Cell structure formation in a two-dimensional density-based dislocation dynamics model

TL;DR

This paper presents a minimal two-dimensional dislocation density model that analytically and numerically investigates the formation of cellular patterns during plastic deformation, revealing their connection to strain hardening.

Contribution

It introduces a simplified analytical model for dislocation pattern formation, linking cell structures directly to strain hardening mechanisms.

Findings

Analytical stability criteria for cell structure emergence.

Pattern wavelength selection mechanism identified.

Cell formation closely related to strain hardening, independent of cross slip.

Abstract

Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is easily amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate the dynamics of the patterning process and establish the mechanism of pattern wavelength selection. This analysis demonstrates an intimate relationship between hardening and cell structure formation, which appears as an almost inevitable corollary to strain hardening itself. Specific mechanisms such as cross slip, by contrast, turn out to be incidental to the formation of cellular patterns.