Dislocation dynamics and crystal plasticity in the phase field crystal model

Abstract

A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy and show that it obeys the stress strain relation of linear elasticity. Dislocations in a two dimensional hexagonal lattice are shown to be composite topological defects in the amplitude expansion of the phase field, with topological charges given by the Burgers vector. This allows us to introduce a formal relation between dislocation velocity and the evolution of the coarse grained envelopes of the phase field. Standard dissipative dynamics of the phase field crystal model is shown to determine the velocity of the dislocations. When the amplitude equation is valid, we derive the Peach-Koehler force on a dislocation, and compute the associated defect mobility. A numerical integration of the phase field crystal equations in two dimensions is used to compute the motion of a dislocation dipole, and good agreement is found with the theoretical predictions.

11 pages, 3 figures

References in corpus (3)

• Renormalization group theory for the phase field crystal equation
• Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials
• Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model

Cited by in corpus (30)

• Mesoscale model of dislocation motion and crystal plasticity
• A coarse-grained phase-field crystal model of plastic motion
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• A phase field crystal theory of the kinematics of dislocation lines
• Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
• The role of fluid flow in the dynamics of active nematic defects
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Field Dislocation Mechanics and Phase Field Crystal models
• Stress in ordered systems: Ginzburg-Landau type density field theory
• Mechanical relaxation and fracture of phase field crystals
• A unified field theory of topological defects and non-linear local excitations
• Kinematics and dynamics of disclination lines in three-dimensional nematics
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Dislocation nucleation in the phase field crystal model
• Grain rotation and coupled grain boundary motion in two-dimensional binary hexagonal materials
• Defect dynamics in active smectics induced by confining geometry and topology
• Minimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation
• Elasticity versus phase field driven motion in the phase field crystal model
• Substrate curvature governs texture orientation in thin films of smectic block copolymers
• Analytical model for the motion and interaction of two-dimensional active nematic defects
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
• Mesoscale Field Theory for Quasicrystals
• Mesoscale modeling of deformations and defects in thin crystalline sheets
• Explicit temperature coupling in phase-field crystal models of solidification
• Topological defects in polar active matter