Equation of motion for grain boundaries in polycrystals

Luchan Zhang,Yang Xiang,Jian Han,David J Srolovitz

doi:10.1038/s41524-021-00532-6

Abstract

Grain boundary (GB) dynamics are largely controlled by the formation and motion of disconnections (with step and dislocation characters) along with the GB. The dislocation character gives rise to shear coupling; i.e. the relative tangential motion of two grains meeting at the GB during GB migration. In a polycrystal, the shear coupling is constrained by the presence of other grains and GB junctions, which prevents large-scale sliding of one grain relative to the other. We present continuum equations of motion for GBs that is based upon the underlying disconnection dynamics and accounts for this mechanical constraint in polycrystals. This leads to a reduced-order (zero-shear constrained) model for GB motion that is easily implemented in a computationally efficient framework, appropriate for the large-scale simulation of the evolution of polycrystalline microstructures. We validated the proposed reduced-order model with direct comparisons to full multi-disconnection mode simulations.

Highlights

Grain boundaries are major components of polycrystalline microstructures
We recently developed a continuum model for grain boundary (GB) migration that is based upon disconnection migration[14,15]
We proposed a continuum model that accounts for the concurrent migration of GB and the junctions along which they meet in a disconnectionbased framework[16,17]

Summary

Introduction

Grain boundaries (interfaces between domains/grains of different crystallographic orientations) are major components of polycrystalline microstructures. Traditional models for isotropic GB dynamics are based on capillarity-driven GB migration; i.e., the driving force for migration is proportional to the local GB mean curvature κ2,3 such that the normal GB velocity vn (isotropic limit) is vn = MGBγκ, where MGB is the GB mobility and γ is the GB energy. Motion by mean curvature-based continuum models are unable to adequately account for many GB migration phenomena such as stress-driven GB motion associated with disconnection dynamics. We recently developed a continuum model for GB migration that is based upon disconnection migration[14,15] These models naturally include GB migration under a wide range of driving forces (internal and applied stress, chemical potential jumps, capillarity), as well as the effect of temperature. We proposed a continuum model that accounts for the concurrent migration of GB and the junctions along which they meet in a disconnectionbased framework[16,17]

Methods

Results

Conclusion