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Continuum dislocation dynamics (CDD) aims at representing the evolution ofsystems of curved and connected dislocation lines in terms of density-likefield variables. Here we discuss how the processes of dislocationmultiplication and annihilation can be described within such a framework. Weshow that both processes are associated with changes in the volume density ofdislocation loops: dislocation annihilation needs to be envisaged in terms ofthe merging of dislocation loops, while conversely dislocation multiplicationis associated with the generation of new loops. Both findings point towards theimportance of including the volume density of loops (or 'curvature density') asan additional field variable into continuum models of dislocation densityevolution. We explicitly show how this density is affected by loop mergers andloop generation. The equations which result for the lowest order CDD theoryallow us, after spatial averaging and under the assumption of unidirectionaldeformation, to recover the classical theory of Kocks and Mecking for the earlystages of work hardening.

Annihilation and sources in continuum dislocation dynamics (CDD)