A study of the mechanical behavior of thermo-oxidized composite lamina

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1 Revue des Energies Renouvelables CISM 08 Ou El Bouaghi (2008) A study of the echanical behavior of thero-oxidized coposite laina A. Yousfi 1*, S. Fréour 2, F. Jacquein 2, M. Rahani 1, H. Osani 3 and R. Guillen 2 1 Departent of Mechanical Engineering, University Aar Tilidji, Laghouat, Algeria 2 GeM Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 6183, Université de Nantes - Ecole Centrale de Nantes, France 3 Non Metallic Materials Laboratory, University Ferhat Abbas, Setif, Algeria Abstract - The ai of this work is the study of the echanical behavior of polyer atrix coposites reinforced with carbon fiber, which have undergone a thero-oxidation process. The purpose of this work is the ulti-scale analysis of the consequences of oxidation of epoxy atrices on the intrinsic echanical properties of the external coposite ply, on the one hand, and on the internal echanical states experienced by the structure as a function of the considered echanical load, on the other hand. Effective echanical properties of oxidized coposite plies are deterined according to Eshelby- Kröner self-consistent hoogenization procedure, depending on the progress of the oxidation process. The results are copared to the corresponding properties estiated by the finite eleent ethod. The acroscopic echanical states are calculated for T300/5208 unidirectional coposite and lainates. The acroscopic stresses undergone by each ply of the structure was deduced fro the classical laination theory and by the finite eleent ethod, whereas the local stresses in both constituents (carbon fiber and epoxy atrix) were calculated for each ply of structure, through an analytical stress concentration relation previously deonstrated in [1], which satisfies the atheatical fraework of Eshelby-Kröner self-consistent odel. The local stresses have also been copared with the results obtained using the finite eleent ethod: the two approaches predict close together results. Résué - L objectif de ce travail est l étude du coporteent écanique des coposites à atrice polyère renforcée avec la fibre de carbone, qui ont subi un processus de thero-oxydation. Le but de ce travail est l analyse ulti-échelle des conséquences de l oxydation de la atrice époxy sur les propriétés écaniques intrinsèques de la couche extérieure en coposite, d une part, et sur la écanique interne des états, par la structure en fonction de la charge écanique considéré, d autre part. Les propriétés écaniques effectives du coposite oxydé plies sont déterinées en fonction de la procédure d hoogénéisation de Eshelby-Kröner auto-cohérent, et en fonction de l avanceent du processus d oxydation. Les résultats sont coparés aux propriétés correspondantes estiées par la éthode des éléents finis. Les écaniques acroscopiques sont calculées pour les états T300/5208 coposites unidirectionnels et stratifiés. Le stress subi par acroscopique de chaque pli de la structure a été déduite de la théorie classique de lainage et par la éthode des éléents finis, alors que coe il le souligne à la fois, les constituants (fibre de carbone et de résine époxy atrice) ont été calculées pour chaque pli de la structure, par le biais d une analyse du stress concentration, relation déjà déontrée dans [1], qui répond aux athéatiques qu au odèle auto-cohérent de Eshelby-Kröner odèle auto-cohérent. Les stress locaux ont égaleent été coparés avec les résultats obtenus en utilisant la éthode des éléents finis: les deux approches prédisent des résultats proches. Keywords: Thero-oxidation - Polyer atrix coposites - Scale transition odels - Local stress. * youah@yahoo.fr 299

