Influence of free edge intralaminar stresses on damage process in CFRP laminates under thermal cycling conditions

COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 66 (2006) 1354–1365 www.elsevier.com/locate/compscitech

Influence of free edge intralaminar stresses on damage process in CFRP laminates under thermal cycling conditions M.C. Lafarie-Frenot *, N.Q. Ho Laboratoire de Me´canique et de Physique des Mate´riaux, Umr CNRS No. 6617, Ensma, Teleport 2, 1 Av. Cle´ment Ader, B.P. 40109, 86961 Futuroscope, Chasseneuil Cedex, France Received 7 February 2005; received in revised form 31 August 2005; accepted 12 September 2005 Available online 3 November 2005

Abstract The purpose of this study is to understand the damage mechanisms of CFRP laminate subjected to repeated thermo-mechanical loads. Thermal cycling tests in oxygen show that the oxidation at high temperature associated with the ‘‘fatigue’’ phenomenon due to the cyclic thermal stresses lead to many matrix cracks. By means of optical microscopy and X-ray technique, some observations permit to characterize and quantify the initiation, build-up and propagation kinetics of these transverse cracks. A thermo-elastic calculation of the initial intralaminar transverse thermal stresses has been carried out in 3D finite-element models of the undamaged specimens. The comparison of experimental data and FEM results highlights a significant ‘‘free edge effect’’ on transverse matrix cracking onset, depending on both the direction of the edge referred to the fibres and the position of the layer in the lay-up. From this observation, a scenario of damage development dealing with a coupling between the local transverse stresses and the oxidation process is proposed.  2005 Elsevier Ltd. All rights reserved. Keywords: B. Durability; B. Matrix cracking; B. Environmental degradation; C. Laminates

1. Introduction Within the framework of the French ‘‘Aeronautical Supersonic Research’’ program supported by the Ministry of Research, the Ministry of Equipment, of Transport and Housing, one project concerned the ‘‘durability of CFRP laminates subjected to repeated thermo-mechanical loading’’. The work presented in this paper is part of the collaborative research conducted by three laboratories which have approached this project according to their field of competences: the LTVP (ENSAM Paris) was charged with the ageing and oxidation kinetics modelling of carbon-fibres epoxy–matrix unidirectional composites, the damage mechanisms of laminates submitted to thermal cycling in more or less oxidative atmospheres were identified and characterized in our laboratory (LMPM – ENSMA *

Corresponding author. Tel.: +33 5 4949 8229; fax: +33 5 4949 8238. E-mail address: [email protected] (M.C. Lafarie-Frenot).

0266-3538/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.09.006

Poitiers), and the LMT-ENS Cachan took charge of the damage modelling of the laminates under such thermomechanical conditions. In this context, this paper is dealing with the damage processes of CFRP laminates subjected to thermal cycling in an oxidative atmosphere and focuses on the free edge effects on the damage development. During a flight presenting subsonic and supersonic phases, the airplane cell is subjected to temperature variations. As far as CFRP laminates are concerned, these temperature variations may induce high stress variations due to the anisotropic thermo-mechanical behaviour of the material. Because one flight corresponds to one thermal cycle and because numerous flights are planned, in such conditions, the constitutive plies of a CFRP laminate would be subjected to a ‘‘thermal fatigue’’ loading. Moreover, in the supersonic phase of flight, the temperature experienced by the cell material is sufficiently high to activate a possible process of polymer matrix ageing, in particular by oxidation.

M.C. Lafarie-Frenot, N.Q. Ho / Composites Science and Technology 66 (2006) 1354–1365

Damage mechanisms in CFRP laminates have been widely studied for many years [1–20]. In laminates subjected to uniaxial fatigue loading, matrix cracking is usually the first damage observed and acts as nucleus for further damage types (delamination, longitudinal splitting) [12–15]. Initiated at free edges, cracks then propagate towards the core of laminated composite plates, building up a non-homogenous damage distribution across the specimenÕs width [6,11]. During thermal cycling tests, thermal effects and local stresses due to anisotropic characteristics of composite laminates have been investigated [5,18–20]. Lafarie-Frenot and Rouquie [5] highlighted the accelerating effect of an oxidative atmosphere: the higher the oxygen concentration, the more significant the acceleration of the cracking development. Rouquie et al. [20] pointed out the influence of layer orientation on the transverse cracking damage of CFRP laminates. Although thermo-elastic calculations give identical stress values in the interior of three different lay-ups submitted to a thermal loading, the damage observed on the polished edges of the samples highly depends on the stacking sequence. From such observations, it appears that free edge effects become essential elements for analyzing the damage mechanisms in composite CFRP laminates subjected to either mechanical or thermal fatigue loading. Stress perturbations at free edges of composite laminates may induce initial failure events and accelerate damage growth, eventually reducing ultimate strength in tensile tests as well as in thermal loading ones. The influence of edge effects in composite laminates has been investigated experimentally and/or analytically [21–39]. Many studies have focused on free edges effects in tensile loading. In [21], the tensile strengths of 12 composite layups were measured. A novel approach to account for the edge influence on the ultimate strength value was also proposed. Chan and Wang [22] confirmed the fact that, in uniaxial quasi-static tension loading, the nature of the 90 ply used as the core layer in cross-plied and angle-plied laminates has a definite effect on matrix cracking and onset of delamination in the laminate. It is well known that the initiation and growth of transverse cracks depend on the intrinsic properties of the 90 ply in the laminate. For the delamination problem at the free edge, the interlaminar stresses can be relieved by reducing the difference in stiffness of adjacent layers in the direction normal to the free edge. A soft 90 ply core layer minimizes the mismatch in properties along the transverse direction between the core layer and the load-bearing layer. As a result, it provides a higher laminate performance under the intended loading. Using numerical techniques, some problems concerning the free edge stress distribution in composite laminates under uniaxial tension were approached [23,24]. On the other hand, few investigations have dealt with free edge influence in thermal loading conditions [25,26]. Recently, the free edge stresses in general cross-ply composite laminates under tensile and thermal loading have been studied by Tahani and Nosier [26]. The formulation was restricted to linear elastic material behaviour, small

