Macroscopic properties of an orthotropic elastic medium containing arbitrarily oriented cracks: application to damage

TL;DRAbstract

An analytical method for the determination of the Eshelby tensor S associated with an arbitrarily oriented crack in an orthotropic elastic medium is first presented. The crack is modelled as an infinite cylinder (with low aspect ratio) along one symmetry axis of the solid matrix. The proposed methodology yields explicit expressions of the Eshelby tensor (or equivalently the Hill tensor P) which show the interaction between the structural anisotropy and the cracks-induced anisotropy. These results are then introduced into a Mori–Tanaka homogenization scheme in order to determine the macroscopic quantities (stiffness tensor, energy) of the cracked media. A last part of the study is devoted to the formulation of an anisotropic damage model based on the micromechanical results. The ability of this model to describe the inelastic behaviour of brittle matrix composites is demonstrated. Moreover, quantitative comparisons with experimental data on a Ceramic Matrix Composite (unidirectional SiC

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