5 research outputs found
Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach
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.Comment: v1: 11 pages, 4 figures. v2: title changed, extensive rewriting, and
new material added; 19 pages, 12 figures (content as published