Generalised continuum modelling of grain size effects in polycrystals

The effect of the dislocation density tensor is introduced into the classical crystal plasticity framework by means of the micromorphic theory of single crystals. A computational homogenisation strategy is presented in order to describe the global and local responses of two-dimensional polycrystalline aggregates for grain sizes ranging from 1 to 200 microns. The model is shown to naturally predict a size-dependent kinematic hardening behaviour which is responsible for the observed strong size effects. The yield stress at a given averaged plastic strain is shown to follow a power law scaling relation for grain sizes larger than a critical one. The field of plastic deformation is also strongly affected by grain size, whereby micron-size grains lead to the formation of intense slip bands crossing several grains.