Composites: Part A 44 (2013) 114–121

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Composites: Part A

journal homepage: www.elsevier .com/locate /composi tesa

The effect of thermo-oxidation on matrix cracking of cross-ply [0/90]S

composite laminates

Dinh-Quy Vu, Marco Gigliotti ⇑, Marie Christine Lafarie-FrenotInstitut Pprime, Département Physique et Mécanique des Matériaux, CNRS, ENSMA – Université de Poitiers, UPR 3346, 1, Avenue Clément Ader, BP 40109, F86961 FuturoscopeChasseneuil Cedex, France

a r t i c l e i n f o

Article history:Received 8 March 2012Received in revised form 5 August 2012Accepted 8 August 2012Available online 31 August 2012

Keywords:A. Polymer–matrix composites (PMCs)B. Environmental degradationC. Numerical analysisD. Mechanical testing

1359-835X/$ - see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.compositesa.2012.08.013

⇑ Corresponding author. Tel.: +33 549498340.E-mail address: marco.gigliotti@ensma.fr (M. Gigli

a b s t r a c t

The present article focuses on the effects of thermo-oxidation on matrix cracking in cross-ply [0/90]S

composite laminates. IM7/977-2 carbon/epoxy samples were firstly aged at 150 �C under 1.7 bars of oxy-gen for 24 h, 48 h and 96 h, respectively. Quasi-static tensile tests were then carried out on un-aged andaged samples. The number of matrix cracks was counted during the tensile tests in order to establish theevolution of the crack density as a function of the applied stress and a numerical model was employed toevaluate the critical energy release rate of un-aged and aged laminates. A reduction of the critical energyrelease rate of aged samples was measured compared to un-aged sample. Scanning Electron Microscopy(SEM) observations were carried out by replicas of the sample surfaces in order to identify a possible rela-tionship between the thermo-oxidation induced damage at the local scale and the onset of matrix crack-ing at ply scale.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Composite materials have been increasingly integrated withinaerospace structures as they possess very interesting specificmechanical properties (strength and stiffness) and very good fati-gue resistance. In the next future composite materials are expectedto be employed in structural parts subjected to rather severe ther-mal conditions. For instance, composite structures for aero-enginescan be exposed to oxidative environments at high temperatures(>120 �C); under such conditions oxidation reaction/diffusion phe-nomena take place within the polymer material and threaten theintegrity of the structure.

Thermo-oxidation of organic matrix composites has been thesubject of specific studies over the past 30 years [1–3]. The emer-gence of new advanced aerospace applications (‘‘hot’’ structures)has given new impetus to the development of studies on thebehavior of carbon/epoxy composites at high temperature, andespecially on the thermo-oxidation [4–9]: it consists of a coupledoxygen diffusion/reaction phenomenon which affects a relativelythin layer (up to a few hundred of micrometers, depending onthe resin system) leading to matrix chemical shrinkage strainsdue to the departure of volatile species and to mechanicalproperties changes – local stiffness increase and toughnessdecrease – due to chemical modifications (mainly chain scissions)of the polymer network [10]. In [7], by using micro-indentation,

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otti).

Olivier et al. shown mechanical properties changes which aredue to chemical modifications of the polymer network and takeplace within a few hundred of micrometers from the external sur-faces exposed to the environment.

Chemical shrinkage strains may contribute significantly to thedevelopment of internal stresses leading possibly to damage atthe microscopic scale (the scale of the fiber), such as fiber/matrixdebonding.

Fig. 1 [11] shows the damage state of the surface of a compositesample aged under atmospheric air for 1000 h: resin shrinkage andfiber/matrix debonding are clearly visible. It is also clearly demon-strated in [11] that the development of these degradations de-pends on the type of environment (atmospheric air, oxygenpressure, and on the aging time, since longer exposition to a moreaggressive environment means systematically more fiber/matrixdebonding sites. It has been also proved [11,12] that the resinshrinkage is deeper and the fiber/matrix debonding sites are morenumerous in resin-rich zones, that is, zones with low fiber volumefraction.

