Abstract Three-dimensional grain growth behaviors under anisotropic (misorientation-dependent) grain boundary energy and mobility are investigated via phase-field simulations. Based on a multi-phase-field model and parallel graphics-processing unit computing on a supercomputer, very large-scale simulations with more than three million grains are achieved, enabling reliable statistical evaluation of anisotropic grain growth. The anisotropic boundary properties are introduced by the classical Read-Shockley and sigmoidal models; the threshold misorientation angle, Δθh, included in these models is used as a quantity to determine the anisotropy strength of the system. Systematic simulations are performed for different Δθh values, through which the correlations between the anisotropy strength and grain growth characteristics such as grain size and misorientation distributions are examined. The obtained results show that anisotropic grain growth reaches the steady-state regime irrespective of the Δθh value. However, the kinetics and microstructural morphology during the steady-state growth are largely dependent on Δθh. Furthermore, by comparison with the simulated results, the applicability of analytical grain growth theories to anisotropic systems are tested. The tests reveal that the steady-state microstructure in anisotropic growth cannot be well captured by the existing theories, which is likely because the basic assumptions of the theories do not hold for anisotropic systems.

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各向异性晶粒生长的大规模相场研究：依赖于错误取向的晶界能量和迁移率的影响

摘要 通过相场模拟研究了在各向异性（依赖于错误取向）晶界能量和迁移率下的三维晶粒生长行为。基于超级计算机上的多相场模型和并行图形处理单元计算，实现了超过 300 万个晶粒的超大规模模拟，从而能够对各向异性晶粒生长进行可靠的统计评估。各向异性边界属性由经典的 Read-Shockley 和 sigmoidal 模型引入；这些模型中包含的阈值取向角 Δθh 用作确定系统各向异性强度的数量。对不同的 Δθh 值进行系统模拟，通过它可以检查各向异性强度与晶粒生长特征（例如晶粒尺寸和取向差分布）之间的相关性。获得的结果表明，无论 Δθh 值如何，各向异性晶粒生长均达到稳态状态。然而，稳态生长期间的动力学和微观结构形态在很大程度上取决于 Δθh。此外，通过与模拟结果的比较，检验了分析晶粒生长理论对各向异性系统的适用性。测试表明，现有理论无法很好地捕捉各向异性生长中的稳态微观结构，这可能是因为这些理论的基本假设不适用于各向异性系统。获得的结果表明，无论 Δθh 值如何，各向异性晶粒生长均达到稳态状态。然而，稳态生长期间的动力学和微观结构形态在很大程度上取决于 Δθh。此外，通过与模拟结果的比较，检验了分析晶粒生长理论对各向异性系统的适用性。测试表明，现有理论无法很好地捕捉各向异性生长中的稳态微观结构，这可能是因为这些理论的基本假设不适用于各向异性系统。获得的结果表明，无论 Δθh 值如何，各向异性晶粒生长均达到稳态状态。然而，稳态生长期间的动力学和微观结构形态在很大程度上取决于 Δθh。此外，通过与模拟结果的比较，检验了分析晶粒生长理论对各向异性系统的适用性。测试表明，现有理论无法很好地捕捉各向异性生长中的稳态微观结构，这可能是因为这些理论的基本假设不适用于各向异性系统。测试了分析晶粒生长理论对各向异性系统的适用性。测试表明，现有理论无法很好地捕捉各向异性生长中的稳态微观结构，这可能是因为这些理论的基本假设不适用于各向异性系统。测试了分析晶粒生长理论对各向异性系统的适用性。测试表明，现有理论无法很好地捕捉各向异性生长中的稳态微观结构，这可能是因为这些理论的基本假设不适用于各向异性系统。