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179 originally published online 28 August 2012 2013 227:Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications

Satrio Wicaksono and Gin Boay ChaiA review of advances in fatigue and life prediction of fiber-reinforced composites

  

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Review Article

A review of advances in fatigue and lifeprediction of fiber-reinforced composites

Satrio Wicaksono and Gin Boay Chai

Abstract

This contribution is an attempt to provide a thorough review of past and current research work on fatigue and life

prediction of fiber-reinforced composites. In order to summarize and present a comprehensive overview of the current

state-of-the-art published works, the reviews in this contribution are broadly summarized into four groups of review;

(1) fatigue of fiber-reinforced composites, (2) composite damage mechanism, (3) composite failure criteria and, (4) com-

posite fatigue modeling and life prediction. The review will begin with a discussion of inherent and environmental factors

affecting the fatigue of composites. This is followed by a rather extensive description of the composite damage mech-

anism and a summary of commonly used failure criteria for life prediction. And towards the end, models and methods for

fatigue and life prediction of composites are summarized and discussed.

Keywords

Fatigue, composites, laminates, time–temperature superposition, life prediction

Date received: 29 November 2011; accepted: 19 July 2012

Introduction

The reasons for the increasing popularity of compos-ites in weight critical application are their high specificstiffness and strength. Some examples of engineeringapplication where composites have become indispens-able are in the area of sporting goods, aircraft andaerospace, automobile and marine. In these applica-tions, cyclic and fluctuating loads are common andthis type of loading condition will eventually causedfatigue in structures. The subject of fatigue and lifeprediction of materials and structures are usuallyintertwined. The current knowledge on fatigue andthe prediction of life of composite structures is stillat its infancy.

In the 1960s and 1970s, many engineers andresearchers knew that metals suffered from fatigueand there was a misconception then that compositesdo not suffer from fatigue. There were, however, ahandful of published literatures on the fatigue behav-ior of glass-fiber composites. These composites exhibita form of degradation in service that can be describedas ‘fatigue’. A simplistic description of this ‘fatigue’phenomenon is that under cyclic loading condition,the load-bearing capacity of the materials falls withtime and this results in failures at stress levels, whichare often well below the normal engineering strength.The mechanisms by which this deterioration occurs incomposites are completely different from those whichare responsible for the fatigue phenomena in metals.Not only are these mechanisms different, they are

more complicated too. From the engineer’s point ofview, the challenge is to choose the appropriate mater-ial for a specific structural application so as to avoideither material or structural failure within the designlife of a component or structure. Thus there is a needto understand the mechanisms of degradation in ser-vice and to be able to predict the life of a given com-posite under particular design condition.

Some of the earlier notable literature published inthe area of fatigue response of fiber-reinforced com-posites were by Boller1 in the early 1970s, followed byOwen and his collaborators.2 Then Baker and co-workers3,4 were also laying down the foundationsthat describe the fatigue behavior of metal matrixcomposites (MMCs). While much of these earlyworks on fatigue are focused on phenomenologicalstudies, it quickly became apparent that an under-standing of the microstructural damage mechanismsresponsible for failure under cyclic loading is a pre-requisite for the development of new fatigue-resistantmaterials and also vital in the prediction of fatiguelife. Researchers such as Reifsnider and Talreja5,6

School of Mechanical and Aerospace Engineering, Nanyang

Technological University, Singapore

Corresponding author:

Gin Boay Chai, School of Mechanical and Aerospace Engineering,

Division of Aerospace Engineering, Nanyang Technological University,

50 Nanyang Avenue, Singapore 639798, Singapore.

Email: mgbchai@ntu.edu.sg

Proc IMechE Part L:

J Materials: Design and Applications

227(3) 179–195

! IMechE 2012

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are associated with the key developments in the emer-ging field of damage mechanics. The build-up of fati-gue damage is essentially a stochastic process and vitalstatistical interpretations of fatigue behavior in con-junction with life prediction of composites were pub-lished by Hahn,7 Whitney8 and Yang and Jones.9 Inrecent times, artificial neural networks (ANN), whichis basically an adaptive computer program that haslearning capabilities, was developed for fatigue lifeprediction of fiber-reinforced composites. Leeet al.,10 Al-Assaf and El Kadi11,12 are among someof the earliest researchers in the area of ANN appliedto fatigue of composites.

The early research into the fatigue behavior offiber-reinforced composites is largely dominated bythe aerospace industry, and much of the work wasfunded by the aerospace industry and also by the gov-ernment. In the half-century or so since compositeswere first developed, the picture, as far as applicationsare concerned, has changed substantially and aero-space is now only one of several industries that isseeking and using the latest of these materials whichoffer them the desirable benefits of high strength andstiffness combined with low density. It is perhaps forthis reason more than any other that it seems anappropriate time to produce a new survey of our cur-rent level of knowledge of the Achilles heel – the fati-gue behavior and life prediction of composites.

It is now appreciated that the behavior of compos-ite under fatigue loading is completely different fromthat of metal. Fatigue in metal occurs by the initiationof single crack, which propagates until catastrophicfailure occurs. In contrast to metal, damage buildup in composite is in global fashion rather than inlocalized fashion. Composites have several damageaccumulation mechanism, fiber–matrix debonding,matrix cracking, delamination and fiber fracture.These damage mechanisms can occur independentlyor interactively depending on material properties andtesting conditions.13

The purpose of this literature review is to gather,compile and review the notable published researchworks on fatigue and life prediction of compositematerials and structures. This contribution will serveas a guide and a stepping stone in the right directionto the next level of technological development in thisarea of research. The reviews will now be presented inthe following order: (1) fatigue of fiber-reinforcedcomposites, (2) composite damage mechanism, (3)composite failure criteria, and (4) composite fatiguemodeling and life prediction.

