基于CAFE模型的镍基合金定向凝固过程显微组织模拟
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摘要
采用CAFE模型(Cellular automata finite element method)模拟第二代镍基高温合金CMSX4凝固过程中的晶粒生长,并探讨浇注温度和冷却速度对凝固组织的影响。结果表明:凝固开始时,首先在铸锭底部会形成一层取向随机的细小等轴晶,由于晶粒间的竞争生长,晶粒数目减小,晶粒尺寸增大,?001?晶向与热流方向偏离角较大的晶粒逐渐被偏离角较小的晶粒淘汰。浇注温度的提高会使晶粒尺寸变大、晶粒数目变小,而冷却速度的升高却会使晶粒尺寸变小,与理论分析一致。
CAFE model was adopted to simulate the grain growth during solidification process of the second generation nickel-based superalloy CMSX4, and then the influences of casting temperature and cooling rate on the solidification structure were discussed. The results show that at the beginning of solidification, a layer of fine equiaxed grains with random orientation forms first. Due to the competition between the grain growth, the number of grains decreases, the grain size increases, and the grains with bigger deviation angle of the ?001? crystal orientation deviating from the direction of heat flow are gradually eliminated by the grains with small deviation angle. The increase of pouring temperature will make the grain size bigger, the number of crystal grains decreases, while the increase of cooling rate can make the grain size smaller. The results are consistent with the theoretical analysis.
CAFE model was adopted to simulate the grain growth during solidification process of the second generation nickel-based superalloy CMSX4, and then the influences of casting temperature and cooling rate on the solidification structure were discussed. The results show that at the beginning of solidification, a layer of fine equiaxed grains with random orientation forms first. Due to the competition between the grain growth, the number of grains decreases, the grain size increases, and the grains with bigger deviation angle of the ?001? crystal orientation deviating from the direction of heat flow are gradually eliminated by the grains with small deviation angle. The increase of pouring temperature will make the grain size bigger, the number of crystal grains decreases, while the increase of cooling rate can make the grain size smaller. The results are consistent with the theoretical analysis.
引文
[1]GANDIN C A,CHARBON C,RAPPAZ M.Stochastic modeling of solidification grain structure[J].ISIJ International,1995,35:651.
[2]ZAEEM M A,YIN H,FELICELLI S D.Modeling dendritic solidification of Al-3%Cu using cellular automaton and phase-field methods[J].Applied Mathematical Modelling,2013,37(5):3495-3503.
[3]张红伟,NAKAJIMA K,王恩刚,赫冀成.Al-Si合金宏观偏析、凝固组织演变的元胞自动机-控制容积法耦合模拟[J].中国有色金属学报,2012,22(7):1883-1895.ZHANG Hong-wei,NAKAJIMA K,WANG En-gang,HE Ji-cheng.Simulation of macrosegregation and solidification microstructure evolution for Al-Si alloy by coupled cellular automaton-finite volume model[J].The Chinese Journal of Nonferrous Metals,2012,21(7):1883-1895.
[4]GANDIN C H A,RAPPAZ M.Probabilistic modeling of microstructure formation in solidification processes[J].Acta Metallurgy Material,1993,39(2):345.
[5]GANDIN C H A,RAPPAZ M.A coupled finite element-cellular automaton model for the predict ion of dendritic grain structure in solidification processes[J].Acta Metallurgy Material,1994,40(7):2233.
[6]王松,谢明,王塞北,付作鑫,沈月,杜文佳,薄存继.基于CAFE法的Cu-Cr-Zr-Ag合金凝固组织模拟[J].贵金属,2013,34(3):50-54.WANG Song,XIE Ming,WANG Sai-bei,FU Zuo-xin,SHEN Yue,DU Wen-jia,BO Cun-ji.Simulation of solidified microstructures of Cu-Cr-Zr-Ag alloy based on CA-FE method[J].Precious Metals,2013,34(3):50-54.
[7]JING Cai-liang,XU Zhi-gang,WANG Ying,WANG Wan-jun.Simulation on solidification structure of 72A tire cord steel billet using CAFE method[J].China Foundry,2012,9(1):53.
