composites Science and Technology, Vol. 65 (2005), pp. 2575-2587 

[14] Takeda S., Okabe Y., Takeda N. Delamination detection in CFRP laminates with embedded small-diameter fiber Bragg grating sensors. 

Composites: Part A 33, Vol. 33 (2002), pp. 971-980

Abstract 

Residual life predictions of repaired fatigue cracks 

H Wu *, A Imad, N Benseddi 

Mechanics Laboratory of Lille, Ecole Polytech’Lille, France 

The stop-hole method is a simple and economic repair technique widely used to retard or even to stop the propagation 

of a fatigue crack that cannot be replaced immediately after the detection of the crack. Its principle is to drill a hole at or 

close to the crack tip to eliminate the stress concentration there and so stop the crack propagation. To study the 

effectiveness of this repair method, classical N techniques are adapted to explain the results of several experiments 

carried out on aluminium plates, taking into account short crack concepts. This is a simple and reliable calculation 

method to predict beforehand the results of this practical emergency repair which can be quite useful in real-life situations. 

The aim of the present work is to predict the fatigue crack initiation lives by employing the analytical modelling based on 

the classical N theory and short crack theory for aluminium 6082 T6. The comparison among the experimental and the 

calculation results show that the life increment caused by the stop-holes can be effectively predicted in this way. 

Keywords: stop-hole; crack repair; N method; short cracks 


The stop-hole method is a popular emergency repair technique to extend the fatigue life of cracked 

structural components [1]. A simple and reliable calculation method to predict beforehand the results of 

this practical emergency repair technique can be quite useful in real-life situations. However, the 

appropriate modelling of this problem is not that simple. As a general rule, the increase of the stop-hole 

diameter contributes to decrease the value of the stress concentration factor Kt of the resulting notch, but 

it also increases the nominal stresses in the residual ligament of the repaired component. While small 

stop-hole diameters are associated with smaller notch sensitivities q, which decrease the resulting Kt 

effect in the fatigue crack (re)initiation life. This effect is quantified by the so-called fatigue stress 

concentration factor Kf, classically defined by [2-3] 

Kf = 1 + q(Kt- 1) (1) 

However, when a long crack is repaired by a relatively small stop-hole, it forms an elongated notch 

with a high Kt, which is associated with a steep stress/strain gradient around its root. Consequently, its 

notch sensitivity q cannot be well predicted by the classical Peterson recipe [4]. Therefore, the model 

for predicting the residual fatigue life of repaired cracked structures must take this fact into account, as 

shown below. 

* E-mail address: wuhao-2009@hotmail.com

368 

2. Experimental program 


A set of experiments was carried out on SE(T) specimens with thickness B = 8 mm and width W = 80 

mm, (see Fig. 1), to measure the delays associated with the re-initiation of a fatigue crack after drilling a 

stop-hole centred at the crack tip of length a. The tested material was an Al alloy 6082 T6. The 

specimens were cut on the LT direction, and the fatigue tests were carried out under constant load range 

P at R = Pmin/Pmax = 0.57. This high R-ratio was chosen to avoid any crack closure interference on the 

crack propagation behavior. 

The 2, 5 or 6 mm stop-holes were carefully centered and drilled at the fatigue crack tips. The load 

range P was always maintained constant, before and after the drilling of the stop-holes. 

3 The basic stop-hole model 

Fig. 1. The tested specimens. 

The fatigue crack re-initiation lives at the stop-hole roots can be modeled by N local strain 

procedures, using (i) the cyclic properties of the 6082 T6 Al alloy, H’ = 443 MPa, h’ = 0.064, ’f = 485 

MPa, b=-0.0695, ’f = 0.733, c =-0.827, where ’f, b, ’f and c are the Coffin-Manson parameters and 

H’ and h’ are the coefficient and the exponent of the cyclic stress-strain curve fitted by 

Ramberg-Osgood; (ii) the nominal stress history (see table 3); and (iii) the stress concentration factor Kt 

of the notches generated by repairing the cracks drilling a stop-hole at their tips. Such factors can be 

estimated by Inglis, giving for hole radii =1, 2.5 or 3 mm, respectively 

Kt 1 + 2 a / = 11.49, 7.63 or 7.06 (2) 

The classical N models neglect hardening transients, supposing that the fatigue behavior can be 

described by an unique Ramberg-Osgood cyclic stress/strain curve, whose parameters H’ and h’ can 

also be used to describe the elastic-plastic hysteresis loop curves. These equations should model 

both the nominal and the notch root cyclic stress/strain behavior, to avoid the logical inconsistency of

H Wu, A Imad, N Benseddi / Residual life predictions of repaired fatigue cracks 

using two different models for describing the same material (Hookean for the nominal and 

Ramberg-Osgood for the notch root stresses), and also to avoid the significant prediction errors that can 

be introduced at higher nominal loads by such a regrettably widespread practice [5]. 

All the required fatigue life calculations were made using the ViDa software. For the two bigger 

stop-holes the predictions reproduce quite well the measured fatigue crack re-initiation lives. But the 

predictions obtained by the same calculation procedures for the smaller stop-hole with = 1.0mm are 

much more conservative. 