Reviews on fatigue of fiber-reinforcedcomposites

The several factors of inherent and external naturethat affect the fatigue behavior of fiber-reinforcedcomposites are compiled in Figure 1. Each of these

factors will be discussed in some details in subsequentsections.

Types of fiber

As the main load carrier in composites, the type offibers used will affect the composites fatigue behavioras the fibers carry most of the load. Figure 2 showstypical plots of peak tensile stress versus log cycles tofailure for three common fiber-reinforced composites.The S-N curve of glass fiber-reinforced plastic(GFRP) shows a more drastic drop in its fatiguestrength than that of carbon fiber-reinforced plastic(CFRP). The use of very stiff carbon fiber limits thestrain in the composite and thus prevents largedeformation in the matrix which can lead to prema-ture initiation of damage. On the other hand, the useof less stiff glass fiber allows for large deformation inthe matrix giving rise to fatigue failure. The fatigueperformance of kevlar fiber-reinforced plastic(KFRP) is more complicated than that of CFRPand GFRP due to the fact that kevlar fiber is fatiguesensitive.14 The task of compiling a fatigue databasefor composites can be rather daunting consideringthat there are many different types of fiber materialsavailable in the market. Some typical glass fibers thatare found in the market are E-glass, ECR-glass,C-glass and S-glass fibers. S-glass, for example, hashigher stiffness and strength in comparison with theother glass fibers. Each of these glass fibers react dif-ferently under corrosive environment as well.15 Theeffect of corrosion on fatigue of composites will bediscussed later. There are several different types ofcarbon fibers such as T300, AS4 and IM6. Amongthese three types of carbon fibers, IM6 has smallerfiber diameter but higher stiffness and strength.16,17

Types of matrix

Several researchers have shown that the fatiguestrength of glass fiber-reinforced composites is signifi-cantly depended on the properties of the resin.1,2

Fatigue damage in the form of crack initiation willusually starts in the matrix region. There areresearches that show the advantage of thermoplasticresin over thermoset resin in terms of ductility andtoughness.18–20 These resulted in considerably longerfatigue life of thermoplastics resin.20 The other advan-tage of a tougher resin is its higher interlaminar frac-ture toughness which will result in increased fatigueresistance against delamination.21 The fracture tough-ness of fiber-reinforced composite is affected by theinterface between matrix and fiber as well. Weakerinterface tends to improve the fracture toughness byresisting the crack to propagate through the matrix,and also reduces the effectiveness of the stress trans-fer.22 In order to get the desirable performance,interfacial adhesion can be controlled by surface

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treatment, such as plasma treatment, fiber sizing andcoating, electro-discharge, dry and wet oxidation.23

Resistance to crack propagation in the matrixmaterial can also be increased by adding rubber par-ticle in the resin.24 Adding nanoparticles in the matrixmaterial can increase the composite tensile strength,impact strength and fatigue life quite significantly.25

The addition of nanoparticles such as carbon nano-tubes in polymer matrices will allow damage sensingvia electrical signals. Microscale damages such asinter-fiber failure and matrix microcracking andmacroscopic damages such as delamination and rup-ture of fiber bundles can be detected using thisdamage sensing method.26,27 Besides being able tosense damages, its piezoresistive properties alsomakes it possible to measure strain-rate in carbonnanotube–polymer composites.26,28

Stacking sequence and type of reinforcement

Fatigue damage mechanism of composites depends ontheir stacking sequence and reinforcement type, thusdefining the unique fatigue properties of stacked com-posites. The effect of stacking sequence and reinforce-ment type on fatigue damage mechanism of compositematerials will be discussed later in section on compos-ite damage mechanism.

Loading conditions

The fatigued damage and failure response of compos-ites to loads depend largely on the loading

Fatigue of

Fibre-Reinforced Composites

External factors

1. Loading conditions

-Tension

-Compression

-Shear

-Combine loads

2. Environments

-Temperature

-Moisture

-Corrosion

-Combined effects

Inherent factors

1. Type of fibre

-Glass fibres

-Carbon fibres

-Kevlar fibres

2. Type of matrix

-Thermoplastic resin

-Thermoset resin

3. Stacking sequence

-Symmetric

-Antisymmetric

-Unsymmetric

4. Type of reinforcement

-Unidirectional

-Woven

-Braiding

-Stitching

-Pinning

Figure 1. Factors affecting the fatigue of fiber-reinforced composites.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

–2 0 2 4 6 8

Log Cycle to Failure

Pea

k S

tres

s (M

Pa)

CFRP

GFRP

KFRP

Figure 2. Typical S-N fatigue data for unidirectional

composite materials.14

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conditions.14,29–31 For instance, the fatigue perform-ances of a particular composite under tension–tensionfatigue will be different from those under tension–compression or compression–compression fatigue.29

Fiber failure is the main failure mode in unidirectionalcomposites under tension–tension fatigue.14 However,during tension–compression and purely compressivecycling, cracks propagate through the spreading offiber buckling failure zones.29–31 In various combin-ation of axial tension–compression cycling, the fatigueresistance of unidirectional composites decreases asthe compressive stress increases.29 Due to the poorcompression response of aramid fiber composites,the compression stress will be likely to be even moredamaging to composite containing aramid fiber thanthose of carbon fiber and glass fiber.32

Environmental conditions

The effect of three environmental conditions, i.e. tem-perature, moisture and corrosion, on fiber-reinforcedcomposites properties have been studied and will bediscussed in the following.

