A crystal symmetry-invariant Kobayashi--Warren--Carter grain boundary model and its implementation using a thresholding algorithm

Jaekwang Kim, M. Jacobs, S. Osher, N. Admal
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引用次数: 2

Abstract

One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme thermomechanical loads. A unified framework to study the coevolution of grain boundaries with bulk plasticity has recently been developed by Admal et al. (2018), which is based on modeling grain boundaries as continuum dislocations governed by an energy based on the Kobayashi--Warren--Carter (KWC) model (Kobayashi et al., 1998, 2000). While the resulting unified model demonstrates coupled grain boundary motion and polygonization (seen in recrystallization), it is restricted to grain boundary energies of the Read--Shockley type, which applies only to small misorientation angles. In addition, the implementation of the unified model using finite elements inherits the computational challenges of the KWC model that originate from the singular diffusive nature of its governing equations. The main goal of this study is to generalize the KWC functional to grain boundary energies beyond the Read--Shockley-type that respect the bicrystallography of grain boundaries. The computational challenges of the KWC model are addressed by developing a thresholding method that relies on a primal dual algorithm and the fast marching method, resulting in an O(NlogN) algorithm, where N is the number of grid points. We validate the model by demonstrating the Herring angle relation, followed by a study of the grain microstructure evolution in a two-dimensional face-centered cubic copper polycrystal with crystal symmetry-invariant grain boundary energy data obtained from the lattice matching method of Runnels et al. (2016a,b).
晶体对称不变的Kobayashi- Warren- Carter晶界模型及其阈值算法实现
晶界建模最重要的目的之一是预测在极端热机械载荷下发生的异常晶粒生长、耦合晶界运动和再结晶等现象中大量晶粒的演化。Admal等人(2018)最近开发了一个统一的框架来研究晶界与体塑性的共同演化,该框架基于将晶界建模为由基于Kobayashi- Warren- Carter (KWC)模型的能量控制的连续位错(Kobayashi et al., 1998,2000)。虽然所得的统一模型显示了耦合的晶界运动和多边形化(见于再结晶),但它仅限于Read- Shockley类型的晶界能量,这仅适用于小的取向偏差角。此外,使用有限元的统一模型的实现继承了KWC模型的计算挑战,这些挑战源于其控制方程的奇异扩散性质。本研究的主要目的是将KWC泛函推广到考虑晶界双晶学的Read—shockley型之外的晶界能。KWC模型的计算挑战通过开发一种阈值方法来解决,该方法依赖于原始对偶算法和快速前进方法,从而产生O(NlogN)算法,其中N是网格点的数量。我们通过展示Herring角关系验证了该模型,然后利用Runnels等人(2016a,b)的晶格匹配方法获得的晶体对称性不变晶界能量数据,研究了二维面心立方铜多晶的晶粒微观结构演变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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