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.
Highlights
Since the discovery of dislocations as carriers of plastic deformation, developing a continuum theory for motion and interaction of dislocations has been a challenging task
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 dislocation multiplication is associated with the generation of new loops
Unlike theories based on the Kröner-Nye tensor which measures the excess dislocation density, in Continuum dislocation dynamics (CDD), dislocations of different orientation can coexist within an elementary volume
Summary
Since the discovery of dislocations as carriers of plastic deformation, developing a continuum theory for motion and interaction of dislocations has been a challenging task. Such a theory should address two interrelated problems: how to represent in a continuum setting the motion of dislocations, the kinematics of curved and connected lines, and how to capture dislocation interactions. The classical continuum theory of dislocation (CCT) systems dates back to Kröner (1958) and Nye (1953) This theory describes the dislocation system in terms of a rank-2 tensor field α defined as the curl of the plastic distortion, α = ∇ × βpl.
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