Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum plasticity theory

Abstract

Due to recent successes of a statistical-based nonlocal continuum crystal plasticity theory for single-glide in explaining various aspects such as dislocation patterning and size-dependent plasticity, several attempts have been made to extend the theory to describe crystals with multiple slip systems using ad-hoc assumptions. We present here a mesoscale continuum theory of plasticity for multiple slip systems of parallel edge dislocations. We begin by constructing the Bogolyubov-Born-Green-Yvon-Kirkwood (BBGYK) integral equations relating different orders of dislocation correlation functions in a grand canonical ensemble. Approximate pair correlation functions are obtained for single-slip systems with two types of dislocations and, subsequently, for general multiple-slip systems of both charges. The effect of the correlations manifests itself in the form of an entropic force in addition to the external stress and the self-consistent internal stress. Comparisons with a previous multiple-slip theory based on phenomenological considerations shall be discussed.

12 pages, 3 figures

References in corpus (2)

• Dislocation Glasses: Aging during Relaxation and Coarsening
• Mesoscale theory of grains and cells: crystal plasticity and coarsening

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• Cell structure formation in a two-dimensional density-based dislocation dynamics model
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