温度梯度区域熔化作用下熔池迁移的元胞自动机模拟
|
摘要
本文采用耦合凝固和熔化效应的二维元胞自动机(cellular automaton, CA)模型,对温度梯度区域熔化(temperature gradient zone melting, TGZM)效应引起的熔池在固液两相区中的迁移现象进行模拟研究.模拟分析了抽拉速度、熔池初始位置、温度梯度和合金成分等因素对TGZM动力学的影响,并将模拟结果与解析模型的预测结果进行比较验证.通过模拟发现,在温度梯度作用下,熔池总是向着高温方向迁移;当抽拉速度低于或高于临界抽拉速度时,熔池朝向移动的液相线或固相线迁移;对于给定的抽拉速度,位于糊状区内临界位置以上的熔池会迁移进入液相,而位于临界位置以下的熔池会逐步靠近固相线.此外,温度梯度越高,合金成分越低,熔池的迁移速度越快.
Directional solidification is a common and important process in both scientific research and industrial practice. Owing to the presence of temperature gradients during directional solidification, local remelting and solidification in the mushy zone occurs, resulting in some typical phenomena such as temperature gradient zone melting(TGZM). The TGZM influences the solidifying microstructure and microsegregation significantly. In the present work, a two-dimensional(2 D) cellular automaton(CA) model involving the mechanism of both solidification and melting is adopted to investigate the migration phenomena of molten liquid pools in the mushy zone due to the TGZM. The effect of pulling velocity, initial liquid pool position, temperature gradient,and alloy composition on the TGZM kinetics are studied. The simulation results are compared with the analytical predictions, and good agreement between two models is obtained. It is found that under a temperature gradient, the liquid pool always migrates towards the high temperature direction. When the pulling velocity is lower than the critical velocity, the liquid pool migrates through the liquidus into the bulk liquid and the time required for a liquid pool to reach the liquidus increases with pulling velocity increasing. On the other hand, when a pulling velocity higher than the critical value is adopted, the liquid pool moves towards the solidus and the time required for migrating liquid pool to reach the solidus decreases with pulling velocity increasing. For a given pulling velocity, the liquid pools located above the critical position move towards the liquidus, while the others gradually approach to the solidus. When a molten liquid pool migrates towards the liquidus, the migration velocity and liquid pool thickness are found to gradually increase, while the liquid pool composition decreases with time. Inversely, for the molten liquid pool that moves towards the solidus, the migration velocity and liquid pool thickness gradually decrease, while the liquid pool composition increases with time going by. The average migration velocity of liquid pool caused by the TGZM effect increases with temperature gradient increasing and alloy composition decreasing. The CA simulations provide an insight into the complicated interactions among the local temperature, solute distribution and diffusion, and the kinetics of local remelting and solidification in the TGZM process.
Directional solidification is a common and important process in both scientific research and industrial practice. Owing to the presence of temperature gradients during directional solidification, local remelting and solidification in the mushy zone occurs, resulting in some typical phenomena such as temperature gradient zone melting(TGZM). The TGZM influences the solidifying microstructure and microsegregation significantly. In the present work, a two-dimensional(2 D) cellular automaton(CA) model involving the mechanism of both solidification and melting is adopted to investigate the migration phenomena of molten liquid pools in the mushy zone due to the TGZM. The effect of pulling velocity, initial liquid pool position, temperature gradient,and alloy composition on the TGZM kinetics are studied. The simulation results are compared with the analytical predictions, and good agreement between two models is obtained. It is found that under a temperature gradient, the liquid pool always migrates towards the high temperature direction. When the pulling velocity is lower than the critical velocity, the liquid pool migrates through the liquidus into the bulk liquid and the time required for a liquid pool to reach the liquidus increases with pulling velocity increasing. On the other hand, when a pulling velocity higher than the critical value is adopted, the liquid pool moves towards the solidus and the time required for migrating liquid pool to reach the solidus decreases with pulling velocity increasing. For a given pulling velocity, the liquid pools located above the critical position move towards the liquidus, while the others gradually approach to the solidus. When a molten liquid pool migrates towards the liquidus, the migration velocity and liquid pool thickness are found to gradually increase, while the liquid pool composition decreases with time. Inversely, for the molten liquid pool that moves towards the solidus, the migration velocity and liquid pool thickness gradually decrease, while the liquid pool composition increases with time going by. The average migration velocity of liquid pool caused by the TGZM effect increases with temperature gradient increasing and alloy composition decreasing. The CA simulations provide an insight into the complicated interactions among the local temperature, solute distribution and diffusion, and the kinetics of local remelting and solidification in the TGZM process.
