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

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.

arXiv comment16 pages, 7 figures

References in corpus (34)

• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals
• Phase-field Crystals with Elastic Interactions
• Derivation of the phase field crystal model for colloidal solidification
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Amplitude expansion of the binary phase field crystal model
• Deformation of crystals: Connections with statistical physics
• Renormalization group theory for the phase field crystal equation
• Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
• Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models
• Grain growth beyond the Mullins model, capturing the complex physics behind universal grain size distributions
• Consistent Hydrodynamics for Phase Field Crystals
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
• Mesoscale model of dislocation motion and crystal plasticity
• Phase-field-crystal models and mechanical equilibrium
• Renormalization group approach to multiscale modelling in materials science
• Non-singular dislocation continuum theories: Strain gradient elasticity versus Peierls-Nabarro model
• Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
• Finite element approximation of the fields of bulk and interfacial line defects
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Mechanical relaxation and fracture of phase field crystals
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Elastic constants of stressed and unstressed materials in the phase field crystal model
• Measuring strain and rotation fields at the dislocation core in graphene
• Yielding and jerky plasticity of tilt grain boundaries in high-temperature graphene

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• 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
• 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
• Field Dislocation Mechanics and Phase Field Crystal models
• Stress in ordered systems: Ginzburg-Landau type density field theory
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Dislocation nucleation in the phase field crystal model
• Inelastic rotations and pseudo-turbulent plastic avalanches in crystals
• Grain rotation and coupled grain boundary motion in two-dimensional binary hexagonal materials
• Homogeneous nucleation of dislocations as a pattern formation phenomenon
• Minimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Anomalous grain dynamics and grain locomotion of odd crystals
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• 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
• Modeling dislocations in quasicrystals through amplitude equations