4. Analytical prediction of the notch sensitivity 

Long cracks grow under a given and R set when K = (a)f(a/w) > Kth(R), where Kth(R) 

is the propagation threshold at that R-ratio. Therefore, short cracks (which have a 0) must propagate in 

an intrinsically different way, as otherwise K(a 0, R) > Kth(R) , which is a non-sense, as 

a stress range > 2SL(R) can generate and propagate a fatigue crack, where SL(R) is the fatigue limit 

of the material at R. To conciliate the fatigue limit (e.g.) at R = 0, S0 = 2SL(0), with the propagation 

threshold under pulsating loads K0 = Kth(0), a small “short crack characteristic size” a0 were summed 

to the actual crack size a in [6] so as to obtain 

2 

1 K 

K (a a ), where a 

0 

I = + 0 0 = 

f ( a w ) S0 

 

These equations correctly predicted that the biggest stress range, which does not propagate a 

microcrack, is the fatigue limit: if a

370 


initiate at the notch root but do not propagate if 2SL Kt 2SL K f [5]. E.g., the stress intensity 

factor of a crack that departs from a circular hole of radius in a Kirsh (infinite) plate loaded in mode I 

is given by [8] 

where (a/) (x) is given by: 

( ) ( ) 

KI = a a = 1.1215 a a 

(7) 

2 3 

0.2 0.3 x x x 

 

( 

x ) = 1+ + 2- 

2.354 + 1.206 -0.221 

 

(1 x ) (1 x ) 

6 

 

+ + 

1+ x 1+ x 1+ x 

 

Note that lim KI = 1.1215 3 a and lim KI = a 2 , exactly as expected. Thus, if a0 = 

a0 a 

(K0/S0) 2 , any crack departing from a Kirsh hole will propagate when 

/2 

-1/ 

 

KI = ( a ) a Kth = K0 

1+ ( a0 a) 

 

 

The propagation criterion for these fatigue cracks can then be rewritten as [5] 

( ) 

K0 S0 

 

a S0 

a S0 K 

 

 

 

g , , 

0 

, 

 

 

 

1/ 

 

 

S0 

a K 

0 

 

 

 

 

+ 

S0 

 

In other words, if x a/ and K0/S0, a fatigue crack departing from a Kirsch hole grows 

whenever (x) > g(x, S0/, , ) /g > 1. Fig. 4 plots some /g functions for several fatigue 

strength to loading stress range ratios S0/ as a function of the normalized crack length x a/, 

assuming a material/notch combination with = 1.5 and = 6. 

For high applied stress ranges , the strength to load S0/ ratio is small, and the corresponding 

/g curve is always higher than 1, which means that cracks will initiate and propagate from the Kirsch 

hole border, without stopping during this process. One example of such a case is the upper curve in Fig. 

2, which shows the function /g1.4 obtained for S0/ = 1.4. On the other hand, small stress ranges 

with load ratios S0/ Kt = 3 have /g functions which are smaller than 1, meaning that no crack 

will initiate from the Kirsch hole, and that small enough cracks will not propagate from it at such lo 

loads. This is illustrated by curves /g3, associated with the limit case S0/ = 3, and /g4, associated 

with S0/ = 4. 

But three other cases must be noted in Fig.2. The first crosses once the /g = 1 line, see the /g2.3 

curve, meaning such an intermediate load range can initiate and propagate a fatigue crack from the 

notch border until the decreasing /g2.3 value reaches 1, where the crack stops. Thus, this loading level 

generates a non-propagating fatigue crack at the notch border due to the crack tip stress gradient effect, 

with a size given by the corresponding a = x abscissa. 

(8) 

(9) 

(10)


Fig. 2. The fatigue stress concentration factor Kf can be obtained by finding the function /g which is tangent to the /g =1 line, 

thus in this case Kf = 1.64. 

The second, illustrated in Fig. 2 by the /g1.85 curve, intersects the /g =1 line twice. Therefore, this 

load level will also generate a fatigue crack at the Kirsch hole border, which will propagate until 

reaching the maximum size obtained from the abscissa of the first intersection point (on the left), where 

the crack stops. Moreover, cracks longer than the size defined by the abscissa of the second intersection 

point will re-start propagating by fatigue under = S0/1.85 until eventually fracturing the Kirsch 

plate. However, the crack initiated by fatigue under such load cannot propagate between these two 

intersection points by fatigue alone (assuming remains constant). Hence, it can only grow in this 

region if driven by a different mechanism, such as corrosion or creep, for example. 

These two cases seem different, yet they are similar: the /g2.3 curve will cross the /g =1 line twice 

if the graph is extended to larger x a/ values, because a sufficiently long crack can always propagate 

by fatigue under a given (even if small) range whenever its SIF range K = (a) grows with 

the crack size a, as in this Kirsch plate. In fact, all /g curves start at Kt/S0 and a = 0, and become 

higher than 1 for sufficiently large a/ values. 

