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

Abstract

A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to account for core-width generalized stacking-fault energy effects. The degrees of freedom of the solution of the latter equation are reduced by means of the collective-variable method, well-known in soliton theory, which we reformulate in a way suitable to the problem at hand. Through these means, two coupled governing equations for the dislocation position and core width are obtained, which are combined into one single complex-valued equation of motion, of compact form. The latter equation embodies the history dependence of dislocation inertia. It is employed to investigate the motion of an edge dislocation under uniform time-dependent loading, with focus on the subsonic/transonic transition. Except in the steady-state supersonic range of velocities-which the equation does not address-our results are in good agreement with atomistic simulations on tungsten. In particular, we provide an explanation for the transition, showing that it is governed by a loading-dependent dynamic critical stress. The transition has the character of a delayed bifurcation. Moreover, various quantitative predictions are made, that could be tested in atomistic simulations. Overall, this work demonstrates the crucial role played by core-width variations in dynamic dislocation motion.

The mechanisms governing the activation of dislocation sources in aluminum at different strain rates

“…For screw dislocations, a rigorous treatment of inertia can be found in Ni and Markenscoff (2008), where an expression of the dislocation effective mass for regularised dislocation cores can be found. For edge dislocations, Pellegrini (2014) has provided a complete treatment of dislocation drag including inertial effects based on a regularised core, using a dynamic Peierls-Nabarro model. Previously, Pillon et al (2007), again within the Peierls-Nabarro framework, provided an approximate equation of motion for edge and screw components that accounted for retardation effects.…”

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

“…The mobility law of dislocations is adjusted to account for the likely presence of high speed dislocations [1,18,21,[23][24][25][26][27][28]; data about the mobility of dislocations is extracted from MD simulations of aluminum [22] (see Supplementary Materials).…”

Fourier‐based numerical approximation of the Weertman equation for moving dislocations

“…Several branches may exist, as the model allows one to consider intersonic regimes. 7,32 Physical results on v lie outside the scope of the article and will be reported elsewhere. 21…”

“…Indeed, the initial conditions and long-time steady-state regimes of the dynamic PN equation are solutions to the latter equation. 32 However, we emphasize that (6) is only an algorithmic tool that has no relationship whatsoever with the actual dynamics of dislocations.…”