A new simulator for real-scale dislocation plasticity based on dynamics of dislocation-density functions

Abstract

Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today’s computing power. Dislocation-density based approaches are a way forward but most schemes published to-date give a heavier weight on the consideration of geometrically necessary dislocations (GNDs), while statistically stored dislocations (SSDs) are either ignored or treated in ad hoc manners. In reality, however, the motions of GNDs and SSDs are intricately linked through their mutual (e.g. Taylor) interactions. A correct scheme for dislocation dynamics should therefore be an 'all-dislocation' treatment that is equally applicable for all dislocations, with a rigorous description of the interactions between them. In this talk, a new formulation for computational dynamics of dislocation-density functions, based on the above 'alldislocation' principle, is discussed. The dynamic evolution laws for the dislocation densities are derived by coarsegraining the individual density vector fields of all the discrete dislocation lines in the system, without distinguishing between GNDs and SSDs. Elastic interactions between dislocations in 3D are treated in full in accordance with Mura’s formulation for eigen stress. Dislocation generation is considered as a consequence of dislocations to maintain their connectivity, and a special scheme is devised for this purpose. The model is applied to simulate a number of intensive microstructures involving discrete dislocation events, including loop expansion and shrinkage under applied and self stress, dipole annihilation, and Orowan looping. The scheme can also handle high densities of dislocations present in extensive microstructures.