2 300 A. Yousfi et al. 1. INTRODUCTION Due to their very interesting specific echanical properties, carbon-reinforced epoxy lainates are considered as serious candidates for the replaceent of etals, etallic alloys and cerets for industrial applications such as structural parts for the next generation supersonic aircrafts [2]. The lifetie scheduled for the structural eleents of supersonic aircraft approxiately corresponds to 20,000 cycles in a range of teperatures varying between 55 C and 120 C, with a total length of the plateau at 120 C of 80,000 h (10 years) [3]. Such high teperatures over long periods cause a theral ageing of the resin of eleents coposite of structure leading to theral oxidation of external ply of aterial. Before 1990, few studies have been conducted on theral aging of organic atrix coposites reinforced with carbon fiber. Indeed, before this date, the use of these aterials has been liited to a field of rather low teperatures between -50 C and +70 C, which correspond to the theral load experienced in service by structural parts of, for exaple, subsonic aircraft and helicopters. Recently, the proble arose when such organic atrix coposites have been considered for applications under severe environental conditions fro a theral point of view (teperatures of about 250 C, air pressure higher than 1 atosphere) [4, 5]. The lainated coposites exposed to high teperatures are subject to degradation caused ainly by theral oxidation of their organic atrix. It induces the growth of oxidized layer of reduced thickness in the subsurface of the coposite parts. This superficial phenoenon leads to weight loss and alters the echanical behavior [6, 7]. The diffusion-reaction odel coupled to a echanistic schee has been proposed in [8], in order to predict the behaviour of epoxy atrices experiencing theral ageing. It can predict the oxidation products concentration profiles, fro which the oxidized layer thickness and weight losses are deterined. The theral oxidation of atrix induces a fragility of the near surface area fro which the echanical properties are different to those of the bulk, unaffected by oxidation aterial. The purpose of this work is the ulti-scale analysis of the consequences of the theral-oxidation of epoxy atrices on the intrinsic echanical properties of the external coposite ply, on the one hand, and on the internal echanical states of coposite structure according to the considered echanical loading, on the other hand. This work includes five sections. The first section is dedicated to the influence of theral oxidation on the echanical properties of coposite ply. The second section presents the Eshelby-Kröner self-consistent odel: its constitutive laws are given for the estiation of effective theral elastic properties of coposite ply (stiffness tensor and coefficient of theral expansion). The third section is devoted to the coupling of the classical laination theory and analytical scale-transition relations for local stress deterination in both constituents of coposite plies subjected to a thero-elastic loading. The fourth section describes the conclusions of the present study, while the fifth offers a nuber of perspectives for future developents in this field of research.

3 CISM 2008: A study of the echanical behaviour of thero-oxidized coposite EFFECTIVE PROPERTIES OF A THERMOOXIDIZED COMPOSITE PLY Oxydation odel and results Various odel enabling to achieve the nuerical coputation of oxidation process in pure epoxies or epoxy atrix coposites have been proposed in the literature [9, 10]. Siulations of isotheral aging at 150 C of an epoxy resin during various ageing lengths deonstrated that the oxidized layer thickness was not growing beyond 200 µ whereas the oxidation products concentration were continuously increasing in the affected layer [8]. Results obtained through ultra-icro indentation tests on epoxy resin, after 100 h, 600 h and 1000 h of isotheral aging at 150 C show that a polynoial relation between elastic indentation odulus and oxidation products concentration occurs (1) [8]: Y = 57.4Q Q (1) where Y is the elastic odulus of the epoxy atrix, expressed in GPa, Q is the oxidation products concentration (ol/l) which is space and tie dependent. The evolution of the Young s odulus of the atrix during the theral oxidation process is displayed on figure 1. The atrix is considered as an isotropic aterial, which Poisson s ratio ν = is assued due to the lack of available inforation on its evolution, as independent of state of theral oxidation process, while its shear odulus is deducted fro the classical relation: G Y = (2) 2(1 + Y ) Fig. 1: Evolution of the elastic odulus as a function of the oxidation products concentration Coparison with the behavior of unaffected atrix The theral oxidized atrix is stiffer than the unaffected atrix in a ratio varying between 1 and The atrix properties of a therally oxidized ply can be very different fro those of the corresponding unaffected ply, so that three ain consequences due to the theral oxidation of coposite structure can be expected: a