Temperature. One of the earliest and perhaps mostresearched about environmental condition that affectsthe fatigue properties of composites is temperature.Temperature is known to degrade and age the mech-anical properties of the resin material. The type ofresin used will therefore affect the fatigue performanceof composites at high temperature.33 Miyanoet al.34–37 used the strong relationship between timeand temperature in composite fatigue performance tobuild an accelerated testing methodology. This meth-odology allows one to predict the fatigue strength ofcomposite materials under arbitrary temperature, fre-quency and load ratio. The four hypotheses used inMiyano’s accelerated testing methodology34,38 are:

1. same failure mechanism for static, creep and fati-gue failures;

2. same time–temperature superposition principle forall strength;

3. the linear cumulative damage law for monotoneloading; and,

4. linear dependence of fatigue strength upon stressratio.

When these hypotheses are met, the fatigue strengthunder arbitrary combination of frequency, stress ratioand temperature can be determined. The tests andsteps that are needed in order to fully characterizethe fatigue properties of a composite material basedon Miyano’s accelerated testing methodology are pre-sented in a flowchart as shown in Figure 3.

The author used Miyano’s methodology ofFigure 3 to characterize L-930 flame-retardantwoven carbon-epoxy fatigue properties in tension–tension fatigue. Using the accelerated testing method-ology, zero stress ratio tension–tension fatiguestrength master curve for this material was establishedas shown in Figure 4. To validate the curves, testswere performed at 80 �C, 4Hz and a load ratio¼ 0.5.The results showed good agreement with the predic-tion as shown in Figure 5. This result shows thatMiyano’s accelerated testing methodology is veryeffective in fully characterizing fatigue properties ofthis specific type of composite materials.

One note of caution here is that Miyano’s method-ology has two known limitations. The first is that themethodology uses linear cumulative damage (LCD)law, which is generally unsatisfactory except for con-stant strain rate to failure.39 The other is thatMiyano’s methodology cannot be used when thereare hysteretic heating,40 and hysteretic heating nor-mally occurs at high frequency fatigue test (10 Hz ormore).

Moisture. Moisture is known to affect the properties ofresin but not those of the fiber. Thermoset resin ismore sensitive towards moisture than thermoplasticresin. Moisture affects the thermomechanical

Storage Modulus Master Curve

Time-Temperature Shift Factor

Master Curve of

Zero Stress Ratio Fatigue Strength

Fatigue Strength at Arbitrary Frequency,

Temperature and Stress Ratio

Master Curve of Creep Strength

Master Curve of Constant Strain

Rate (CSR) Strength

Constant Strain Rate (CSR) Test

at Several

Temperatures

Zero Stress Ratio Fatigue Test at Several

Temperatures and Load Magnitudes

Dynamic Mechanical Analysis (DMA) Test

Figure 3. Flowchart of all the tests and steps needed for accelerated testing methodology.

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properties of the resin through plasticization orhydrolytic or chemical degradation of the resin net-work. This will in turn reduce the composites life andmaximum service temperature (moisture lowers theglass transition temperature of the resin). One import-ant parameter in defining the effect of moisture is themoisture diffusion rate. Several factors that affect themoisture diffusion rate are:41

. the polarity of the molecular structure;

. the degree of crosslinking;

. the degree of crystallinity in the case of a thermo-plastic matrix; and,

. the presence of residuals in the material.

Corrosion. Fiber-reinforced composites are well knownfor their high corrosion resistance compared tometals. Thus fiber-reinforced composites are foundin many structural applications of corrosive naturesuch as components like pipe, scrubber, beam, etc.15

Several recent research showed that fiber-reinforcedcomposites are susceptible to acidic corrosive environ-ment.15,42 It was discovered that polymer matrixdegrade faster in the acidic environment42 and fiber,especially E-glass fiber, failed at a much lower loadthan the design load due to environmental stress cor-rosion cracking (ESCC).15 The problem of ESCCescalates at higher acid concentration coupled withtemperature and load. There are several glass fiberssuch as ECR, C and S-glass fibers that give betterresistance against ESCC.15 ECR-glass essentially isboron- and fluorine-free E-glass. With the removalof boron and fluorine, the chemical resistance – espe-cially acid resistance – of ECR-glass fiber is vastlyimproved.43 And C-glass fiber was developed specif-ically to resist chemical attack and S-glass fiber is ahigh strength glass fiber that gives stability underextreme corrosive environments as well.15

Reviews on composite damagemechanism

The damage mechanism of composites in fatigueenvironment will be reviewed and discussed in

500

600

700

800

900

1000

1100

-5 0 5 10 15 20 25

Log (tf') (Log(min))

Max

Str

ess

(MP

a)

Figure 4. Zero stress ratio tension–tension fatigue strength master curve for L-930 flame retardant woven carbon-epoxy.

0

200

400

600

800

1000

1200

-2 0 2 4 6 8

Log (Nf)

Fat

igu

e S

tren

gth

(M

Pa)

Prediction

Validation

Figure 5. L-930 flame-retardant woven carbon-epoxy ten-

sion–tension fatigue strength validation (80 �C, 4 Hz and

SR¼ 0.5).

