Phase-field simulation for the evolution of solid/liquid interface front in directional solidification process

doi:10.1016/j.jmst.2018.12.009

Abstract

Abstract:

In this study, the phase field method was used to study the multi-controlling factors of dendrite growth in directional solidification. The effects of temperature gradient, propelling velocity, thermal disturbance and growth orientation angle on the growth morphology of the dendritic growth in the solid/liquid interface were discussed. It is found that the redistribution of solute leads to multilevel cavity and multilevel fusion to form multistage solute segregation, and the increase of temperature gradient and propelling velocity can accelerate the dendrite growth of directional solidification, and also make the second dendrites more developed, which reduces the primary distance and the solute segregation. When the temperature gradient is large, the solid-liquid interface will move forward in a flat interface mode, and the thermal disturbance does not affect the steady state behavior of the directionally solidified dendrite tip. It only promotes the generation and growth of the second dendrites and forms the asymmetric dendrite. Meanwhile, it is found that the inclined dendrite is at a disadvantage in the competitive growth compared to the normal dendrite, and generally it will disappear. When the inclination angle is large, the initial primary dendrite may be eliminated by its secondary or third dendrite.

Key words: Phase field method, Directional solidification, Interface morphology, Multi-control factors

Yuhong Zhao, Bing Zhang, Hua Hou, Weipeng Chen, Meng Wang. Phase-field simulation for the evolution of solid/liquid interface front in directional solidification process[J]. J. Mater. Sci. Technol., 2019, 35(6): 1044-1052.

Figures/Tables 15

Table 1 Material properties chosen for simulation.

Property	Value in simulation
m_e (K·(wt%)^-1)	-170
k_e	0.45
T_M (K)	933
D_L (m²·s^-1)	1.2 × 10^-8
D_S (m²·s^-1)	1.2 × 10^-9
P (kg·m^-3)	2.9 × 10³
L_f (J·mol^-1)	10676

Fig. 1. Evolution of dendrite tip selection constant of Al-0.5%Zn alloy during directional solidification (G = 20 K/mm, VP = 4 mm/s).

Fig. 2. Morphology evolution of the liquid/solid interface frontier of Al-0.5%Zn alloy during directional solidification (G = 20 K/mm, Vp = 4 mm/s), (a) t = 50τ0, (b) t = 100τ0, (c) t = 200τ0, (d) t = 300τ0.

Fig. 3. Solute field changes of the liquid/solid interface frontier of Al-0.5%Zn alloy during directional solidification (G = 20 K/mm,Vp = 4 mm/s), (a) t = 50τ0, (b) t = 100τ0, (c) t = 200τ0, (d) t = 300τ0.

Fig. 4. (a) Solute field and (b) morphology distributions of the single grain liquid/solid interface frontier of Al-0.5%Zn alloy during directional solidification at t = 700τ0 (G = 20 K/mm, Vp = 4 mm/s).

Fig. 5. Solute concentration change of the left of yellow line in Fig. 4 at X-axis direction.

Fig. 6. Directional solidification dendritic morphology with different temperature gradient at t = 300τ0 and Vp = 4 mm/s. (a) G = 20 K/mm; (b) G = 40 K/mm; (c) G = 100 K/mm.

Fig. 7. Directional solidification dendrite with temperature gradients of (a) 200 K/mm and (b) 2000 K/mm, respectively, at t = 300τ0 and VP = 4 mm/s.

Fig. 8. Dendritic morphologies at different interface pulling velocities at G = 20 K/mm and t = 400τ0, (a) VP = 1 mm/s; (b) VP = 2 mm/s; (c) VP = 4 mm/s; (d) VP = 8 mm/s.

Fig. 9. Changes of tip radius (a) and growth velocity (b) of solid-liquid interface frontier at different pulling velocities.

Fig. 10. Directional solidification dendrites under (a) unperturbed and (b) perturbed conditions.

Fig. 11. Comparison of the outlines of the directional dendritic dendrite with perturbed, the black, blue and green contours correspond to 200τ0, 300τ0 and 400τ0, respectively.

Fig. 12. Comparison of the outlines of the directional dendrites with unperturbed and perturbed, the black contour is perturbed, and the green one is unperturbed.

Fig. 13. Dendrite growth morphology at the angle of (a) 0°, (b) 18°, (c) 35°, and (d) 45° between preferred growth direction and temperature gradient direction at Vp = 2 mm/s, G = 10 K/mm, and t=400τ0.

Fig. 14. Dendrite growth process (VP = 2 mm/s, G = 10 K/mm) at 45° between preferred growth direction and temperature gradient direction, (a) t = 50τ0, (b) t = 200τ0, (c) t = 400τ0, (d) t = 600τ0, (e) t = 800τ0 and (f) t = 1000τ0.