引文
[1] Rettenmayr M 2009 Int. Mater. Rev. 54 1
[2] Pfann W G 1955 Trans. AIME 203 961
[3] Tiller W A 1963 J. Appl. Phys. 34 2757
[4] Allen D J, Hunt J D 1976 Metall. Mater. Trans. A 7 767
[5]KinoshitaK,AraiY,InatomiY,TsukadaT,MiyataH,Tanaka R 2016 J. Cryst. Growth 455 49
[6] Wang H, Li S, Li X, Zhong H 2017 J. Cryst. Growth 466 56
[7] Ma X, Yoshikawa T, Morita K 2014 Sci. Adv. Mater. 6 1697
[8] Shirzadi A A, Wallach E R 1999 Acta Mater. 47 3551
[9]Nguyen-Thi H, Reinhart G, Buffet A, Schenk T, Mangelinck Noel N, Jung H, Bergeon N, Billia B, Hartwig J, Baruchel J2008 J. Cryst. Growth 310 2906
[10] Buchmann M, Rettenmayr M 2005 J. Cryst. Growth 284 544
[11]B?senbergU,BuchmannM,RettenmayrM2007J. Cryst.Growth 304 281
[12]L?ffler A, Reuther K, Engelhardt H, Liu D, Rettenmayr M2015 Acta Mater. 91 34
[13]Liu D M, Li X Z, Su Y Q, Peng P, Luo L S, Guo J J, Fu H Z 2012 Acta Mater. 60 2679
[14]Liu D M, Li X Z, Su Y Q, Rettenmayr M, Guo J J, Fu H Z2014 Appl. Phys. A 116 1821
[15]Pan S Y, Zhang Q Y, Zhu M F, Rettenmayr M 2015 Acta Mater. 86 229
[16] Zhu M F, Tang Q Y, Zhang Q Y, Pan S Y, Sun D K 2016Acta Metall. Sin. 52 1297(in Chinese)[朱鸣芳,汤倩玉,张庆宇,潘诗琰,孙东科2016金属学报52 1297]
[17]Chen R, Xu Q Y, Liu B C 2014 Acta Phys. Sin. 63 188102(inChinese)[陈瑞,许庆彦,柳百成2014物理学报63188102]
[18]Zhang Y P, Lin X, Wei L, Wang M, Peng D J, Huang W D2012 Acta Phys. Sin. 61 228106(in Chinese)[张云鹏,林鑫,魏雷,王猛,彭东剑,黄卫东2012物理学报61 228106]
[19]JiangHX,ZhaoJZ2011Acta Metall. Sin.471099(in Chinese)[江鸿翔,赵九洲2011金属学报47 1099]
[20] Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[21] Pan S, Zhu M 2010 Acta Mater. 58 340
[22] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477(in Chinese)[李强,李殿中,钱百年2004物理学报53 3477]
[23]Wei L, Lin X, Wang M, Huang W D 2015 Chin. Phys. B 24078108
[24]Zhang Q Y, Fang H, Xue H, Pan S Y, Rettenmayr M, Zhu M F 2017 Sci. Rep. 7 17809
[25]Zhu M F, Xing L K, Fang H, Zhang Q Y, Tang Q Y, Pan S Y 2018 Acta Metall. Sin. 54 789(in Chinese)[朱鸣芳,邢丽科,方辉,张庆宇,汤倩玉,潘诗琰2018金属学报54 789]
[26]ZhangQY,XueH,TangQY,PanSY,RettenmayrM,Zhu M F 2018 Comput. Mater. Sci. 146 20
[27]ZhangQY,FangH,XueH,TangQY,PanSY,Rettenmayr M, Zhu M F 2018 Scr. Mater. 151 28
[28] Farup I, Drezet J M, Rappaz M 2001 Acta Mater. 49 1261