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strains and displacements, and to the case of a known temperature field. It was shown that the edge effect problem in such laminates is actually a quasi-three-dimensional problem and its stress analysis can be restricted to a generic two-dimensional cross-section of the laminates. Edge effects in laminated composites may result in delamination and transverse cracking. Various methods for determining the free edge stresses are documented in the literature. Using numerical methods for the analysis of free edge stresses in composite laminates, authors employed finite-difference techniques [27,28], finite-element modelling [24,29] or boundary element solutions [23]. On the other hand, many analytical methods have been employed to examine the free edge effects problem. For example, a layerwise theory was used by Tahani and Nosier [26] to investigate analytically the interlaminar stresses near the free edges of general cross-ply composite laminates. Cho and Kim [25] proposed an iterative method to analyze free edge interlaminar stresses in composites subjected to tension, bending, twisting and/or thermal loads. Matrix cracking and edge delamination in composites laminates have been studied widely. According to personal interests, these two types of damage were often studied separately by researchers. Dealing with the coupling between the two types of damage, Xu [30] showed that there exists an interaction between matrix cracking and edge delamination. Matrix cracking may lead to local delamination; delamination may induce matrix cracking. Another study by analytical technique for this type of coupling was approached in [31]. Rebiere et al. [32] proposed an energetic criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates. Recently, Ladeveze et al. [33,34] have proposed a bridge between the descriptions on the micro- and mesoscales of damaged laminated composites, dealing with the in-plane as well as the out-of-plane behaviour of the laminate. The out-of-plane interlaminar stress distribution at free edges in composite laminates has been studied for numerous years. Indeed, laminated composites subjected to tension develop interlaminar stress concentrations near the free edge region. Such stresses due to the anisotropic behaviour of adjacent plies induce several damage mechanisms in composite laminates. There are two major failure modes at a free edge: the first one, opening mode delamination caused by excessive interlaminar normal stress rzz and the second one, shear-dominated interlaminar failure by interlaminar shear stresses rxz and ryz. The former failure mode is a stable crack growth mode; i.e., the delamination crack extends as loading increases. In contrast, the latter mode often occurs in a sudden and catastrophic manner [35]. In order to increase the mechanical strength of a laminate, efforts in laminate design have been directed toward suppressing or delaying delamination by controlling the composite fracture toughness and reducing free edge outof-plane interlaminar stresses. A number of methods for suppressing free edge failure in laminated composites in tension have been proposed. Sun and Chu [36] used narrow

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and shallow notches along the straight edges of the coupon specimen in order to disrupt the load path along the free edges. Chan et al. [37] used adhesive films placed along interfaces in order to increase interfacial toughness in laminates which are prone to opening mode delamination. We have just mentioned some methods for reducing free edge effects by edge modification, but some investigators have suggested other methods dealing with fibre modification. A technique to reduce the free edge interlaminar stresses by varying the fibre volume fraction near the free edge was presented by Shiau and Chue [38]. Finally, Suvorov and Dvorak [39] used optimized prestressed fibres for reducing free edge stresses in composite laminates. In summary, this literature survey shows that many authors have studied the delamination process in composite laminates subjected to thermal and/or mechanical loading. As a consequence, the calculations near a free edge of a laminate generally concerned only the out-of-plane interlaminar stress–strain fields. The results presented here relate to the matrix cracking damage process which is the first one observed in CFRP laminates subjected to thermal cycling [20]. Moreover, it has been shown previously that, during thermal cycling, matrix cracks initiate on free edges of laminate samples. Therefore, it appears necessary to evaluate the free edge effects on in-plane intralaminar transverse stresses which are mainly responsible for transverse matrix crack onset. By means of experimental and numerical tools, the present study permits a better understanding of the damage mechanisms in composite laminates subjected to thermal cycling loading in a more or less oxidative environment. 2. Material and experimental conditions All the specimens used in the present study have been cut from composite plates which were provided and processed by CCR-EADS (Corporate Research Centre – France – of the European Aeronautic Defence and Space Company). Laminate coupons of stacking sequence [03/903]S have been used. The composite material made of an epoxy/amine matrix (ref 977-2) is reinforced by continuous carbon fibres (ref type IM7). The plates have been elaborated in an autoclave, according to a specific polymerization cycle, optimized for

