Computational homogenization to study the effect of microscopic cracks on the macroscopic strength of polycrystalline materials

In this paper, the capability of computational homogenization technique in the prediction of the macroscopic yield surface of polycrystalline materials at the presence of microscopic damage is investigated. In order to perform the computational homogenization, the irregular shape representative volume elements (RVE) composed of two dimensional grains is used. The grains are considered as an undamageable linear elastic material while the grain boundaries are modeled by a nonlinear cohesive interface law. To study the effect of initial microscopic damages, three different shapes of fully damaged cracks are inserted at the center of RVEs. The Drichlet’s boundary conditions extracted from a macroscopic strain tensor is imposed on the boundary of RVEs and gradually increased until the full failure of samples. The results show that initial damages can dramatically reduce the material strength and give rise to an asymmetric yield surface whereas they have no effect on the macroscopic modulus of elasticity.