A Flux Boundary Condition for Grain Boundary-Dislocation Interaction Using All-Dislocation Density Dynamics (ADD)

Grain boundaries (GBs) play a crucial role in the plasticity of polycrystalline materials, yet mesoscopic simulation methods to study their effects remain scarce. During plastic deformation, dislocations interact with GBs in various ways—they may transfer to adjacent grains, reflect back, or be absorbed—depending on the GB's properties. Past attempts to understand these effects have predominantly relied on atomistic simulation with limited spatiotemporal scales. Here, we exploit an "all-dislocation density" (ADD) dynamics framework to simulate plasticity within grains and at GBs. We derived a flux boundary condition for ADD that incorporates the dislocation density flux at the GB and implements it numerically on a rhombus mesh structure. The dislocation flux is computed using a mathematically robust framework that rigorously accounts for factors affecting slip transfer. The numerical scheme examines the effects of misorientation angle and grain size on slip transfer under constant stress, as well as constant stress and strain rate conditions. The results reveal that lower misorientation angles lead to higher plastic strain and mobile dislocation density. Furthermore, plastic strain is inversely proportional to the square root of the grain size, aligning with the Hall-Petch relationship. Strain hardening intensifies with increasing grain boundary misorientation, reflecting reduced slip transfer through less permeable boundaries. The study also investigates how mobility and initial dislocation density influence lattice resistance and GB strengthening, revealing transitions between hardening mechanisms. These expected results confirm that the ADD framework is appropriate for mesoscopic simulation of GB effects in dislocation plasticity.