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The purpose of this work is to present various application of statistical scale transition models to the analysis of polymer-matrix composites submitted to thermo-hygro-mechanical loads. In order to achieve such a goal, two approaches, classically used in the field of modelling heterogeneous material are studied: Eshelby-Kröner self-consistent model on the one hand and Mori-Tanaka approximate, on the second hand. Both models manage to handle the question of the homogenization of the microscopic properties of the constituents (matrix and reinforcements) in order to express the effective macroscopic coefficients of moisture expansion, coefficients of thermal expansion and elastic stiffness of a uni-directionally reinforced single ply. Inversion scale transition relations are provided also, in order to identify the effective unknown behaviour of a constituent. The proposed method entails to inverse scale transition models usually employed in order to predict the homogenised macroscopic elastic/hygroscopic/thermal properties of the composite ply from those of the constituents. The identification procedure involves the coupling of the inverse scale transition models to macroscopic input data obtained through either experiments or in the already published literature. Applications of the proposed approach to practical cases are provided: in particular, a very satisfactory agreement between the fitted elastic constants and the corresponding properties expected in practice for the reinforcing fiber of typical composite plies is achieved. Another part of this work is devoted to the extensive analysis of macroscopic mechanical states concentration within the constituents of the plies of a composite structure submitted to thermo-hygro-elastic loads. Both numerical and a fully explicit version of Eshelby-Kröner model are detailed. The two approaches are applied in the viewpoint of predicting the mechanical states in both the fiber and the matrix of composites structures submitted to a transient hygro-elastic load. For this purpose, rigorous continuum mechanics formalisms are used for the determination of the required time and space dependent macroscopic stresses. The reliability of the new analytical approach is checked through a comparison between the local stress states calculated in both the resin and fiber according to the new closed form solutions and the equivalent numerical model: a very good agreement between the two models was obtained. The purpose of the final part of this work consists in the determination of microscopic (local) quadratic failure criterion (in stress space) in the matrix of a composite structure submitted to purely mechanical load. The local failure criterion of the pure matrix is deduced from the macroscopic strength of the composite ply (available from experiments), using an appropriate inverse model involving the explicit scale transition relations previously obtained for the macroscopic stress concentration at microscopic level. Convenient analytical forms are provided as often as possible, else procedures required to achieve numerical calculations are extensively explained. Applications of this model are achieved for two typical carbon-fiber reinforced epoxies: the previously unknown microscopic strength coefficients and ultimate strength of the considered epoxies are identified and compared to typical expected values published in the literature.

Colloque avec actes et comité de lecture. Internationale.; International audience; Cette étude vise à examiner la validité du modèle autocohérent de Kröner-Eshelby dans le cas où plusieurs morphologies d’inclusions coexistent au sein d’un même volume élémentaire représentatif. Une étude des deux formulations utilisables et de leurs limites conduit à proposer une formulation mixte qui satisfait les principes de moyennes de Hill. Les résultats de cette approche originale sont alors décrits dans le cas d’un chargement thermo-mécanique.

International audience; In order to predict the long-term durability of polymer matrix composite materials submitted to humid environments, the moisture diffusion behavior has to be investigated. The knowledge of the effective diffusivity is actually required, for estimating the moisture content of polymer-based fiber-reinforced materials, even when a basic behavior such as Fick's law is assumed to occur. The original contribution of the present work is to provide new analytical solutions for the effective diffusivities from the solving of unit cell problems on representative volume elements by means of several multi-scale approaches. Composite materials with impermeable or permeable fibers are extensively investigated. The proposed approaches are extended to the practical case of composite materials containing realistic voids volume fractions.

International audience; The aim of this work is the study of the mechanical behavior of polymer matrix composites reinforced with carbon fiber, which have undergone a thermo-oxidation process. The purpose of this work is the multi-scale analysis of the consequences of oxidation of epoxy matrices on the intrinsic mechanical properties of the external composite ply, on the one hand, and on the internal mechanical states experienced by the structure as a function of the considered mechanical load, on the other hand. Effective mechanical properties of oxidized composite plies are determined according to Eshelby-Kröner self-consistent homogenization procedure, depending on the progress of the oxidation process. The results are compared to the corresponding properties estimated by the finite element method. The macroscopic mechanical states are calculated for T300/5208 unidirectional composite and laminates. The macroscopic stresses undergone by each ply of the structure was deduced from the classical lamination theory and by the finite element method, whereas the local stresses in both constituents (carbon fiber and epoxy matrix) were calculated for each ply of structure, through an analytical stress concentration relation previously demonstrated in [1], which satisfies the mathematical framework of Eshelby-Kröner self-consistent model. The local stresses have also been compared with the results obtained using the finite element method: the two approaches predict close together results.; L’objectif de ce travail est l’étude du comportement mécanique des composites à matrice polymère renforcée avec la fibre de carbone, qui ont subi un processus de thermo-oxydation. Le but de ce travail est l’analyse multi-échelle des conséquences de l’oxydation de la matrice époxy sur les propriétés mécaniques intrinsèques de la couche extérieure en composite, d’une part, et sur la mécanique interne des états, par la structure en fonction de la charge mécanique considéré, d’autre part. Les propriétés mécaniques effectives du composite oxydé plies sont déterminées en fonction de la procédure d’homogénéisation de Eshelby-Kröner auto-cohérent, et en fonction de l’avancement du processus d’oxydation. Les résultats sont comparés aux propriétés correspondantes estimées par la méthode des éléments finis. Les mécaniques macroscopiques sont calculées pour les états T300/5208 composites unidirectionnels et stratifiés. Le stress subi par macroscopique de chaque pli de la structure a été déduite de la théorie classique de laminage et par la méthode des éléments finis, alors que comme il le souligne à la fois, les constituants (fibre de carbone et de résine époxy matrice) ont été calculées pour chaque pli de la structure, par le biais d’une analyse du stress concentration, relation déjà démontrée dans [1], qui répond aux mathématiques qu’au modèle auto-cohérent de Eshelby-Kröner modèle auto-cohérent. Les stress locaux ont également été comparés avec les résultats obtenus en utilisant la méthode des éléments finis: les deux approchesprédisent des résultats proches.