4 302 A. Yousfi et al. variation of i- the effective acroscopic properties of coposite plies, ii- the profiles of acroscopic stress in the structure and iii- the localization of the acroscopic echanical states (stress and strain) in both constituents of each ply (fiber and atrix). The three above listed expected consequences of thero-oxidation are ulti scale phenoena, either explicitly, in the case of ites i- and iii-, (i- being an hoogenization proble, whereas iii- is related to localization proble), or iplicitly, in the case of ite ii-, which iplies the knowledge of the acroscopic effective properties of the coposite ply (resulting fro the estiates achieved in i-). In order to be able to treat each of these aspects, a scale-transition odel is required. This odel is described below in section MULTI-SCALE ANALYSIS 3.1 Introduction Scale transition odels are based on a ultiscale representation of aterials. In the case of coposite aterials, for instance, a two-scale odel is sufficient: - The properties and echanical states of either the resin or its reinforceents are respectively indicated by the superscripts and f. These constituents define the so-called pseudo acroscopic scale of the aterial [11]. - Hoogenization operations perfored over its aforeentioned constituents are assued to provide the effective behavior of the coposite ply, which defines the acroscopic scale of the odel. It is denoted by the superscript I. This definition also enables to consider an uni-directional reinforceent at acroscopic scale, which is a satisfactorily realistic stateent, copared to the present design of coposite structures. As for the coposite structure, it is actually constituted by an assebly of the above described coposite plies, each of the possibly having the principal axis of their reinforceents differently oriented fro one to another. This approach enables to treat the case of ulti-directional lainates, as shown, for exaple, in [1]. Within scale transition odeling, the local properties of the i-superscripted constituents are usually considered to be known (i.e. the pseudo acroscopic stiffness, i i L and coefficients of theral expansion M ), whereas the corresponding effective acroscopic properties of the coposite structure (respectively, L I I and M ) are a priori unknown and results fro (often nuerical) coputations. Aong the nuerous, available in the literature scale transition odels, able to handle such a proble, ost involve rough-and-ready theoretical fraeworks: Voigt [12], Reuss [13], Neerfeld-Hill [14, 15], Tsai-Hahn [16] and Mori-Tanaka [17, 18] approxiates fall in this category. This is not satisfying, since such a odel does not properly depict the real physical conditions experienced in practice by the aterial. In spite of this lack of physical realis, soe of the aforeentioned odels do nevertheless provide a nuerically satisfying estiation of the effective properties of a coposite ply, by coparison with the experiental values or others, ore rigorous odels. Both Tsai-Hahn and Mori-Tanaka odels fulfil this interesting condition [19, 20]. Nevertheless, in the field of scale transition odelling, the best candidate reains Kröner-Eshelby self-consistent odel [21, 22], because only this odel takes into account a rigorous treatent of the therohygro-elastic interactions between the

5 CISM 2008: A study of the echanical behaviour of thero-oxidized coposite 303 hoogeneous acroscopic ediu and its heterogeneous constituents, as well as this odel enables handling the icrostructure (i.e. the particular orphology of the constituents, especially that of the reinforceents). 3.2 Deterination of the effective acroscopic thero-elastic properties of coposite plies According to Eshelby-Kröner self consistent odel, the hoogenization relation enabling to deterine the acroscopic elastic stiffness of a coposite ply fro the properties of the constituents is: [ E I :( L i L I ) + I ] I i 1 L = L : (3) i= f, In equation (3), I stands for the fourth-order identity tensor, whereas the nae given to the tensor E I often changes fro one article to another (it is called, for exaple, Hill tensor, or Morris tensor, depending on which work fro [28, 29] is considered). Morris s tensor expresses the dependence of the localization tensor on the orphology assued for the atrix and its reinforceents [28]. It can be expressed as a function of Eshelby tensor S I esh, through E I = S I I esh : L It has to be underlined that both Hill s and Eshelby s tensor coponents are functions of the acroscopic stiffness I L (soe exaples are given in [23, 24]). The hoogenization relation satisfied by the acroscopic coefficients of theral expansion of a coposite ply writes as follows: [ I i I E :( L L ) + I ] I I 1 1 i i M = L : :L :M (4) i = f, Only a few study studies were dedicated to the oxidation effects on the echanical behavior of organic atrix coposites. It was nevertheless shown in [25] that the properties of carbon fibers are stable below 300 C. As a consequence, the variation of echanical properties of thero-oxided lainates only depend on the evolution of the atrix properties. Table 1 displays the local properties of carbon fiber considered in order to achieve the hoogenization calculations. Table 1: Local properties of carbon fiber T300 [26] Y 1 (GPa) Y 2, Y 3(GPa) ν 12, ν 13 G 12 (GPa) G 23 (GPa) Evolutions of the effective longitudinal and transverse acroscopic elastic oduli, as a function of the oxidation products concentration are shows on figures 2 and 3, for a coposite containing a carbon fiber volue fraction equal to 60 %. The effective echanical properties of the oxidized coposite ply were deterined, during the oxidation process, through Eshelby-Kröner self-consistent hoogenization procedure (3) (curve KESC ). The results were copared to the corresponding properties estiated according to the finite eleent ethod (FEM "curve").