[8]卜晓兵,李落星,张立强,朱必武,王水平.Al-Cu合金凝固微观组织的三维模拟及优化[J].中国有色金属学报,2011,21(9):2195-2201.BU Xiao-bing,LI Luo-xing,ZHANG Li-qiang,ZHU Bi-wu,WANG Shui-ping.Three-dimensional numerical simulation and optimization of solidification structure of Al-Cu alloy[J].The Chinese Journal of Nonferrous Metals,2011,21(9):2195-2201.
[9]仲红刚,曹欣,陈湘茹,张捷宇,翟启杰.Al-Cu合金水平单向凝固组织预测及实验观察[J].中国有色金属学报,2013,23(10):2792-2799.ZHONG Hong-gang,CAO Xin,CHEN Xiang-ru,ZHANG Jie-yu,ZHAI Qi-jie.Numerical and experimental investigation of solidification structure in horizontal directional solidification process of Al-Cu Alloy[J].The Chinese Journal of Nonferrous Metals,2013,23(10):2792-2799.
[10]张华,倪红卫,陈光友,成日金,刘吉刚.Al-Si合金凝固组织的三维模拟及预测[J].过程工程学报,2009,9(1):92-96.ZHANG Hua,NI Hong-wei,CHENG Guang-you,CHENG Ri-jin,LIU Ji-gang.Three-dimensional numerical simulation and prediction of solidification structure of Al-Si alloy[J].The Chinese Journal of Process Engineering,2009,9(1):92-96.
[11]MOHSEN A Z,HEBI Y,SERGIO D F.Modeling dendritic solidification of Al-3%Cu using cellular automaton and phase-field methods[J].Applied Mathematical Modelling,2013,37:3495-3503.
[12]RAVINDRA S S,GANESH N R,SUMITESH D.Cellular automata finite element(CAFE)model to predict the forming of friction stir welded blanks[J].Computational Materials Science,2012,58:87-100.
[13]SAUNDERS N,MIODOWNIK A P.Calculation of phase diagrams:A comprehensive guide[J].London:Oxford University Press,1998:33.
[14]庞瑞鹏,王福明,张国庆,李长荣.基于3D-CAFE法对430铁素体不锈钢凝固热参数的研究[J].金属学报,2013,49(10):1234-1242.PANG Rui-peng,WANG Fu-ming,ZHANG Guo-qing,LI Chang-rong.Study of solidification thermal parameters of 430ferrite stainless steel based on 3D-CAFE method[J].Acta Metallurgica Sinica,2013,49(10):1234-1242.
[15]KURZ W,GIOVANOLA B,TRIVEDI R.Theory of microstructural development during rapid solidification[J].Acta Metall Mater,1986,34(5):823-830.
[16]王金龙,赖朝彬,王福明,张炯明,任嵬.CAFE模型机理及应用[J].钢铁研究学报,2009,21(10):60-63.WANG Jin-long,LAI Chao-bin,WANG Fu-ming,ZHANG Jiong-ming,REN Wei.Mechanism and application of CAFE method[J].Journal of Iron and Steel Research,2009,21(10):60-63.
[17]宋迎德,郝海,古松伟,张爱民,张兴国.枝晶生长速度对微观组织数值模拟的影响研究——Ivantsov函数近似方法的确定[J].铸造技术,2011,32(1):34--38.SONG Ying-de,HAO Hai,GU Song-wei,ZHANG Ai-min,ZHANG Xing-guo.Research on the microstructure simulation determination of the approximation of Ivantsov Function[J].Foundry Technology,2011,32(1):34-38.
[18]王金龙,王福明,李长荣,程慧静.基于CAFE法优化易切削钢9SMn28锰硫比[J].热加工工艺,2009,38(5):10-13.WANG Jin-long,WANG Fu-ming,LI Chang-rong,CHENG Hui-jing.Optimization of rate of manganese to sulfur for free-cutting steel 9SMn28 based on CAFE methods[J].Hot Working Technology,2009,38(5):10-13.
