元胞自动机法模拟铝合金三维枝晶生长

Simulating the Three-Dimensional Dendritic Growth of Al Alloy Using the Cellular Automata Method

以元胞自动机模型为基础,基于晶粒形核和生长的物理过程及热质传输过程,建立了铝合金凝固过程微观组织形成及枝晶形貌演化的三维元胞自动机模型。与传统的元胞自动机不同,该模型不仅考虑了温度场扩散而且考虑了固液相中的溶质扩散、曲率过冷等重要因素。枝晶尖端生长速度与局部过冷度的关系采用KGT(Kurz-Giovanola-Trivedi)模型,温度场和浓度场计算采用有限差分法。使用该模型模拟了单晶生长和多晶生长。模拟结果表明,所建立的模型能够合理反映质点形核、单晶粒生长和多晶粒生长,微观组织形貌的模拟计算结果合理。

Based on physical process of nucleation and growth of grains and basic transfer equations such as heat and solute transfer equations, we develop a Cellular Automaton (CA) model for the three-dimensional simulation of microstructure, microsegregation and free dendritic growth of aluminium alloys. The growth of the dendritic is controlled by CA method. Different from the classical cellular automata in which only the temperature field is calculated, this model includes both the solute diffusion in liquid and in solid and curvature undercooling, which have vital influence on the evolution of microstructure. The relationship between the growth velocity of a dendrite tip and the local undercooling is calculated according to the KGT (Kurz-Giovanola-Trivedi) model. The finite difference method is used to calculate the temperature and solute fields in the calculation domain. The model is applied to predict the microstructure, such as growth of single crystal, growth of multi-crystal. Simulated results show that the nucleation, growth of single crystal, and multi-crystal and microstructure evolution of free dendritic crystal could be predicted reasonably. The calculated results are coincident with actual phenomena.