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

Vincent Monchiet 1 I. C. Gruescu 2 O. Cazacu 3 D. Kondo 4
1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 LML - Laboratoire de Mécanique de Lille - FRE 3723
3 MAE - Department of Mechanical and Aerospace Engineering [Shalimar]
4 DALEMBERT - Institut Jean Le Rond d'Alembert
Abstract : 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 a closed-form solution of the Eshelby tensor corresponding to cracks in an elastic anisotropic medium. In this study, we begin to present closed form expressions of the Eshelby tensor $\tensq{S}$ that we derived for a cylindrical crack embedded in an orthotropic material. The 3D obtained expressions reduce to existing results in the 2D case or in particular 3D cracks configurations. The effective compliance of an orthotropic medium containing arbitrarily oriented cracks is then derived by using the new 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).
Keywords : Homogenization Eshelby tensor Anisotropy Damage Brittle materials Ceramic Matrix Composites Micromechanics Cracks
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Vincent Monchiet, I. C. Gruescu, O. Cazacu, D. Kondo. A micromechanical approach of crack-induced damage in orthotropic media : application to a brittle matrix composite. Engineering Fracture Mechanics, Elsevier, 2012, 83 (-), pp.40-53. ⟨10.1016/j.engfracmech.2011.11.011⟩. ⟨hal-00687861⟩

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