Study of size effects in thin films by means of a crystal plasticity theory based on DiFT

S. Limkumnerd, E. Van der Giessen*

*Corresponding author for this work

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Abstract

In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide given by Yefimov et al. [2004b. A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity simulations. J. Mech. Phys. Solids 52, 279-300]. In this dislocation field theory (DiFT) the transport equations for both the total dislocation density and geometrically necessary dislocation (GND) density on each slip system were obtained from the Peach-Koehler interactions through both single and pair dislocation correlations. The effect of pair correlation interactions manifested itself in the form of a back stress in addition to the external shear and the self-consistent internal stress. We here present the study of size effects in single crystalline thin films with symmetric double slip using the novel continuum theory. Two boundary value problems are analyzed: (1) stress relaxation in thin films on substrates subject to thermal loading, and (2) simple shear in constrained films. In these problems, earlier discrete dislocation simulations had shown that size effects are born out of layers of dislocations developing near constrained interfaces. These boundary layers depend on slip orientations and applied loading but are insensitive to the film thickness. We investigate the stress response to changes in controlled parameters in both problems. Comparisons with previous discrete dislocation simulations are discussed. (c) 2008 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)3304-3314
Number of pages11
JournalJournal of the Mechanics and Physics of Solids
Volume56
Issue number11
DOIs
Publication statusPublished - Nov-2008

Keywords

  • Dislocations
  • Thin films
  • Size effects
  • Continuum plasticity
  • Dislocation correlations
  • DISCRETE DISLOCATION PLASTICITY
  • STRAIN-GRADIENT PLASTICITY
  • SINGLE-CRYSTAL
  • NONLOCAL CONTINUUM
  • LENGTH-SCALE
  • PREDICTIONS
  • MECHANICS
  • ENERGY
  • MODEL
  • VISCOPLASTICITY

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