the needs of a supersonic use which requires a stable material without any effect of overheating or evolution of properties. This polymerization cycle consisted of a 3 h long gelation phase at 150 C followed by a polymerization phase at 180 C, 2 h long with a 7 bar pressure. A post cure cycle, 2 h long at 210 C, was also added in order to improve the characteristics of the material. The plateÕs thickness is equal to 1.68 mm. Rectangular and octagonal specimens were cut from this plate according to the directions indicated in Fig. 1. We have carried out two thermal cycling tests in two atmospheres: neutral (pure dry nitrogen) and oxidative (pure dry oxygen). For the two tests, small rectangular specimens of dimensions 35 · 25 · 1.68 mm3 were used. Especially, for the test performed in oxygen, we also used larger rectangular specimens whose dimensions were 50 · 70 · 1.68 mm3 and octagonal samples which had the same surface as that of the large rectangular ones. Let us insist on the fact that when the octagonal specimenÕs edges are observed, apparent stacking sequence differs according to the edge considered. Three successive edges of the octagon would, respectively, correspond to ‘‘stacking sequences’’ [03/903]S, [+453/453]S and [903/03]S (cf. Fig. 1). This classification only concerns the edges of the specimens, because the lay-up is the same (two external 3 ply thick layers, crossed with one central 6 ply thick layer), regardless of the sample geometry. To compare the edge stress values and observations presented in the following sections, it will be more relevant to characterize the edge by the angle which exists between the cutting plane and the fibre direction of the layer. Depending on the specimen edge considered, this angle is equal to 0, 90, and ±45, which leads to the above-mentioned ‘‘edge stacking sequences’’. The polished and dried specimens are placed into a specific thermal cycling device which has been developed to control both the environment and the temperature during tests. In order that all the faces undergo the same effects due to temperature and gas flow, the specimens are placed vertically on racks. These racks are then put within an enclosure of low volume and small thermal inertia. An overpressure of 20 mbar is imposed in this enclosure in order to make the gas circulate. Finally, this enclosure is placed inside a thermal equipment allowing controlled temperature variations to be prescribed.

Fig. 1. Cutting diagram of the specimens and aspect of the edges according to their orientation.

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Two thermal cycling tests either in pure dry nitrogen or in pure dry oxygen consisted of 1000 triangular cycles with constant cooling and heating rates of 4 C/min, the maximum and minimum temperatures being, respectively, of 150 and 50 C. The maximum temperature, 150 C, is approximately 55 C lower than the glass transition temperature of the composite material. During tests, some specimens have been removed regularly from the thermal cycling oven to observe damage development: on free edges by optical microscopy and inside the specimens by means of penetrant enhanced X-radiography. 3. Thermal loading (50/150 C) simulation Due to the mismatch in values of the coefficients of thermal expansion, the temperature variation imposed during the thermal cycling tests (50/150 C) induces thermal stresses in each ply of the laminate. For our composite material, the coefficients of thermal expansion of the unidirectional ply in the longitudinal and transverse directions are: al = 0.23 · 106 C1, at = 30 · 106 C1, respectively, and the stress-free temperature has been taken equal to the polymerization one, i.e. 180 C. We will consider here the case of a constant temperature distribution in our composite specimens. Transverse thermal ply tresses (r22) in the core of a ply can be estimated by a thermoelastic calculation of an infinite plate of the laminate, which gives an order of magnitude of the stresses present in each ply for a given temperature. In the case of a thermal cycling between 50 and 150 C, these calculations lead to transverse thermal stress values which lie between 7 and 53 MPa, and which are identical in the different layers of the [03/903]S stacking sequence. A two-dimensional simulation using the finite-element method implemented in the ABAQUS software for estimating the transverse thermal stresses gives the same results. In Fig. 2, these transverse thermal stresses (r22) are put in correspondence with the temperature variation: the cyclic temperature variation induces in each ply of the laminate cyclic transverse stress variations with a 100 min period, which is equivalent to a

T˚C

sort of thermally driven ‘‘fatigue’’ with the temperature variation DT analogous to the change in stress. 3.1. Free edge stress calculation by FEM 3D In Fig. 2, it is shown that at the lowest temperature of 50 C, the stresses due to the restrained differential expansions are the most important. Then, in order to state the effect of the free edge on the in-plane transverse thermal stress distribution, a three-dimensional modelling of the octagonal specimen subjected to a ‘‘thermal loading’’ of 50 C has been carried out by using the finite-element method. Because of the problem symmetries, we have modelled only one-eighth of the specimen and replaced the symmetric planes by relevant boundary conditions. With regard to the grid, C3D20R type element was used and we created a finer grid in the areas beside the edges where the free edge effects may appear when the specimen undergoes a ‘‘thermal load’’ (cf. Fig. 3). Moreover, the model thickness corresponds to the height of 12 C3D20R elements. In Fig. 4, the calculated values of the transverse thermal stresses r22 are plotted against the ratio of the distance from the edge to the plate thickness. First of all, it is important to note that, close to the edge, the values of the inplane intralaminar transverse thermal stress r22 depend on both the location of the layer in the lay-up (internal or external) and on the cutting plane orientation referred to the fibre direction (90 or ±45). This figure points out some important free edge effects on the in-plane transverse ply stress distribution due to the thermal loading. It is shown that these effects extend to a distance which is approximately 1.5 times the plate thickness. The threedimensional calculation highlights over-stresses at the free edges when the plane of the edge is perpendicular to the fibre direction. This overstress is close to 66 MPa in the central 6 ply thick layer and to 56 MPa in the two external 3 ply thick layers (Fig. 4). Conversely, if the edges are cut at ±45 with respect to the fibres, regardless of the layer position in the stacking (internal or external), on the edges we find a value of transverse stress much lower than that far away from the edges (23 MPa against 53 MPa) (Fig. 4).

150˚ C time -5 C -50˚

σ22

53 MP a

7 MPa

time

100 mins

Fig. 2. Schematic representation of the prescribed thermal cycles and corresponding transverse ply stresses in each layer of the laminate.

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Fig. 3. Modelling of the octagonal specimen in ABAQUS.