The effect of thermo-oxidation at the microscopic (fiber/matrix)and mesoscopic (ply) scales is twofold: from one side, the occur-rence and the development of microscopic damage (fiber/matrixdebonding or micro-cracks for instance) give rise to the onset ofoxidized/damaged layers which propagates along the compositeplies [13,14]: the presence of fiber/matrix debonding andmicro-crack generates additional surface exposed to oxygen andaccelerates the kinetics of degradation [15,16]. From another side,thermo-oxidation produces embrittlement and toughness decrease

fibre/matrix debonding

matrix shrinkage

Fig. 1. SEM observations (45� tilted) on the edges of samples isothermally aged at150 �C under atmospheric air 1000 h [11].

.

Fig. 2. Sample geometry and dimensions. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

0h

48h

a

c

d

b

Fig. 3. Observations surface sample after aging, before tensile test: (a) un-aged; (b)aged under 1.7 bars O2 48 h; (c and d) zoom on matrix shrinkage and fiber–matrixdebonding.

24h

96h e

c

d

a

b

D.-Q. Vu et al. / Composites: Part A 44 (2013) 114–121 115

of the affected surfaces. In all cases, the produced changes tend toaffect thin layers close to the exposed surfaces (few hundred ofmicrometers), whose extent may be very small with respect tothe sample dimensions.

Past research is mainly concerned with the effects of thermo-oxidation on composite at the microscopic [5,7,11,12] and meso-scopic [13,16] scale. The present article focuses on the effects ofthermo-oxidation on matrix microcracking of cross-ply [0/903/0]IM7/977-2 composite specimens, aiming at establishing a link be-tween degradation at the microscopic/mesoscopic scale, includingoxidized/damaged layers, and the development of matrix micro-cracking at the laminate scale.

Samples were first subjected to isothermal aging tests at 150 �Cunder 1.7 bars of oxygen and then to quasi-static tensile tests up torupture. The sample polished edges were observed at regular inter-vals during the tensile test by a traveling optical microscopemounted on the tensile machine in order to count the number ofmatrix transverse cracks appearing in the 90� layers.

Replicas of the sample surface edges were also observed by SEMto establish a possible link between thermo-oxidation damage atthe microscopic scale (fiber/matrix debonding) and the onset oftransverse matrix cracks in the 90� layers.

Fig. 4. Observations surface sample after aging, before tensile test: (a) aged under1.7 bars O2 24 h; (b) aged under 1.7 bars O2 96 h; (c–e) zoom on thermo-oxidation-induced micro-cracks.

2. Experimental setup

2.1. Sample type and preparation

Samples (dimensions: 180 mm � 20 mm � 1.25 mm) were cutout from a [0/903/0] IM7/977-2 composite plate and polished auto-matically by an optimized procedure, set up to minimize the im-pact of polishing (see Fig. 2). The reader is referred to Ref. [11]for more details concerning the polishing setup: the procedure ischosen in order not to induce damage at the microscopic scaleon virgin (unaged) samples. After polishing, the samples were sub-jected to isothermal aging tests at 150 �C under 1.7 bars oxygenpressure in a climatic chamber [8] before undergoing quasi-statictensile tests.

Figs. 3 and 4 show optical microscopy observations of specimen’ssurfaces after polishing (0 h) and after aging under 1.7 bar of oxygen

for 24 h, 48 h and 96 h, respectively. No damage is observed on sur-face of unaged specimen (Fig. 3a), even at the microscopic scale.Thermo-oxidation induced matrix shrinkage (Fig. 3c) and fiber/ma-trix debonding onset (Fig. 3d) is observed on the surface of samplesaged under 1.7 bars oxygen for 48 h. Some thermo-oxidation in-duced microcracks are visible on aged samples (Fig. 4c–e), startingfrom around 24 h conditioning: these microcracks are not localizedand have no preferred direction. By comparing Fig. 4c with Fig. 4dand e, we see that microcracks in samples aged for 96 h are moreopen than those in samples aged for 24 h.

The material elastic properties of the unidirectional laminate –measured by independent tests – are given in Table 1.

It has to be noted that – in this type of samples – the centralblock of 90� plies is relatively thick and such that – under static

Table 1Properties of the unidirectional laminate.

