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 f(ξ)=t-η(ξ)-b(x-ξ)2+z2 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*|1/2log|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.