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Transverse stress (MPa)

70 60 50 40 internal layer; edge perpendicular to fibers external layer; edge perpendicular to fibers

30

internal and external layer; edge at+/-45˚ to fibers 20 0

1

2

3

4

5

6

7

8

9

10

Distance from edge over plate thickness

Fig. 4. Results of FEM simulations, transverse ply-stresses at 50 C, in the different plies of an undamaged octagonal specimen.

4. Experimental results Thermal cycling tests induce various types of damages, depending to a certain extent on the orientation and the thickness of the layers in the lay-up, but essentially on the more or less oxidative environment of the specimen. The main features of the different sorts of damage observed in thermal cycling tests have been described in detail in a previous paper [5]. In the series of thermal cycling tests presented in this paper, we found the same differences in damage mechanisms and kinetics of development according to the atmosphere of the test: • In oxygen, some matrix shrinkage, which appears as a difference of level between matrix and fibres, was already observed on the edges of samples which have experienced 100 thermal cycles. On the contrary, the edges of coupons tested in nitrogen remain as flat as they were just after the polishing, up to the end of the 1000 thermal cycles. • The transverse matrix cracking process initiated very earlier during test performed in oxygen, compared to that carried out in nitrogen: the first transverse cracks were observed after 200 thermal cycles in oxygen and only after 600 cycles in nitrogen (cf. Fig. 5). • As the number of thermal cycles increased, transverse matrix cracks increased steadily in number and length, but the kinetics of their development were observed much faster in oxygen than in nitrogen. In this section, we describe the characteristics of the transverse cracks and of their development according to the specimen geometry and to the test atmosphere, neutral or oxidative. To characterize the transverse crack development, two different techniques were used: optical microscopy to count the number of these cracks and to measure their opening on the polished edges of the specimens and X-radiography for measuring their length along the ply width. X-ray technique enables the cracks to be observed inside the core of the coupons but, in order to make the cracks more visible on X-radiographs, a zinc iodide solu-

Fig. 5. (50/150 C), microscopic observations of the edges; examples of transverse matrix cracks: (a) 200 cycles in oxygen; (b) 600 cycles in nitrogen.

tion is used to enhance the contrast between the cracks and the composite material. In these conditions, the sensitivity of the radiography method has been evaluated at around 0.6 mm. In the following, we will take into account only the cracks crossing the entire layer thickness and discriminate them according to their location in the lay-up: either in the 6 ply internal layer or in the two external layers of 3 plies. 4.1. Thermal cycling test in nitrogen Two batches of small rectangular samples, differing by the orientation of their cutting out from the [03/903]S laminated plate, have been subjected to 1000 thermal cycles (50/150 C) in nitrogen. This thermal cycling test is performed in a neutral atmosphere in order to put in light the damaging effect of the cyclic thermal stresses only. The comparison with the same test performed in oxygen will reveal the effect of oxidation on the damage processes. This will be shown in the next section. During this test in nitrogen, no crack has been observed before 600 cycles, neither on the edge by optical microscopic observations nor elsewhere on X-radiographs. During the last 400 cycles of the test, few transverse cracks appear and in Fig. 6, we present X-radiographs of specimens cut in two different ways which have experienced 1000 cycles in nitrogen. In these pictures, the vertical and horizontal lines correspond, respectively, to transverse cracks in the internal and external layers.

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Fig. 6. Examples of X-ray pictures of rectangular specimens after 1000 thermal cycles (50/150 C) in nitrogen.

One can see in Fig. 6 that the damage level of the specimens, even after 1000 thermal cycles is very low. It is the reason why the reader of this paper must consider the following comments and results as general trends which have been confirmed on other specimens but with a large scatter concerning the values of crack number and length. As a consequence the damage patterns cannot be quantitatively described with great confidence because of the too few data. In Fig. 6, the X-ray pictures show that the damage states induced by the thermal fatigue depend on the orientation of the cutting out – either 90 or 45 with respect to the fibre direction. Indeed, in the external layers of both specimens, one can observe some long transverse cracks whereas some few short cracks are only observed in the central layer of the sample cut orthogonally to the fibres. Not a single crack has been seen in the central layer of the specimen cut with a ±45 angle from the fibre direction! This absence of matrix crack in that configuration has been confirmed by both microscopic observations of the edges and X-radiographs. For the different rectangular specimens which have experienced 1000 thermal cycles (50/150 C) in nitrogen, the values of the cracked surface areas have been estimated and presented in Table 1. As for the internal layers, only the one whose edges are perpendicular to the fibres was damaged. Concerning the external layers, the cracked surface area values are found higher and nearly independent of the orientation of the edges. However, let us insist on the very important dispersion over the samples considered, leading to a great scatter in measurements, not shown in this table. However, these results obtained at the end of the thermal cycling test in nitrogen put in light some free edge effects on the damage development.

Table 1 Small rectangular specimens, cracked surface areas measured in the internal and external layers, according to the orientation of the edge plane, 1000 cycles (50/150 C); nitrogen Layer

Edges 90 to fibres (mm2)

Edges ±45 to fibres (mm2)

Internal External

24.8 55.2

0 54.8

4.2. Thermal cycling test in oxygen In this section which concerns the thermal cycling tests in oxygen, most of experimental results have been obtained with the large specimens (rectangular and octagonal). However, in order to compare them with the results obtained and presented above, in nitrogen, the small rectangular ones have been used only for X-ray observations and measurements of cracked surface areas. 4.2.1. Opening of transverse cracks In Fig. 7, examples of transverse matrix cracks observed on the polished edges after 1000 cycles (50/150 C) in oxygen are presented. In the case of edges perpendicular to fibres (Fig. 7(a) and (b)), matrix cracks have an overall direction which is perpendicular to the interfaces between the crossed layers. The crack opening appears the largest in the centre of the internal layer (cf. Fig. 7(a)) and at the margins of the external layers (cf. Fig. 7(b)). Whereas on the edges cut at ±45 to fibres, matrix cracking was detected only in the external layers. Compared to the cracks observed on the edges perpendicular to fibres, those appear slightly slanted, much less opened and, especially, more sinuous (cf. Fig. 7(c)).

