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

Classical homogenization techniques are not designed to predict the e€ect of the size of the constituents on the e€ective 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 di€erent from that observed on the constituent alone (say the single crystal). Cosserat single crystal plasticity is used in this work to describe the in¯uence of grain size on the e€ective hardening behaviour of polycrystals. For that purpose, three-dimensional ®nite element calculations of periodic Cosserat multi-crystalline aggregates of di€erent grain sizes are provided. The polycrystal is regarded as a heterogeneous Cosserat medium and speci®c techniques for the estimation of the e€ective 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.