Motion of grain boundaries incorporating dislocation structure

Abstract

In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion of grain boundaries (i.e., motion of the constituent dislocations in the grain boundary normal direction) and equations for the dislocation structure evolution on the grain boundaries. This model is derived from the discrete dislocation dynamics model. The long-range elastic interaction between dislocations is included in the continuum model, which ensures that the dislocation structure on a grain boundary is consistent with the Frank's formula. These evolutions of the grain boundary and its dislocation structure are able to describe both normal motion and tangential translation of the grain boundary and grain rotation due to both coupling and sliding. Since the continuum model is based upon dislocation structure, it naturally accounts for the grain boundary shape change during the motion and rotation of the grain boundary by motion and reaction of the constituent dislocations. Using the derived continuum grain boundary dynamics model, simulations are performed for the dynamics of circular and non-circular two dimensional grain boundaries, and the results are validated by discrete dislocation dynamics simulations.

A Continuum Multi-Disconnection-Mode model for grain boundary migration

“…Cahn and Taylor (Cahn and Taylor, 2004;Taylor and Cahn, 2007) proposed a description that couples curvature-driven GB motion to mechanical stresses and describes grain boundary sliding and grain rotation. Zhang and Xiang (2018) developed a continuum model for shear coupling in low-angle GBs in terms of the motion and reaction of the constituent dislocations that constitute the GB structure.…”

“…Substantial experimental and atomistic simulation evidence exists for the presence of shearcoupled migration in high-angle GBs (Winning et al, 2001;Gottstein et al, 2001;Winning et al, 2002;Rupert et al, 2009;Molteni et al, 1996Molteni et al, , 1997Hamilton and Foiles, 2002;Chen and Kalonji, 1992;Shiga and Shinoda, 2004;Sansoz and Molinari, 2005;Trautt et al, 2012;Homer et al, 2013). Zhang and Xiang (2018) developed a continuum model for shear coupling in low angle GBs in terms of the motion and reaction of the constituent dislocations that constitute the GB structure. Recent experiments and simulations demonstrated that the shear-coupling of highangle GBs (Rajabzadeh et al, 2013a,b;Mompiou et al, 2015) is associated with the motion of line defects known as disconnections (Bollmann, 1970;Ashby, 1972;Hirth and Pond, 1996).…”

A Three-Dimensional Continuum Simulation Method for Grain Boundary Motion Incorporating Dislocation Structure

“…[35] by a dislocation model and experimental observations that conservation and annihilation of the constituent dislocations may lead to cancelation of the coupling and sliding motions of the grain boundary, leading to the classical motion by curvature. A continuum model has been developed based on the motion and reaction of the constituent dislocations for the dynamics of low angle grain boundaries in two dimensions [50]. Their model can describe both the coupling and sliding motions of low angle grain boundaries.…”

“…In this paper, we generalize the two-dimensional continuum model for grain boundary dynamics in Ref. [48,50] to three dimensions, where grain boundaries and their constituent dislocations are curved in general. The three-dimensional continuum model for the dynamics of grain boundaries incorporates the motion and reaction of the constituent dislocations, and is able to describe both coupling and sliding motions of the grain boundaries, to which the classical motion by mean curvature model does not apply.…”

Atomistic survey of grain boundary-dislocation interactions in FCC nickel

“…Researchers have developed mesoscale models, like the discrete dislocation dynamics model [28][29][30] to model the dislocation-GB interactions seen experimentally and have shown that the Hall-Petch relationship is dependent on the ability of dislocations to transmit. Another model, developed by Lim et al, utilizes a two-scale model called the Superdislocation (SD) model, to model the Hall-Petch effect in polycrystals using Finite Element Method (FEM) techniques [15].…”