Fig. 7. Microscopic observations of transverse matrix cracks on specimen edges according to the orientation of the edge and the location of the layer in the lay-up; 1000 cycles (50/150 C); oxygen: (a) edge at 90 to fibres, internal; (b) edge at 90 to fibres, external; (c) edge at 45 to fibres, external.

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oxygen. The following remarks are valid for Figs. 8 and 9 on which transverse cracks edge densities are presented according to the number of thermal cycles: for each specimen, cracks are counted on the entire length of the free edge observed. Densities are expressed in cracks per cm and per layer. As there are two external layers with the same orientation and thickness in each specimen, crack densities of these layers are calculated as the average of the densities measured in each of both external layers. Moreover, each value is the average of the numbers of cracks per cm counted on the free edges of three identical specimens. In Fig. 8, the edge crack densities of the six unidirectional ply internal layer are plotted against the number of cycles. The values reported in this figure have been obtained on the different edges of the rectangular and octagonal specimens. On the one hand, we note in this figure that not a single transverse crack was detected on the edges whose cut is at ±45 to fibres: this configuration was found either in the rectangular specimens cut in directions of ±45 (2) or in the octagonal ones (2 0 ). On the other hand, from 200 cycles on, we observed some cracks on the edges perpendicular to fibres in rectangular (1) and octagonal (1 0 ) samples. Thereafter, the crack density increases gradually between 200 cycles and 600 cycles and then, continues to increase slightly up to a saturation state of approximately 8 cracks per cm at 1000 cycles. Crack densities counted on the edges of the external layers are shown in Fig. 9. First of all, it must be noted that

The crack opening values of some transverse cracks have been measured by using an optical microscope. For each crack, the measurement has been carried out at seven different sites of the most opened part. As these measurements have been done on five transverse cracks, each crack opening value corresponds therefore to the average of 35 measurements. In Table 2, the crack opening values measured on the edges of specimens which have experienced 1000 cycles thermal in oxygen are collected. In this table, the crack opening values are classified according to the location of the layer concerned and to the orientation of the edge. It is shown in Table 2 that on the edges whose cut is perpendicular to fibres, the cracks in the internal layer (18 lm) are more widely opened than those in the external layers (13 lm). On the other hand, the cracks observed on the edges oriented at 45 with respect to the fibres are much less opened (65 lm), and even closed in places. 4.2.2. Edge crack density In this section, we are going to quantify the transverse crack number evolution during the thermal cycling test in

Table 2 Opening of cracks after 1000 cycles (50/150 C) in oxygen Position

Opening (lm)

90 to fibres, internal 90 to fibres, external 45 to fibres, external

18 ± 0.6 13 ± 0.5 65

10 1

Cracks/cm

8

1'

2

1’

2'

90˚ cut

1

6

INTERNAL

4 2’

2

2 2

45˚ cut

0 0

400

200

600

800

1000

1200

cycles Fig. 8. Internal layer, density of cracks on free edges versus number of (50/150 C) thermal cycles; oxygen.

10 1

Cracks/cm

8

1'

2

2'

1’ 1

6 EXTERNAL

4

90˚ cut

2’ 2

45˚ cut

2 2

0 0

200

400

600 cycles

800

1000

1200

Fig. 9. External layers, density of cracks on free edges versus number of (50/150 C) thermal cycles; oxygen.

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cracks have been found in external layers regardless of their edge orientation. However, the crack densities have been found systematically lower on the edges cut at ±45 than on those perpendicular to fibres. In both cases, the growth curves are S-shaped and it seems that the saturation has not yet been reached after 1000 cycles. Compared to the internal layer, the crack densities values measured in external layers are lower and this is right whatever the number of cycles. For example at 1000 cycles, we observe 6 cracks per cm in the external layers (Fig. 9) against 8 cracks per cm in the internal layer (Fig. 8). In both Figs. 8 and 9, we note that for a given cutting orientation, the edge crack density values are very close whatever the specimen geometry. Therefore, the kinetics of the increase in crack number on the edges does not depend on the specimen geometry but it definitely depends on the cutting direction referred to fibres as well as the layer position (internal or external). Indeed, these observations show that on the edges perpendicular to fibres, matrix crack build-up is much earlier and much faster than that on the edges cut at ±45. Moreover, when observing the edges perpendicular to fibres, the internal layer appears more cracked than the external layers, while for the edges whose cut is at ±45 to fibres, the opposite prevails. 4.2.3. Observations by X-radiography In Fig. 10, we present X-radiographs of small rectangular specimens cut in two different ways and which have experienced 1000 cycles in oxygen. The vertical and horizontal lines correspond, respectively, to transverse cracks in the internal and external layers. Cracked surface areas in two small rectangular specimens have been estimated and gathered in Table 3. In accordance with the microscopic edge observations, we note in Fig. 10 that no crack is visible in the internal layer with edges cut at 45 to fibres. For external layers, there is a little bit of difference in cracked surface areas (271.1 mm2 against 217.3 mm2) and it seems that the cracked area depends on the direction of edges with respect to fibres. From data in Tables 1 and 3, we can compare the damage levels in terms of cracked surface area according to the test atmosphere. In Fig. 11, the cracked surface area values are represented as functions of the layer position and the cutting direction with respect to fibres. The significant dif-