[19]ZHU M F,HONG C P.A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys[J].ISIJ International,2001.
[20]王永聚,付建华,闫红红,张家齐.42Cr Mo钢环件凝固过程与组织的变化数值模拟[J].热加工工艺,2012,41(19):50-52.WANG Yong-ju,FU Jian-hua,YAN Hong-hong,ZHANG Jia-qi.Numerical simulation on solidification process and structure changes of 43Cr Mo steel ring casting[J].Hot Working Technology,2012,41(19):50-52.
[21]YANG Zhi-jun,ZHAO Xiao-hua,KOU Hong-chao,LI Jin-shan,HU Rui,ZHOU Lian.Numerical simulation of temperature distribution and heat transfer during solidification of titanium alloy ingots in vacuum arc remelting process[J].Transactions of Nonferrous Metals Society of China,2010,20(10):1957-1962.
[22]SEO S M,KIM I S,LEE J H,JO C Y,MIYAHARA H,OGI K.Grain structure prediction of Ni-base superalloy castings using the cellular automaton-finite element method[J].Materials Science and Engineering A,2007,449(13):713-716.
[2]ZAEEM M A,YIN H,FELICELLI S D.Modeling dendritic solidification of Al-3%Cu using cellular automaton and phase-field methods[J].Applied Mathematical Modelling,2013,37(5):3495-3503.
[3]张红伟,NAKAJIMA K,王恩刚,赫冀成.Al-Si合金宏观偏析、凝固组织演变的元胞自动机-控制容积法耦合模拟[J].中国有色金属学报,2012,22(7):1883-1895.ZHANG Hong-wei,NAKAJIMA K,WANG En-gang,HE Ji-cheng.Simulation of macrosegregation and solidification microstructure evolution for Al-Si alloy by coupled cellular automaton-finite volume model[J].The Chinese Journal of Nonferrous Metals,2012,21(7):1883-1895.
[4]GANDIN C H A,RAPPAZ M.Probabilistic modeling of microstructure formation in solidification processes[J].Acta Metallurgy Material,1993,39(2):345.
[5]GANDIN C H A,RAPPAZ M.A coupled finite element-cellular automaton model for the predict ion of dendritic grain structure in solidification processes[J].Acta Metallurgy Material,1994,40(7):2233.
[6]王松,谢明,王塞北,付作鑫,沈月,杜文佳,薄存继.基于CAFE法的Cu-Cr-Zr-Ag合金凝固组织模拟[J].贵金属,2013,34(3):50-54.WANG Song,XIE Ming,WANG Sai-bei,FU Zuo-xin,SHEN Yue,DU Wen-jia,BO Cun-ji.Simulation of solidified microstructures of Cu-Cr-Zr-Ag alloy based on CA-FE method[J].Precious Metals,2013,34(3):50-54.
[7]JING Cai-liang,XU Zhi-gang,WANG Ying,WANG Wan-jun.Simulation on solidification structure of 72A tire cord steel billet using CAFE method[J].China Foundry,2012,9(1):53.
[8]卜晓兵,李落星,张立强,朱必武,王水平.Al-Cu合金凝固微观组织的三维模拟及优化[J].中国有色金属学报,2011,21(9):2195-2201.BU Xiao-bing,LI Luo-xing,ZHANG Li-qiang,ZHU Bi-wu,WANG Shui-ping.Three-dimensional numerical simulation and optimization of solidification structure of Al-Cu alloy[J].The Chinese Journal of Nonferrous Metals,2011,21(9):2195-2201.
[9]仲红刚,曹欣,陈湘茹,张捷宇,翟启杰.Al-Cu合金水平单向凝固组织预测及实验观察[J].中国有色金属学报,2013,23(10):2792-2799.ZHONG Hong-gang,CAO Xin,CHEN Xiang-ru,ZHANG Jie-yu,ZHAI Qi-jie.Numerical and experimental investigation of solidification structure in horizontal directional solidification process of Al-Cu Alloy[J].The Chinese Journal of Nonferrous Metals,2013,23(10):2792-2799.
