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

TL;DR

This paper introduces a phase-field crystal model that accurately describes defect dynamics and dislocation motion in crystalline materials, integrating elastic and plastic deformation analysis with a finite element approach.

Contribution

The paper develops a coarse-grained phase-field crystal model with a finite element method to analyze dislocation behavior and stress regularization in crystalline structures.

Findings

Regularization of stresses near dislocation cores

Dislocation dipole motion due to internal interactions

Grain shrinkage observed in simulations

Abstract

The phase-field crystal model in its 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 the elastic distortion and stress regularization at a dislocation core 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 the 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 also 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.