定向凝固糊状区枝晶粗化和二次臂迁移的实验和模拟
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摘要
采用透明合金原位观察实验和元胞自动机(CA)模拟,对丁二腈-丙酮(SCN-ACE)合金在定向凝固过程中糊状区的枝晶形貌演化进行了分析研究。实验和模拟均观察到了由于小枝晶臂重熔、相邻枝晶臂从尖端或根部合并的3种枝晶臂粗化模式,以及由于温度梯度区域熔化(TGZM)效应所引起的二次枝晶臂向高温方向的迁移现象。结果表明,枝晶臂的迁移速率随温度梯度的提高而加快;随保温时间的延长,枝晶臂的迁移速率降低。实验值和解析解吻合良好。通过模拟证实了必须有熔化效应才能实现枝晶臂迁移和小枝晶臂重熔的粗化模式。此外,熔化效应对由相邻枝晶臂合并引起的粗化模式也有显著的促进作用。
Directional solidification is a common and important process in both scientific research and industrial practice. Dendrites are the most frequently observed microstructures in the directional solidification. It is known that dendrite coarsening in mushy zones is an unavoidable phenomenon that influences microstructures and thereby properties significantly. Moreover, the presence of temperature gradients during directional solidification leads to temperature gradient zone melting(TGZM), which yields dendrite arm migration towards higher temperatures. In the present work, the evolution of dendrite microstructures in the mushy zone during directional solidification is investigated through in situ experiments and cellular automaton(CA) simulations for a transparent succinonitrile-acetone(SCN-ACE) alloy. The phenomena of dendrite coarsening and the secondary dendrite arm migration toward high temperature direction due to TGZM have been observed by both experiment and simulation. Dendrite coarsening is found to be caused by three modes, including the remelting of small dendrite arms, and dendrite arm coalescence through the advancement of interdendritic grooves and joining of dendrite arm tips. The experimental measurements indicate that the average migration velocity of the secondary dendrite arm increases with increasing the temperature gradient. For a fixed temperature gradient, dendrite arm migration becomes slower with time. The experimental data agree reasonably well with the analytical predictions. The present CA model involving the mechanisms of both solidification and melting can effectively reproduce the typical features of secondary dendrite arm migration and dendrite coarsening as observed in experiments. The simulation results show that the local liquid concentrations near the lateral side of big arms and in the "valleys" between side arms are relatively higher than that at the tips of small arms. This drives solute diffusion and leads to the dissolution of small arms, the growth of thick arms, and advancement of interdendritic groove bases. However, at the groove between two relatively narrow and long adjacent side arms, the solute diffusion is obstructed. In this case, dendrite arm coalescence through joining arm tips together with an entrapped liquid droplet in the solid can be observed. The role of melting for microstructure evolution in mushy zones is investigated by comparing the simulation results using CA models with and without melting effect. It is demonstrated that remelting is one of the dominant mechanisms for dendrite arm migration and dendrite coarsening by the mode of small dendrite arm remelting. Moreover, remelting also promotes dendrite coarsening by the mode of dendrite arm coalescence.
Directional solidification is a common and important process in both scientific research and industrial practice. Dendrites are the most frequently observed microstructures in the directional solidification. It is known that dendrite coarsening in mushy zones is an unavoidable phenomenon that influences microstructures and thereby properties significantly. Moreover, the presence of temperature gradients during directional solidification leads to temperature gradient zone melting(TGZM), which yields dendrite arm migration towards higher temperatures. In the present work, the evolution of dendrite microstructures in the mushy zone during directional solidification is investigated through in situ experiments and cellular automaton(CA) simulations for a transparent succinonitrile-acetone(SCN-ACE) alloy. The phenomena of dendrite coarsening and the secondary dendrite arm migration toward high temperature direction due to TGZM have been observed by both experiment and simulation. Dendrite coarsening is found to be caused by three modes, including the remelting of small dendrite arms, and dendrite arm coalescence through the advancement of interdendritic grooves and joining of dendrite arm tips. The experimental measurements indicate that the average migration velocity of the secondary dendrite arm increases with increasing the temperature gradient. For a fixed temperature gradient, dendrite arm migration becomes slower with time. The experimental data agree reasonably well with the analytical predictions. The present CA model involving the mechanisms of both solidification and melting can effectively reproduce the typical features of secondary dendrite arm migration and dendrite coarsening as observed in experiments. The simulation results show that the local liquid concentrations near the lateral side of big arms and in the "valleys" between side arms are relatively higher than that at the tips of small arms. This drives solute diffusion and leads to the dissolution of small arms, the growth of thick arms, and advancement of interdendritic groove bases. However, at the groove between two relatively narrow and long adjacent side arms, the solute diffusion is obstructed. In this case, dendrite arm coalescence through joining arm tips together with an entrapped liquid droplet in the solid can be observed. The role of melting for microstructure evolution in mushy zones is investigated by comparing the simulation results using CA models with and without melting effect. It is demonstrated that remelting is one of the dominant mechanisms for dendrite arm migration and dendrite coarsening by the mode of small dendrite arm remelting. Moreover, remelting also promotes dendrite coarsening by the mode of dendrite arm coalescence.
