A coarse-grained phase-field crystal model of plastic motion

Marco Salvalaglio, Luiza Angheluta, Zhi Feng Huang, Axel Voigt, Ken R. Elder, Jorge Viñals

Research output: Contribution to journalArticle

Abstract

The phase-field crystal model in an amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail stress regularization at a dislocation core given by the model, and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for a consistent separation of plastic and elastic time scales in this framework. A finite element method is introduced to solve the combined amplitude and elasticity equations, which is applied to a few prototypical configurations in two spatial dimensions for a crystal of triangular lattice symmetry: i) the stress field induced by an edge dislocation with an analysis of how the amplitude equation regularizes stresses near the dislocation core, ii) the motion of a dislocation dipole as a result of its internal interaction, and iii) the shrinkage of a rotated grain. We compare our results with those given by other extensions of classical elasticity theory, such as strain-gradient elasticity and methods based on the smoothing of Burgers vector densities near defect cores.

Original languageEnglish (US)
Article number103856
JournalJournal of the Mechanics and Physics of Solids
Volume137
DOIs
StatePublished - Apr 2020

Fingerprint

crystal field theory
Elasticity
Burgers vector
plastics
Plastics
Crystals
elastic properties
Edge dislocations
Crystal symmetry
Dislocations (crystals)
Crystal lattices
Crystalline materials
edge dislocations
Finite element method
Defects
shrinkage
smoothing
stress distribution
finite element method
dipoles

Keywords

  • coarse-graining
  • crystal plasticity
  • dislocation motion
  • finite element method
  • phase-field crystal

Cite this

A coarse-grained phase-field crystal model of plastic motion. / Salvalaglio, Marco; Angheluta, Luiza; Huang, Zhi Feng; Voigt, Axel; Elder, Ken R.; Viñals, Jorge.

In: Journal of the Mechanics and Physics of Solids, Vol. 137, 103856, 04.2020.

Research output: Contribution to journalArticle

Salvalaglio, Marco ; Angheluta, Luiza ; Huang, Zhi Feng ; Voigt, Axel ; Elder, Ken R. ; Viñals, Jorge. / A coarse-grained phase-field crystal model of plastic motion. In: Journal of the Mechanics and Physics of Solids. 2020 ; Vol. 137.
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