Pattern formation in a minimal model of continuum dislocation plasticity

TL;DR

This paper introduces a minimal continuum model showing that strain hardening and dislocation kinematics alone can lead to the formation of heterogeneous dislocation patterns during plastic deformation.

Contribution

It presents a simplified, fundamental model demonstrating that basic physical mechanisms are sufficient for dislocation pattern formation.

Findings

Dislocation patterns emerge from strain hardening and dislocation kinematics.

The model reproduces patterns consistent with the principle of similitude.

Pattern formation occurs without complex interactions or additional mechanisms.

Abstract

The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect communities, there is no general consensus regarding the physical mechanism which leads to the formation of dislocation patterns. In order to establish the fundamental mechanism, we formulate an extremely simplified, minimal model to investigate the formation of patterns based on the continuum theory of fluxes of curved dislocations. We demonstrate that strain hardening as embodied in a Taylor-type dislocation density dependence of the flow stress, in conjunction with the structure of the kinematic equations that govern dislocation motion under the action of external stresses, is already sufficient for the formation of dislocation patterns that are consistent with the principle of similitude.