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Analysis for a dislocation (screw/edge) accelerating through the shear-wave speed


Supersonic motion of dislocation in solids is a topic of hot current research endeavor. The approach is mostly based on molecular dynamics and computer simulation. There is concurring evidence that dislocations cross the shear wave speed barrier, in particular under shock loading condition. Here the analytic solution is presented for a dislocation, both screw and edge, accelerating through the shear-wave speed barrier. The analysis is based on solution for general motion of a Volterra dislocation, obtained and evaluated at the instant when the velocity of the dislocation is equal to the shear-wave speed, but acceleration is present. At this transition, the Mach wave cone is starting to form and the roots of the function that defines the interval of the dislocation motion the wavelets from which contribute to the wave-front change from complex conjugate to real, and the coefficient of the delta function of the stress at the forming Mach wave cone is logarithmic-over-square-root singular. While the step discontinuity of the displacement of a Volterra dislocation is too strong of a dislocation model for the crystal dislocation, the solution is useful because it is the kernel for a variable core model, which removes the singularity as shown here. Moreover, except in the neighborhood of the core, the analytic solution can provide comparisons for the molecular dynamics simulation solutions

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