Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches
Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches
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三元共晶相场模拟与分析 3D JacksonâHunt 方法的定量比较
DOI：
10.1007/s11663-017-1142-2
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Nestler
中科院分区：
文献类型：
--
作者：
P. Steinmetz;M. Kellner;J. Hötzer;B. Nestler
对于三元共晶定向凝固过程中过冷度、片层间距和生长速度之间关系的解析描述，文献中报道了基于杰克逊和Hunt理论的不同扩展。除了解析方法外，相场法已被建立来研究共晶合金凝固过程中空间复杂的组织演变。了解的基本机制控制的形态发展，在多相，多组分系统的高度兴趣。为此，在一个理想的三元共晶系的定向凝固的解析扩展和三维相场模拟之间的比较。根据观察到的一致性，在二维验证的情况下，实验报告，固有的三维链状图案进行了广泛的模拟研究。结果进行了定量比较与文献中报道的分析结果，并与新派生的方法，使用相等的过冷度。结果表明，基于Grand势方法的相场模型能够较好地描述三元共晶系定向凝固过程中过冷度与片层排列之间的关系。
For the analytical description of the relationship between undercoolings, lamellar spacings and growth velocities during the directional solidification of ternary eutectics in 2D and 3D, different extensions based on the theory of Jackson and Hunt are reported in the literature. Besides analytical approaches, the phase-field method has been established to study the spatially complex microstructure evolution during the solidification of eutectic alloys. The understanding of the fundamental mechanisms controlling the morphology development in multiphase, multicomponent systems is of high interest. For this purpose, a comparison is made between the analytical extensions and three-dimensional phase-field simulations of directional solidification in an ideal ternary eutectic system. Based on the observed accordance in two-dimensional validation cases, the experimentally reported, inherently three-dimensional chain-like pattern is investigated in extensive simulation studies. The results are quantitatively compared with the analytical results reported in the literature, and with a newly derived approach which uses equal undercoolings. A good accordance of the undercooling–spacing characteristics between simulations and the analytical Jackson–Hunt apporaches are found. The results show that the applied phase-field model, which is based on the Grand potential approach, is able to describe the analytically predicted relationship between the undercooling and the lamellar arrangements during the directional solidification of a ternary eutectic system in 3D.
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