Is Intersonic Dislocation Motion Possible? Singularity Analysis for an Edge Dislocation Accelerating through the Shear Wave Speed Barrier

Abstract

The analysis of Markenscoff and Clifton (J Mech Phys Solids 29:253–262, 1981) for a generally nonuniformly moving Volterra edge dislocation, valid both for subsonic and intersonic/supersonic motion, is focused on the instant in which the dislocation accelerates through the shear-wave speed barrier. Mathematically, the roots (of the argument of the step function \(f\left( \xi \right) = t - \eta \left( \xi \right) - rb\) that defines the intervals of the path of the motion that contribute to the field point) change from a pair of complex conjugate to a double real, splitting into two real ones, and, at the instant of the transition to intersonic motion, the stress analysis is performed at this double root maximum of \(f\left( \xi \right)\). The stress at the forming Mach front contains a \(\frac{{\log \left| {\xi - \xi ^* } \right|}}{{\left| {\xi - \xi ^* } \right|^{\tfrac{1}{2}} }}\) singularity in the coefficient of the delta function, which can be removed by a ramp-core (delta sequence rather than delta function) model of the core displacement.