Properties 20 �C

E11 (GPa) 157E22 (GPa) 8.5m12 0.29G12 (GPa) 5a1 (1 �C�1) 0.23 � 10�6

a2 (1 �C�1) 30 � 10�6

long distance QUESTAR microscope

Camera

Fig. 5. ‘‘In situ’’ observation setup for crack counting during the tensile test. (Forinterpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)

mold

Fig. 6. Experimental setup for applying the replica onto specimen surface duringtensile tests. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

116 D.-Q. Vu et al. / Composites: Part A 44 (2013) 114–121

monotonic loading – the matrix microcracking developing in 90�plies span over the entire thickness and width of the sample[17,18].

Original

a

Fig. 7. SEM observations of the sample external surfaces:

Moreover, it should be emphasized that for the samples inFigs. 3 and 4, the thickness of the oxidized/damaged layer is ofthe order of 100 lm [9], which is negligible with respect to thesamples dimensions, but sufficient to activate embrittlement ofthe sample surfaces.

2.2. Testing machine

Tensile tests were carried out on a hydraulic Instron 4505 ma-chine (maximal load 100 kN). All tests were conducted at the rateof 0.1 mm/min.

In situ observations of polished samples edges were performedduring the tensile test without dismounting the sample by meansof a video camera and a long distance Questar microscope (Fig. 5).The camera transfers the images to a computer screen and trans-verse cracks can be counted at each stage of the loading. We canmove the setup vertically to count the number of cracks within afixed distance (4 cm for example).

2.3. Replica technique

The replica technique was used in [19] to monitor the initiationand propagation of cracks on the outer surface of specimens. In thisstudy, we will use this technique to register the state of specimensurface during tensile tests without having to dismount and re-mount the specimen each time. A mold adapting to the geometryof the specimen and to the experimental setup was produced tofacilitate the holding during the polymerization step of the resin(about 5 min) (see Fig. 6). Then, the replicas are coated and inves-tigated by SEM.

Fig. 7 presents SEM observations of the external surface of anaged sample performed on the original sample (Fig. 7a) and onthe corresponding replica (Fig. 7b). We can note that the replicagives a ‘‘negative’’ view of the sample surface.

Fig. 8 shows SEM observations of fiber/matrix debonding on theoriginal sample (Fig. 8a) and on the replica (Fig. 8b). We can notethat the replica technique is able to detect fiber/matrix debonding,thus is effective at the microscopic scale.

In conclusion, SEM observations show that the replica tech-nique is effective for characterizing the specimen surface, both atthe macroscopic and the microscopic (fiber/matrix) scales.

3. Numerical simulation of matrix cracking in [0/90]S cross-plycomposite laminate under static tensile test

Matrix cracking in off-axis plies is usually the first type of dam-age appearing in composite laminates. A lot of experimental workhas been carried out on [0/90]S cross-ply laminates in order toidentify and characterize the physical and geometrical parameters

Replica

b

(a) original specimen and (b) corresponding replica.

Original Replicaa b

Fig. 8. SEM observations of fiber/matrix debonding on the sample external surfaces: (a) original specimen and (b) corresponding replica.

Fig. 9. Schematics of the model employed for the calculation of the energy releaserate.

D.-Q. Vu et al. / Composites: Part A 44 (2013) 114–121 117

governing the onset, propagation and saturation of matrix cracksunder mechanical or thermal loading. Based on the experimentalresults, researchers have proposed models to predict these phe-nomena. The mechanical analysis of damage evolution in the com-posite consists of two main steps:

– The first step aims at describing the stress field in the [0/90]S

laminate in the presence of damage.– The second step involves using a failure criterion to predict

damage evolution.

In the literature, different methods for calculating the stressfield in [0/90]S cross-ply laminates have been presented. Amongthem, the ‘‘shear-lag’’ model is one of the most used Nairn andMendels [20] have recently classified the ‘‘shear-lag’’ – based mod-els by developing elastic calculations of general multi-layer sys-tems in which matrix cracking in [0/90]S cross-ply laminates is aparticular case. The authors show that, whatever the stress distri-butions along the thickness, all the approaches lead to a fundamen-tal ‘‘shear-lag’’ equation:

d2s�xzðxÞdx2 � a2s�xzðxÞ ¼ 0 ð1Þ

�L 6 x 6 þL (Fig. 9); s�xzðxÞ is shear stress at layers interface; ‘‘a’’ is a‘‘shear-lag’’ parameter:

a2 ¼ 1h1E22

þ 1h2E11

� �h1kR

G23þ h2kL

G13

� ��1

ð2Þ

As shown in Fig. 9, 2h1 and 2h2 represent, respectively, the totalthickness of the 90� and the 0� plies. E11, E22, G23 and G13 are theelastic mechanical properties of the unidirectional laminate; kR

and kL are constants which depend on the distribution of shearstress sxz along the thickness.