Finally, the /g1.64 curve is tangent to the /g =1 line, meaning that this = S0/1.64 is the smallest 

stress range that can cause crack initiation and propagation without arrest from the notch border. In 

other words, by definition, the Fig. 2 Kirsch hole fatigue SCF is given by Kf = S0/ = 1.64. Moreover, 

the abscissa xmax of the tangency point between the /g1.64 curve and the /g =1 line gives the largest 

non-propagating crack that can arise from it by fatigue alone, amax = xmax. Therefore, the Kf and amax 

can be found by solving the system. 

Therefore, Kf = S0/ can be calculated from the material fatigue limit S0 and crack propagation 

threshold K0, and from the geometry of the cracked piece by 

( a ) = g( a , S 0 

, K0 S 0 , ) 

 

 

( a ) 

 

 

= g( a , S 0 

, K0 S 0 , ) 

a a 

371 

(11)

372 


The stress intensity factor of a crack a which departs from such a notch with semi-axes b e c, with a and 

b in the same direction perpendicular to the (nominal) stress , is given by: 

K = F ( a b ,c b) a 

(12) 

I 

where = 1.1215 is the free surface correction factor and F(a/b, c/b) is the geometric factor associated 

to the notch stress concentration, which can be calculated as a function of the non-dimensional 

parameter s = a/(a + b) and of Kt, given by [8] 

( ) 

K 1 2 

b 

1 

0.1215 

t = + + 

 

c 

(1 c b ) 

2.5 

+ 

An analytical expression for the F(a/b, c/b) of deep semi-elliptical notches with c b was fitted to a 

series of finite element numerical calculations 

(13) 

2 

a c 1- exp( -K s ) 

F( , ) f ( K ,s) K 

t 

 

b b 

t = t 

, for c b (14) 

K2 t s 

Making g = and g/a = /a in (11), one can calculate the smallest stress range required to 

initiate and propagate a crack from the notch root at a given combination of and K0/S0, which 

can be used to calculate Kf = S0/ and q. Indeed, a short crack a < ast departing from the notch 

boundary stops when it reaches 

5. Notch sensitivity for semi-elliptical notches 

2 

1/ 

K I ( a st ) ast K0 

1 ( a0 a st ) 

 

- 

= = + 

 

 

Traditional notch sensitivity estimates assume that q depends only on the notch root and on the 

material ultimate strength SU. Thus, similar materials with the same SU but different K0 should have 

identical notch sensitivities, according to these estimates. And it also happens to the materials with 

shallow and deep or elongated notches of identical tip radii. However, it must be mentioned that well 

established empirical relations relate the fatigue limit S0 to SU, but there is no such relation between 

the FCP threshold K0 and SU. Moreover, it is also important to point out that the q estimation for 

elongated notches by the traditional procedures can generate questionable Kf values, as discussed above. 

The proposed model, on the other hand, recognizes that the q values of semi-elliptical notches, not only 

depend on , S0, K0 and , but also strongly depend on the c/b ratio, see Fig.3. The curves shown in 

this figure are calculated for typical aluminum alloys which have mean SU = 225MPa, fatigue limit SL = 

90MPa S0 = 2SLSR/(SL + SR) = 129MPa, propagation threshold K0 = 2.9MPam, = 6, and short 

crack length parameter a0 = 0.26mm. Their corresponding Peterson‟s curve is well approximated by the 

semi-circular c/b = 1 notch, but this curve is not applicable for high c/b ratios. Therefore, the proposed 

predictions indicate that these old estimates should not be used for elongated notches, a prediction 

experimentally verifiable, as discussed in the following section. 

(15)


Fig. 3. Notch sensitivity q as a function of the semi-elliptical notch root radius = c 2 /b for aluminum alloys having a0 = 0.26mm (Su 225MPa). 

6. The improved stop-hole model 

An improved model for predicting the effect of the stop holes on the crack re-initiation fatigue lives 

can be generated by using: (i) a semi-elliptical notch with b = 27.5mm and = c 2 /b = 1, 2.5 or 3mm to 

simulate the stop-hole repaired specimens; (ii) the mechanical properties of the 6082 T6 Al alloy studied 

in this work; (iii) equation (11) to calculate the notch sensitivity and equation (15) for the stress 

intensity factor of the repaired specimens; and finally (iv) Kf instead of Kt in the N model. 

The predictions generated by such an improved model are presented in Fig. 4-6. Since q 1 for the 

= 3.0 and = 2.5mm stop-holes, the predictions obtained using their calculated Kf = 7.0 and Kf = 7.2, 

respectively, are as good as those obtained using their estimated Kt. However, the overly conservative 

initial predictions for the smaller = 1mm stop-hole, which were generated using its estimated Kt 11.5, 

are much improved when the notch sensitivity effect quantified by its properly calculated Kf = 8.3 is 

used in the fatigue crack re-initiation calculations. 

Fig. 4. Predicted and measured crack re-initiation lives at the stop-holes roots of radius = 3.0mm, using the Kf (instead of Kt) of the repaired 

crack. 

373

374 


Fig. 5. Predicted and measured crack re-initiation lives at the stop-holes roots of radius = 2.5mm, using the Kf (instead of Kt) of the repaired 

crack. 

