Please wait a minute...
金属学报  2019, Vol. 55 Issue (5): 664-672    DOI: 10.11900/0412.1961.2018.00427
  本期目录 | 过刊浏览 |
定向凝固糊状区枝晶粗化和二次臂迁移的实验和模拟
方辉1,薛桦1,汤倩玉1,张庆宇1,潘诗琰2,朱鸣芳1()
1. 东南大学材料科学与工程学院江苏省先进金属材料高技术研究重点实验室 南京 211189
2. 南京理工大学材料科学与工程学院 南京 210094
Dendrite Coarsening and Secondary Arm Migration in the Mushy Zone During Directional Solidification:
Hui FANG1,Hua XUE1,Qianyu TANG1,Qingyu ZHANG1,Shiyan PAN2,Mingfang ZHU1()
1. Jiangsu Key Laboratory of Advanced Metallic Materials, School of Materials Science and Engineering, Southeast University, Nanjing 211189, China
2. School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
全文: PDF(7613 KB)   HTML
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。

关键词 定向凝固枝晶温度梯度区域熔化元胞自动机    
Abstract

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.

Key wordsdirectional solidification    dendrite    temperature gradient zone melting    cellular automaton
收稿日期: 2018-09-10      出版日期: 2019-01-22
ZTFLH:  TG113.12,TG111.4  
基金资助:国家自然科学基金项目(51371051);国家自然科学基金项目(51501091);中央高校基本科研业务费专项资金项目(2242016K40008);东南大学优秀博士论文培育基金项目(YBJJ1627)
通讯作者: 朱鸣芳     E-mail: zhumf@seu.edu.cn
Corresponding author: Mingfang ZHU     E-mail: zhumf@seu.edu.cn
作者简介: 方 辉,女,1995年生,博士生

引用本文:

方辉,薛桦,汤倩玉,张庆宇,潘诗琰,朱鸣芳. 定向凝固糊状区枝晶粗化和二次臂迁移的实验和模拟[J]. 金属学报, 2019, 55(5): 664-672.
Hui FANG,Hua XUE,Qianyu TANG,Qingyu ZHANG,Shiyan PAN,Mingfang ZHU. Dendrite Coarsening and Secondary Arm Migration in the Mushy Zone During Directional Solidification:. Acta Metall Sin, 2019, 55(5): 664-672.

链接本文:

http://www.ams.org.cn/CN/10.11900/0412.1961.2018.00427      或      http://www.ams.org.cn/CN/Y2019/V55/I5/664

图1  透明材料定向凝固原位观察实验装置示意图
ParameterUnitValue
Gibbs-Thomson coefficient, Γ℃·m6.48×10-8
Diffusion coefficient in liquid, Dlm2·s-11×10-9
Diffusion coefficient in solid, Dsm2·s-11×10-12
Partition coefficient, k-0.1
Liquidus slope, ml℃·%-1 (mass fraction)-2.8
Melting point of the pure solvent, Tm58.081
表1  本工作采用的物性参数[23,34]
图2  SCN-2.0%ACE合金在温度梯度G=9 ℃/mm、抽拉速率Vp=0条件下保温不同时间时二次枝晶臂迁移的原位实验观察照片
图3  温度梯度区域熔化(TGZM)原理示意图

Temperature gradient

℃·mm-1

Average migrating velocity / (μm·s-1)