[10]张华,倪红卫,陈光友,成日金,刘吉刚.Al-Si合金凝固组织的三维模拟及预测[J].过程工程学报,2009,9(1):92-96.ZHANG Hua,NI Hong-wei,CHENG Guang-you,CHENG Ri-jin,LIU Ji-gang.Three-dimensional numerical simulation and prediction of solidification structure of Al-Si alloy[J].The Chinese Journal of Process Engineering,2009,9(1):92-96.
[11]MOHSEN A Z,HEBI Y,SERGIO D F.Modeling dendritic solidification of Al-3%Cu using cellular automaton and phase-field methods[J].Applied Mathematical Modelling,2013,37:3495-3503.
[12]RAVINDRA S S,GANESH N R,SUMITESH D.Cellular automata finite element(CAFE)model to predict the forming of friction stir welded blanks[J].Computational Materials Science,2012,58:87-100.
[13]SAUNDERS N,MIODOWNIK A P.Calculation of phase diagrams:A comprehensive guide[J].London:Oxford University Press,1998:33.
[14]庞瑞鹏,王福明,张国庆,李长荣.基于3D-CAFE法对430铁素体不锈钢凝固热参数的研究[J].金属学报,2013,49(10):1234-1242.PANG Rui-peng,WANG Fu-ming,ZHANG Guo-qing,LI Chang-rong.Study of solidification thermal parameters of 430ferrite stainless steel based on 3D-CAFE method[J].Acta Metallurgica Sinica,2013,49(10):1234-1242.
[15]KURZ W,GIOVANOLA B,TRIVEDI R.Theory of microstructural development during rapid solidification[J].Acta Metall Mater,1986,34(5):823-830.
[16]王金龙,赖朝彬,王福明,张炯明,任嵬.CAFE模型机理及应用[J].钢铁研究学报,2009,21(10):60-63.WANG Jin-long,LAI Chao-bin,WANG Fu-ming,ZHANG Jiong-ming,REN Wei.Mechanism and application of CAFE method[J].Journal of Iron and Steel Research,2009,21(10):60-63.
[17]宋迎德,郝海,古松伟,张爱民,张兴国.枝晶生长速度对微观组织数值模拟的影响研究——Ivantsov函数近似方法的确定[J].铸造技术,2011,32(1):34--38.SONG Ying-de,HAO Hai,GU Song-wei,ZHANG Ai-min,ZHANG Xing-guo.Research on the microstructure simulation determination of the approximation of Ivantsov Function[J].Foundry Technology,2011,32(1):34-38.
[18]王金龙,王福明,李长荣,程慧静.基于CAFE法优化易切削钢9SMn28锰硫比[J].热加工工艺,2009,38(5):10-13.WANG Jin-long,WANG Fu-ming,LI Chang-rong,CHENG Hui-jing.Optimization of rate of manganese to sulfur for free-cutting steel 9SMn28 based on CAFE methods[J].Hot Working Technology,2009,38(5):10-13.
[19]ZHU M F,HONG C P.A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys[J].ISIJ International,2001.
[20]王永聚,付建华,闫红红,张家齐.42Cr Mo钢环件凝固过程与组织的变化数值模拟[J].热加工工艺,2012,41(19):50-52.WANG Yong-ju,FU Jian-hua,YAN Hong-hong,ZHANG Jia-qi.Numerical simulation on solidification process and structure changes of 43Cr Mo steel ring casting[J].Hot Working Technology,2012,41(19):50-52.
[21]YANG Zhi-jun,ZHAO Xiao-hua,KOU Hong-chao,LI Jin-shan,HU Rui,ZHOU Lian.Numerical simulation of temperature distribution and heat transfer during solidification of titanium alloy ingots in vacuum arc remelting process[J].Transactions of Nonferrous Metals Society of China,2010,20(10):1957-1962.
[22]SEO S M,KIM I S,LEE J H,JO C Y,MIYAHARA H,OGI K.Grain structure prediction of Ni-base superalloy castings using the cellular automaton-finite element method[J].Materials Science and Engineering A,2007,449(13):713-716.