Discrete Dislocation Dynamics for Crystal RVEs. Part 1: Periodic Loop Kinematics

TL;DR

This paper introduces a new method for implementing dislocation flux boundary conditions in discrete dislocation dynamics, ensuring continuity across periodic boundaries using a dual topological description, with tests confirming its effectiveness.

Contribution

It presents a novel dual-space topological approach for flux boundary conditions in discrete dislocation dynamics within periodic RVEs, enhancing modeling accuracy.

Findings

Boundary nodes have negligible impact on dislocation motion in bulk plasticity.

The approach effectively enforces dislocation continuity across periodic boundaries.

Test cases validate the proposed boundary condition implementation.

Abstract

A novel implementation of the dislocation flux boundary condition in discrete dislocation dynamics is presented. The continuity of the individual dislocation loops in a periodic representative crystal volume (RVE) is enforced across the boundary of the RVE with the help of a dual topological description for representing dislocation line kinematics in two equivalent spaces representing the deforming crystal, the RVE and the unbounded crystal spaces. The former describes the motion of the dislocations in the simulated crystal RVE whereas the latter represents the motion of dislocations in an infinite space containing all replicas of the RVE. A mapping between the two spaces forms the basis of the implementation of flux boundary condition. The implementation details are discussed in the context of statistical homogeneity of bulk crystals undergoing macroscopically homogeneous plastic deformation. Some test cases are presented and discussed to establish the proposed approach. It has been observed that the boundary nodes associated with dislocation segments bear no relevance in the motion of the dislocation segments from the standpoint of bulk crystal plasticity modeling throughout the deformation history of the crystal.