Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

TL;DR

This paper provides a comprehensive theoretical and numerical analysis of Gurtin's grain-boundary model, incorporating grain misorientation and orientation, with finite element implementation and comparison of kinematic measures.

Contribution

It introduces an alternative kinematic measure for grain boundary impediment and demonstrates the model's application through 3D numerical examples.

Findings

Different kinematic measures impact the model's predictions

The alternative measure offers a new perspective on grain boundary behavior

Numerical examples validate the theoretical framework

Abstract

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory.