Upscaling modeling of effective elastic properties and anisotropic damage propagation in fractured materials regarded as homogenized media

A model combining the micromechanical reasoning with macroscopic thermodynamic concepts is formulated in this paper for damage evolution in microfractured materials. Fractures correspond to a region of small thickness, along which mechanical and physical properties of the material are degraded. Unlike cracks, fractures are discontinuities able to transfer stress and, therefore, can be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. The present paper consists of employing a micromechanical approach to formulate the homogenized elastic behavior of fractured media. In the context of Eshelby’s equivalent inclusion theory, the approach employs the Mori–Tanaka scheme to estimate the homogenized elastic moduli of materials with multiple fracture families. According to classical references, fractures are geometrically modeled as oblate spheroids endowed with appropriate elastic properties. In order to evaluate the damage evolution in materials with several families of microfractures, a damage model is formulated by combining the above results with a classical thermodynamics approach. Particular emphasis is dedicated to the representation of anisotropic damage, induced by a load applied in a specific direction to a material with an isotropic fracture distribution. The ability of the damage model to describe the response of a material under any loading is demonstrated through a comparison with available experimental data for a ceramic matrix composite silicon carbide reinforced with silicon carbide fibers (SiC–SiC).