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Table 3 Small rectangular specimens, cracked surface areas measured in the internal and external layers, according to the orientation of the edge plane, 1000 cycles (50/150 C); oxygen Layer

Edges at 90 to fibres (mm2)

Edges at ±45 to fibres (mm2)

Internal External

256.2 271.1

0 217.3

ferences in cracked surfaces measured in specimens tested either in nitrogen or in oxygen highlight the role of oxidation in damage enhancement. In Fig. 12, some X-radiographs of large rectangular and octagonal specimens which have experienced 1000 thermal cycles [50/150 C] in oxygen are presented. They enable us to visualize and compare the damage state in each layer of the samples of different geometries at the end of the test. As in Figs. 6 and 10, in Fig. 12, the horizontal black lines correspond to cracks present in the two external layers of each specimen, whereas vertical lines correspond to cracks in the internal layer of the coupon. These X-ray pictures confirm that the damage state of the external layers and that of the internal layer are very different, regardless of the specimen geometry. Moreover, we note that in the octagonal specimen we can recover the damage patterns of both rectangular samples. Indeed, according to the layer position (internal or external) and to the direction of the edges with respect to fibres (90 or ±45), the matrix crack distribution observed

Fig. 11. Small rectangular specimens, cracked areas after 1000 cycles (50/150 C) in oxygen and nitrogen versus the layer position and the edgesÕ plane direction.

Fig. 10. X-ray pictures after 1000 cycles (50/150 C) in oxygen of small rectangular specimens.

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Fig. 12. X-ray pictures of large specimens after 1000 cycles (50/150 C) in oxygen.

in the rectangular specimens are combined in the octagonal one. As a consequence, the following comments and measurements which will concern the octagonal samples would be very similar for the rectangular geometry. In Fig. 12, the X-ray picture of the octagonal specimen obviously shows that the transverse crack distribution is very inhomogeneous in the internal layer, while it seems much more uniform in the external layers. To analyze quantitatively these differences, we have counted the cracks at certain distances from the edges, according to horizontal lines for the internal layer (di) or to vertical lines for the

external layers (de) (cf. Fig. 13). Then, these measurements have been discriminated according to zones whose edge is perpendicular to fibres ( ) or oriented at ±45 to fibres ( ). Finally, the densities expressed in cracks per cm and per layer were deduced for each distance considered and are presented in Fig. 14. In Fig. 14, crack densities are presented as functions of the relative distance from the centre of the octagonal specimen, 0 and 1 corresponding to the centre and to the edges of the specimen, respectively. It can be seen in Fig. 14 that, in the external layers ( in Fig. 14), transverse crack distributions are quite uniform; however, more cracks are observed in the region whose edge is perpendicular to fibres ( , 6 cracks per cm) than in the region whose edge is at ±45 to fibres ( , 4 cracks per cm). It must be noted that these values are identical or very close to those measured in small and large rectangular coupons. On the other hand, it can be noted that the internal layer is damaged only in the median part of the specimen whose edge is perpendicular to fibres ( ). Indeed, it appeared clearly in the X-ray picture of the octagonal specimen shown in Fig. 12 that in the internal layer, there is not a single crack in the region whose edge is cut at ±45 to fibres ( )! In the median part, we observe a very important gradient of crack distribution between the edges and the centre of the specimen, no crack reaching the centre of the specimen ( ). The crack density increases in a regular way when the edge is approached up to a value of about 7 cracks per cm.

2

0,5 length

di Internal

External de

4

3

1

4 2

0.5 length

0.5 length

Fig. 13. Method of quantitative analysis of the crack distribution in the octagonal specimen.

8

Cracks/cm

Margin

Internal, 90˚ tofibers

6

4

1

External, 90˚ to fibers

2

External, 45˚ to fibers

3

2

Center

Internal, 45˚ tofibers

4

0 0

0.2

0.4 0.6 di or de/0.5 length

0.8

1

Fig. 14. X-ray pictures, crack distributions in the octagonal specimen after 1000 (50/150 C) cycles in oxygen.

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ply stress is not sufficient to explain the extreme difference in damage level between the external and internal layers with edge oriented at ±45 to the fibre direction. Particularly, when the test was performed in oxygen, a very regular dense array of cracks is observed in the external layers, whereas there is not a single crack in the internal one. In both cases, the FEM calculations have given exactly the same intralaminar stress values (cf. Fig. 4). This last remark leads us to think that, in order to analyze the experimental results obtained in oxygen, it is not only necessary to take into account these stresses but also the location of the layers with respect to the atmosphere. With such an idea in mind, we propose a scenario dealing with the coupling between ‘‘stresses’’ and ‘‘oxidation’’ (cf. Fig. 15) with four configurations as listed below:

5. Damage scenario: coupling between ‘‘stresses and oxidation’’ On one hand, the preceding results concerning the transverse matrix cracking induced by thermal cycling show that the presence of an oxidative atmosphere (oxygen compared to nitrogen) accelerates the damage process. After 1000 thermal cycles (50/150 C) in oxygen, cross-ply laminate coupons are damaged in a regular way, whereas in nitrogen, only very few transverse cracks are observed. However, regardless of the environment, the transverse matrix cracking onset as well as its development throughout the thermal cycling tests is found to depend significantly on the ply configuration: In the internal layer:

Fig. 15(1): Internal layer, edge at 90 with respect to fibres • When the free edge is orthogonal to the fibre direction, cracks initiate on the edge and grow towards the centre of the laminate. • When the free edge orientation is equal to ±45 with respect to the fibre direction, not a single crack is found!