Fig. 6. Predicted and measured crack re-initiation lives at the stop-holes roots of radius = 1.0mm, 

using the Kf (instead of Kt) of the repaired crack. 

The Al 6082 T6 fatigue limit and fatigue crack propagation threshold under pulsating loads required 

to calculate Kf are estimated as K0 = 4.8 MPam and S0 = 110MPa, following traditional structural 

design practices [7-8], and the Bazant‟s exponent was chosen, as recommended by [5], as = 6. 

7. Conclusion 

Classical N techniques were used with properly estimated properties to reproduce the measured 

fatigue crack re-initiation lives after stop-hole repairing several modified SEN(T) specimens. The 

predicted lives were not too dependent on the mean load N model, and the larger stop-hole measured 

lives could be well reproduced using the stress concentration factor Kt in the Neuber/Ramberg-Osgood 

system. But such an approach yielded grossly conservative prediction for the smaller stop-hole life 

improvements. This problem was solved using the fatigue stress concentration factor Kf of the resulting 

notch instead of Kt in that system. The predicted notch sensitivities reproduce well the classical


Peterson‟s q estimates for circular holes or approximately semi-circular notches, but it is found that the 

notch sensitivity of elongated slits has a very strong dependence on the notch aspect ratio, defined by 

the ratio c/b of the semi-elliptical notch that approximates the slit shape having the same tip radius. 

These predictions are confirmed by experimental measurements of the re-initiation life of long fatigue 

cracks repaired by introducing a stop-hole at their tips, using their calculated Kf and appropriate N 

procedures. 

References 

[1] SONG, P.S.; SHIEH, Y.L. Stop drilling procedure for fatigue life improvement. Int. J. Fatigue v.26(12), p.1333-1339, 2004. 

[2] PETERSON, R.E. Stress Concentration Factors, Wiley 1974. 

[3] SHIGLEY, J.E.; MISCHKE, C.R.; BUDYNAS, R.G. Mechanical Engineering Design, 7th ed., McGraw-Hill 2004. 

[4] MEGGIOLARO, M.A.; MIRANDA, A.C.O.; CASTRO, J.T.P. Short crack threshold estimates to predict notch sensitivity factors in 

fatigue. Int. J. Fatigue v.29(9-11), p.2022-2031, 2007. 

[5] MEGGIOLARO, M.A.; CASTRO, J.T.P. Evaluation of the errors induced by high nominal stresses in the classical N method, in 

Blom,AF ed. Fatigue 2002(2), p.1451-1458, EMAS 2002. 

[6] EL HADDAD, M.H.; TOPPER, T.H.; SMITH, K.N. Prediction of non-propagating cracks. Eng. Fract. Mech. v11, p.573-84, 1979. 

[7] BAZANT, Z.P. Scaling of quasibrittle fracture: asymptotic analysis. Int. J. Fracture v.83(1), p.19-40, 1997. 

[8] TADA, H.; PARIS, P.C.; IRWIN, G.R. The stress analysis of cracks handbook. Del Research; 1985. 

375

Monotonic and cyclic deformation behavior of ultrasonically 

welded hybrid joints between light metals and carbon fiber 

reinforced polymers (CFRP) 

Abstract: 

F Balle *, D Eifler 

Institute of Materials Science and Engineering, University of Kaiserslautern, Kaiserslautern 67663, Germany 

In the present work, hybrid joints between the aluminum alloy 5754 and carbon fiber reinforced polyamide 66 has 

been joined by ultrasonic metal welding. Selected surface pre-treatments of the metallic surface were investigated to 

increase the joint strength and optimize the ageing behavior of the welds. Light and scanning electron microscopy were 

used to understand the bonding mechanisms in detail. Beside the monotonic properties the cyclic deformation behavior of 

ultrasonic welded aluminum/CFRP-joints were investigated in this work. Therefore load-increase- as well as single-step 

tests were performed with a servohydraulic testing system at a frequency of 5 Hz. The endurance limit of 

AA5754/CF-PA66-joints under cyclic tensile shear load (R > 0) was determined to about 35% of the monotonic tensile 

shear strength. 

Keywords: Ultrasonic welding; multi-material design; fatigue of welded structures; load increase tests 


The current demand for lightweight structures leads to an increasing application of materials like 

aluminum, magnesium and fiber reinforced polymers (FRP) and their combinations. Hence the 

predominant aim of innovative products in the automotive and aircraft industry but also in railway 

transportation and engineering in general is the reduction of the weight of the components. For the 

development of new lightweight products a detailed knowledge of monotonic and cyclic deformation 

behavior of joints made of dissimilar materials is obligatory. To fulfill these challenges appropriate 

joining techniques are necessary. 

