Annihilation and sources in continuum dislocation dynamics (CDD)

TL;DR

This paper explores how dislocation multiplication and annihilation can be modeled within continuum dislocation dynamics by focusing on the volume density of dislocation loops, enhancing the theoretical framework for plasticity.

Contribution

It introduces the volume density of dislocation loops as a new field variable in continuum models, linking loop processes to dislocation density evolution.

Findings

Dislocation annihilation corresponds to merging of loops.

Dislocation multiplication relates to generation of new loops.

The model recovers classical work hardening theory under certain conditions.

Abstract

Continuum dislocation dynamics (CDD) aims at representing the evolution of systems of curved and connected dislocation lines in terms of density-like field variables. Here we discuss how the processes of dislocation multiplication and annihilation can be described within such a framework. We show that both processes are associated with changes in the volume density of dislocation loops: dislocation annihilation needs to be envisaged in terms of the merging of dislocation loops, while conversely dislocation multiplication is associated with the generation of new loops. Both findings point towards the importance of including the volume density of loops (or 'curvature density') as an additional field variable into continuum models of dislocation density evolution. We explicitly show how this density is affected by loop mergers and loop generation. The equations which result for the lowest order CDD theory allow us, after spatial averaging and under the assumption of unidirectional deformation, to recover the classical theory of Kocks and Mecking for the early stages of work hardening.