International audience; The effects related to the evolution of the moisture-dependent hygroelastic properties of composite plies constituting a fiber-reinforced epoxy laminate on the predicted stress states in the structure during the transient stage of hygroscopic loading are investigated. The approach proposed involves the coupling of the classical continuum mechanics formalism to the Eshelby-Kroner self-consistent scale transition model. An inverse scale transition model is used to describe the evolution of local hygroelastic properties of the epoxy matrix as the process of moisture diffusion proceeds. The scale transition relations allow one to determine the local distribution of stresses in the constituents (fiber and matrix) of each ply of the laminates considered from the distribution of macroscopic stresses. Numerical simulations show that the account (or not) of softening of the composite structure under hygroscopic loadings significantly affects the multiscale stress states predicted.

International audience; The aim of this work is to propose an analytical model for transient hygro-elastic stresses in transversely isotropic multi-layered cylinders. This approach allows one to calculate the time and space dependent hygro-elastic stresses in fiber-reinforced composite submitted to hygroscopic fields by applying the classical continuum mechanics formalism. Application of the proposed model to the case of an embedded optical fiber shows interesting results, concerning the stress field perturbation occurring in the composite in the vicinity of the intrusive optical fiber. The model proposed in this study provides a detailed stress analysis of the inclusion which is required to correctly interpret the data collected through the optical fiber and deduce stresses experienced by the host material.

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Stress analyses are performed in unidirectional fiber-reinforced composites, exposed to ambient fluid, byextending a classical self-consistent model to hygro-elastic solicitations. Constitutive laws are given for themacroscopic elastic properties and Coefficients of Moisture Expansion (CME) by considering a jump inmoisture content between the fiber and the matrix. The macroscopic (ply) and local (fiber and matrix) internalstress states are evaluated for various moisture content ratios between the matrix and the ply. The macroscopicstresses are calculated by using continuum mechanics formalisms and the local stresses are deduced from thescale transition model

International audience; This article deals with the prediction of residual stresses due to plastic solicitations in twophases materials. Reliability of simplified models is evaluated by a comparison between calculations and measurements realized on plastically pre-strained perlitic steels. Two kinds of models are investigated: the classical predictive method and inverse approaches. A semiempiric model based on Dvorak and Benveniste formalism is proposed in order to solve the problem of the excessively high stiffness predicted by the classical models. This method improves results obtained by the others studied approaches and achieves to reproduce curves of residual stresses in each phase and macroscopic stress-strain response, for a single set of hardening parameters.; Cet article apporte une contribution à la prévision des contraintes résiduelles d'origine plastique dans les matériaux biphasés. Les performances de modèles simplifiés sont évaluées par une confrontation avec des mesures réalisées sur des aciers perlitiques prédéformés. Deux manières de piloter les modèles sont envisagées : la méthode prédictive classique et une approche inverse. Devant le constat de la trop grande raideur des modèles, une approche semi-empirique, basée sur le modèle de Dvorak et Benveniste, est proposée. Cette méthode franchit les verrous des formalismes classiques en parvenant à reproduire pour un seul jeu de paramètres d'écrouissage, les courbes de contraintes résiduelles de chacune des phases ainsi que celle correspondant au chargement imposé au polycristal biphasé.

International audience; The development of thermal residual stresses was investigated in polycrystalline materials. Two complementary ways were used: the experimental values obtained by X-ray diffraction were compared to the results predicted by self-consistent scale transition approaches. First, single-phase materials were considered. The model was checked through the experimental study of rolled textured polycrystalline α-Zr and α-Ti with hexagonal closed packed structure. The level and the influence of the thermal stresses on the macroscopic behaviour have been quantified. In a second part, the model was extended to the case of two-phase materials. A new approach was developed in order to characterize the coefficient of thermal expansion (CTE) of phases embedded in multiphase materials. The analysis of the problem was based on the coupling of numerical simulations with thermo-elastic scale transition models and experiments. The whole approach was finally checked through the study of an Al-50%vol.-SiC-50%vol. MMC. The CTE of Silicon Carbide were determined as a function of the temperature. Simulated results obtained show a very good agreement with experimental values available in the literature.

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