本文在已有的二元初生相元胞自动机(CA)方法的基础上, 针对二元共晶凝固过程提出了改进的元胞自动机(MCA)模型. 该模型考虑成分过冷和曲率过冷对界面形态的影响, 通过界面溶质浓度守恒来获得共晶α相和β相生长速率, 模拟了层片的湮灭、分叉与稳态生长. 为了验证模型的可靠性, 对常见的 CBr4-C2Cl6共晶透明合金进行了模拟, 研究了抽拉速率对共晶层片间距大小的影响, 模拟结果与文献中的实验结果吻合良好; 同时模拟了共晶层片间距调整过程的形貌演化以及层片振荡不稳定性现象. 本文将 MCA模型扩展到三维定向凝固过程中, 研究了共晶形态的层--棒状转变机制.
Eutectic microstructures are one of the most common solidification patterns in the binary or multi-component alloy systems. Due to the fine periodic microstructures of the eutectic alloys, the commercial applications of the eutectic alloys can improve the mechanical properties of the castings. The solidification mechanism of eutectic alloys has been widely studied by a lot of experimental works and theoretical analysis over the years. Recently, numerical models were used to study the mechanisms of formation of phase patterns and selection dynamics of the lamellar eutectic, such as phase field (PF) and cellular automaton (CA) model, which can promote the development of eutectic growth theory. Based on the existing CA method for binary primary α phase, a modified cellular automaton (MCA) model was developed for the simulation of binary eutectic growth. In this model, the influence of constitutional and curvature undercooling on the interface morphology was considered. The growth rate of eutectic interface was calculated by the solute conservation at the $\alpha$/liquid and $\beta$/liquid interfaces. The model could simulate the phenomenon of overgrowth, splitting and steady state growth of the eutectic lamellar. CBr4-C2Cl6 eutectic transparent alloy was chosen to validate the model. The simulated results showed that the increasing pulling rate lead to a smaller eutectic lamellar spacing, which had a good agreement with the Jackson--Hunt theory and the experimental results from the literature. Eutectic morphology evolution was simulated under a constant pulling rate and temperature gradient, which showed that the stable lamellar structures existed when the initial lamellar spacing was in a finite range between the minimum stable spacing λm and the limiting maximum stable spacing λm. A smaller initial lamellar spacing would lead to lamellar annihilation. Conversely, a larger initial lamellar spacing could lead to the lamellar nucleation due to the appearance of solute rich concave at the center of the α/liquid interface. Meanwhile, the oscillatory instability of the eutectic lamellar was also reappeared by the MCA model. The MCA model was easily extended to 3D, and the lamellar-rod transition during directional solidification was simulated, which showed that the ratio of volume fraction of α and β phase was smaller than 1/Π tend to form lamellar-rod transition when the initial lamellar spacing was smaller than λm.
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