引文
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[2]Allen D J,Hunt J D.Melting during solidification[J].Metall.Mater.Trans.,1976,7A:767
[3]Ruvalcaba D,Mathiesen R H,Eskin D G,et al.In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy[J].Acta Mater.,2007,55:4287
[4]Limodin N,Salvo L,Boller E,et al.In situ and real-time 3-Dmicrotomography investigation of dendritic solidification in an Al-10wt.%Cu alloy[J].Acta Mater.,2009,57:2300
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[7]Jackson K A,Hunt J D.Transparent compounds that freeze like metals[J].Acta Metall.,1965,13:1212
[8]Huang W D,Wang L L.Solidification researches using transparent model materials-A review[J].Sci.China:Technol.Sci.,2012,55:377
[9]B?yük U,Ke?lio?lu K,Erol M,et al.Measurement of solid-liquid interfacial energy in succinonitrile-pyrene eutectic system[J].Mater.Lett.,2005,59:2953
[10]Akbulut S,Ocak Y,B?yük U,et al.Solid-liquid interfacial energy of pyrene[J].J.Appl.Phys.,2006,100:123505
[11]Stalder I,Bilgram J H.The measurement of the solid-liquid surface free energy of xenon[J].J.Chem.Phys.,2003,118:7981
[12]Akamatsu S,Bottin-Rousseau S,Faivre G.Experimental evidence for a zigzag bifurcation in bulk lamellar eutectic growth[J].Phys.Rev.Lett.,2004,93:175701
[13]Bottin-Rousseau S,Perrut M,Picard C,et al.An experimental method for the in situ observation of eutectic growth patterns in bulk samples of transparent alloys[J].J.Cryst.Growth,2007,306:465
[14]Ludwig A,Mogeritsch J,Grasser M.In-situ observation of unsteady peritectic growth modes[J].Trans.Indian Inst.Met.,2009,62:433
[15]Huang W D,Lin X,Li T,et al.A time-dependent interface stability during directional solidification of a single phase alloy(II)-Comparison with experimental results[J].Acta Phys.Sin.,2004,53:3978(黄卫东,林鑫,李涛等.单相合金凝固过程时间相关的界面稳定性(Ⅱ)实验对比[J].物理学报,2004,53:3978)
[16]Melendez A J,Beckermann C.Measurements of dendrite tip growth and sidebranching in succinonitrile-acetone alloys[J].J.Cryst.Growth,2012,340:175
[17]Wang X B,Lin X,Wang L L,et al.Influence of liquid flow on cellular and dendritic spacings[J].Acta Phys.Sin.,2013,62:078102(王贤斌,林鑫,王理林等.液相对流对定向凝固胞/枝晶间距的影响[J].物理学报,2013,62:078102)
[18]Jiang T N,Georgelin M,Pocheau A.Wave dynamics on directional solidification interfaces swept by a flow in a thin sample[J].J.Cryst.Growth,2015,417:37
[19]Wang L L,Wang X B,Wang H Y,et al.Effect of crystallographic orientation on instability behavior of planar interface in directional solidification[J].Acta Phys.Sin.,2012,61:148104(王理林,王贤斌,王红艳等.晶体取向对定向凝固平界面失稳行为的影响[J].物理学报,2012,61:148104)
[20]Wang X B,Lin X,Wang L L,et al.Effect of crystallographic orientation on dendrite growth in directional solidification[J].Acta Phys.Sin.,2013,62:108103(王贤斌,林鑫,王理林等.晶体取向对定向凝固枝晶生长的影响[J].物理学报,2013,62:108103)
[21]Shi Y F,Xu Q Y,Gong M,et al.Simulation of NH4Cl-H2O dendritic growth in directional solidification[J].Acta Metall.Sin.,2011,47:620(石玉峰,许庆彦,龚铭等.定向凝固过程中NH4Cl-H2O枝晶生长的数值模拟[J].金属学报,2011,47:620)
[22]Benielli D,Bergeon N,Jamgotchian H,et al.Free growth and instability morphologies in directional melting of alloys[J].Phys.Rev.,2002,65E:051604
