( 1. 南昌大學(xué) 材料科學(xué)與工程學(xué)院， 南昌 330047;
2. 南昌大學(xué) 機(jī)電工程學(xué)院， 南昌 330029)
摘 要: 通過引入溶質(zhì)再分配、 溶質(zhì)擴(kuò)散、界面能各向異性和界面曲率， 構(gòu)建了描述合金凝固微觀組織形態(tài)演變的元胞自動(dòng)機(jī)模型。 在介觀和微觀尺度上的模擬結(jié)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(jié)果清晰地再現(xiàn)了與實(shí)測(cè)結(jié)果相一致的枝晶形態(tài)和生長(zhǎng)現(xiàn)象。 根據(jù)分形理論采用分維定量比較了模擬結(jié)果和實(shí)驗(yàn)結(jié)果， 兩者的計(jì)盒維數(shù)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(jié)果表明熔體過冷度和樹枝晶的計(jì)盒維數(shù)呈近似拋物線關(guān)系。
關(guān)鍵字: 微觀組織模擬； 多尺度； 元胞自動(dòng)機(jī)； 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
