Mesoscale theory of grains and cells: crystal plasticity and coarsening

TL;DR

This paper develops a mesoscale continuum theory explaining how dislocation structures such as grains and cells form and evolve in crystalline solids, capturing phenomena like wall formation and coarsening at different temperatures.

Contribution

It introduces a novel mesoscale model based on a microscopic order parameter that describes dislocation dynamics and topological conservation, explaining wall formation and coarsening.

Findings

The theory predicts formation of sharp dislocation walls in finite time.

It accounts for dislocation climb and glide in different temperature regimes.

The model aligns with observed microstructural evolution in crystalline materials.

Abstract

Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simple, continuum explanation for the evolution of dislocations into sharp walls. We present here a mesoscale theory of dislocation motion. It provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The resulting theory is shown to form sharp dislocation walls in finite time, both with and without dislocation climb.