Scale transition rules applied to crystal plasticity

Abstract : Homogenization methods adapted to polycrystalline aggregates are discussed. The description of the transition rule using the self-consistent scheme and based on the assumption of time-independent plasticity are first detailed. A few alternative propositions that simplify the general rate form of the relation given by Hill are also presented, with their limitations. A second part recalls several key ideas used to transfer the problem to time-dependent behavior. A final part is devoted to the comparison of several mean-field models and CPFEM simulations in the case of an equiaxed polycrystalline aggregate with an uniform or heterogeneous local elastic behavior. A significant effect of non-uniform elastic properties is exhibited on the macroscopic behavior, specifically on the apparent yield stress, and also on stress and strain fields