Shock-driven nucleation and self-organization of dislocations in the dynamical Peierls model

Dynamic nucleation of dislocations caused by a stress front ("shock") of amplitude sigma(alpha) moving with speed V is investigated by solving numerically the dynamic Peierls equation with an efficient method. Speed V and amplitude sigma(alpha) are considered as independent variables, with V possibly exceeding the longitudinal wave speed c(L). Various reactions between dislocations take place such as scattering, dislocation-pair nucleation, annihilation, and crossing. Pairs of edge dislocation are always nucleated with speed upsilon greater than or similar to c(L) (and likewise for screws with c(L) replaced by c(S), the shear wave speed). The plastic wave exhibits self-organization, forming distinct "bulk" and "front" zones. Nucleations occur either within the bulk or at the zone interface, depending on the value of V. The front zone accumulates dislocations that are expelled from the bulk or from the interface. In each zone, dislocation speeds and densities are measured as functions of simulation parameters. The densities exhibit a scaling behavior with stress, given by [(sigma(alpha)/sigma th)(2) - 1](beta), where sigma th represents the nucleation threshold and 0 < beta < 1.