改进元胞自动机法数值模拟高温合金凝固过程枝晶生长行为
Numerical Simulation of Dendritic Growth Behavior in Solidification of Superalloy by an Improved Cellular Automaton Method
摘 要
提出了一种改进元胞自动机方法，该法充分考虑了溶质场和热扩散对枝晶生长的作用，并基于溶质场方程的27点离散格式，对多元高温合金凝固时的枝晶生长行为进行了数值模拟和试验对比，研究了枝晶生长形貌演变和单晶叶片铸件杂晶形成规律。结果表明：增大过冷度能促进枝晶快速生长，但由于溶质富集，单晶粒枝晶尖端生长速率随时间延长而逐渐减小；当冷却速率较低时，铸件等截面区域偏离热流取向的枝晶会淘汰与热流取向相同的枝晶；在定向凝固枝晶生长中，等温线内凹温度场中的变截面区域易形成杂晶；上述模拟计算结果和试验结果及相关文献的研究结果一致，该改进元胞自动机方法具有一定的有效性和实用性。
高温合金
枝晶生长
数值模拟
cellular automaton
superalloy
dendritic growth
numerical simulation
Abstract
An improved cellular automata method, fully considering the combined effect of solute field and thermal diffusion on dendrite growth, was proposed. Based on the 27-point discrete scheme of solute field equation, the numerical simulation of the dendritic growth behavior in multi-element superalloy solidification was carried out and compared with the experimental results. The dendritic growth morphology evolution and the stray grain formation in single crystal blade casting were studied. The results show that increasing the undercooling degree could promote the dendritic growth, but the growth rate of the single crystal dendrite tip gradually decreased with time due to solute enrichment. At low cooling rates, dendrites deviating from the heat flow direction eliminated dendrites with the same orientation as the heat flow. In the process of directional solidification dendritic growth, the stray grains were easy to form in the variable cross-section region with the concave isotherm. The simulation results are consistent with the experimental results and the research results of related literatures, indicating that the improved cellular automaton method is effective and practical.
中图分类号 TG244.3 DOI 10.11973/jxgccl202002013
所属栏目 物理模拟与数值模拟
基金项目 国家自然科学基金资助项目（51475181）；先进航空轻质合金材料精密铸造联合实验室资助项目
收稿日期 2019/2/26
修改稿日期 2020/1/7
网络出版日期
作者单位点击查看
备注郭钊(1988-),男,湖北咸宁人,博士研究生
引用该论文: GUO Zhao,ZHOU Jianxin,SHEN Xu,YIN Yajun,JI Xiaoyuan,WANG Sheng. Numerical Simulation of Dendritic Growth Behavior in Solidification of Superalloy by an Improved Cellular Automaton Method[J]. Materials for mechancial engineering, 2020, 44(2): 65～72
郭钊,周建新,沈旭,殷亚军,计效园,王圣. 改进元胞自动机法数值模拟高温合金凝固过程枝晶生长行为[J]. 机械工程材料, 2020, 44(2): 65～72
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参考文献
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【2】霍苗,刘林,黄太文,等. 镍基单晶高温合金小角度晶界的形成机制、影响因素与控制措施[J]. 材料导报,2018,32(19):3394-3404.
【3】高翔,燕群,杭超,等. 涡轮叶片高温振动特性试验技术研究[J]. 装备环境工程,2018,15(9):61-65.
【4】STEFANESCU D M. Length-scale in solidification analysis[M]//Science and Engineering of Casting Solidification. Cham:Springer International Publishing, 2015.
【5】RAPPAZ M,GANDIN A.Probabilistic modelling of microstructure formation in solidification processes[J].Acta Metallurgica et Materialia, 1993,41(2):345-360.
【6】DILTHEY U, PAVLIK V. Numerical simulation of dendrite morphology and grain growth with modified cellular automata[C]//Modeling of Casting, Welding and Advanced Solidification Processes VIII. San Diego,CA:Minerals, Metals & Naterials Society, 1998.
【7】NASTAC L. Simulation of microstructure evolution during solidification processes[D]. Tuscaloosa:University of Alabama, 1995.
【8】NASTAC L. Numerical modeling of solidification morphologies and segregation patterns in cast dendritic alloys[J].Acta Materialia, 1999,47(17):4253-4262.
【9】SHIN Y H, HONG C P. Modeling of dendritic growth with convection using a modified cellular automaton model with a diffuse interface[J].ISIJ International, 2002,42(4):359-367.
【10】BELTRAN-SANCHEZ L,STEFANESCU D M. Growth of solutal dendrites:A cellular automaton model and its quantitative capabilities[J]. Metallurgical and Materials Transactions A, 2003, 34(2):367-382.
【11】BELTRAN-SANCHEZ L, STEFANESCU D M.A quantitative dendrite growth model and analysis of stability concepts[J].Metallurgical and Materials Transactions A,2004,35(8):2471-2485.
【12】ZHU M,STEFANESCU D.Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys[J].Acta Materialia, 2007, 55(5):1741-1755.
【13】PAN S Y,ZHU M F.A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth[J].Acta Materialia, 2010, 58(1):340-352.
【14】WANG W,LEE P D,MCLEAN M.A model of solidification microstructures in nickel-based superalloys:Predicting primary dendrite spacing selection[J].Acta Materialia, 2003, 51(10):2971-2987.
【15】XU Q Y,ZHANG H,QI X,et al.Multiscale modeling and simulation of directional solidification process of turbine blade casting with MCA method[J].Metallurgical and Materials Transactions B, 2014, 45(2):555-561.
【16】YUAN L, LEE P D.A new mechanism for freckle initiation based on microstructural level simulation[J].Acta Materialia, 2012, 60(12):4917-4926.
【17】ZHANG X F,ZHAO J Z,JIANG H X,et al.A three-dimensional cellular automaton model for dendritic growth in multi-component alloys[J].Acta Materialia,2012,60(5):2249-2257.
【18】王锦程,郭春文,李俊杰,等.定向凝固晶粒竞争生长的研究进展[J].金属学报,2018,54(5):657-668.
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