Modelling dislocation structures and size effects in deformed bicrystal based on continuum approaches

Dislocation patterning and size effects present significant challenges to conventional constitutive models in plasticity, which typically lack microscopic information. To address these limitations, continuum dislocation dynamics has been developed as a physics-based framework for describing plastic deformation, originally derived from discrete dislocation dynamics. In this study, continuum dislocation dynamics is applied to model dislocation motion in bicrystals, incorporating order parameters inspired by the phase-field method to represent grain boundaries. For small grains, dislocations are depleted from the grain interior and accumulate at grain boundaries, leading to increased back stress and elevated local yield stress. This reproduces the experimentally observed size effect, in which finer grains exhibit higher strength. In large grains, dislocations self-organize into cell structures, and these patterns become smeared-out near grain boundaries. By combining formulation of order parameters and continuum dislocation dynamics, the present approach enables simulating dislocation motion in polycrystals via continuum approaches, extending physics-based plasticity models to a broader range of materials.