[23]Pan S Y,Zhang Q Y,Zhu M F,et al.Liquid droplet migration under static and dynamic conditions:Analytical model,phase-field simulation and experiment[J].Acta Mater.,2015,86:229
[24]Pan S Y,Zhu M F.A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth[J].Acta Mater.,2010,58:340
[25]Shi Y F,Xu Q Y,Liu B C.Simulation and experimental research of melt convection on dendrite morphology evolution[J].Acta Phys.Sin.,2011,60:126101(石玉峰,许庆彦,柳百成.对流作用下枝晶形貌演化的数值模拟和实验研究[J].物理学报,2011,60:126101)
[26]Zhao J Z,Jiang H X.A three-dimensional cellular automaton simulation for dendritic growth[J].Acta Metall.Sin.,2011,47:1099(赵九洲,江鸿翔.枝晶生长的三维元胞自动机模拟[J].金属学报,2011,47:1099)
[27]Chen R,Xu Q Y,Liu B C.Simulation of dendritic competitive growth during directional solidification using modified cellular automaton method[J].Acta Phys.Sin.,2014,63:188102(陈瑞,许庆彦,柳百成.基于元胞自动机方法的定向凝固枝晶竞争生长数值模拟[J].物理学报,2014,63:188102)
[28]Zhu M F,Hong C P.A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys[J].ISIJInt.,2001,41:436
[29]Li Q,Li D Z,Qian B N.Modeling of dendritic growth by means of cellular automaton method[J].Acta Phys.Sin.,2004,53:3477(李强,李殿中,钱百年.元胞自动机方法模拟枝晶生长[J].物理学报,2004,53:3477)
[30]Zhang H,Xu Q Y,Shi Z X,et al.Numerical simulation of dendrite grain growth of DD6 superalloy during directional solidification process[J].Acta Metall.Sin.,2014,50:345(张航,许庆彦,史振学等.DD6高温合金定向凝固枝晶生长的数值模拟研究[J].金属学报,2014,50:345)
[31]Zhang Y P,Lin X,Wei L,et al.Effect of surface tension anisotropy on the growth patterns of cellulars in directional solidification[J].Acta Phys.Sin.,2012,61:228106(张云鹏,林鑫,魏雷等.用CA方法模拟界面能各向异性对胞晶生长形态的影响[J].物理学报,2012,61:228106)
[32]Wei L,Lin X,Wang M,et al.Effects of physical parameters on the cell-to-dendrite transition in directional solidification[J].Chin.Phys.,2015,24B:078108
[33]Zhu M F,Stefanescu D M.Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys[J].Acta Mater.,2007,55:1741
[34]Farup I,Drezet J M,Rappaz M.In situ observation of hot tearing formation in succinonitrile-acetone[J].Acta Mater.,2001,49:1261
[35]Zhu M F,Tang Q Y,Zhang Q Y,et al.Cellular automaton modeling of micro-structure evolution during alloy solidification[J].Acta Metall.Sin.,2016,52:1297(朱鸣芳,汤倩玉,张庆宇等.合金凝固过程中显微组织演化的元胞自动机模拟[J].金属学报,2016,52:1297)
[36]Zhang Q Y,Fang H,Xue H,et al.Interaction of local solidification and remelting during dendrite coarsening-Modeling and comparison with experiments[J].Sci.Rep.,2017,7:17809
[37]Zhu M F,Xing L K,Fang H,et al.Progresses in dendrite coarsening during solidification of alloys[J].Acta Metall.Sin.,2018,54:789(朱鸣芳,邢丽科,方辉等.合金凝固枝晶粗化的研究进展[J].金属学报,2018,54:789)
[38]Zhang Q Y,Xue H,Tang Q Y,et al.Microstructural evolution during temperature gradient zone melting:Cellular automaton simulation and experiment[J].Comput.Mater.Sci.,2018,146:204
[39]Zhang Q Y,Fang H,Xue H,et al.Modeling of melting and resolidification of equiaxed microstructures in a temperature gradient[J].Scr.Mater.,2018,151:28
[40]Flemings M C,Kattamis T Z,Bardes B P.Dendrite arm spacing in aluminum alloys[J].AFS Trans.,1991,176:501
[2]Allen D J,Hunt J D.Melting during solidification[J].Metall.Mater.Trans.,1976,7A:767
