A discrete dislocation dynamics framework for modeling polycrystal plasticity with hardening

Abstract

A two-dimensional discrete dislocation dynamics (DDD) framework is extended to model plastic deformation in polycrystalline materials having realistic grain morphology in finite geometries. The formulation includes constitutive rules to represent intra-grain dislocation mechanisms as well as dislocation/slip transmission across grain boundaries. Rules for intra-granular interactions mimic key three-dimensional dislocation mechanisms, such as line tension and dynamic junction and source formation, in addition to other short-range dislocation interactions. Various effects of idealized three-dimensional dislocation mechanisms on the mechanical response in tension are explored. The scaling of flow strength with grain size is investigated with and without slip transmission at grain boundaries. To aid in the analysis, spatial mappings of relevant stress components and geometrically necessary dislocation density are produced, which bring out competing dislocation-based strengthening mechanisms leading to the observed grain size effect in polycrystals.