Monday, July 22, 2013

1307.5244 (Yves-Patrick Pellegrini)

Collective-variable dynamics and core-width variations of dislocations
in a Peierls model

Yves-Patrick Pellegrini
The method of collective variables, reformulated by means of d'Alembert's principle, is employed to set up a systematic perturbative approach to the solution of the dynamical Peierls equation for rectilinear screw and edge dislocations. In this nonlinear, history-dependent, and dissipative integro-differential equation which includes radiation reaction, the slip function is a dynamically-evolving field. Its degrees of freedom are reshuffled by equating it to the sum of a "mean-field" arctangent ansatz, exact for steady motion, in which the collective variables are the time-dependent dislocation position and core width, and a residual term. Two constraints determine the collective variables. Equations for the latter and for the residual are obtained. To leading order, a known equation of motion for the dislocation position is retrieved, together with the yet unknown associated governing equation for the core width. Both equations are combined into one single complex-valued equation for a complex coordinate, of real part the dislocation position and of imaginary part its half-width. The model allows for transient supersonic states inasmuch as they relax to subsonic ones. Numerical calculations show that a loading-dependent dynamical critical stress governs the forward subsonic-to-transonic transition of the edge dislocation. Its dependence with respect to the viscosity coefficient is investigated in the case of abrupt loading. The model reproduces the phenomenology of velocity and core width variations during the decay of transient transonic states to subsonic ones, previously observed in molecular-dynamics simulations by Gumbsch and Gao [P. Gumbsch and H. Gao, Dislocations faster than the speed of sound, Science 283, 965 (1999)].
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