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

A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading

“…A procedure similar to that of Markenscoff was used by Jokl et al [39] to solve the injection of a static screw dislocation. Recently, Pellegrini [40] has expanded the Peierls-Nabarro equations into a fully dynamic formulation.…”

Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

“…Apparently first noticed in the context of dynamic crack-motion theory, 51 it was independently rediscovered in the context of the DPE by the author. 35 Albeit superficially dissipative-like and of the same form as the drag term (9) it is non-phenomenological, and uniquely associated to K. It compensates for a contribution emanating from the latter in the equal-time limit ∆t → 0. 24,35,36 As it remains operative in steady motion, it should not be attributed the character of an acceleration/braking radiation term.…”

“…Equation (6) introduces a slight modification with respect to previous work, 24,35 and is further commented at the end of this Section.…”

“…For edge dislocation components of the "climb" type 52 the prefactor of the "local" loss term differs from the one in (10). 35,53 For brevity, climb edge dislocations are not considered further hereafter.…”

On the core width and Peierls stress of bubble rafts dislocations within the framework of modified Peierls-Nabarro model

“…As is well known, the P-N model can predict the core width and Peierls stress of dislocations analytically [12][13][14][15][16]. However, the fundamental dislocation equation in the P-N model is derived from the balance between the nonlinear interaction from the misfit gluing and the linear interaction form the deformation, which is obtained by the assumption that the crystal is taken to be elastic continuum.…”