[3]Ruvalcaba D,Mathiesen R H,Eskin D G,et al.In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy[J].Acta Mater.,2007,55:4287
[4]Limodin N,Salvo L,Boller E,et al.In situ and real-time 3-Dmicrotomography investigation of dendritic solidification in an Al-10wt.%Cu alloy[J].Acta Mater.,2009,57:2300
[5]Li B,Brody H D,Kazimirov A.Synchrotron microradiography of temperature gradient zone melting in directional solidification[J].Metall.Mater.Trans.,2006,37A:1039
[6]Nguyen-Thi H,Reinhart G,Buffet A,et al.In situ and real-time analysis of TGZM phenomena by synchrotron X-ray radiography[J].J.Cryst.Growth,2008,310:2906
[7]Jackson K A,Hunt J D.Transparent compounds that freeze like metals[J].Acta Metall.,1965,13:1212
[8]Huang W D,Wang L L.Solidification researches using transparent model materials-A review[J].Sci.China:Technol.Sci.,2012,55:377
[9]B?yük U,Ke?lio?lu K,Erol M,et al.Measurement of solid-liquid interfacial energy in succinonitrile-pyrene eutectic system[J].Mater.Lett.,2005,59:2953
[10]Akbulut S,Ocak Y,B?yük U,et al.Solid-liquid interfacial energy of pyrene[J].J.Appl.Phys.,2006,100:123505
[11]Stalder I,Bilgram J H.The measurement of the solid-liquid surface free energy of xenon[J].J.Chem.Phys.,2003,118:7981
[12]Akamatsu S,Bottin-Rousseau S,Faivre G.Experimental evidence for a zigzag bifurcation in bulk lamellar eutectic growth[J].Phys.Rev.Lett.,2004,93:175701
[13]Bottin-Rousseau S,Perrut M,Picard C,et al.An experimental method for the in situ observation of eutectic growth patterns in bulk samples of transparent alloys[J].J.Cryst.Growth,2007,306:465
[14]Ludwig A,Mogeritsch J,Grasser M.In-situ observation of unsteady peritectic growth modes[J].Trans.Indian Inst.Met.,2009,62:433
[15]Huang W D,Lin X,Li T,et al.A time-dependent interface stability during directional solidification of a single phase alloy(II)-Comparison with experimental results[J].Acta Phys.Sin.,2004,53:3978(黄卫东,林鑫,李涛等.单相合金凝固过程时间相关的界面稳定性(Ⅱ)实验对比[J].物理学报,2004,53:3978)
[16]Melendez A J,Beckermann C.Measurements of dendrite tip growth and sidebranching in succinonitrile-acetone alloys[J].J.Cryst.Growth,2012,340:175
[17]Wang X B,Lin X,Wang L L,et al.Influence of liquid flow on cellular and dendritic spacings[J].Acta Phys.Sin.,2013,62:078102(王贤斌,林鑫,王理林等.液相对流对定向凝固胞/枝晶间距的影响[J].物理学报,2013,62:078102)
[18]Jiang T N,Georgelin M,Pocheau A.Wave dynamics on directional solidification interfaces swept by a flow in a thin sample[J].J.Cryst.Growth,2015,417:37
[19]Wang L L,Wang X B,Wang H Y,et al.Effect of crystallographic orientation on instability behavior of planar interface in directional solidification[J].Acta Phys.Sin.,2012,61:148104(王理林,王贤斌,王红艳等.晶体取向对定向凝固平界面失稳行为的影响[J].物理学报,2012,61:148104)
[20]Wang X B,Lin X,Wang L L,et al.Effect of crystallographic orientation on dendrite growth in directional solidification[J].Acta Phys.Sin.,2013,62:108103(王贤斌,林鑫,王理林等.晶体取向对定向凝固枝晶生长的影响[J].物理学报,2013,62:108103)
[21]Shi Y F,Xu Q Y,Gong M,et al.Simulation of NH4Cl-H2O dendritic growth in directional solidification[J].Acta Metall.Sin.,2011,47:620(石玉峰,许庆彦,龚铭等.定向凝固过程中NH4Cl-H2O枝晶生长的数值模拟[J].金属学报,2011,47:620)
[22]Benielli D,Bergeon N,Jamgotchian H,et al.Free growth and instability morphologies in directional melting of alloys[J].Phys.Rev.,2002,65E:051604