For a material similar to ours, by using kR = 0.3300 andkL = 0.3070, Nairn and Mendels [20] showed that the stresses cal-culated by ‘‘shear-lag’’ models are very close to finite element re-sults. Using an approach proposed by Lee and Daniel [21],Berthelot et al. [22] found a good agreement with the finite ele-ment calculations for kR ¼ 1

3 and kL ¼ 13. The study by Nairn and

Mendels shows the high efficiency and the simplicity of ‘‘shear-lag’’ models. In the present paper, we will take kR ¼ 1

3 and kL ¼ 13

to calculate the stress field.A failure criterion is necessary to predict damage evolution. In

this study, we employ an energetic approach: we assume that acrack forms when the energy release rate due to the creation ofnew crack exceeds the critical energy release rate of the laminate.The crack appears on the edge of the specimen and propagatesinstantaneously across the entire thickness and width. The studyis limited to the elastic case but takes into account the influenceof thermal stresses on the calculation of the energy release rate.The general procedure for the calculation of the energy release rateof composite systems has been presented by Nairn [23]. We applythese results to an elementary cell between two matrix cracks,obtaining an expression for the energy release rate due to the onsetof a new crack between two existing cracks (Fig. 9). We note thatthe calculation of the energy release rate follow a deterministic ap-proach since it is assumed that a new crack forms always midwaybetween two existing cracks. It is also important to note that themodel implicitly assumes that a new crack – when it forms – spansover the entire sample thickness and width. As noted in Section 2.1,this condition is satisfied experimentally for both un-aged andaged samples employed in the present study, due to the geometri-cal arrangement of the specimen.

Within the elementary cell (Fig. 9), the energy release rate canbe calculated using two different definitions. The first uses the con-cept of discrete facture mechanics [23,24] and calculates the en-ergy release rate, G, through the expression:

G ¼ �DEDA

ð3Þ

E is the total potential energy of the plate taking into account resid-ual thermal stress due to the curing process; DA is the discrete var-iation of damaged area (the area of a new crack).

In this case, the expression of energy release rate associatedwith the apparition of new crack in the middle of two existingcracks can be written as a function of the applied stress, r, andof the crack density, d ¼ 1

2L, see Fig. 9:

Gðr; dÞ ¼ GmaxðrÞ � fdðdÞ ð4Þ

With:

GmaxðrÞ ¼1a

E22

Ex

1E11ð1þ h12Þ r� 1

1þ h12E11Da21DT

� �2

ð5Þ

118 D.-Q. Vu et al. / Composites: Part A 44 (2013) 114–121

fdðdÞ ¼ 2 tanha

4d

� �� tanh

a2d

� �ð6Þ

a is calculated by (Eq. (2)), Ex ¼ E11þh12E221þh12

,h12 ¼ h1h2

,Da21 ¼ a2 � a1, DT

is the temperature differential between the curing temperature(210 �C in our case) and room temperature (20 �C).

The second definition uses the notions of classical fracturemechanics, for which the expression of the energy release rateassociated with the appearance of a new crack between two exist-ing cracks is:

G ¼ � @

@A½E� ð7Þ

Eq. (7) gives an expression which is similar to Eq. (4) with a differ-ent fd(d):

fdðdÞ ¼ tanha

2d

� �� a

2d1� tanh2 a

2d

� �h ið8Þ

The two expressions, Eqs. (6) and (8), are slightly different. Theexperimental results do not help finally deciding in favor of one oranother. However, the last expression, Eq. (8), is employed in ourstudy.

Since the thickness of the thermo-oxidized/damaged layer is ofthe order of few micrometers, its impact on the elastic propertiesof the ply is negligible: therefore Eq. (5) is calculated by employingthe elastic properties of the pristine ply.

