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

TL;DR

This study numerically investigates shock-driven dislocation nucleation and self-organization in a dynamic Peierls model, revealing how dislocation behaviors depend on stress front speed and amplitude, with distinct zone formations and scaling laws.

Contribution

It introduces a numerical approach to analyze dislocation nucleation and self-organization under shock conditions, highlighting new insights into dislocation dynamics at high speeds.

Findings

Dislocation pairs nucleate with speeds near or exceeding wave speeds.

Plastic waves self-organize into bulk and front zones.

Dislocation densities follow a specific stress-dependent scaling law.

Abstract

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 $0<\beta<1$.