Abstract：A new two-dimensional cellular automata and finite difference (CA-FD) model of dendritic growth was improved, which a perturbation function was introduced to control the growth of secondary and tertiary dendrite, the concentration of the solute was clearly defined as the liquid solute concentration and the solid-phase solute concentration in dendrite growth processes, and the eight moore calculations method was used to reduce the anisotropy caused by the shape of the grid in the process of redistribution and diffusion of solute. Single and multi equiaxed dendrites along different preferential direction, single and multi directions of columnar dendrites of Al-4% Cu alloy were simulated, as well as the distribution of liquid solute concentration and solid solute concentration. The simulation results show that the introduced perturbation function can promote the dendrite branching, liquid/solid phase solute calculation model is able to simulate the solute distribution of liquid/solid phase accurately in the process of dendritic growth, and the improved model can realize competitive growth of dendrite in any direction.
HE Y Z, DING H L, LIU L F, et al. Computer simulation of 2D grain growth using a cellular automata model based on the lowest energy principle[J]. Materials Science and Engineering:A, 2006, 429(1-2):236-246.
陈晋.基于元胞自动机方法的凝固过程微观组织数值模拟[D].南京:东南大学,2005. CHEN J. Numerical simulation on solidification microstructures using cellular automaton method[D]. Nanjing:Southeast University,2005.
HONG C P, ZHU M F, LEE S Y. Modeling of dendritic growth in alloy solidification with melt convection[J]. Tech Science Press, 2006, 2(4):247-260.
LI Q, GUO Q Y, LI R D. Numerical simulation of dendrite growth and microsegregation formation of binary alloys during solidification process[J]. Chinese Physics, 2006, 15(4):778-791.
LI J J, WANF J C, YANG G C. Phase-field simulation of microstructure development involving nucleation and crystallographic orientations in alloy solidification[J]. Journal of Crystal Growth, 2007, 309(1):65-69.
LI D, LI R, ZHANG P W. A cellular automaton technique for modelling of a binary dendritic growth with convection[J]. Applied Mathematical Modelling, 2007,31(6):971-982.
YIN H, FELICELLI S D. Dendrite growth simulation during solidification in the lens process[J]. Acta Materialia, 2010, 58(4):1455-1465.
陈守东,陈敬超,吕连灏. 基于CA-FE的双辊连铸纯铝凝固组织模拟[J]. 材料工程, 2012, (10):48-53. CHEN S D, CHEN J C, LU L H. Numerical simulation of solidified microstructure of Twin-roll continuous casting pure aluminum based on CA-FE method[J]. Journal of Materials Engineering, 2012, (10):48-53.
MINORU Y, YUKINOBU N, HIROSHI H, et al. Numerical simulation of solidification structure formation during continuous casting in Fe-0.7mass%C alloy using cellular automaton method[J]. ISIJ International, 2006, 46(6):903-908.
付振南,许庆彦,熊守美. 基于概率捕获模型的元宝自动机方法模拟镁合金枝晶生长过程[J]. 中国有色金属学报, 2007,17(10):1567-1573. FU Z N, XU Q Y, XIONG S M. Numerical simulation on dendrite growth process of Mg alloy using cellular automaton method based on probability capturing model[J]. The Chinese Journal of Nonferrous Metals, 2005, 41(6):583-587.
ZHAN X H, WEI Y H, DONG Z B. Cellular automaton simulation of grain growth with different orientation angles during solidification process[J]. Journal of Materials Processing Technology, 2008, 208(1-3):1-3.
HAKAN H, MATTI R. Microstructure evolution influenced by dislocation density gradients modeled in a reaction diffusion system[J]. Computational Materials Science, 2013, 67:373-383.
MOHSEN A Z, HEBI Y. Comparison of cellular automaton and phase field models to simulate dendrite growth in hexagonal crystals[J]. Materials Science Technology, 2012, 28(2):137-146.
ZHU M F, DAI T, LEE S Y, et al. Modeling of solutal dendritic growth with melt convection[J]. Computers and Mathematics with Applications, 2008, 55(7):1620-1628.
LUO S, ZHU M Y. A two-dimensional model for the quantitative simulation of the dendritic growth with cellular automaton method[J]. Computational Materials Science, 2013, 71:10-18.