4. Results and discussions

In order to introduce the issue let us first discuss the followingexperimental observation. Fig. 10 presents microscopy observa-tions of a [452/�454/+452/010/9010]S composite sample before con-ditioning (un-aged, Fig. 10a), after an aging test for 48 h at 150 �Cunder 5 bars oxygen (O2) (Fig. 10b) and nitrogen (N2) (Fig. 10c).In the un-aged sample, three transverse matrix cracks are visibleon the 90� layer. These cracks are related, on one hand, to the man-ufacturing process, in particular to the cooling step from post-curetemperature (210 �C) to room temperature (�20 �C) and on the

Fig. 10. Microscopy observation of the surface of a quasi-isotropic compositesample: (a) un-aged; (b) aged under 5 bars O2 48 h; (c) aged under 5 bars N2 48 h.

other hand, to the sample preparation step (sample polishing, forexample). The 5 bar O2 aged sample presents additional transversecracks on the 90� layer which are absent in the 5 bar N2 aged sam-ple. The source of these new cracks is related to thermal stress in-duced by the cooling step from aging temperature (150 �C) to roomtemperature but also to the thermo-oxidation induced degradationinduced under O2 environment at 150 �C, which is absent in a neu-tral N2 environment.

4.1. Evaluation of critical energy release rate

Fig. 11 shows the evolution of the matrix crack density as afunction of the applied stress measured on four different samples:un-aged, aged at 150 �C under 1.7 bars oxygen for 24 h, 48 h and96 h, respectively. Two test series were carried out to ensure thereproducibility of the experimental results. During the test, it isverified experimentally – through visual inspection and RX pat-terns – that the 90� matrix microcracks span over the entire sam-ple thickness and width, for both un-aged and aged samples.

Fig. 11 shows that there is a clear gap between the behavior ofthe un-aged samples and that of aged samples. For a given appliedstress, the aged specimens have a higher crack density (for in-stance, around 25% for an applied stress of 600 MPa) comparedto un-aged specimens. However, it is shown that the crackingkinetics is similar for all the aged samples (24 h, 48 h and 96 h).We deduce that the aged samples have all the same matrix crack-ing behavior, in spite of their different aging time.

Fig. 11 shows the embrittlement of thermo-oxidation aged sam-ples with respect to matrix microcracking. As mentioned in theintroduction section, this embrittlement could be related to twodistinct effects: thermo-oxidation induced micro damage – in par-ticular fiber/matrix debonding – prior to mechanical loading,depending on aging time, and thermo-oxidation induced materialchanges, particularly toughness decrease, close to the exposed sur-faces, over a thermo-oxidized layer whose thickness is almostindependent of aging time. The relative importance of these twoscenarios on the observed embrittlement will be investigated inmore detail in Section 4.2. Through comparison between theexperimental data and the microcracking model, the next subsec-tions are dedicated to the identification of the critical values ofthe energy release rate, for both un-aged and aged samples.

4.1.1. Failure criterion with Gc constant (G(d) = Gc)From the experimental data, the critical energy release rate, Gc,

of the samples can be evaluated using a failure criterion of the typeG = Gc. Fig. 12 shows the results of numerical calculations carried

0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000 1200Stress (Mpa)

Cra

ck d

ensi

ty (

1/cm

)

0h-1 24h-1 48h-1

0h-2 24h-2 48h-2

Un-Aged Aged 96h

un-aged

aged (24h, 48h et 96h)

Fig. 11. Evolution of matrix crack density as a function of the applied stress in [0/903/0] laminates: un-aged (0 h), and aged under 1.7 bars oxygen at 150 �C (24 h,48 h and 96 h) samples. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000 1200Stress (Mpa)

Cra

ck d

ensi

ty (

1/cm

)

un-agedaged (24h,48h,96h)

un-aged

aged (24h,48h,96h)

))d3.2exp(1(196237)d(Gc −−+=

))d3.2exp(1(122209)d(Gc −−+=

Fig. 13. Experimental–numerical evolutions of crack density in function of appliedstress (Gc varying with crack density according to (Eq. (10))). (For interpretation ofthe references to color in this figure legend, the reader is referred to the web versionof this article.)