Ultrasonic welding is a pressure welding technique, whereby the formation of the bond occurs as a 

result of a static welding force and a superimposed ultrasonic oscillation [1]. In comparison to other 

joining techniques like adhesive bonding or brazing, ultrasonic welding is characterized by a low energy 

input, consequently low temperatures in the welding zone and short welding times. Current applications 

of this technology are plastic as well as metal welding [2, 3]. Until now ultrasonic plastic welding is 

typically used to join FRP to each other, but in the case of metal/FRP-joints the ultrasonic plastic 

welding method only enables joints between metal and polymer matrix and not directly with the load 

bearing fibers of the FRP. Recent results show, that beside compact glass also glass or carbon fiber 

textiles with or even without thermoplastic as well as thermosetting matrix can be welded to metals by 

* E-mail address: balle@mv.uni-kl.de. Tel: +49-(0)631-205 2413.

F Balle, D Eifler / Monotonic and cyclic deformation behavior of ultrasonically welded hybrid joints between light metals and CFRP 

ultrasonic metal welding [3-7]. Recent investigations at the WKK show that ultrasonic metal welding is 

a suitable alternative to join CFRP with sheet metals like aluminum alloys or aluminum plated steel 

[8-10]. In this paper the ultrasonic welding technology was investigated systematically for joining 

aluminium alloys to carbon fiber reinforced thermoplastic polymers (CFRP). In the following the 

ultrasonic metal welding technology as well as monotonic and fatigue properties of the realized joints 

are presented. 

2. Materials and methods 

2.1 Parent Materials 

Within the scope of the present work aluminum sheets are welded directly on the fiber reinforcement 

of the CFRP organic sheets. The aluminum wrought alloy (AA5754) was used to be welded onto the 

thermoplastic composite made of polyamide 66 (PA66) with a satin fabric of carbon fibers (Toray 

T300J). Selected mechanical properties of the parent materials are summarized in table 1. The tensile 

tests were performed in rolling direction of the Al-sheet and in filling direction of the carbon fabric in 

case of the CFRP sheet. 

Young´s 

Modulus 

E 

[GPa ] 

Table 1. Monotonic mechanical properties of the base materials 

0.2 % Yield 

Strength 

R p0.2 

[MPa ] 

Ultimate 

Tensile Strength 

UTS 

[MPa] 

AA5754 H22 70 177 250 13.5 

CF-PA66 55 / 580 1.1 

Ultimate 

Elongation 

A 

[%] 

The Al-sheets AA5754 were welded in work-hardened, thermal-softened and quarter-hard condition 

(H22). The rolling direction is clearly shown by elongated grains in the longitudinal section of AA5754, 

see Figure 1a). Furthermore small intermetallic precipitations of type (Fe, Mn)Al 6 (Fe, Mn)3SiAl12, 

Mg2Si and Al3Mg2 were determined in previous TEM studies [4]. 

a) b) 

Fig. 1. Micrographs of the parent materials: a) AA5754 H22, b) CFRP (matrix: PA66). 

In Figure 1b) a cross section of the CFRP organic sheet is shown. The fiber reinforcement of the 

CFRP is a C-textile Satin 5H-fabric with a weight per unit area of 285 g/m². The fiber volume fraction 

of the 2 mm thick organic sheets is about 48%. It was manufactured in an autoclave process by using six 

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layers of CF-fabric at the University of Kaiserslautern in the framework of the research unit 524 

supported by the German Research Foundation (DFG). 

2.2 Ultrasonic welding system, specimen geometry and design of experiments 

For the present investigations modified and optimized industrial ultrasonic spot metal welding 

systems were used to join the aluminum wrought alloy (AA5754) and carbon fiber reinforced 

thermoplastic composites (CFRP) with PA66 matrix. One essential requirement is to control the welding 

force during the joining process accurately by an integrated force measuring device. Therefore a special 

clamping system was developed at the WKK, see Figure 2a). Furthermore, the welding system is 

equipped with several measuring devices to enable a high-resolution measurement of the main process 

parameters like welding force and welding energy. The specimen geometry is shown in Figure 2b). The 

welding area of the sonotrode is 10 x 10 mm². Since it is not possible to determine the exact geometry 

of the joining area the shear strength is calculated by the ratio of the achieved tensile shear force related 

to the nominal sonotrode contact area. 

(a) (b) 

Fig. 2. a) Ultrasonic spot welding system for hybrid joints, b) Specimen geometry. 

To identify suitable welding parameters for Al/CFRP-joints a statistical model named "central 

composite design circumscribed (CCC)" was used. In comparison to a stepwise variation of each 

welding parameter, this model for non-linear relationships allows to find the optimum parameters with 

considerably less welding steps. A further important advantage of the CCC-model is the description of 

the mutual dependence of the three central welding parameters oscillation amplitude, welding force and 

energy in relation to the achievable tensile shear strength of the joints [10]. The design of the 

CCC-model is based on the three significant process parameters mentioned above with five different 

settings for each. The suitable ranges of the process parameters, which allow high strength joints, were 

estimated in preliminary investigations. For joints of AA5754 and CF-PA66 composites appropriate 

welding parameters for the force FUS ranges between 100 N and 220 N, for the amplitude u between 

37 µm up to 43 µm and for the energy WUS between 1700 Ws and 2300 Ws. The used CCC-model leads 

to 18 different parameter triples and allows to reduce the necessary welds at a factor of 7 in comparison 

to a conventional stepwise procedure. Simultaneously the reproducibility of the joint strength could be


improved. All combinations of the welding parameters were proved in tensile shear tests. For each 

parameter combination twelve welds were performed at least. 