6 304 A. Yousfi et al. Fig. 2: Longitudinal acroscopic effective elastic odulus of a coposite ply, as a function of the oxidation products concentration Fig. 3: Transverse acroscopic effective elastic odulus of a coposite ply, as a function of the oxidation products concentration Figure 4 shows the evolutions obtained for the effective acroscopic coefficients of theral expansion of a coposite ply, according to (4), during the theral oxidation process experienced by the epoxy. Fig. 4: Evolution of the longitudinal (M 11 ) and transverse (M 22 ) acroscopic coefficients of theral expansion, as a function of the oxidation products concentration

7 CISM 2008: A study of the echanical behaviour of thero-oxidized coposite 305 According to figure 2 and 4, the longitudinal effective properties (i.e. in the direction parallel to axis of the reinforcing fibers), are, in first approxiation, independent fro the state of theral oxidation process of the polyer atrix constituting the considered coposite ply. Actually, a relative deviation weaker than 1 % is observed at the end of the oxidation process for the Young s odulus, while the longitudinal acroscopic coefficient of theral expansion reains alost constant (and tends towards zero). This result is explained by the fact that in the fiber direction, a unidirectional ply presents thero-echanical properties which are controlled by the properties of a single constituent: the fiber. Experiental results on coposite plies in siilar circustances, i.e. in cases when the carbon fibers exhibit constant properties, while those of the atrix significantly vary, corroborates the results of our siulations: longitudinal effective acroscopic properties of coposite plies do not vary as a function of the properties polyer atrix (at least in the case that the coposite ply contains a high volue fraction of fibers) [27]. On the contrary, the effective acroscopic properties of a coposite ply, in the direction transverse to the reinforceents axis, do significantly depend on the state of theral oxidation process experienced by the polyer atrix constituting the ply. In fact, the relative variation of transverse Young odulus of oxidized ply copared to the reference value (unaffected ply) can reach 12 % at the ter of oxidation process (and spreads so that the variation for transversal coefficient of theral expansion is 3.5%). The reader will notice that this relative variation depends hi even on the volue fraction of reinforceents in the coposite ply and ay reach 38 % in the pure atrix at the end of the oxidation process. 4. STUDY OF THE MULTI-SCALE MECHANICAL STATES EXPERIENCED BY THE COMPOSITE STRUCTURE Deterination of echanical states within the constituents of a coposite ply subjected to thero-elastic loading Analytical relations satisfying the fundaental assuptions of Eshelby-Kröner selfconsistent odel, enabling to proceed to the localization of the acroscopic strains within the atrix were established in [1]. Due to the length of these equations, they will not be provided in the present work, so that the interested reader should refer to (18) - (19) of [1]. The corresponding stress tensor experienced by the atrix can be deduced fro its strain state through: σ 11 2 L 44 ε 12 2 L 44 ε 13 σ = 2 L ε σ ε L (5) 2 L ε ε σ L With σ 11 = L 11 ε 11 + L 12 ( ε 22 + ε 33 ) M 11 ( L L 12 ) T σ 22 = L 11 ε 22 + L 12 ( ε 11 + ε 33 ) M 11 ( L L 12 ) T (6) σ = L ε + L ( ε + ε ) M ( L + 2 L ) T

