Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Abstract

The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the `glide' and `climb' type, by means of Mura's eigenstrains method. These equations are of the integro-differential type and feature a non-local kernel in space and time. The equation for the screw differs by an instantaneous term from a previous attempt by Eshelby. Those for both types of edges involve in addition an unusual convolution with the second spatial derivative of the displacement jump. As a check, it is shown that these equations correctly reduce, in the stationary limit and for all three types of dislocations, to Weertman's equations that extend the static Peierls-Nabarro model to finite constant velocities.

14 pages, 1 figure. A few minor typos in published version corrected here (in red)

References in corpus (5)

• Dislocation Core Energies and Core Fields from First Principles
• Supersonic dislocations observed in a plasma crystal
• Dynamic Peierls-Nabarro equations for elastically isotropic crystals
• Equation of motion for dislocations with inertial effects
• The gauge theory of dislocations: a uniformly moving screw dislocation

Cited by in corpus (20)

• Dynamic Peierls-Nabarro equations for elastically isotropic crystals
• Velocity dependent dislocation drag from phonon wind and crystal geometry
• Analytic model of the remobilization of pinned glide dislocations: including dislocation drag from phonon wind
• Dislocation drag from phonon wind in an isotropic crystal at large velocities
• Properties of dislocation drag from phonon wind at ambient conditions
• Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach
• Line tension of a dislocation moving through an anisotropic crystal
• Distributional and regularized radiation fields of non-uniformly moving straight dislocations, and elastodynamic Tamm problem
• Stability of pulse-like earthquake ruptures
• Screw and edge dislocations with time-dependent core width: from dynamical core equations to an equation of motion
• Causal Stroh formalism for uniformly-moving dislocations in anisotropic media: Somigliana dislocations and Mach cones
• Uniformly-moving non-singular dislocations with elliptical core shape in anisotropic media
• Reply to "Comment on 'Dynamic Peierls-Nabarro equations for elastically isotropic crystals' "
• On the Structure of Linear Dislocation Field Theory
• On the gradient of the Green tensor in two-dimensional elastodynamic problems, and related integrals: Distributional approach and regularization, with application to nonuniformly moving sources
• A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry
• Elastic Liénard-Wiechert potentials of dynamical dislocations from tensor gauge theory in 2+1 dimensions
• Shock-driven nucleation and self-organization of dislocations in the dynamical Peierls model
• Fourier-based numerical approximation of the Weertman equation for moving dislocations
• Properties of accelerating edge dislocations in arbitrary slip systems with reflection symmetry