( 1. 南昌大学 材料科学与工程学院， 南昌 330047;
2. 南昌大学 机电工程学院， 南昌 330029)
摘 要: 通过引入溶质再分配、 溶质扩散、界面能各向异性和界面曲率， 构建了描述合金凝固微观组织形态演变的元胞自动机模型。 在介观和微观尺度上的模拟结果表明， 该模型可有效地解决微观组织形成的多尺度问题。模拟结果清晰地再现了与实测结果相一致的枝晶形态和生长现象。 根据分形理论采用分维定量比较了模拟结果和实验结果， 两者的计盒维数分别为1.703和1.694， 阐述了分维定量表征枝晶形貌的物理含义。 模拟结果表明熔体过冷度和树枝晶的计盒维数呈近似抛物线关系。
关键字: 微观组织模拟； 多尺度； 元胞自动机； 分维
（ 1. School of Materials Science and Engineering, Nanchang University,Nanchang 330047, China；
2. School of Mechanical and Electronic Engineering, Nanchang University,Nanchang 330029, China）
Abstract: A modified model was built up by adopting solute diffusion, solute redistribution, interface anisotropy and interface curvature at S/L interface. Simulation results at mesoscopic and microscopic levels exhibit a number of experimental features, which indicate that the present model can effectively solve the multi-scale problem during solidification. Based on the fractal theory, the dendritic morphologies from simulation and experiment were compared using fractal dimension, the box counting dimensions of simulation and experiment results are 1.703 and 1.694 respectively. The physical meanings of fractal dimension characterizing dendritic morphology was discussed. The results of simulations indicate that the relationship between melt undercooling and box counting dimension of dendrite is close to parabola.
Key words: microstructure modeling； multi-scale； cellular automaton； fractal dimension
