Deformation band patterns and dislocation structures in finite strain crystal viscoplasticity

TL;DR

This paper investigates deformation band patterns and dislocation structures in single crystals and polycrystals using a finite strain crystal viscoplasticity model, revealing the influence of material parameters, boundary conditions, and strain gradient plasticity on microstructure formation.

Contribution

It introduces a comprehensive model incorporating strain gradient plasticity to predict pattern sizes and demonstrates the generality of deformation patterns in both single crystals and polycrystals.

Findings

Deformation patterns depend on material and numerical parameters.

Strain gradient plasticity introduces a length scale controlling pattern size.

Patterns are observed in both 2D and 3D crystal structures.

Abstract

Deformation band patterning in single crystals is investigated using a finite strain crystal viscoplasticity model based on the evolution of dislocation densities. In the presence of strong latent hardening and weak rate dependence, the deformation organizes into laminate microstructures consisting of single-slip regions separated by dislocation walls. The influence of material and numerical parameters on the nucleation and morphology of these patterns is analyzed in 2D single crystals under plane strain compression. Pattern formation is also observed in 3D single-crystal cylinders subjected to tension, where the characteristic size of deformation microstructures is found to depend on mesh size and boundary conditions in the absence of an intrinsic material length scale. To address this limitation, strain gradient plasticity is introduced, providing a length scale that governs the size of the patterns. Finally, we demonstrate that deformation patterns and dislocation structures also emerge in 2D and 3D polycrystals, highlighting the generality of the phenomenon.