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this section. The particular case of fiber-reinforcedcomposites subjected to cyclic tensile–tensile loadwill be emphasized. The two main microstructuraldamage mechanisms commonly observed in compos-ites under cyclic loading are fiber failure and matrixfailure.6,44 The failure process as a result of thesedamages depends on the type of reinforcement inthe composites; unidirectional, multi-directional,woven and three-dimensional (3D) reinforcement.

Fiber failure

Fiber failure in composites regardless of static or fati-gue failure is classified into two modes of failure: ten-sile and compressive fiber failure.44 The typical tensilefiber failure modes are fiber pull-out, fiber fractureand debonding. Fiber pull-out failure occurs whereboth fiber and matrix are brittle.45

For a composite in tension, local fiber fractureoccurs in the early loading stage and stress redistribu-tion follows. After which, debonding of fiber frommatrix occurs and this is followed by fibers breakagethat lead to the final failure.44 Compressive fiber fail-ure is, however, less dependent on fiber strength anddepends more on fiber stability such as fiber micro-buckling and kinking. Free edge and area in the vicin-ity of void are the places where fiber microbucklingusually initiates.44 And compressive fiber failure isalso affected by fiber misalignment. It has beenreported that a 0.25� fiber misalignment can reducethe compressive strength of a unidirectional compos-ite up to 70% of its initial value.44

Matrix failure

Matrix failure can be distinguished into two possiblemodes of failure: matrix failure in a ply (inter-fiberfracture) and matrix failure in between plies (delam-ination).46 Inter-fiber fracture would usually start atfiber–resin interface then propagates to the resin.Delamination on the other hand is caused by interla-minar stress, which is a direct effect of microcracks inthe resin.44 Free edges of multi-directional laminate

generally produce interlaminar shear stress singulari-ties that initiate microcrack. In general, the severity ofthe free-edge effect depends on the ply orientation oftwo adjacent plies.

Unidirectional composites

The fatigue response of unidirectional compositesunder tension–tension fatigue load is typically a func-tion of the fiber properties of the composites and thealignment of the fiber from the loading axis. In theearly stage of the fatigue response of composites withfibers aligned in the loading direction, matrix crackswill initiate in the direction along the fibers.47,48 Asthe cyclic load continues, the cracks grow and accu-mulate into several stress concentration hot spots.When the maximum cyclic load reaches the residualstrength, fiber matrix breakage will cause total failure.The damage mechanism of unidirectional compositesaligned at smaller ply angle (less than 20�) will be theessentially the same as the damage mechanism of uni-directional composites aligned at 0�.49 However, thefinal failure of unidirectional composites aligned atlarger ply angle (20� or more) will most likely to bedominated by matrix failure.49.

Multidirectional composites

Two types of multidirectional composites will be dis-cussed here, namely the cross-ply laminate and angle-ply laminate.

Figure 6 illustrates the progression of damage in across-ply laminate subjected to tension–tension cyclicloading condition.50 The initiation of fatigue damageis the appearance of matrix cracks perpendicular toloading direction. This is followed by matrix cracksalong the fiber in the transverse plies. As the laminateis further stressed, the crack density increases and thisis followed by crack coupling and fiber/matrixdebonding (debonding here depends on the interfacialstrength between fiber and matrix). The next stage ofdamage mechanism is in the form of delamination.Delamination will initiates near the free edges because

1

Crack initiationMatrix cracking

2 Fibre breakingCrack coupling

4

Delamination growthLocalized fibre breaking

3

Interfacial debondingDelamination

Fibre breaking

5FractureFailure

Figure 6. Damage development in a cross-ply laminate during tension–tension fatigue.50

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of high edge interlaminar stresses. As the loading con-tinues, the size of delamination will grow. The laststage of damage mechanism is breakage of the fibersaligned in the loading direction.

The corresponding graph of damage accumulationversus life for a cross-ply laminate under tension–ten-sion fatigue loading is shown in Figure 7. Thisdescription of damage mechanism and their progres-sion is also applicable to the unidirectional laminatedcomposites.

Fatigue damage mechanism in angle-ply laminateis, however, very dependent on its ply orientation withmatrix failure dominating for larger ply angle. Thefinal failure in the form of fiber breakage is morecommon in smaller ply angle in angle-ply laminate.More intensive and detailed study in this area ismuch needed, especially in understanding the relationbetween ply orientation and fatigue properties ofpractical laminates.

Woven composites

Woven composites have so many advantages com-pared to unidirectional and multi-directional compos-ites. Some of these advantages are better impactresistance, damage tolerance, dimensional stabilityover a large range of temperature and ease of manu-facturing. They have, however, lower overall in-planeproperties than unidirectional composites.50 Thestructural behavior of woven composites is affectedby the fiber material, matrix material, weave pattern,fabric geometry, fiber volume fraction and laminateconfiguration.51–55

The microstructural damages that occur in wovencomposites under fatigue loading are normally in theform of matrix microcracking, fiber breakage, crackcoupling and fiber–matrix interfacial debonding.50

Transverse crack (fill direction of the weave), shearfailure (warp direction of the weave), pure-matrixregion cracks, delamination between fill and warp,delamination between adjacent layers and warp

tensile failure are the usual macroscopic damagemechanisms.50

Figure 8 shows the modulus decay and damageaccumulation in woven-fabric composites during fati-gue life. It also shows that fatigue life of woven com-posites is typically divided into three stages; the initialstage, middle stage and final stage. Microstructuraldamages and transverse cracks in the fill direction ofthe weave are formed during the initial stage of thefatigue life. There is also rapid decay of modulusduring this stage, which is mainly caused by strainand stress concentrations in the geometrically repeat-ing unit cell.50 In the middle stage of the fatigue life,the main damage mechanisms are shear failure(warp), cracks (resin) and, delamination between filland warp as well as between adjacent layers. In thefinal stage of the fatigue life, all the damage modeswill grow rapidly. At the stress concentration loca-tions, fibers will fracture resulting in the final failureof the composite.50