• Presence of a thermal transverse overstress at the edge: the edge is a favourable site to crack initiation, the crack opening is wide, making the diffusion of oxygen in cracks easier, thus accelerating their propagation from the edge towards the core of the layer.

In the external layer: Fig. 15(2): External layers, edges at 90 with respect to fibres

• The matrix cracks spontaneously appear longer, compared to those in the inner layer, and their increase in number and length is a little faster when the free edge is orthogonal to the fibre direction.

• Presence of a smaller thermal transverse overstress at the edges but especially presence of oxygen over all the external surfaces: initiation, accumulation and growth of cracks can occur everywhere on the laminate skin, where the matrix is rapidly oxidized.

On the other hand, the calculation of the transverse ply stresses induced by a ‘‘thermal loading’’ in that cross-ply laminate, have shown significant free edge effects, which depend on both the location of the ply (internal or external) and of the edge orientation with respect to the fibre direction. These two remarks show that, on the edge, there is an obvious connection between the level of the transverse ply stresses and the onset and accumulation of matrix cracks. Nevertheless, this free edge effect on transverse

Fig. 15(3): Internal layer, edge at ±45 with respect to fibres • Presence of a thermal lower-stress at the edge: crack initiation as well as diffusion of oxygen at the edge of this layer is more difficult; in our test, no crack was observed in this configuration, even at the end of the test.

Internal layer

External layers Oxygen

2

1 Cut at 90˚˚

3

2 1

3

σ22

2 1

σ22 Oxygen

Oxygen

Oxygen

4

3 3

Cut at 45˚

3

2

2

σ22

σ22

1

1 Oxygen

Fig. 15. Scenario of damage: coupling between ‘‘stresses’’ and ‘‘oxidation’’.

Oxygen

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Fig. 15(4): External layers, edges at ±45 with respect to fibres • Presence of the same thermal lower-stress at the edge as for the inner layer but presence of oxygen over all external surfaces: cracks initiate and accumulate preferentially far away from the edge, and then rapidly cross the length of the ply, the cracking soon concerning an oxidized – degraded – polymer matrix. These observations put forwards the need of threedimensional modelling and computation. Indeed, the laminate edge modifies the degradation process through both a mechanical and a chemical influence, since the stress field as well as the oxidation process are edge-sensitive. A simplified approach for such problem is proposed by Lubineau et al. [40]. It is based on the complete 3D computation of the degradation using a hybrid modelling. Effect of environment is taken into account through a modification of the ply tenacity, which is assumed to be the alone affected parameter. At any point and at a given time, the critical values of the material tenacity are modified by fatigue and by oxidation, and transverse micro cracking develops naturally according to the static evolution law. 6. Conclusion Specimens of various geometries were cut in a carbon/ epoxy laminated plate [03/903]S. Subjected to 1000 thermal cycles (50/150 C) under nitrogen or oxygen, they were gradually damaged by transverse matrix cracks which accumulated and propagated during the test. Observations by means of microscopy and X-radiography as well as a quantitative analysis of the opening, density and distribution of the cracks were carried out. The results highlighted important free edge effects on the transverse matrix cracking of composite laminates submitted to thermal cycles which depends not only on the orientation of the edges referred to fibres, but also on the location of the layers in the lay-up. These observations were related to the initial transverse stress level on the edges which has been evaluated by a 3D FEM calculation of an undamaged specimen: the higher the transverse stress level, sooner is the matrix crack onset, and faster is the matrix crack accumulation on the edges. Moreover, when thermal cycling is performed in an oxidative atmosphere, there exists a coupling between thermal transverse stresses and oxidation which enhances the importance of the location of the layers with respect to the atmosphere. Acknowledgements The authors acknowledge the financial support of the French Research Department, the French Transport Department, and EADS (CCR Surenes, France) for supplying the composite plates and samples.

