Numerical Simulation and Experimental Validation of Nondendritic Structure Formation in Magnesium Alloy Under Oscillation and Ultrasonic Vibration

A Correction to this article was published on 30 September 2019

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In this study, the formation of nondendritic structures in the primary phase of magnesium alloy solidified under oscillation and ultrasonic vibration was investigated by numerical simulation and experimentally. The growth and motion of a dendrite during solidification was simulated by a combination of the lattice Boltzmann method and the phase-field method. The simulation and experimental results indicated that higher oscillation amplitudes and acoustic streaming made the microstructures change from dendritic to nondendritic in the α-Mg primary phases. A sufficient shear stress and an appropriate flow time in the barrel should be satisfied when a given inclined angle is selected. The effects of the flow and the thermal field on the nucleation behavior, the constitutional undercooling, and the growth morphology are also discussed. It was found that a high shear rate and high turbulence can help homogenize the temperature and the concentration fields and collide and rotate the α-Mg primary phases.

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  • 30 September 2019

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  1. 1.

    D.B. Spencer, R. Mehrabian, and M.C. Flemings: Mater. Trans. A, 1972, vol. 3, pp. 1925-32.

    Article  Google Scholar 

  2. 2.

    R. Rojas, T. Takaki, and M. Ohno: J. Comput. Phys., 2015, vol. 298, pp. 29-40.

    CAS  Article  Google Scholar 

  3. 3.

    L. Liu, S. Pian, Z. Zhang, Y. Bao, R. Li, and H. Chen: Comput. Mater. Sci., 2018, vol. 146, pp. 9-17.

    CAS  Article  Google Scholar 

  4. 4.

    G. Reinhart, H. Nguyen-Thi, N. Mangelinck-Noël, J. Baruchel, and B. Billia: JOM., 2014, vol. 66, pp. 1408-14.

    CAS  Article  Google Scholar 

  5. 5.

    H. Yasuda, T. Nagira, M. Yoshiya, M. Uesugi, N. Nakatsuka, M. Kiire, A. Sugiyama, K. Uesugi, and K. Umetani: In IOP Conf: Mater. Sci. Eng., 2012, vol. 27, pp. 012084.

    Google Scholar 

  6. 6.

    N. Shevchenko, S. Boden, G. Gerbeth, and S. Eckert: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 3797-3808.

    Article  Google Scholar 

  7. 7.

    S. Eckert, P.A. Nikrityuk, B. Willers, D. Räbiger, N. Shevchenko, H. Neumann-Heyme, V. Travnikov, S. Odenbach, A. Voigt, and K. Eckert: Eur. Phys. J. Spec. Top., 2013, vol. 220, pp. 123-37.

    CAS  Article  Google Scholar 

  8. 8.

    G. Lesoult: Mater. Sci. Eng. A, 2005, vol. 413, pp. 19-29.

    Article  Google Scholar 

  9. 9.

    A. Bogno, H. Nguyen-Thi, G. Reinhart, B. Billia, and J. Baruchel: Acta Mater., 2013, vol. 61, pp. 1303-15.

    CAS  Article  Google Scholar 

  10. 10.

    A.A. Buffet, G. Reinhart, T. Schenk, H. Nguyen-Thi, J. Gastaldi, N. Mangelinck-Noël, H. Jung, J. Härtwig, J. Baruchel, and B. Billia: Phys. Status Solidi A, 2007, vol. 204, pp. 2721-7.

    CAS  Article  Google Scholar 

  11. 11.

    W.J. Boettinger, J.A. Warren, C. Beckermann, and A. Karma: Ann. Rev. Mater. Res., 2002, vol. 32, pp. 163-94.

    CAS  Article  Google Scholar 

  12. 12.

    M. Zhu, D. Sun, S. Pan, Q. Zhang, and D. Raabe: Modell. Simul. Mater. Sci. Eng., 2014, vol. 22, pp. 034006.

    Article  Google Scholar 

  13. 13.

    V.R. Voller: Appl. Math. Model., 1987, vol. 11, pp. 110-6.

    Article  Google Scholar 

  14. 14.

    L. Tan and N. Zabaras: J. Comput. Phys., 2006, vol. 211, pp. 36-63.

    Article  Google Scholar 

  15. 15.

    S. Karagadde, A. Bhattacharya, G. Tomar, and P. Dutta: J. Comput. Phys., 2012, vol. 231, pp. 3987-4000.

    Article  Google Scholar 

  16. 16.

    B. Jelinek, M. Eshraghi, S. Felicelli, and J.F. Peters: Comput. Phys. Commun., 2014, vol. 185, pp. 939-47.

    CAS  Article  Google Scholar 

  17. 17.