Curtis and Moore56 compared the behavior oflaminated woven composites with that of equivalentnon-woven composite laminates under reversed axialcyclic loading. Three different stacking sequenceswere reported: Lay-up A – [90�,0�,0�,90�]s, lay-up B– [þ45�,�45�,0�,90�]s and lay-up C – [0�,90�,þ45�,�45�]s. The S-N diagrams of these test specimensare presented in Figure 9. Transverse cracks wereobserved to develop in the early stage of the fatigueresponse of non-woven coupon with lay-up A.Longitudinal interlaminar cracks and delaminationbetween 0� and 90� layers then started to appear,and finally the specimen failed with evidence of fiberbreakage. Similar failure mechanism and process canbe observed in the woven coupon with lay-up A con-figuration, but damage and failure were confined toindividual tow of fibers.56 Figure 9(a) shows that thefatigue curve of woven coupon is lower than that ofthe non-woven coupon for specimens with lay-up A.One reason for this is that woven coupon has greaterfiber instability meaning the buckling of 0� fibers will

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

Percentage of Life

Mod

ulus

Dec

ay

Dam

age

Damage

Modulus Decay

Figure 8. Modulus decay and damage accumulation in woven-

fabric composites during fatigue life.50

0 20 40 60 80 100

Percentage of Life

Dam

age

Figure 7. Damage accumulation in laminated composites

made of unidirectional layers during fatigue life.50

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create high shear stress at the resin and interfaceregion of the buckled 0� fibers.56

In the case of the non-woven coupons with lay-upB configuration, damage initiates in the þ45� and�45� layers leading to delamination between the inter-face between the þ45� and 0� layers. For the wovencoupons with lay-up B, initial damage in the form ofdelamination occurs between 0� and 90� layers fol-lowed by transverse cracks in 90� tows and cracks inthe resin rich regions between tows.56 The damageand failure mechanisms of both woven and non-woven specimens with lay-up C configuration aresimilar to those of specimens of lay-up B. Figure9(b) and (c) show similar fatigue response for bothnon-woven and woven specimens.

Three-dimensional composites

Some recent composites developed for structuralapplication are the 3D composites. Examples ofthese are the woven, stitched, z-pinned, braided andknitted composites. In comparison to 2D composites,3D composites are known to have higher delamin-ation toughness and impact damage resistant.57–59

The introduction of z-binders in 3D composites will,however, induce resin-rich region around z-binders,

and this will give rise to microstructural damages inthe form of local in-plane distortion, fiber breakageand crimping.57 Under in-plane fatigue loading, theseinitial microdamages will grow into macroscopic dam-ages before final failure. As a result, the in plane fati-gue properties of 3D composites are considerably lessfrom those of 2D composites.57

Reviews on composite failure criteria

Composites can fail through several different individ-ual damage mechanisms as described in earliersections. To complicate matters, one damage mechan-ism can interact with another damage mechanism.Therefore to predict the failure of composites underloading, a suite of failure criteria may be needed.Many researchers have contributed towards settingup a database of composite failure criteria.60–63 Theextensive published failure criteria can be classifiedinto two major research groups64–66 as illustrated inFigure 10.

Conventional notations are used in the subsequentdiscussion on the failure criteria. Three normal stres-ses of �ij and six components of shear stresses �ij(where i, j¼ 1, 2, 3) shown in Figure 11 representthe general state of stresses at a material point.

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1(a) (b)

(c)

Log Nf

Pea

k S

tres

s R

atio

[0,90,90,0]s

Lay-up A

0

0.1

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1

Log Nf

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k S

tres

s R

atio

[+45,-45,0,90]s

Lay-up B

0

0.1

0.2

0.3

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0.9

1

0 1 2 3 4 5 6 7 8 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8

Log Nf

Pea

k S

tres

s R

atio

[0,90,+45,-45]s

Lay-up C

Figure 9. Fatigue life comparison between unidirectional laminates (dashed line) and satin weaved fabric composites (solid line)

under tension–compression fatigue loading.56

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The corresponding normal and shear strains aredefined by "ij and �ij respectively, and the Poisson’sratios are denoted by �ij. Subscripts c and t in thestress or strain component indicate compressive andtensile respectively and subscript u indicates the ultim-ate stress or strain component.