[23]Pan S Y,Zhang Q Y,Zhu M F,et al.Liquid droplet migration under static and dynamic conditions:Analytical model,phase-field simulation and experiment[J].Acta Mater.,2015,86:229
[24]Pan S Y,Zhu M F.A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth[J].Acta Mater.,2010,58:340
[25]Shi Y F,Xu Q Y,Liu B C.Simulation and experimental research of melt convection on dendrite morphology evolution[J].Acta Phys.Sin.,2011,60:126101(石玉峰,许庆彦,柳百成.对流作用下枝晶形貌演化的数值模拟和实验研究[J].物理学报,2011,60:126101)
[26]Zhao J Z,Jiang H X.A three-dimensional cellular automaton simulation for dendritic growth[J].Acta Metall.Sin.,2011,47:1099(赵九洲,江鸿翔.枝晶生长的三维元胞自动机模拟[J].金属学报,2011,47:1099)
[27]Chen R,Xu Q Y,Liu B C.Simulation of dendritic competitive growth during directional solidification using modified cellular automaton method[J].Acta Phys.Sin.,2014,63:188102(陈瑞,许庆彦,柳百成.基于元胞自动机方法的定向凝固枝晶竞争生长数值模拟[J].物理学报,2014,63:188102)
[28]Zhu M F,Hong C P.A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys[J].ISIJInt.,2001,41:436
[29]Li Q,Li D Z,Qian B N.Modeling of dendritic growth by means of cellular automaton method[J].Acta Phys.Sin.,2004,53:3477(李强,李殿中,钱百年.元胞自动机方法模拟枝晶生长[J].物理学报,2004,53:3477)
[30]Zhang H,Xu Q Y,Shi Z X,et al.Numerical simulation of dendrite grain growth of DD6 superalloy during directional solidification process[J].Acta Metall.Sin.,2014,50:345(张航,许庆彦,史振学等.DD6高温合金定向凝固枝晶生长的数值模拟研究[J].金属学报,2014,50:345)
[31]Zhang Y P,Lin X,Wei L,et al.Effect of surface tension anisotropy on the growth patterns of cellulars in directional solidification[J].Acta Phys.Sin.,2012,61:228106(张云鹏,林鑫,魏雷等.用CA方法模拟界面能各向异性对胞晶生长形态的影响[J].物理学报,2012,61:228106)
[32]Wei L,Lin X,Wang M,et al.Effects of physical parameters on the cell-to-dendrite transition in directional solidification[J].Chin.Phys.,2015,24B:078108
[33]Zhu M F,Stefanescu D M.Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys[J].Acta Mater.,2007,55:1741
[34]Farup I,Drezet J M,Rappaz M.In situ observation of hot tearing formation in succinonitrile-acetone[J].Acta Mater.,2001,49:1261
[35]Zhu M F,Tang Q Y,Zhang Q Y,et al.Cellular automaton modeling of micro-structure evolution during alloy solidification[J].Acta Metall.Sin.,2016,52:1297(朱鸣芳,汤倩玉,张庆宇等.合金凝固过程中显微组织演化的元胞自动机模拟[J].金属学报,2016,52:1297)
[36]Zhang Q Y,Fang H,Xue H,et al.Interaction of local solidification and remelting during dendrite coarsening-Modeling and comparison with experiments[J].Sci.Rep.,2017,7:17809
[37]Zhu M F,Xing L K,Fang H,et al.Progresses in dendrite coarsening during solidification of alloys[J].Acta Metall.Sin.,2018,54:789(朱鸣芳,邢丽科,方辉等.合金凝固枝晶粗化的研究进展[J].金属学报,2018,54:789)
[38]Zhang Q Y,Xue H,Tang Q Y,et al.Microstructural evolution during temperature gradient zone melting:Cellular automaton simulation and experiment[J].Comput.Mater.Sci.,2018,146:204
[39]Zhang Q Y,Fang H,Xue H,et al.Modeling of melting and resolidification of equiaxed microstructures in a temperature gradient[J].Scr.Mater.,2018,151:28
[40]Flemings M C,Kattamis T Z,Bardes B P.Dendrite arm spacing in aluminum alloys[J].AFS Trans.,1991,176:501
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