( 1. 南昌大學 材料科學與工程學院， 南昌 330047;
2. 南昌大學 機電工程學院， 南昌 330029)
摘 要: 通過引入溶質再分配、 溶質擴散、界面能各向異性和界面曲率， 構建了描述合金凝固微觀組織形態(tài)演變的元胞自動機模型。 在介觀和微觀尺度上的模擬結果表明， 該模型可有效地解決微觀組織形成的多尺度問題。模擬結果清晰地再現了與實測結果相一致的枝晶形態(tài)和生長現象。 根據分形理論采用分維定量比較了模擬結果和實驗結果， 兩者的計盒維數分別為1.703和1.694， 闡述了分維定量表征枝晶形貌的物理含義。 模擬結果表明熔體過冷度和樹枝晶的計盒維數呈近似拋物線關系。
關鍵字: 微觀組織模擬； 多尺度； 元胞自動機； 分維
（ 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
