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
Cite this article:
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.
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.
Fund: National Natural Science Foundation of China(51371051);National Natural Science Foundation of China(51501091);Fundamental Research Funds for the Central Universities(2242016K40008);Scientific Research Foundation of Graduate School of Southeast University(YBJJ1627)
Fig.1 Schematic of in situ experimental observation setup for directional solidification of transparent materials
Parameter
Unit
Value
Gibbs-Thomson coefficient, Γ
℃·m
6.48×10-8
Diffusion coefficient in liquid, Dl
m2·s-1
1×10-9
Diffusion coefficient in solid, Ds
m2·s-1
1×10-12
Partition coefficient, k
-
0.1
Liquidus slope, ml
℃·%-1 (mass fraction)
-2.8
Melting point of the pure solvent, Tm
℃
58.081
Table 1 The physical parameters used in the present work[23,34]
Fig.2 In situ experimental observation regarding the secondary dendrite arm migration of a SCN-2.0%ACE (mass fraction) alloy at G=9 ℃/mm and Vp=0 for the holding time of 0 s (a), 36 s (b) and 60 s (c) (G—temperature gradient, Vp—withdrawal rate, T1—temperature of left side)
Fig.3 Schematic of temperature gradient zone melting (TGZM) (T—temperature, C—concentration, S—solidus, L—liquidus, $C^{h}_{L}$ and $C^{c}_{L}$—equilibrium liquid concentrations in the hot and cold sides, respectively)
Temperature gradient
℃·mm-1
Average migrating velocity / (μm·s-1)
Experiment
Analytical
solution
Relative
error / %
7
0.61±0.064
0.74
17.6
8
0.72±0.076
0.85
15.3
9
0.85±0.094
0.96
11.5
10
0.89±0.073
1.07
16.8
11
0.94±0.076
1.18
20.3
Table 2 Comparisons of experimental data and analytical predictions regarding the average migrating velocity within 18 s as a function of temperature gradient for a SCN-2.0%ACE alloy at Vp=0 μm/s and initial position y0=5037 μm (Dimensionless initial position =0.9)
Fig.4 Comparisons of experimental measurements and analytical predictions regarding the average migration velocity varying with time (t) for a SCN-2.0%ACE alloy at Vp=7.8 μm/s, $\tilde{y}_{0}=0.94$, and G=7 and 9 ℃/mm (Lines: analytical solutions; symbols: experimental data)
Fig.5 In situ experimental observation regarding the dendrite arm coalescence of a SCN-2.0%ACE alloy at G=9 ℃/mm for the holding time of 6 s (a) and 30 s (b) (Boxes 1 and 2: dendrite arm coalescence through joining dendrite arm tips, box 3: advancement of interdendritic grooves)
Fig.6 In situ experimental observation regarding the dendrite arm coarsening of a SCN-2.0%ACE alloy at G=9 ℃/mm and Vp=0 for the holding time of 7 s (a) and 67 s (b) (The arrows indicate the melting of small dendrite arms)
Fig.7 Simulated dendrite arm migration, coarsening and coalescence using CA model involving both melting and solidification mechanisms for a SCN-2.0%ACE alloy at G=9 ℃/mm for the holding time of 0 s (a), 20 s (b) and 40 s (c) (Box 1: melting of small dendrite arms, box 2: advancement of interdendritic grooves, box 3: joining of dendrite arm tips, CA—cellular automaton)
Fig.8 Simulated dendrite microstructures using CA model without melting for a SCN-2.0%ACE alloy at G=9 ℃/mm for the holding time of 20 s (a) and 40 s (b) (Boxes 1~3 are corresponding to the locations in Fig.7)
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
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
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
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
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
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
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
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
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