In basic investigations it was proved that thermoplastic carbon fiber composites can be welded to 

aluminum alloys by using ultrasonic plastic or ultrasonic metal welding. In comparison to ultrasonic 

plastic welding, 100% higher tensile shear strengths can be achieved by using ultrasonic metal welding 

[6]. The advantage of an ultrasonic oscillation parallel to the surface of the joining partners, which is 

typical for ultrasonic metal welding, is the possibility to realise a direct contact between the metal and 

the load bearing fibers of the reinforced composite. Thereby the welding process does not damage any 

fibers. By scanning electron micrographs (SEM) of the welding zones it is shown that the ultrasonic 

metal welding process removes the matrix between the fiber reinforcement and the metal, whereby the 

metallic surface gets into contact to the fibers [7-10]. 

2.3 Setup for fatigue testing 

A servo-hydraulic testing system of the type MTS 858 was used to examine the fatigue behavior of 

ultrasonically welded Al/CFRP-joints. For single overlap samples the hydraulic grip was modified and 

adjusted by a bending strut to avoid bending stresses (see figure 3a). A constraint in loading direction is 

prohibited by the use of Teflon disks. The cyclic loading was performed with a frequency of 5 Hz. A 

stress ratio of R ≥ 0 was selected to realize application-oriented conditions for single overlap joints. 

First, the cyclic deformation behavior was investigated by stepwise load increase tests (LIT). 

Therefore the force amplitude Fa was increased stepwise at125 N from an initial value of 100 N up to 

the failure of the joint. The length of each load step was fixed with 10 4 cycles. The maximum number of 

cycles was 2 × 10 6 . 

Based on the LIT selected single step tests (SST) were performed with the same test conditions. The 

cyclic displacement was measured as a function of the force amplitude with strain gauges mounted onto 

the surface of the aluminum and CFRP sheets in the area of the sonotrode tip, see figure 3b). 

a) b) 

Fig. 3. a) Fatigue testing system for single overlap joints, b) Displacement measurement setup (schematic). 

Data logging and evaluation were realized with a LabView-based software, which was developed at 

the Institute of Materials Science and Engineering (University of Kaiserslautern). 

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3.1 Monotonic properties of ultrasonically welded AA5754/CF-PA66-joints 

In this paper selected results of joints between AA5754 and the composite CF-PA66 are represented. 

Figure 4 shows the tensile shear strengths for a constant welding energy WUS of 2160 Ws. Tensile 

strengths are calculated by the ratio of the achieved tensile shear force related to the area of the welding 

tool, the sonotrode with 100 mm². 

Fig. 4. Contour plot (WUS = 2160 Ws) to find suitable process parameters for A5754/CF-PA66-joints. 

A maximum average tensile shear strength of 31.5 MPa can be determined slightly right to the centre 

of the diagram. However two-dimensional cuts of the diagram are necessary to ascertain the welding 

parameters exactly. In Figure 5 the course of the tensile shear strength for the three important process 

parameters welding force, oscillation amplitude and welding energy are shown separately. In every case 

two process parameters are constant. For example, on the left-hand side the oscillation amplitude u was 

varied between 38 and 42 µm. Besides the course of the average tensile shear strength the lower and 

upper confidential interval for 95 % is specified. An increasing amplitude up to 40.5 µm causes an 

increased displacement of the matrix of the CFRP and a better contact between the metal sheet and the 

fibers. As a result the tensile shear strength of the joints increases. After the peak value a damage of the 

textile and thus a decrease of the tensile shear strength occur at still higher oscillation amplitudes. An 

optimum range appears for values around 40 µm. The variation of the welding energy and the welding 

force shows nearly the same tendencies. 

By using mechanical (corundum blasting, CB) and/or chemical (acid pickling, AP) surface 

pre-treatments of the aluminum sheets, the tensile shear strength of the joints can be increased up to 

54 MPa and furthermore the long-term stability can be improved significantly [8]. The surfaces of the 

pre-treated aluminium sheets were characterized by electron microscopy and described quantitatively by 

interferometry. In Figure 6 the four different surface conditions are shown. A comparison of as rolled 

surface with corundum blasted surface show a macroscopic roughness. The mean surface roughness R a 

is increased from 0.3 µm to 3.0 µm, see table 2. By acid pickling, the surface roughness is nearly not


affected in a macroscopic manner, so that only selected peaks were removed and only the roughness 

profile Rt falls from 1.7 to 1.2 µm. A combined pre-treatment leads to a surface with both effects. The 

ultrasonic spot welded joints were tested after ageing of one and four weeks at different temperatures 

and humidity. For a pure mechanical and a combined pre-treatment of the aluminum sheets (corundum 

blasting and pickling in nitric acid, CB&AP) nearly no decrease of the tensile shear strength was 

determined [9]. 

Fig. 5. Single evaluation of oscillation amplitude, welding force and energy for AA5754/CF-PA66-joints by using statistical test planning. 

