Instability origin of subgrain formation in plastically deformed materials

The review is focused on two methods of formulation and solution of the subgrain formation problem: an energetic approach and a model of incremental deformations. Both methods are based on a reduced single slip version of crystal plasticity. The mathematical analysis of the energetic approach is done for a single slip model only; in the incremental approach the deformation are assumed small, hence, multi slip can be treated as a sum of single slips. The energetic approach has been employed in analysis of the crystal plasticity model of shear and kink bands. The incremental higher strain gradient model provides an insight into an initial stage of the subgrain formation and the mechanism controlling the subgrain size.