8 306 A. Yousfi et al. The echanical states experienced by the reinforceents can be deduced fro Hill s averages relations over stresses and strains [28]: f 1 I ν σ = σ σ ; f 1 I ν ε = ε ε (7) ν f ν f ν f ν f The variation of the internal acroscopic stresses σ 11 I and σ I 22 have been calculated during the one edge theral oxidation process of a coposite lainate subitted to either a longitudinal or a transverse external load. The results obtained for the acroscopic echanical states were localized within the constituents using the above described scale transition relations. The curves for both the acroscopic and local stresses experienced by the external ply have been displayed on figures 5-6 (in the cases that a longitudinal or a transverse external load was considered, respectively). On the sae figures, the stress states predicted for the thero-oxidized lainate were copared to the corresponding stresses calculated for the unaffected aterial. The echanical states predicted fro the effective acroscopic properties provided by Eshelby-Kröner Self-Consistent odel were copared to the echanical states calculated fro the effective acroscopic properties deduced fro finite eleents analysis. Figures 5 and 6 underline the consequences of a theral oxidation on the ulti-scale echanical states. In the case that the coposite structure is subitted to a longitudinal external load, the ulti-scale internal stresses experienced by the oxidized ply are independent fro the oxidation process state. This result coes fro the independence fro the oxidation state exhibited by the acroscopic effective properties in the longitudinal direction (see section 4 of the present work). On the contrary, in the case when the coposite plate is subitted to a transverse echanical loading, the internal stresses experienced by the oxidized ply and its very constituents differ fro those that would have been undergone by an unaffected ply: the acroscopic stress increases during the theral oxidation, as a consequence of the increased effective stiffness of the thero-oxided ply. Oxidized ply Unaffected ply

9 CISM 2008: A study of the echanical behaviour of thero-oxidized coposite 307 Fig. 5: Longitudinal ( σ 11 ) and transverse ( σ 22 ) stresses concentrations in the constituents of the external ply, the coposite structure being subjected to a longitudinal stress σ 11 = 100 MPa At the scale of the constituents: i) the stress concentration in the reinforcing fiber does not vary at all as a function of the oxidation products concentration, since the properties of the carbon fibers are unchanged during the theral-oxidation process. ii) the epoxy atrix experiences an increasing stress state during the theral oxidation process, which can be attributed to the increased stiffness of this constituent induced by the theral-oxidation. Actually, coposites are generally designed so that the reinforceents concentrate the stresses. Moreover, in practice, daage and failure initially often takes place in the subsurface of a echanical part. Thus, an increased stress experienced by the resin of the external ply is, a priori not favourable to the durability of the coposite structure. These considerations can help to explain the worst durability of therooxided coposite structures, observed in practice, by coparison with the reference behaviour of the unaffected by oxidation structure. Oxidized ply Unaffected ply

10 308 A. Yousfi et al. Fig. 5: Longitudinal ( σ 11 ) and transverse ( σ 22 ) stresses concentrations in the constituents of the external ply, the coposite structure being subjected to a longitudinal stress σ 22 = 50 MPa ST: Scale-transition; cop: coposite; at: atrix; FEM: finite eleent ethod 5. CONCLUSIONS In this work, the consequences due to the theral oxidation of the epoxy resin constituting a coposite structure were investigated, for the first tie, through a scale transition approach. The results obtained through the scale transition ethod were copared to finite eleents calculations, with a rather good agreeent. The scale transition approach deonstrates that the effective properties and echanical states of the external ply of a coposite structure having experienced a theral oxidation process do not strongly differ fro the corresponding reference values of the ply unaffected by the theral oxidation. On the opposite, the local properties and echanical states of the atrix constituting the ply affected by theral oxidation do strongly vary as a function of the theral oxidation process state. It was deonstrated that both the evolutions of the echanical properties and echanical states in the epoxy after the theral oxidation were not copatible with an enhanced durability of the structure, especially in the case that a transverse external load had to be undergone. 6. PERSPECTIVES The scope of the present study was liited to the consequences of the theral oxidation of the polyer atrix on the evolutions of the properties and echanical states of coposite aterials during a subsequent loading at abient teperature. Nevertheless, the coposite experiencing theral ageing are often subjected to theral echanical loads at high teperature. Under these conditions, the polyer atrix exhibits a visco-elastic behavior. This leads to an effective visco-elastic behavior of the coposite plies at acroscopic scale. In order to take into account these physical phenoena, a visco-elastic scale transition odel will be developed. This odel will be used in order to achieve the prediction of the effective theroechanical behaviour (stiffness tensor and coefficients of theral expansion) of the coposite plies as a function of tie and teperature. Thereafter, it will be possible to

