Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials

Abstract

Classical homogenization techniques are not designed to predict the effect of the size of the constituents on the effective mechanical behaviour of heterogeneous materials. They usually take the volume fraction and, in some cases, the morphology of phase distribution into account. This shortcoming is related to the fact that, in crystals, the elastoviscoplastic behaviour of each constituent within the aggregate may be different from that observed on the constituent alone (say the single crystal). Cosserat single crystal plasticity is used in this work to describe the influence of grain size on the effective hardening behaviour of polycrystals. For that purpose, three-dimensional finite element calculations of periodic Cosserat multi-crystalline aggregates of different grain sizes are provided. The polycrystal is regarded as a heterogeneous Cosserat medium and specific techniques for the estimation of the effective properties are presented. The approach is then applied to the case of two-phase single crystal materials for which the behaviour of one phase as a matrix turns out to be much harder than the isolated phase.