Annihilation and sources in continuum dislocation dynamics

Mehran Monavari, Michael Zaiser
2018 Materials Theory  
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
more » ... 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. This fundamental setting provided by the classical continuum theory of dislocation systems has, over the past two decades, inspired many models (e.g. (Sedláček et al. 2003; Xiang 2009; Zhu and Xiang 2015) ). Irrespective of the specific formulation, a main characteristic of the CCT is that, in each elementary volume, the dislocation tensor can measure
doi:10.1186/s41313-018-0010-z fatcat:ovifrdavebferh63k76c3l7lvi