[2] Pfann W G 1955 Trans. AIME 203 961
[3] Tiller W A 1963 J. Appl. Phys. 34 2757
[4] Allen D J, Hunt J D 1976 Metall. Mater. Trans. A 7 767
[5]KinoshitaK,AraiY,InatomiY,TsukadaT,MiyataH,Tanaka R 2016 J. Cryst. Growth 455 49
[6] Wang H, Li S, Li X, Zhong H 2017 J. Cryst. Growth 466 56
[7] Ma X, Yoshikawa T, Morita K 2014 Sci. Adv. Mater. 6 1697
[8] Shirzadi A A, Wallach E R 1999 Acta Mater. 47 3551
[9]Nguyen-Thi H, Reinhart G, Buffet A, Schenk T, Mangelinck Noel N, Jung H, Bergeon N, Billia B, Hartwig J, Baruchel J2008 J. Cryst. Growth 310 2906
[10] Buchmann M, Rettenmayr M 2005 J. Cryst. Growth 284 544
[11]B?senbergU,BuchmannM,RettenmayrM2007J. Cryst.Growth 304 281
[12]L?ffler A, Reuther K, Engelhardt H, Liu D, Rettenmayr M2015 Acta Mater. 91 34
[13]Liu D M, Li X Z, Su Y Q, Peng P, Luo L S, Guo J J, Fu H Z 2012 Acta Mater. 60 2679
[14]Liu D M, Li X Z, Su Y Q, Rettenmayr M, Guo J J, Fu H Z2014 Appl. Phys. A 116 1821
[15]Pan S Y, Zhang Q Y, Zhu M F, Rettenmayr M 2015 Acta Mater. 86 229
[16] Zhu M F, Tang Q Y, Zhang Q Y, Pan S Y, Sun D K 2016Acta Metall. Sin. 52 1297(in Chinese)[朱鸣芳,汤倩玉,张庆宇,潘诗琰,孙东科2016金属学报52 1297]
[17]Chen R, Xu Q Y, Liu B C 2014 Acta Phys. Sin. 63 188102(inChinese)[陈瑞,许庆彦,柳百成2014物理学报63188102]
[18]Zhang Y P, Lin X, Wei L, Wang M, Peng D J, Huang W D2012 Acta Phys. Sin. 61 228106(in Chinese)[张云鹏,林鑫,魏雷,王猛,彭东剑,黄卫东2012物理学报61 228106]
[19]JiangHX,ZhaoJZ2011Acta Metall. Sin.471099(in Chinese)[江鸿翔,赵九洲2011金属学报47 1099]
[20] Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[21] Pan S, Zhu M 2010 Acta Mater. 58 340
[22] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477(in Chinese)[李强,李殿中,钱百年2004物理学报53 3477]
[23]Wei L, Lin X, Wang M, Huang W D 2015 Chin. Phys. B 24078108
[24]Zhang Q Y, Fang H, Xue H, Pan S Y, Rettenmayr M, Zhu M F 2017 Sci. Rep. 7 17809
[25]Zhu M F, Xing L K, Fang H, Zhang Q Y, Tang Q Y, Pan S Y 2018 Acta Metall. Sin. 54 789(in Chinese)[朱鸣芳,邢丽科,方辉,张庆宇,汤倩玉,潘诗琰2018金属学报54 789]
[26]ZhangQY,XueH,TangQY,PanSY,RettenmayrM,Zhu M F 2018 Comput. Mater. Sci. 146 20
[27]ZhangQY,FangH,XueH,TangQY,PanSY,Rettenmayr M, Zhu M F 2018 Scr. Mater. 151 28
[28] Farup I, Drezet J M, Rappaz M 2001 Acta Mater. 49 1261
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |