Abstract.
The growth of hexagonal columnar dendrite during directional solidification with respect to the multi-controlling parameters such as anisotropy, cooling rate, temperature gradient and orientation angle were investigated by a quantitative phase-field method, respectively. The simulation results show that the increase of anisotropy, cooling rate and temperature gradient can accelerate the solidification velocity of columnar dendrites. Among them, the cooling rate has the most significant effect on the solidification velocity of columnar dendrite. In contrast, the solidification velocity of columnar dendrite slows down with the increase of the orientation angle. Meanwhile, the primary dendrite spacing decreases with the increase of cooling rates and temperature gradient, and the primary dendrite arms are smooth. The primary dendrite spacing increases with the increase of anisotropy and orientation angle, which provides space for the development of secondary dendrite arms. In addition, the effects of cooling rate and temperature gradient on the solid volume fraction were also studied.
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References
L.Q. Chen, Annu. Rev. Mater. Res. 32, 113 (2002)
J. Eiken, Int. J. Cast Met. Res. 22, 86 (2009)
F.I. Versnyder, M.E. Shank, Mater. Sci. Eng. 6, 213 (1970,)
H. Soda, A. McLean, Z. Wang et al., J. Mater. Sci 30, 5438 (1995)
J. Wang, C. Guo, J. Li, Z. Wang, Acta Metall. Sin. 54, 657 (2018)
T. Takaki, S. Sakane, M. Ohno et al., Acta Mater. 118, 230 (2016)
Sansan Shuai, Jiang Wang, Zhongming Ren, Mater. China 01, 068 (2019)
W.J. Boettinger, J.A. Warren, C. Beckermann et al., Annu. Rev. Mater. Res. 32, 163 (2002)
X. Dong, H. Xing, K. Weng et al., J. Iron Steel Res. Int. 24, 865 (2017)
Sensen Jia, Yongbiao Wang, Yanqiu Xiao, Yujuan Wu, Mater. Rep. 33, 3306 (2019)
J.C. Wang, J.J. Li, Y.J. Yang et al., Sci. China Ser. E: Technol. Sci. 51, 362 (2008)
W. Zhi-Jun, W. Jin-Cheng, Y. Gen-Cang, Chin. Phys. B 19, 017305 (2010)
M. Amoorezaei, S. Gurevich, N. Provatas, Acta Mater. 58, 6115 (2010)
T. Takaki, M. Ohno, T. Shimokawabe et al., Acta Mater. 81, 272 (2014)
D. Tourret, A. Karma, Acta Mater. 82, 64 (2015)
A.J. Clarke, D. Tourret, Y. Song et al., Acta Mater. 129, 203 (2017)
Y. Kang, Y. Jin, Y. Zhao et al., J. Iron Steel Res. Int. 24, 171 (2017)
W. Xiao, S. Li, C. Wang et al., Mater. Des. 164, 107553 (2019)
C. Zhu, S. Xu, L. Feng et al., Comput. Mater. Sci. 160, 53 (2019)
Y. Zhao, B. Zhang, H. Hou et al., J. Mater. Sci. Technol. 35, 1044 (2019)
H. Xing, M. Ji, X. Dong et al., Mater. Des. 185, 108250 (2020)
S. Tang, R. Backofen, J. Wang et al., J. Cryst. Growth 334, 146 (2011)
B. Böttger, J. Eiken, I. Steinbach, Acta Mater. 54, 2697 (2006)
M. Wang, Y. Xu, Q. Zheng et al., Metall. Mater. Trans. A 45, 2562 (2014)
F. Gonzales, M. Rappaz, Metall. Mater. Trans. A 37, 2797 (2006)
Janin Eiken, Int. J. Mater. Res. 101, 503 (2010)
D. Montiel, L. Liu, L. Xiao et al., Acta Mater. 60, 5925 (2012)
M. Amoorezaei, S. Gurevich, N. Provatas, Acta Mater. 60, 657 (2012)
S. Gurevich, M. Amoorezaei, D. Montiel et al., Acta Mater. 60, 3287 (2012)
M. Chen, X.D. Hu, D.Y. Ju et al., Comput. Mater. Sci. 79, 684 (2013)
J. Du, A. Zhang, Z. Guo et al., Acta Mater. 161, 35 (2018)
J. Du, A. Zhang, Z. Guo et al., Phys. Rev. Mater. 2, 083402 (2018)
Alain Karma, Phys. Rev. Lett. 87, 115701 (2001)
Y. Chen, A.A. Bogno, N.M. Xiao, B. Billia, X.H. Kang, H. Nguyen-Thi, X.H. Luo, D.Z. Li, Acta Mater. 60, 199 (2012)
Y. Chen, B. Billia, D.Z. Li, H. Nguyen-Thi, N.M. Xiao, A.A. Bogno, Acta Mater. 66, 219 (2014)
Y. Wang, S. Jia, M. Wei et al., J. Alloys Compd. 815, 152385 (2020)
I. Steinbach, Acta Mater. 56, 4965 (2008)
Z. Wang, J. Li, J. Wang, Y. Zhou, Acta Mater. 60, 1957 (2012)
H. Xing, X.L. Dong, C.L. Chen, J.Y. Wang, L.F. Du, K.X. Jin, Int. J. Heat Mass Transfer 90, 911 (2015)
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Wang, Y., Wei, M., Liu, X. et al. Phase-field study of the effects of the multi-controlling parameters on columnar dendrite during directional solidification in hexagonal materials. Eur. Phys. J. E 43, 41 (2020). https://doi.org/10.1140/epje/i2020-11964-9
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DOI: https://doi.org/10.1140/epje/i2020-11964-9