Dislocation distribution near a wall within the framework of the continuum theory of curved dislocations

TL;DR

This paper develops a continuum dislocation theory incorporating an evolving length scale and validates it against discrete dislocation dynamics simulations near a wall, accurately capturing dislocation pile-up behavior.

Contribution

It introduces a parameter-identified continuum model for curved dislocations and validates it against detailed DDD simulations in a wall geometry.

Findings

Continuum theory accurately predicts dislocation pile-up near a wall.

Parameters governing back stress and density gradients are quantitatively determined.

Model serves as a benchmark for validating mesoscale dislocation simulations.

Abstract

A recently proposed generalised continuum theory of curved dislocations describes the spatial and temporal evolution of statistically stored and geometrically necessary dislocation densities as well as the curvature. The dynamics follow from a scalar plastic potential that constrains the allowed velocity fields and leads to a phase field like formulation with a nontrivial mobility function. Although conceptually related to strain gradient plasticity, the theory differs by introducing an intrinsic, evolving length scale given by the dislocation spacing. In this paper, we determine three key material independent parameters of this continuum theory by quantitatively comparing its predictions with discrete dislocation dynamics (DDD) simulations. To achieve this, we impose a narrow impenetrable wall inside the simulation volume, which blocks dislocation motion and generates characteristic spatial variations of the dislocation density fields under external loading. We show that for this geometry, the continuum equations reduce to a form that can be solved efficiently via direct numerical integration. The resulting stationary distributions of total and geometrically necessary dislocation densities are then compared to extensive 2D and 3D DDD simulations. This comparison allows us to extract the parameters that govern the back stress, the density gradient coupling, and the flow stress relation. Our results demonstrate that the continuum theory quantitatively captures the DDD observed structure of the dislocation pile up near the wall and therefore provides a reliable mesoscale description. The wall loading setup further serves as a benchmark problem to validate numerical implementations of the continuum theory in more general geometries.