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 $\sigma_{\rm a}$ moving with speed $V$ is investigated by solving numerically the Dynamic Peierls Equation with an efficient method. Speed $V$ and amplitude $\sigma_{\rm a}$ are considered as independent variables, with $V$ possibly exceeding the longitudinal wavespeed $c_{\rm L}$. Various reactions between dislocations take place such as scattering, dislocation-pair nucleation, annihilation, and crossing. Pairs of edge dislocation are always nucleated with speed $v\gtrsim c_{\rm L}$ (and likewise for screws with $c_{\rm L}$ replaced by $c_{\rm S}$, the shear wavespeed). 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 $((\sigma_a/\sigma_{\rm th})^2-1)^\beta$, where $\sigma_{\rm th}$ represents the nucleation threshold and $0<\beta<1$.