References

[1]	W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35 (1964) 345-352.
[2]	J.A. Warren, J.S. Langer, Phys. Rev. E 47 (1993) 2702-2712.
[3]	C.W. Guo, J.J. Li, Y. Ma, J.C. Wang, Acta. Phys. Sin-Ch. 64 (2015) 329-336, (in Chinese).
[4]	R.Z. Xiao, C.S. Zhu, G.S. An, Z.P. Wang, J. Lanzhou. Univ. Technol. 40 (2014) 9-13, (in Chinese).
[5]	H. Xing, L. Zhang, K. Song, Int. J. Heat. Mass. Trans. 104 (2017) 607-614.
[6]	H. Xing, K. Ankit, X. Dong, Int. J. Heat. Mass. Trans. 117 (2018) 1107-1114.
[7]	K.D. Noubary, M. Kellner, Comp. Mater. Sci. 138 (2017) 403-411.
[8]	D. Tourret, Y. Song, A.J. Clarke, A. Karma, Acta Mater. 122 (2017) 220-235.
[9]	H.W. Pan, Z.Q. Han, B.J. Liu, J. Mater. Sci. Technol. 32 (2016) 68-75.
[10]	G.W. Wang, J.J. Liang, Y.Z. Zhou, T. Jin, X.F. Sun, Z.Q. Hu, J. Mater. Sci. Technol. 33 (2017) 499-506.
[11]	H. Hou, D.Y. Ju, Y.H. Zhao, J. Cheng, J. Mater. Sci. Technol. 20 (2004) 45-48.
[12]	B. Echebarria, A. Karma, S. Gurevich, Phys. Rev. E, 81 (2010), Article 021608.
[13]	J. Ghmadh, J.M. Debierre, J. Deschamps, M. Georgelin, A. Pocheau, Acta Mater. 74 (2014) 255-267.
[14]	J. Li, Z. Wang, Y. Wang, J. Wang, Acta Mater. 74 (2012) 1478-1493.
[15]	D. Tourret, A.J. Clarke, S.D. Imhoff, P.J. Gibbs, W. John, A. Karma, JOM 67 (2015) 1776-1785.
[16]	J. Pereda, F.L. Mota, L. Chen, B. Billia, D. Tourret, Y. Song, J.M. Debierre, R. Guerin, A. Karma, R. Trivedi, N. Bergeon, Phys. Rev. E, 95 (2017), Article 012803.
[17]	N. Bergeon, D. Tourret, L. Chen, J. Debierre, R. Guerin, A. Ramirez, B. Billia, A. Karma, R. Trivedi, Phys. Rev. Lett. 110 (2013), Article 226102.
[18]	D. Tourret, J.M. Debierre, Y. Song, F. Mota, N. Bergeon, R. Guerin, R. Trivedi, B. Billia, A. Karma, Phys. Rev. E, 92 (2015), Article 042401.
[19]	M. Amoorezaei, S. Gurevich, N. Provatas, Acta Mater. 58 (2010) 6115-6124.
[20]	A. Pocheau, M. Georgelin, Epl. 76 (2006) p. 291.
[21]	A.J. Clarke, D. Tourret, Y. Song, S.D. Imhoff, P.J. Gibbs, J.W. Gibbs, K. Fezzaa, A. Karma, Acta Mater. 29 (2017) 203-216.
[22]	Y.S. Kang, Y.C. Jin, Y.H. Zhao, J. Iron. Steel. Res. Int. 24 (2017) 171-176.
[23]	Y.S. Kang, Y.H. Zhao, H. Hou, L.W. Chen, Acta. Phys. Sin-Ch. 65 (2016), Article 188102.
[24]	C.J. Hou, Y.C. Jin, Y.H. Zhao, Chin. J. Nonferrous Met. 26 (2016) 60-65.
[25]	Y.H. Zhao, W.J. Liu, H. Hou, Chin. J. Nonferrous Met. 43 (2014) 841-845.
[26]	A. Semoroz, Y. Durandet, M. Rappaz, Acta Mater. 49 (2001) 529-541.
[27]	F. Gonzales, M. Rappaz, Metall. Mater. Trans. A 39 (2008) 2148-2160.
[28]	M. Ohno, K. Matsuura, Acta Mater. 58 (2010) 5749.
[29]	M. Ohno, K. Matsuura, Phys. Rev. E 79 (2009) 031603-031615.
[30]	A.A. Wheeler, W.J. Boettinger, G.B. Mcfadden, Phys. Rev. E 47 (1993) 1893.
[31]	A. Karma, W.J. Rappel, Phys. Rev. E 60 (1999) 3614-3625.
[32]	B. Echebarria, R. Folch, A. Karma, M. Plapp, Phys. Rev. E, 70 (2004), Article 061604.
[33]	Y. Xie, H.B. Dong, J.A. Dantzig, ISIJ Int. 54 (2014) 430-436.
[34]	J.C. Ramirez, C. Beckermann, A. Karma, Phys. Rev. E, 69 (2004), Article 051607.
[35]	J.A. Dantzig, P.D. Napoli, J. Friedli, Metall. Mater. 44 (2013) 5532-5543.
[36]	A.J. Melendez, C. Beckermann, J. Cryst.Growth 340 (2012) 175-180.
[37]	X.B. Wang, X. Lin, L.L. Wang, B.B. Bai, M. Wang, W.D. Huang, Acta Phys. Sin. 62 (2013), Article 108103.
[38]	W. Kurz, D.J. Fisher, Fundamentals of Solidification, Switzerland, (2010), pp. 1-243.