A micropolar continuum model of diffusion creep

TL;DR

This paper extends traditional diffusion creep models by incorporating grain rotation through a micropolar continuum approach, providing more comprehensive constitutive laws for different creep mechanisms and illustrating their effects with a 2D grain model.

Contribution

It introduces a micropolar (Cosserat) continuum model for diffusion creep, including grain rotation, and derives new constitutive laws from homogenization of discrete grain physics.

Findings

Derived constitutive tensors for Coble and Nabarro-Herring creep.

Illustrated coupling between grain rotation and translation in a 2D grain model.

Identified degeneracy in pure boundary diffusion modes and ways to address it.

Abstract

Solid polycrystalline materials undergoing diffusion creep are usually described by Cauchy continuum models with a Newtonian viscous rheology dependent on the grain size. Such a continuum lacks the rotational degrees of freedom needed to describe grain rotation. Here we provide a more general continuum description of diffusion creep that includes grain rotation, and identifies the deformation of the material with that of a micropolar (Cosserat) fluid. We derive expressions for the micropolar constitutive tensors by a homogenisation of the physics describing a discrete collection of rigid grains, demanding an equivalent dissipation between the discrete and continuum descriptions. General constitutive laws are derived for both Coble (grain-boundary diffusion) and Nabarro-Herring (volume diffusion) creep. Detailed calculations are performed for a two-dimensional tiling of irregular hexagonal grains, which illustrates a potential coupling between the rotational and translational degrees of freedom. If only the plating out or removal of material at grain boundaries is considered, the constitutive laws are degenerate: modes of deformation that involve pure tangential motion at the grain boundaries are not resisted. This degeneracy can be removed by including the resistance to grain-boundary sliding, or by imposing additional constraints on the deformation.