Fig. 6. Surface structure of pre-treated AA5754 sheets: a) initial state, as rolled (R); b) corundum blasted (CB); c) acid pickled (AP); d) CB & AP. 

Table 2. Comparison of induced roughness (in µm) by surface pre-treatment of AA5754 

AA5754 R CB AP CB & AP 

Mean surface roughness Ra 0.3 3.0 0.3 2.5 

Arithmetical roughness profile Rt 1.7 12.5 1.2 12.7 

3.2 Microstructure of ultrasonically welded AA5754/CF-PA66-joints 

To understand the microstructure of ultrasonically welded hybrid joints, it is necessary to evaluate the 

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initial state of the polymer joining partner. According to the satin fabric (Atlas 1/4) the polyamide layer 

thickness near the surface depends on the position in the CFRP sheet. The transition zone of the crimped 

fiber bundles is characterized by periodically returning layer thicknesses of about 250 µm. Nevertheless, 

the differently thick, but the fiber reinforcement covering polymer layer, is displaced by the ultrasonic 

transversal waves, in particular in the influencing area of the sonotrode, see figure 7. 

Fig. 7. Microstructure of the CF-PA66 sheet before and after ultrasonic welding. 

Digital image analysis clearly shows the reduction of the layer thickness within the range of the 

crimped fiber bundles by the ultrasonic welding process, but not a complete displacement overall. In 

Figure 8 micrographs of the two characteristic zones are shown. Especially on roughness peaks a direct 

contact between the carbon fibers and the aluminum surface was examined, see Figure 8a). In zones 

with a polymer layer up to 100 µm in thickness before welding, a direct contact is rarely possible. In 

zones between chaining and filling thread a polymer layer with a thickness of about 100 µm remains 

because of the maximum layer thickness in the initial state before welding, see figure 8b). So there is no 

direct contact between fibers and metal surface. In the polymer-rich zones an interface very similar to 

conventional plastic welding technique will be realized, therefore only adhesive bonding between 

polymer and aluminum occurs. 

Fig. 8. Micrographs of different positions in the joining zone of AA5754 (CB)/CF-PA66-joints: 

a) polymer poor joining zone, b) polymer rich joining zone.


The ultrasonic metal welding technology differs clearly from conventional procedures to join sheet 

metals to fiber reinforced composites. By using transversal shear waves the interface of polymer poor 

zones is characterized by a high plastic deformation of the aluminum surface. The fracture surface of 

pre-treated AA5754/CFRP-joints shows several fiber bundles, which were pulled out during the tensile 

shear test, see figure 9. Furthermore characteristic marks of the satin fabric were investigated by 

scanning electron microscopy. Filling and chaining direction are labelled in figure 9 by circle and arrow. 

The micrograph with higher magnification on the right-hand side shows the pronounced contact of the 

fibers to the aluminum. 

Fig. 9. Fracture surface of ultrasonic welded AA5754(CB)/CF-PA66-joints after tensile shear test. 

3.3 Cyclic behavior of ultrasonically welded AA5754/CF-PA66-joints 

Beside the monotonic properties, the cyclic deformation behavior of the ultrasonic welded hybrid 

joints was investigated. Therefore only surface pre-treated AA5754 sheets were ultrasonically welded to 

the CFRP to avoid aging effects during cyclic loading. At first the fatigue behavior was observed in 

stepwise load increase tests (LIT) for the three different pre-treated aluminum sheets. The fracture of the 

single overlap joint in figure 10 was evaluated with a force amplitude of 1975 N equivalent to an upper 

force of 4000 N which is correlated to 80% of the monotonic tensile shear strength with 50 MPa. 

Analogue to the monotonic behaviour the fatigue fracture occurs in the joining interface between 

AA5754 and CFRP. 

The displacement was measured with strain gauges near to the tip of the sonotrode. Some cycles 

before failure a pronounced increase of the displacement amplitude was observed. Final failure is 

announced by very pronounced increase of the displacement amplitude. 

On the other hand the displacement amplitude, measured on the aluminum surface, decreases in the 

load step before final failure. This effect can be attributed to the single overlap geometry of the joint 

beside the fatigue damage in the joining zone. An increase of the tensile shear load leads to a gradual 

increase of the bending moment at the overlap ends of the specimens. This geometry induced influence 

was observed in all fatigue tests. A similar behavior was measured for chemical (AP) and combined 

mechanical and chemical pre-treated joints (CB & AP). In figures 11 and 12 the result of a characteristic 

load increase test for each combination are shown. 

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Fig. 10. Load-Increase-Test for corundum blasted AA57547CF-PA66-joint. 

Fig. 11. Load-Increase-Test for an acid pickled AA57547CF-PA66-joint. 

The maximum difference in the realized force amplitudes is in the range of about 125 N. Also in this 

case the fatigue fracture occurs in the ultrasonically welded interface. 

Additionally to the LIT single step tests (SST) with constant force amplitudes were performed to 

determine Woehler curves and fatigue life data. The load levels of each single step test were estimated 

in one load increase test for each surface condition. 

Fig. 12. Load-Increase-Test for an acid pickled and corundum blasted AA57547CF-PA66-joint.


