铝钛二元合金凝固过程数学模型的建立及应用

针对Ti〈0.15%的Al-Ti二元合金,基于三个假设：一个晶核生长过程中所产生的成分过冷为邻近晶粒的形核提供所需的形核过冷度;两个形核事件发生的距离相当于一个晶粒尺寸;忽略界面前沿温度梯度和凝固过程中结晶潜热的析出,在此基础上建立了Al-Ti二元合金凝固过程的数学模型并进行数值计算,计算了成分过冷度与相对晶粒尺寸。应用于电解低钛铝合金和熔配铝钛合金,发现电解低钛铝合金在试验室条件下的形核过冷度ΔTn=0.5~1.0K,低于传统熔配加钛的Al-Ti二元合金（ΔTn=0.8~1.5K）。对于研究电解低钛铝基合金的细化机理提供了数值基础。

Modeling of Solidification of Al-Ti Binary Alloy and Its Application in Grain Refinement

A mathematical model for the solidification of Al-Ti binary alloy with titanium content less than 0.15 wt% is developed. In the model, it is assumed that the constitutional undercooling during a grain growth is equivalent to the undercooling required for nucleation of another adjacent grain; the distance between two nucleation events is defined as the relative grain size in the final microstructure; the temperature gradient at the solid-liquid interface and the latent heat are neglected. Using the model, the constitutional undercooling and the relative grain size of the electrolytic low-titanium aluminium alloy and the traditional Al-Ti alloy are calculated. Model calculation shows that the nucleation undercooling is about 0.5-1.0 K for the electrolytic low titanium aluminum alloy and 0.8-1.5 K for the traditional one. The nucleation undercooling of the electrolytic low titanium aluminum alloys is 0.3-0.5 K lower than that of the traditional Al-Ti binary alloy. This can explain the favorable refining effects of the electrolytic low-titanium aluminium alloy. The modeling results can be used to investigate the grain refinement mechanism for the electrolytic low-titanium aluminium alloy.