D.-Q. Vu et al. / Composites: Part A 44 (2013) 114–121 119

out with different values of Gc (assumed constant with crack den-sity) and a comparison with the experimental results.

We identify a value of Gc = 480 J/m2 for un-aged specimens andGc = 350 J/m2 for aged (24 h, 48 h and 96 h) specimens: aging at150 �C under 1.7 bars oxygen (24 h, 48 h and 96 h) leads to a signif-icant reduction (about 27%) of the sample critical energy releaserate. This reduction is not affected by the aging time and is possiblydue to the material embrittlement induced by thermo-oxidationon the external surface of aged samples, almost independent ofthe aging time.

4.1.2. Failure criterion with Gc depending on crack density(G(d) = Gc(d))

We can note that, using a failure criterion with constant Gc, thegood agreement between experimental measurements and numer-ical calculations is obtained only for high crack density values. Hanet al. [25] and Hahn et al. [26] have shown an increase of the crit-ical energy release rate with increasing crack density. Someauthors [27,28] have also proposed probabilistic criteria to takeinto account this effect.

In this work, we propose a criterion of the form of the followingequation [25,26]:

Gðr;dÞ ¼ GcðdÞ ð9Þ

in which Gc(d) is the critical energy release rate as a function of thematrix crack density.A possible expression of Gc(d) is:

GcðdÞ ¼ Gmin þ Goð1� expð�RdÞÞ ð10Þ

In which Gmin is the critical energy corresponding to appearanceof first crack; G0 and R are parameters with less physical signifi-cance, to be identified. Table 2 presents the parameters of (Eq.(10)) identified for un-aged and aged (24 h, 48 h, 96 h) samples.

It can be noted that Gmin and G0 are significantly affected by theaging process (11% for Gmin and 37% for G0): R is the same for un-aged and aged samples.

Fig. 13 shows a comparison between experimental measure-ments and numerical simulations carried out by employing (Eq.

Gc= 350 (J/m2)

400 (J/m2)

480 (J/m2)

0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000 1200

Stress (Mpa)

Cra

ck d

ensi

ty (

1/cm

)

un-aged

aged (24h,48h,96h)

Fig. 12. Experimental–numerical evolution of matrix crack density as a function ofthe applied stress (Gc taken constant with crack density). (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

Table 2Parameters for Gc(d) (Eq. (10)) identified from the experimental data.

Un-aged Aged (24 h, 48 h, 96 h)

Gmin (J/m2) 237 209G0 (J/m2) 196 122R 2.3 2.3

(10)). The experimental curves are now correctly simulated. Thereis a reduction of critical energy release rate in the aged specimenscompared to un-aged specimens.

4.1.3. Failure criterion with Gc depending on crack density(G(d) = Gc(d)) (probabilistic approach)

The expression (Eq. (10)) is purely phenomenological and it isdifficult to give a proper physical signification to it. Therefore, wewill attempt to identify an expression of Gc(d) which is based ona Weibull-type probabilistic approach [29]. We always assume thata new crack appears in the middle of two pre-existing cracks.When there is a new crack, the volume available between twocracks decreases and the probability of finding a micro-defect forcreating a new crack decreases. Consequently, it takes more energyto create a new crack and the critical energy release rate, Gc, in-crease with increasing crack density. Based on a Weibull-type ap-proach, the probability of creating a crack, Pr, can be expressed as:

Table 3Weibull-type model parameters identified from the experimental data for K takenequal to 0.5.

cmin (J/m2) c0 (J/m2) K a

Un-aged 237 735 0.5 1.5Aged 209 412 0.5 1.5

0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000 1200

Stress (Mpa)

Cra

ck d

ensi

ty (

1/cm

)

Un-Aged Pre-Aged

5.1

1

0c )d)5.0lnL2((10.4209)d(G −+=

5.1

1

0c )d)5.0lnL2((35.7237)d(G −+=

Fig. 14. Experimental–numerical evolution of evolutions of crack density infunction of applied stress (Gc(d) evaluated using the probabilistic approach, (Eq.(12))). (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

thermo-oxidation induced damages at local scale

transverse crack inducedby mechanical loading

thermo-oxidationinduce dresin crack a matrix

crack crossing

the contours

of the fibers in a

zone of high Vf

a b

Fig. 15. SEM observations of replicas registered on specimens aged under 1.7 bars oxygen and then subjected to tensile test.