Figure 13 summarizes the results of single step tests in Fa-N-(Woehler)-Curves for 

AA5754/CF-PA66-joints with three different surface pre-treatments of the aluminum sheets. A cyclic 

force amplitude of 1475 N leads to fatigue failure after 10 5 cycles. At the force amplitude 2475 N the 

welded specimen reached only 10 3 cycles before a spontaneous failure occured. The corresponding 

upper force of 5000 N lies in the range of the maximum monotonic strength of the 

AA5754/CF-PA66-joints. 

The limiting number of cycles in the Woehler tests was 2 × 10 6 . For a force amplitude of 975 N, 2 × 

10 6 cycles were reached without failure. These specimens are marked with arrows. Finally, the 

endurance limit of AA5754/CF-PA66-joints under cyclic tensile shear loading (R > 0) was determined 

to be approximately 35% of the monotonic tensile shear strength. 

Fig. 13. Fa-N (Woehler) -Curves of ultrasonically welded AA5754/CF-PA66-joints for different surface pre-treatments of the metallic joining 

partner. 


For the first time the ultrasonic metal welding technique was successfully applied to join metal sheets 

with CFRP. Due to the ultrasonic welding process causes the polymer matrix is removed out of the 

welding zone. This allows a direct contact between the load bearing carbon fibers and the sheet metal 

without any damage of the carbon fiber reinforcement due to the process. With light and scanning 

electron micrographs as well as digital image analysis the microstructure of the welds was investigated 

in detail. Using the CCC-model it was possible to find optimum welding parameters with only 15% of 

the tests in comparison to a common procedure. Tensile shear strengths of more than 30 MPa were 

realized for suitable process parameters with AA5754/CF-PA66-joints. This value can be increased up 

to 54 MPa by adapted surface pre-treatments of the sheet metal. Furthermore the long-term stability can 

be significantly influenced by these methods. The fatigue behavior of welded hybrid joints was 

investigated in load increase as well as single step tests at a servo-hydraulic test system for single 

overlap joints at a frequency of 5 Hz. The cyclic deformation behavior was described with 

displacement-force measurements with strain gauges on the surface of both joining partners. The 

endurance limit for ultrasonically welded hybrid structures was determined to be approximately 35% of 

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the monotonic strength of surface pre-treated joints. The possibility to join different sheet metals to 

CFRP with high monotonic and cyclic strength allows a considerable extension of the application of the 

ultrasonic metal welding technique. Regarding the efficiency, automation, ecological compatibility and 

the achievable mechanical and technological properties ultrasonic metal welding is an attractive 

alternative to existing polymer joining techniques. 


The authors would like to thank the German Research Society (DFG) for the financial support in the 

framework of the research unit 524. They further thank the state research “Center for Mathematical and 

Computational Modelling (CM)²” at the University of Kaiserslautern for the financial co-support. 

References 

[1] Graff, K. Ultrasonic metal welding. In: New developments in advanced welding, Woodhead Publishing, 2005, 241-269 

[2] Rotheiser, J., Joining of Plastics, Munich: Carl Hanser Verlag, 2004 

[3] Greitmann M.J., Adam T., Holzweißig H.G., et. al., Techn. J. of Welding and all. Proc., DVS-Verlag GmbH, Düsseldorf, 2003, Issue 5, 

268-274 

[4] Brodyanski A., Born Ch., Kopnarski, M. nm-scale resolution studies of the bond interface between ultrasonically welded Al-alloys by an 

analytical TEM: a path to comprehend bonding phenomena? Applied Surface Science 252/1 (2005) 

[5] Gutensohn M., Wagner, G., Eifler D. Ultrasonic Welding of Aluminum Wires. Welding and Cutting, 2007, 59, 550-554 

[6] Krueger S., Wagner, G., D. Eifler D. Ultrasonic Welding of Metal/Composite Joints Adv. Eng. Mat., 2004, 6, No. 3, 157-160 

[7] Balle, F., Wagner, G., Eifler, D. Ultrasonic Spot Welding of Aluminum Sheet/Carbon Fiber Reinforced Polymer – Joints. Mat. Science 

and Eng. Technology, 2007, 38, No. 11, 934-938 

[8] Balle, F., Wagner, G., Eifler, D. Ultrasonic Welding of Aluminium/CFRP-Joints – An Innovative Technology for a Multi-Material Design 

in Lightweight Structures. In: Aluminium Alloys – Their Physical and Mechanical Properties, Wiley (Germany), 2008, 1905-1910 

[9] Balle F., Wagner, G., Eifler, D. Joining of Aluminum 5754 Alloy to carbon fiber reinforced polymers (CFRP) by ultrasonic welding. In: 

Aluminum Alloys: Fabrication, Characterization and Applications II, TMS (The Minerals, Metals & Materials Society), USA, 2009, 

191-196 

[10] Balle, F., Wagner, G., Eifler, D. Ultrasonic Metal Welding of Aluminium Sheets to Carbon Fiber Reinforced Thermoplastic Composites. 

Adv. Eng. Mat., 2009, 11, 35-39

Fatigue behaviour of composite tubes under multiaxial loading

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