References [1] Tsotsis TK, Keller S. Aging of polymeric composite specimens for 5000 hours at elevated pressure and temperature. Compos Sci Technol 2001;61(1):75–86. [2] Lee SH, Nam JD. Thermo-oxidative stability of high performance composites under thermal cycling conditions. J Compos Mater 2001;35(5):433–54. [3] Szyszkowski W, King J. Stress concentrations due to thermal loads in composite materials. Comput Struct 1995;56(2–3):345–55. [4] Biernacki K, Szyszkowski W, Yannacopoulos S. An experimental study of large scale model composite materials under thermal fatigue. Compos Part A 1999;30(8):1027–34. [5] Lafarie-Frenot MC, Rouquie S. Influence of oxidative environments on damage in c/epoxy laminates subjected to thermal cycling. Compos Sci Technol 2004;64(10–11):1725–35. [6] Lafarie-Frenot MC, Henaff-Gardin C, Gamby D. Matrix cracking induced by cyclic ply stresses in composite laminates. Compos Sci Technol 2001;61(15):2327–36. [7] Henaff-Gardin C, Lafarie-Frenot MC. Specificity of matrix cracking development in CFRP laminates under mechanical or thermal loadings. Int J Fatigue 2002;24(2–4):171–7. [8] Henaff-Gardin C, Lafarie-Frenot MC. The use of a characteristic damage variable in the study of transverse cracking development under fatigue loading in cross-ply laminates. Int J Fatigue 2002;24(2–4):389–95. [9] Henaff-Gardin C, Gamby D, Lafarie-Frenot MC. Doubly periodic matrix cracking in composite laminates. Part 2: Thermal biaxial loading. Compos Struct 1996;36(1–2):131–40. [10] Henaff-Gardin C, Gamby D, Lafarie-Frenot MC. Doubly periodic matrix cracking in composite laminates. Part 1: General in-plane loading. Compos Struct 1996;36(1–2):113–30. [11] Gamby D, Henaff-Gardin C, Lafarie-Frenot MC. Propagation of edge cracking towards the centre of laminated composite plates subjected to fatigue loading. Compos Struct 2002;56(2):183–90. [12] Nairn JA, Hu SF, Bark JS. A critical evaluation of theories for predicting microcracking in composite laminates. J Mater Sci 1993;28(18):5099–111. [13] Ladeveze P, Lubineau G. On a damage mesomodel for laminates: micro–meso relationships, possibilities and limits. Compos Sci Technol 2001;61(15):2149–58. [14] Akshantala NV, Talreja R. A micromechanics based model for predicting fatigue life of composite laminates. Mater Sci Eng 2000. [15] Kashtalyan M, Soutis C. The effect of delaminations induced by transverse cracks and splits on stiffness properties of composite laminates. Compos Part A 2000;31:107–19. [16] Lafarie-Frenot MC, Henaff- Gardin C. Formation and growth of 90 ply fatigue cracks in carbon/epoxy laminates. Compos Sci Technol 1990;40(3):307–24. [17] Gamby D, Lafarie-Frenot MC, Henaff- Gardin C. Kinematic waves and nonuniform damage development in composite laminates. Int J Damage Mech 1997;6:51–61. [18] Hancox NL. Thermal effects on polymer matrix composites. Part 1: Thermal cycling. Mater Des 1998;19(3):85–91. [19] Favre JP, et al. Vieillissement des composites a` matrice organique aux tempe´ratures moyennes. Un premier bilan. Paris, France: AMAC. JNC 10; 1996. [20] Rouquie S, et al. Thermal cycling of carbon/epoxy laminates in neutral and oxidative environments. Paris, France: AMAC. JNC 13; 2003. [21] Kress G. Free-edge influence on CFRP laminate strength. Int J Damage Mech 1994;3:192–211. [22] Chan WS, Wang ASD. Effects of a 90 ply on matrix cracks and edge delamination in composite laminates. Compos Sci Technol 1990;38:143–57. [23] Davi G, Milazzo A. Boundary element solution for free edge stresses in composite laminates. Transactions of the ASME. J Appl Mech 1997;64(4):877–84.

M.C. Lafarie-Frenot, N.Q. Ho / Composites Science and Technology 66 (2006) 1354–1365 [24] Gaudenzi P, Mannini A, Carbonaro R. Multi-layer higher-order finite elements for the analysis of free-edge stresses in composite laminates. Int J Numer Methods Eng 1998;41(5):851–73. [25] Cho M, Kim HS. Iterative free-edge stress analysis of composite laminates under extension, bending, twisting and thermal loadings. Int J Solids Struct 2000;37(3):435–59. [26] Tahani M, Nosier A. Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading. Compos Struct 2003;60(1):91–103. [27] Pipes R, Pagano N. Interlaminar stresses in composite laminates under uniform axial extension. J Compos Mater 1970;4:538–48. [28] Altus E, Rotem A, Shmueli M. Free edge effect in angle ply laminates – a new three dimensional finite difference solution. J Compos Mater 1980;14:2–20. [29] Yang HTY, He CC. Three-dimensional finite element analysis of free edge stresses and delamination of composite laminates. J Compos Mater 1994;28(15):1394–412. [30] Xu LY. Interaction between matrix cracking and edge delamination in composite laminates. Compos Sci Technol 1994;50(4):469–78. [31] Zang J, Soutis C. Analytical study of local and edge delamination coupling with transverse ply cracking in laminated composites. University of Leicester, Department of Engineering; 1992. [32] Rebiere J-L, Gamby D. A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates. Compos Sci Technol 2004;64(13–14):2239–50.

1365

[33] Ladeveze P, Lubineau G. An enhanced mesomodel for laminates based on micromechanics. Compos Sci Technol 2002;62(4):533–41. [34] Ladeveze P, Lubineau G, Marsal D. Towards a bridge between the micro- and mesomechanics of delamination for laminated composites. Compos Sci Technol 2005; in press, doi:10.1016/j.compscitech. 2004.12.026. [35] Sun CT, Zhou SG. Failure of quasi-isotropic composite laminates with free edges under off-axis loading. J Reinf Plast Compos 1988;7:515–57. [36] Sun CT, Chu GD. Reducing free edge effect on laminate strength by edge modification. J Compos Mater 1991;25:142–61. [37] Chan WS, Rogers C, Aker S. Improvement of edge delamination strength of composite laminates using adhesive layers. In: Whitney JM, editor. Composite materials: testing and design (7th conference). ASTM STP, vol. 893. Philadelphia: American Society for Testing and Materials; 1986. p. 371–85. [38] Shiau L-C, Chue Y-H. Free-edge stress reduction through fiber volume fraction variation. Compos Struct 1991;19(2):145–65. [39] Suvorov AP, Dvorak GJ. Optimized fiber prestress for reduction of free edge stresses in composite laminates. Int J Solids Struct 2001;38(38–39):6751–86. [40] Lubineau G, Ladeveze P, Violeau D. Durability of CFRP laminates under thermomechanical loading: a micro-meso damage model. Compos Sci Technol 2005; in press, doi:10.1016/j.compscitech.2005. 07.031.