Experiment

Analytical

solution

Relative

error / %

70.61±0.0640.7417.6
80.72±0.0760.8515.3
90.85±0.0940.9611.5
100.89±0.0731.0716.8
110.94±0.0761.1820.3
表2  SCN-2.0%ACE合金在不同温度梯度条件下枝晶臂迁移速率的实验值和解析解比较
图4  SCN-2.0% ACE合金在Vp=7.8 μm/s、G=7和9 ℃/mm时,$\tilde{y}_{0}=0.94$位置的枝晶臂迁移速率随时间(t)变化的实验值和解析解比较
图5  SCN-2.0%ACE合金在G=9 ℃/mm条件下保温时,相邻枝晶臂合并的原位实验观察照片
图6  SCN-2.0%ACE合金在G=9 ℃/mm条件下保温时,枝晶臂粗化的原位实验观察照片
图7  利用包含熔化和凝固效应的CA模型模拟的SCN-2.0%ACE合金在G=9 ℃/mm条件下保温不同时间后的枝晶臂迁移、粗化及合并的形貌
图8  不包含熔化效应的CA模型模拟的SCN-2.0%ACE合金在G=9 ℃/mm条件下保温不同时间后的枝晶形貌
[1] RettenmayrM. Melting and remelting phenomena[J]. Int. Mater. Rev., 2009, 54: 1
[2] AllenD J, HuntJ D. Melting during solidification[J]. Metall. Mater. Trans., 1976, 7A: 767
[3] RuvalcabaD, MathiesenR H, EskinD 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] LimodinN, SalvoL, BollerE, et al. In situ and real-time 3-D microtomography investigation of dendritic solidification in an Al-10wt.% Cu alloy[J]. Acta Mater., 2009, 57: 2300
[5] LiB, BrodyH D, KazimirovA. Synchrotron microradiography of temperature gradient zone melting in directional solidification[J]. Metall. Mater. Trans., 2006, 37A: 1039
[6] Nguyen-ThiH, ReinhartG, BuffetA, et al. In situ and real-time analysis of TGZM phenomena by synchrotron X-ray radiography[J]. J. Cryst. Growth, 2008, 310: 2906
[7] JacksonK A, HuntJ D. Transparent compounds that freeze like metals[J]. Acta Metall., 1965, 13: 1212
[8] HuangW D, WangL L. Solidification researches using transparent model materials—A review[J]. Sci. China: Technol. Sci., 2012, 55: 377
[9] B?yükU, Ke?lio?luK, ErolM, et al. Measurement of solid-liquid interfacial energy in succinonitrile-pyrene eutectic system[J]. Mater. Lett., 2005, 59: 2953
[10] AkbulutS, OcakY, B?yükU, et al. Solid-liquid interfacial energy of pyrene[J]. J. Appl. Phys., 2006, 100: 123505
[11] StalderI, BilgramJ H. The measurement of the solid-liquid surface free energy of xenon[J]. J. Chem. Phys., 2003, 118: 7981
[12] AkamatsuS, Bottin-RousseauS, FaivreG. Experimental evidence for a zigzag bifurcation in bulk lamellar eutectic growth[J]. Phys. Rev. Lett., 2004, 93: 175701
[13] Bottin-RousseauS, PerrutM, PicardC, 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] LudwigA, MogeritschJ, GrasserM. In-situ observation of unsteady peritectic growth modes[J]. Trans. Indian Inst. Met., 2009, 62: 433
[15] HuangW D, LinX, LiT, 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
[15] (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] MelendezA J, BeckermannC. Measurements of dendrite tip growth and sidebranching in succinonitrile-acetone alloys[J]. J. Cryst. Growth, 2012, 340: 175
[17] WangX B, LinX, WangL L, et al. Influence of liquid flow on cellular and dendritic spacings[J].Acta Phys. Sin., 2013, 62: 078102
[17] (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] JiangT N, GeorgelinM, PocheauA. Wave dynamics on directional solidification interfaces swept by a flow in a thin sample[J]. J. Cryst. Growth, 2015, 417: 37
[19] WangL L, WangX B, WangH Y, et al. >Effect of crystallographic orientation on instability behavior of planar interface in directional solidification[J].Acta Phys. Sin., 2012, 61: 148104
[19] (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] WangX B, LinX, WangL L, et al. Effect of crystallographic orientation on dendrite growth in directional solidification[J].Acta Phys. Sin., 2013, 62: 108103
[20] (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] ShiY F, XuQ Y, GongM, et al. Simulation of NH4Cl-H2O dendritic growth in directional solidification[J].Acta Metall. Sin., 2011, 47: 620
[21] (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] BenielliD, BergeonN, JamgotchianH, et al. Free growth and instability morphologies in directional melting of alloys[J]. Phys. Rev., 2002, 65E: 051604
[23] PanS Y, ZhangQ Y, ZhuM 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] PanS Y, ZhuM F. A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth[J]. Acta Mater., 2010, 58: 340
