Analysis for a screw dislocation accelerating through the shear-wave speed barrier

An analysis is performed for an accelerating screw dislocation through the shear-wave speed barrier. At this instant, the function that determines the interval of the path of the dislocation motion that contributes to the wave front has roots that change from a pair of complex conjugate to a double real, which subsequently splits into two real ones. The analysis is performed at this transition to supersonic that occurs at the double root maximum of the function that defines the interval of the dislocation path that contributes to the field points. It is found that the stress has a log|ξ-ξ^*|/|ξ-ξ^*|^1/2 singularity in the coefficient of the delta function of the forming Mach front, implying that for this phenomenon the Volterra dislocation model has too strong a discontinuity (step-function) in the displacement to be meaningful. A ramp-core displacement dislocation model analysis, which removes the singularity in the stress, is presented. These results can be useful in a multiscale dislocation dynamics modeling with inertia effects.