Mode-independent failure criteria

Mode-independent failure criteria are used to predictthe damage and failure of the material without dir-ectly identifying the various modes of failure. Amode-independent failure criterion is usually definedwith only one equation and this makes the criterioneasy to apply. Unfortunately, this type of criteria donot reveal information about the nature of thedamage.64 This group of failure criteria can be furthersub-divided into two groups: polynomial and para-metric criteria.66

Polynomial criteria. One of the earliest and most popularquadratic criterion is Tsai–Hill or Azzi–Tsai criter-ion.62 The earlier yield criterion for isotropic materialwas proposed by Hill,67 this was later modified byAzzi and Tsai,62 and Tsai68 for predicting failure of

fiber-reinforced composites. This criterion states thatthere is material failure in the composite if the follow-ing inequality is violated

�11�11u

� �2

þ�22�22u

� �2

þ�12�12u

� �2

��11�11u

� ��22�22u

� �5 1

ð1Þ

The other popular quadratic criterion is Tsai–Wucriterion61 with the same condition of the violation ofthe inequality of the equation means material failure

F1�11 þ F11�211 þ F2�22 þ F22�

222 þ 2F12�11�22

þ F66�212 5 1

ð2Þ

where

F1 ¼1

�11tu�

1

�11cu; F2 ¼

1

�22tu�

1

�22cu

F11 ¼1

�11tu�11cu; F22 ¼

1

�22tu�22cu; F66 ¼

1

�212u

F12 ¼ �1

2�11tu�11cuð3Þ

Hoffman69 derived a more general form of the quad-ratic equation of the Tsai–Hill62 equation. TheHoffman criterion caters for different tensile and com-pressive strength of the composites. The Hoffman cri-terion is similar to the Tsai–Wu criterion except for69

F12 ¼ �1

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�11tu�11cu�22tu�22cup ð4Þ

Chamis70 also attempted to account for the differ-ences in the tensile and compressive strength by intro-ducing two compensation constants to Tsai–Hillfailure criterion

�11�11u

� �2

þ�22�22u

� �2

þ�12�12u

� �2

�C12C012

�11�11u

� ��22�22u

� �51

ð5Þ

C12 ¼1þ 4�12 � 3�13ð ÞE22 þ 1� �23ð ÞE11ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE11E22 2þ �12 þ �13ð Þ 2þ �21 þ �23ð Þ

p ð6Þ

where E11 and E22 are the longitudinal and transversemodulus elasticity associated with the 1 and 2 direc-tions, respectively. The constant C12 depends only onthe fundamental material properties while the con-stant C012 has different value for each quadrant in fail-ure locus.70

Franklin and Marin71 included the biaxial stresscondition in order to achieve better accuracy in com-posite failure prediction especially when dealing with

11σ 12τ

13τ21τ

22σ23τ31τ

32τ

33σ

1-axis(fibre direction)

2-axis(transverse direction)

3-axis(laminating direction)

X-axis(laminate reference axis)

θply orientation

angle

Figure 11. Three-dimensional state of stresses.

Composite Failure Criteria

Mode Independent Mode Dependent

Polynomial Parametric

Figure 10. Composite failure criteria classification.

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complex stresses. Based on this criterion, material fail-ure occurs if the following inequality is violated71

�211 � C�11�22�11tu�11cu

þ�222

�22tu�22cuþ

�12�12u

� �2

þ �11�11c � �11t�11tu�11cu

þ �22�22c � �22t�22tu�22cu

5 1 ð7Þ

where C is a floating constant that depends on thebiaxial stress condition chosen.

Basically, the accuracy of the prediction of failureincreases with the corresponding increase in the orderof the polynomial. With the higher order polynomialcriteria, the solution gets more complex and labori-ous. For example, there are some successful cubic cri-teria.72,73 As cubic criterion is more flexible inapplication as compared to quadratic criterion, thereare more interaction parameters involved which makethe criterion more complicated.66

Parametric criteria. Parametric criteria utilize a set ofseries (usually of trigonometric function) other thanpolynomial. Some developed the criterion using theFourier expansion74,75 while others used the sineseries.76 The accuracy of parametric criteria dependssignificantly on the number of terms used in the series.66

There are two major drawbacks of mode-indepen-dent failure criteria in comparison with mode-depen-dent failure criteria. The mode-independent criteriacan predict the damage and failure of compositematerials, but they do not reveal the nature of thedamage or failure modes. Also the accuracy of themode-independent criteria in one region of the failureenvelopes cannot be improved without affecting theaccuracy in the other region of the failure envelopes.66

Mode-dependent failure criteria

Mode-dependent failure criteria are sets of criteriathat are used to predict the damage and failure ofmaterial corresponding to each individual mode offailure. These criteria normally come in a set of equa-tions, with each equation for each particular failuremode. Two of the earliest known mode-dependentcriteria are the maximum stress and the maximumstrain criteria.77 Based on the maximum stress criter-ion, composite will not fail until the one of the fol-lowing strain inequalities is violated

�11t5�11tu; �22t5�22tu; �125 �12u; �11c5�11cu

�22c5�22cu ð8Þ

Similarly, in maximum strain criterion, failure incomposite will occur until one of the followinginequalities is violated

"11t 5 "11tu; "22t 5 "22tu; �12 5 �12u; "11c 5 "11cu

"22c 5 "22cu ð9Þ

A more sophisticated mode-dependent failure cri-terion was developed by Hashin.60,78,79 Hashin failurecriterion consisted of four different failure modes asdefined in the following equations (10) to (13).Fiber tension (�1150)

�11�11tu

� �2

þ��12�12u

� �2

41 ð10Þ

Fiber compression (�1140)

�11�11cu

� �2

41 ð11Þ

Matrix tension (�2250)

�22�22tu

� �2

þ�12�12u

� �2

41 ð12Þ

Matrix compression (�2240)

�222�23u

� �2

þ�222�23u

� �2

�1

" #�22�22cuþ

�12�12u

� �2

41 ð13Þ

Based on Hashin criterion, failure in particular modeoccurs if inequality for that particular mode is vio-lated. Several researchers have developed new mode-dependent criteria based on the extension and modi-fication of Hashin criterion. Puck and Schurmann80

extended Mohr’s hypothesis to composite materials.After which Kroll and Hufenbach81 merged Hashincriterion with Puck criterion. More recently, Davilaand Camanho82 have successfully developed a mode-dependent failure criterion by combining several fail-ure criteria for each failure modes. This criterionstates that failure in a particular mode occurs if anyone of the following inequality in equations (14) to(21) is violated.

