Nonconvex energy minimization and dislocation structures in ductile single crystals

摘要: Plastically deformed crystals are often observed to develop intricate dislocation patterns such as the labyrinth, mosaic, fence and carpet structures. In this paper, structures given an energetic interpretation with aid of direct methods calculus variations. We formulate theory in terms deformation fields regard dislocations manifestations incompatibility plastic gradient field. Within framework, we show that incremental displacements inelastic solids follow minimizers a suitably defined pseudoelastic energy function. exhibiting latent hardening, function is nonconvex has wells corresponding single-slip deformations. This favors microstructures consisting locally single slip. Deformation constructed accordance prescription shown be correspondence several commonly Finally, characteristic length scale can built into by taking account self dislocations. The extended leads scaling laws which appear good qualitative quantitative agreement observation.