Mechanical Instability Criterion of Dislocation Structures Based on Discrete Dislocation Dynamics

Abstract

To understand the nature of mechanical instabilities of dislocation structures, e.g., veins and persistent slip bands (PSBs), as an origin of fatigue or plastic behavior in metals, it is essential to evaluate a critical mechanical condition where a dislocation structure collapses. In this paper, we developed an analytical method to describe the instability criterion for arbitrary dislocation structures based on the discrete dislocation dynamics (DDD) concept. According to the proposed method, the mechanical instability starts when the minimum eigenvalue of the Hessian matrix of the potential energy reaches zero. The corresponding eigenvector indicates the displacement of dislocations at the instability. We applied the method to veins and dislocation walls with the Taylor-Nabarro lattices under external loading, and it can successfully describe the onset of instability as well as their displacement mode, regardless of difference of their structure and size. This clearly indicates the validity of the proposed method. The success enables us to address mechanical instability issues on more complicated dislocation structures.