[25] ShiY F, XuQ Y, LiuB C. Simulation and experimental research of melt convection on dendrite morphology evolution[J].Acta Phys. Sin., 2011, 60: 126101
[25] (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] ZhaoJ Z, JiangH X. A three-dimensional cellular automaton simulation for dendritic growth[J].Acta Metall. Sin., 2011, 47: 1099
[26] (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] ChenR, XuQ Y, LiuB C. Simulation of dendritic competitive growth during directional solidification using modified cellular automaton method[J].Acta Phys. Sin., 2014, 63: 188102
[27] (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] ZhuM F, HongC P. A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys[J]. ISIJ Int., 2001, 41: 436
[29] LiQ, LiD Z, QianB N. Modeling of dendritic growth by means of cellular automaton method[J].Acta Phys. Sin., 2004, 53: 3477
[29] (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] ZhangH, XuQ Y, ShiZ X, et al. Numerical simulation of dendrite grain growth of DD6 superalloy during directional solidification process[J].Acta Metall. Sin., 2014, 50: 345
[30] (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] ZhangY P, LinX, WeiL, et al. Effect of surface tension anisotropy on the growth patterns of cellulars in directional solidification[J].Acta Phys. Sin., 2012, 61: 228106
[31] (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] WeiL, LinX, WangM, et al. Effects of physical parameters on the cell-to-dendrite transition in directional solidification[J]. Chin. Phys., 2015, 24B: 078108
[33] ZhuM F, StefanescuD M. Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys[J]. Acta Mater., 2007, 55: 1741
[34] FarupI, DrezetJ M, RappazM. In situ observation of hot tearing formation in succinonitrile-acetone[J]. Acta Mater., 2001, 49: 1261
[35] ZhuM F, TangQ Y, ZhangQ Y, et al. Cellular automaton modeling of micro-structure evolution during alloy solidification[J].Acta Metall. Sin., 2016, 52: 1297
[35] (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] ZhangQ Y, FangH, XueH, et al. Interaction of local solidification and remelting during dendrite coarsening—Modeling and comparison with experiments[J]. Sci. Rep., 2017, 7: 17809
[37] ZhuM F, XingL K, FangH, et al. Progresses in dendrite coarsening during solidification of alloys[J].Acta Metall. Sin., 2018, 54: 789
[37] (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] ZhangQ Y, XueH, TangQ Y, et al. Microstructural evolution during temperature gradient zone melting: Cellular automaton simulation and experiment[J]. Comput. Mater. Sci., 2018, 146: 204
[39] ZhangQ Y, FangH, XueH, et al. Modeling of melting and resolidification of equiaxed microstructures in a temperature gradient[J]. Scr. Mater., 2018, 151: 28
[40] FlemingsM C, KattamisT Z, BardesB P. Dendrite arm spacing in aluminum alloys[J]. AFS Trans., 1991, 176: 501
[1] 孙德建,刘林,黄太文,张家晨,曹凯莉,张军,苏海军,傅恒志. 镍基单晶高温合金叶片模拟件平台处的枝晶生长和取向演化[J]. 金属学报, 2019, 55(5): 619-626.
[2] 唐文书,肖俊峰,李永君,张炯,高斯峰,南晴. 再热恢复处理对蠕变损伤定向凝固高温合金γ′相的影响[J]. 金属学报, 2019, 55(5): 601-610.
[3] 杨燕, 杨光昱, 罗时峰, 肖磊, 介万奇. Mg-14.61Gd合金的定向凝固组织及生长取向[J]. 金属学报, 2019, 55(2): 202-212.
[4] 侯渊, 任忠鸣, 王江, 张振强, 李霞. 纵向静磁场对定向凝固GCr15轴承钢柱状晶向等轴晶转变的影响[J]. 金属学报, 2018, 54(5): 801-808.
[5] 吴国华, 陈玉狮, 丁文江. 高性能镁合金凝固组织控制研究现状与展望[J]. 金属学报, 2018, 54(5): 637-646.
[6] 陈光, 郑功, 祁志祥, 张锦鹏, 李沛, 成家林, 张中武. 受控凝固及其应用研究进展[J]. 金属学报, 2018, 54(5): 669-681.
[7] 王锦程, 郭春文, 李俊杰, 王志军. 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.
[8] 朱鸣芳, 邢丽科, 方辉, 张庆宇, 汤倩玉, 潘诗琰. 合金凝固枝晶粗化的研究进展[J]. 金属学报, 2018, 54(5): 789-800.
[9] 李言祥, 刘效邦. 定向凝固多孔金属研究进展[J]. 金属学报, 2018, 54(5): 727-741.
[10] 康慧君, 李金玲, 王同敏, 郭景杰. 定向凝固Al-Mn-Be合金初生金属间化合物相生长行为及力学性能[J]. 金属学报, 2018, 54(5): 809-823.
[11] 苏彦庆, 刘桐, 李新中, 陈瑞润, 郭景杰, 傅恒志. 籽晶法定向凝固TiAl基合金片层取向控制[J]. 金属学报, 2018, 54(5): 647-656.
[12] 刘林, 孙德建, 黄太文, 张琰斌, 李亚峰, 张军, 傅恒志. 高梯度定向凝固技术及其在高温合金制备中的应用[J]. 金属学报, 2018, 54(5): 615-626.
[13] 王同敏, 魏晶晶, 王旭东, 姚曼. 合金凝固组织微观模拟研究进展与应用[J]. 金属学报, 2018, 54(2): 193-203.
[14] 魏雷, 曹永青, 杨海欧, 林鑫, 王猛, 黄卫东. 粉末床激光重熔条件下Ni-Sn反常共晶微观组织的数值模拟[J]. 金属学报, 2018, 54(12): 1801-1808.
[15] 张洪伟,秦学智,李小武,周兰章. 一种高硼定向凝固合金的初熔行为及其对力学性能的影响[J]. 金属学报, 2017, 53(6): 684-694.