Can dislocations accelerate through the shear-wave speed “barrier”?

Abstract

The question of whether a dislocation can accelerate through the shear-wave speed “barrier” is addressed by analyzing the transient motion of a Volterra dislocation at the instant when the velocity equals the shear-wave speed in the presence of acceleration, which requires an asymptotic analysis at a double root (–at the transition from subsonic to supersonic a pair of complex conjugate roots becomes a double real —). The stresses carried by the forming Mach wave fronts depend on the acceleration at this instant and are found to be O( ln \(r /r^{1/2}\)) singular for a Volterra dislocation both screw and edge. The energy required to push the dislocation through the shear-wave speed “barrier” is determined by means of the “contour-independent” dynamic J integral which defines the self-force on a moving defect, and is obtained as a function of the acceleration as it crosses the “barrier”. While for a Volterra dislocation the energy-rate is singular at this instant, for a more physically realistic ramp-core “smeared” dislocation model, approximating the Volterra dislocation by a delta sequence, this energy rate is obtained by convolution and is finite, with the same result obtained by the theory of distributions. Thus, crossing the “barrier” is theoretically possible as recent experimental evidence in the literature suggests. A “cut-off” constant that remains undetermined will be found in a multiscale analysis by the matching of the self-force based on atomistic calculations modeling the core to the continuum far-field one obtained here. For decelerating motion through the shear-wave speed “barrier” this energy is released as dissipation.