11 CISM 2008: A study of the echanical behaviour of thero-oxidized coposite 309 proceed to the localization of the echanical states within the constituents of each ply of the studied coposite structure. Moreover, practical studies, published in the literature, report an evolution of the yield strength of epoxies during the theral oxidation process. Multi-scale failure criteria, enabling to take into account these experiental results will be developed in further works, in order to rigorously investigate the durability of structures having been subitted to theral oxidation processes. REFERENCES [1] S. Fréour, F. Jacquein and R. Guillen, On an Analytical Self-Consistent Model for Internal Stress Prediction in Fiber-Reinforced Coposites Subitted to Hygroelastic Load, Journal of Reinforced Plastics and Coposites, Vol. 24, N 13, pp , [2] L. Ye, L. Ye, S. Zhongqing and M. Guang, Functionalized Coposite Structures for New Generation Airfraes: a Review, Coposites Science and Technology, Vol. 65, N 9, pp , [3] V. Bellenger, J. Decelle and N. Huet, Ageing of a Carbon Epoxy Coposite for Aeronautic Applications, Coposites Part B: Vol. 36, N 3, pp , [4] P.M. Hergenrother, Developent of Coposites, Adhesives and Sealants for High-Speed Coercial Airplanes, SAMPE Journal, Vol. 36, N 1, pp , [5] M.D. Brunner and T. Cebeci, Proceedings of the 39 th International SAMPE Syposiu and Exhibition, K. Drake, J. Bauer, T. Serafini and P. Cheng, Eds, pp , [6] K.J. Bowles and A. Meyers, Specien Geoetry Effects on Graphite / PMR-15 Coposites during Theral Oxidative Aging, Proceeding of the 32 st International SAMPE Syposiu and Exhibition, pp , [7] M.S. Madhukar, K.J. Bowles and D.S. Papadopoulos, Thero-Oxidative Stability and Fiber Surface Modification Effects on the Inplane Shear properties of Graphite / PMR-15 Coposites, Journal of Coposite Materials, Vol. 31, N 6, pp , [8] N.Q. Ho, F. Pons and M.C. Lafarie-Frenot, 12 th European Conference on Coposite Materials, Biarritz, [9] X. Colin, C. Marais and J. Verdu, A New Method for Predicting the theral Oxidation of Theroset Matrices. Application ton an Aine Crosslinked Epoxy, Polyer Testing, Vol. 20, N 7, pp , [10] G.P. Tandon, K.V. Pochiraju and G.A. Schoeppner, Modeling of Oxidative Developent in PMR-15 Resin, Polyer Degradation and Stability, Vol. 91, N 8, pp , [11] J.M. Sprauel and L. Castex, First European Powder Diffraction International Conference on X-Ray Stress Analysis, Munich, [12] W. Voigt, Lehrbuch der Kristallphysik, Teubner, Leipzig/Berlin, [13] A. Reuss, Zeitschrift für Angewandte und Matheatik und Mechanik, Vol. 9, pp , [14] H. Neerfeld, Mitt. Kaiser-Wilhel-Inst., Eisenforschung Düsseldorf, Vol. 24, pp , [15] R. Hill, Proc. Phys. Soc., Vol. 65, pp , 1952.

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