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

Surachate Limkumnerd*, Erik Van der Giessen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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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-Bom-Green-Yvon-Kirkwood 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.

Original languageEnglish
Article number184111
Number of pages12
JournalPhysical Review. B: Condensed Matter and Materials Physics
Volume77
Issue number18
DOIs
Publication statusPublished - May-2008

Keywords

  • CRYSTAL THIN-FILMS
  • DISCRETE DISLOCATION
  • SINGLE-CRYSTAL
  • 2 DIMENSIONS
  • COMPUTER-SIMULATION
  • FREE-ENERGY
  • MECHANICS
  • BEHAVIOR
  • MODEL
  • SIZE

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