Matrix compression (�2240)

�Teff�T12u

!2

þ�Leff�L12u

!2

41 ð14Þ

where

�Teff ¼ �T�� ��þ �T�n� �

�Leff ¼ �L�� ��þ �L�n� �

ð15Þ

and �n, �T, �L are the normal, transverse shear and

longitudinal shear stress that acts on the fractureplane. The symbols �Tand �L are the correspondinginternal material friction to be determinedexperimentally.Matrix tension (�2250)

1� gð Þ�22�22uþ g

�22�22u

� �2

þ�12�12u

� �2

41 ð16Þ

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g ¼GIc

GIIcð17Þ

where GIc and GIIc are the critical energy release ratein the mode I and II loading respectively.Fiber tension (�1150)

"11"11u

41 ð18Þ

Fiber compression (�1140 and �2240)

�12j j þ �L�22

�12u41 ð19Þ

Fiber compression (�1140 and �2250)

1� gð Þ�22�22uþ g

�22�22u

� �2

þ�12�12u

� �2

41 ð20Þ

Matrix damage in biaxial compression

�mTeff

�T12u

!2

þ�mLeff

�L12u

!2

41 ð21Þ

�mTeff ¼ ��22 cos� sin�� �T cos�

� �� �and

�mLeff ¼ cos� �12j j þ �

T�22 cos�� �� �

ð22Þ

where �mTeff and �mL

eff are the effective transverse andlongitudinal stresses in the misalignment frame. Theparameter � is the fracture angle which is to be deter-mined in an iterative manner.

Although mode-dependent criteria have the advan-tage over mode-independent criteria in terms of theircapability in providing failure mode information, itdoes not means that mode-dependent criteria arealways more accurate than mode-independent cri-teria. The accuracy here is relative. One particularfailure criterion might give better estimation in one

part of the failure envelope but inaccurate estimationin the other part. Thus, choosing appropriate criterionfor particular case is required65 and using a suite offailure criteria is currently the best option.

Reviews on composite fatigue modelingand life prediction

In order to reduce the number of test for predictingcomposite fatigue failure, composite fatigue modelingis needed. There are currently three main groups ofcomposite fatigue models: fatigue life model, phenom-enological model and progressive damage model.Figure 12 illustrates the three main groups and theirassociated composite fatigue models. Each model willbe looked at and discussed with some details in thesubsequent sections.

Fatigue life model

Current fatigue life model normally utilize one of fail-ure criterion as the base and an empirical S-N curve asan input. Such fatigue life model can be used to pre-dict the number of cycle to failure but they do notaccount for the damage accumulation.83 There arecurrently several fatigue life models available in theliterature; Jen and Lee84,85 and Philippidis andVassilopoulos86 developed a deterministic fatigue lifemodel that is basically a modification of Tsai–Hillcriterion, as shown below

�11�11f

� �2

þ�22�22f

� �2

þ�12�12f

� �2

��11�11f

� ��22�22f

� �5 1

ð23Þ

where �11f, �22f and �12f are the fatigue failure stressesin the S-N curves. This criterion can be used to modelfatigue life for any stress ratio and frequency as longas the S-N curves are available for the correspondingstress ratio and frequency.86 Reifsnider and Gao5

presented a fatigue life model based on the

Composite Fatigue Modelling

Fatigue Life Phenomenological Progressive Damage

Damage

Growth

Prediction

Residual

Properties

Prediction

Residual

Strength

Residual

Stiffness

Figure 12. Composite fatigue modeling classification.

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microstructural level. And Fawaz and Ellyin87 devel-oped a model that is able to predict the S-N curve ofunidirectional (UD) laminate with arbitrary ply orien-tation based on S-N curve of a laminate with fibersaligned in one orientation. Paramonov et al.88 suc-cessfully developed a statistical fatigue life modelwhich can predict the minimum and maximumnumber of cycle to failure of a composite structure.

Phenomenological model

Phenomenological model include the description ofthe damage in composites during fatigue loading bymodeling the degradation of one particular propertyof composites. There are two common phenomeno-logical models available: residual stiffness model andresidual strength model.

Residual strength model. This phenomenological modelused experimental observation to describe thestrength loss of composites. This model can be sub-divided into two models: sudden death model andwear-out model. The residual strength in the suddendeath model is kept constant over certain number ofcycle and is then suddenly degraded drastically whenit reaches the critical number of cycle to failure. Onthe other hand, the residual strength in the wear-outmodel is continually decreasing over the number ofcycle following certain predetermined equation.Several researchers have developed and successfullyapplied this model for use in glass fiber-reinforcedcomposites,89,90 and Diao and Mai91 has presented astatistical model of residual strength to predict thefatigue life of composite laminates.

Residual stiffness model. This model describe the stiff-ness loss of composite laminates based on experimentobservation. One major advantage of the residualstiffness model over the residual strength model isthat only the stiffness of composites is needed formaterial characterization. Several notable residualstiffness models have been developed and publishedin the literatures.89,92,93 One such model is byWhitworth93

E nð Þ ¼ E 0ð ÞS

c1Su

� � 1c2

�h ln nþ 1ð Þ þ c1Su

S

� �mc2

" #1m

ð24Þ

where E 0ð Þ, E nð Þ, Su and S respectively are initial stiff-ness, stiffness at n cycle, ultimate strength and appliedstress. The parameters c1, c2, h and m are obtainedfrom experiments.

