A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite

Coupling between initial and damage-induced anisotropies in 3D elastic damaged materials has been so far addressed by homogenization techniques only for particular microcracks configurations. The main difficulty in developing a general 3D micromechanical model lies in the lack of closed-form solutions of the Eshelby tensor corresponding to cracks arbitrarily oriented in an elastic anisotropic medium. In this study, we begin to present analytical expressions of the Eshelby tensor S (equivalently the Hill tensor P ) that we derived for a cylindrical crack embedded in an orthotropic material. The obtained expressions reduce to existing results in the 2D case or in particular 3D cracks configurations. The effective compliance of the orthotropic medium containing arbitrarily oriented cracks is then derived by using the newly derived expressions of the Eshelby tensor. Finally, a damage model is formulated by combining the above results with classical thermodynamics approach. The ability of the model to capture coupling between initial orthotropy and damage induced anisotropy is demonstrated through a comparison with experimental data available for a ceramic matrix composite (unidirectional SiC–SiC).