120 D.-Q. Vu et al. / Composites: Part A 44 (2013) 114–121

Pr ¼ 1� exp � VVo

GCðdÞ � cmin

co

� �a� �ð11Þ

where V is the available volume between two cracks; V0 is the initialvolume; cmin c0 and a are the three parameters associated with theWeibull distribution.

By using K = 1�Pr, we can deduce an explicit expression of Gc(d)in function of K, d (crack density) and the three parameters of theWeibull-type model:

GcðdÞ ¼ cmin þ c0 ð�2L0 ln KÞ:d½ �1a ð12Þ

In which, L0 is the length of specimen and 0 < K < 1.The three parameters of the Weibull-type model can be identi-

fied from experimental data (from applied stress vs. crack densitycurves). Table 3 shows the parameters identified by setting K equalto 0.5 and cmin equal to the value of critical energy release rate cor-responding to the first crack, the same as Gmin used in (Eq. (10)).

Fig. 14 shows the comparison between the experimental mea-sures the numerical simulation using the probabilistic Weibull-type approach. There is a good correlation between experimentalmeasurements and numerical simulations, for both low and highcrack density values.

Again, a reduction of the critical energy release rate (11% forcmin and 44% for c0) is measured in the aged samples comparedto un-aged samples.

4.2. Investigation about a possible link between the microscopic (fiber/matrix) and the mesoscopic (ply) scale

As mentioned in the introduction section, some research studieshave shown that thermo oxidation induces matrix shrinkage andfiber/matrix debonding at the local scale [9,11]. In fact, thermo-oxidation induced shrinkage produces internal stresses which con-tribute to the total stress and may lead to the onset of damage. Inmatrix-rich zones (low Vf) the amount of matrix shrinkage is largeand the fiber/matrix debonding sites are usually more numerous.The extent of fiber/matrix debonding increases also with increas-ing aging time. It is interesting to study whether there is a link be-tween the onset of fiber/matrix thermo-oxidation induceddebonding and the faster development of matrix cracks at theply scale for aged samples, and the related reduction of critical en-ergy release rate.

During tensile tests, the polished edges of the samples were reg-istered by means of polymer replicas allowing microscopic obser-vations of the cracked surfaces. Fig. 15 presents SEMobservations of the replicas taken on the external surface of agedsamples subjected to tensile loads.

Fig. 15a shows damage induced by thermo oxidation at the localscale (resin shrinkage, cracking and fiber/matrix debonding) prior

to any mechanical loading and a matrix microcrack at the ply scalecreated by the tensile load. We can observe that the ply crack is notassociated with thermo-oxidation induced pre-damaged areas.Fig. 15b (tilted 45�) shows a matrix crack crossing the contoursof the fibers in a fiber-rich zone (high Vf) while the extent of ther-mo-oxidation induced damage is important in matrix-rich zones.This result shows that there is no clear link between thermo-oxida-tion induced damage at the local scale and matrix microcracking atthe ply scale. This tend to enforce the hypothesis that the reductionof critical energy release rate in aged samples is mainly due tothermo-oxidation induced resin toughness decrease, almost inde-pendent of aging time.

5. Conclusions

In this work, the effects of thermo oxidation on the matrixcracking of cross-ply [0/90]S laminates were studied. The resultsshow a significant reduction of matrix cracking critical energy re-lease rate of aged specimens compared to the un-aged ones. Thecracking kinetics is identical for the aged specimens. The reductionof the critical energy release rate in aged specimens (embrittle-ment) is related to the material degradation (mainly resin tough-ness decrease) close to the surfaces exposed to the thermooxidative environment, having an effect on the onset and theinstantaneous propagation of the matrix microcracking due to ten-sile loading. On the other hand, SEM observations on replicas showthat there is no direct and clear link between thermo-oxidation in-duced damage at fiber/matrix scale prior to mechanical loadingand matrix microcraking at the ply scale.

Acknowledgement

The authors would like to thank Dr. Jacques Cinquin (EADS IW)for providing the composite material used in this work.

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