Two-scale viscoplastic and damage analysis of a metal matrix composite

Abstract

A damage mechanics model coupled with constitutive equations in elastoviscoplasticity is built up in order to analyze the nonlinear behavior of continuous fibre reinforced metal matrix composites. The resulting macroscopic model is based on homogenization technique which allows to correlate the overall and local mechanical variables together. Using this technique, a material representative cell which includes the fibre and the matrix in their respective volume fractions, can be isolated. Both, the behavior of the fibre and the matrix are considered isotropic with damage effects, but only the matrix will be characterized with elastoviscoplastic constitutive equations (fibers will remain elastic). At this level, a fourth-rank damage tensor is introduced in the formulation. The transition from the microscopic level to the macroscopic one leads to an anisotropic damage evolution induced by the shape of the composite material and by the loading history. Both the strain equivalence and energy equivalence, for the damage formulation, are presented, based on the effective stress concept fully coupled with the material constitutive equations.