Phenomenological model has one common weak-ness. It can only predict the fatigue behavior of com-posite laminates under mono-axial fatigue loadingand cannot account for the complex stress state inreal structure. To get the correct parameters for this

fatigue model, laboratory tests must simulate thesame complex stress state as real structure in orderto fully characterize the material.

Progressive damage model

This model is currently the most advanced modelcompared to the earlier models that were discussed.Progressive damage model is able to predict not onlythe number of cycle to failure but also degradation ofthe properties in the composite structures via the useof fracture criteria. This model can be divided intotwo groups: model predicting damage growth andmodel predicting residual mechanical properties.83

Model predicting damage growth. Since the late 1980s,there were models that can be used to predictdamage growth.94–97 Some models were developedto predict damage growth from either notch94 orholes.95 Bergmann96 developed an empirical delamin-ation propagation model which combine all themodes (mode I tension, mode II shear and mode IIIshear) in one equation. The governing equation ofBergmann model is

dA

dN¼ c1 f Gtð Þð Þ

n¼ c2"

nAm ð25Þ

where Gt is the total of mode I, II and III energyrelease rates, A is the delaminated area and N is therespective number of cycle. The parameters c1, c2, nand m are determined from experiments. By assumingconstant width and a0 as the initial crack length,Bergmann model can be written in the form of

N ¼a 1�mð Þ � a

1�mð Þ

0

1�mð Þc�nð26Þ

Dahlen and Springer97 has successfully built anempirical delamination propagation model thatincludes the effect of shear reversal in mode II delam-ination growth. Shear reversal takes place when thesurfaces bounding the delamination are moving inboth positive and negative direction.97

Model predicting residual mechanical properties. Thismodel require the relationships of the residual mech-anical properties of composites with their damagevariables. Shokrieh98–101 has constructed a model,which is able to predict the fatigue damage progres-sion of complicated composite structures provided theproperties of the composite materials are fully char-acterize using modified Hashin failure criterion. Inorder to fully characterize a composite material,experimental results based on the three loading con-ditions of tension, compression and shear on fibersand resins are needed. For clarity, an illustration ofthe required tests is shown in Figure 13. In order tofully characterize a composite material, for each

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combination of load and fiber or matrix testing, twodifferent set of tests are needed.98

. Fatigue test of specimen until a certain number ofcycle, then followed by a static test until failure.This is to determine the residual stiffness andstrength.

. Fatigue test to failure to form the S-N curve.

In order to make the model less expensive,Paepegem102–110 implemented a cycle jump. The inter-val between two successive cycles where the fatiguedamage law is evaluated, is small in the beginningbut increases as the cycle advances.110 Hochard111

developed a similar progressive fatigue model spe-cially catered for woven composites.

Progressive damage model has more advantagescompare to the other models but it can be very com-plex and expensive in terms of computational solutionas well as in terms of the number of experimentsneeded to fully characterize the material properties.The fatigue life model is rather straight forward andaffordable from the computational solution andexperimental point of view. One has to bear in mindthat fatigue life model can only predict the number ofcycle to first element failure (initial failure), which inpractice may not be the final failure.

Concluding remarks

Thorough reviews of the past and current researchwork on the fatigue and life prediction of fiber-rein-forced composites were carried out and discussed inthis contribution. The factors affecting fatigueresponse and damage mechanism of fiber-reinforcedcomposites subjected to cyclic loads were presentedand discussed in some details. The use of acceleratedtesting methodology to allow for environmentaleffects on the life prediction of composites was alsopresented and discussed with deliberations. In-depthreviews of the available failure criteria for fiber-rein-forced composites were also included.

Progressive fatigue model is perhaps the mostsophisticated model to date compared to the fatiguelife model and the phenomenological model. Coupledwith the sophistication of the model are the complex-ity and economic challenges. Fatigue life model ismuch simpler and easier to apply, as the model canpredict up to the first point of failure without thedetails of stiffness degradation before failure.

The current knowledge on fatigue response and lifeprediction of fiber-reinforced composites is still notyet matured and there are still a lot more work thatneeds to be done. This is especially true in the devel-opment of a failure criterion (or a suite of failurecriteria) that is capable of predicting failure for alltype of fiber-reinforced composite structures and forall type of loading conditions. There is also a need fora progressive fatigue model that is much simpler, inex-pensive computationally and demanding only basicmaterial testing. Current state-of-the-art work ondamage modeling appears to gaining momentumand there are signs that future research work is pro-gressing towards a more sophisticated progressivedamage model coupled with mode-dependent failurecriterion for a more complete prediction of failuremodes and the progression of failure of compositessubject to static and fatigue loads.

Acknowledgement

The financial support in the form of a research student

scholarship provided by Nanyang TechnologicalUniversity, and the permission to use the laboratory andcomputing facilities at the School of Mechanical andAerospace Engineering are truly acknowledged. It must

also be mentioned that the test materials and specimensare provided by Defence Science Organization, Singapore.Last but not least, the many fruitful hours of consultative

discussions with the specialists of Defence ScienceOrganization is greatly acknowledged here.

Funding

This research was funded by grant number NTU-MINDEF

JPP MD-NTU/09/06.

Figure 13. Tests needed in order to fully characterize a composite material.101

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