    X. Zhang, J. Kang, Z. Guo, S. Xiong, and Q. Han: Comput. Phys. Commun., 2018, vol. 223, pp. 18-27.

    CAS  Article  Google Scholar 

  18. 18.

    D. Medvedev, F. Varnik, and I. Steinbach: Procedia Comput. Sci., 2013, vol. 18, pp. 2512-20.

    Article  Google Scholar 

  19. 19.

    T. Takaki, R. Sato, R. Rojas, M. Ohno, and Y. Shibuta: Comput. Mater. Sci., 2018, vol. 147, pp. 124-31.

    CAS  Article  Google Scholar 

  20. 20.

    X.B. Qi, Y. Chen, X.H. Kang, D.Z. Li, and T.Z. Gong: Sci. Rep., 2017, vol. 7, pp. 45770.

    Article  Google Scholar 

  21. 21.

    H.M. Guo, X.J.Yang, and X.Q. Luo: J. Alloys Compd., 2009, vol. 482, pp. 412-5.

    CAS  Article  Google Scholar 

  22. 22.

    A. Karma: Phys Rev Lett., 2001, vol. 87, pp. 115701.

    CAS  Article  Google Scholar 

  23. 23.

    B. Echebarria, R. Folch, A. Karma, and M. Plapp: Phys. Rev. E., 2004, vol. 70, pp. 061604.

    Article  Google Scholar 

  24. 24.

    C. Beckermann, H.J. Diepers, I. Steinbach, A. Karma, and X. Tong: J. Comput. Phys., 1999, vol. 154, pp. 468-96.

    CAS  Article  Google Scholar 

  25. 25.

    R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, and J. Periaux: J. Comput. Phys., 2001, vol. 169, pp. 363-426.

    CAS  Article  Google Scholar 

  26. 26.

    Z.G. Feng and E.E. Michaelides: J. Comput. Phys., 2004, vol. 195, pp. 602-28.

    Article  Google Scholar 

  27. 27.

    GB Mi, LJ He, PJ Li, PS Popel, and IS Abaturov: Chin. J. Nonferrous Met., 2009, 19, 1372-8.

    CAS  Google Scholar 

  28. 28.

    M.W. Wu and S.M. Xiong: Chin. J. Nonferrous Met., 2012, vol. 22, pp. 2212-19.

    CAS  Article  Google Scholar 

  29. 29.

    X. Feng, F. Zhao, H. Jia, Y. Li, and Y. Yang: Ultrason Sonochem., 2018, vol. 40, pp. 113-19.

    CAS  Article  Google Scholar 

  30. 30.

    B. Billia, N. Bergeon, H.N. Thi, H. Jamgotchian, J. Gastaldi, and G. Grange: Phys. Rev. Lett., 2004, vol. 93, pp. 126105.

    Article  Google Scholar 

  31. 31.

    G. Reinhart, A. Buffet, H. Nguyen-Thi, B. Billia, H. Jung, N. Mangelinck-Noel, N. Bergeon, T. Schenk, J. Härtwig, and J. Baruchel: Metall. Mater. Trans. A, 2008, vol. 39, pp. 865-74.

    CAS  Article  Google Scholar 

  32. 32.

    J. Pilling and A. Hellawell: Metall. Mater. Trans. A, 1996, vol. 27, pp. 229-32.

    CAS  Article  Google Scholar 

  33. 33.

    N. Saklakoğlu, S. Gencalp, Ş. Kasman, and İ.E. Saklakoğlu: Adv. Mater. Res. 2011, vol. 264, pp. 272-77.

    Article  Google Scholar 

  34. 34.

    S. Ji and Z. Fan: Metall. Mater. Trans. A, 2002, vol. 33, pp. 3511-20.

    CAS  Article  Google Scholar 

  35. 35.

    X.G. Hu, Q. Zhu, S.P. Midson, H.V. Atkinson, H.B. Dong, F. Zhang, and Y.L. Kang: Acta Mater., 2017, 124, 446-55.

    CAS  Article  Google Scholar 

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This research was supported by a Grant from the National Natural Science Foundation of China (No. 51674144), the Luodi Research Plan of Jiangxi Educational Department (No, KJLD14016), the Nature Science Foundation of Jiangxi Province (Nos. 20122BAB206021, 20133ACB21003), and the Jiangxi Province Young Scientists Cultivating Programs (No. 20122BCB23001).

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Correspondence to Xiangjie Yang.

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Manuscript submitted January 8, 2019.

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Yu, A., Yang, X., Guo, H. et al. Numerical Simulation and Experimental Validation of Nondendritic Structure Formation in Magnesium Alloy Under Oscillation and Ultrasonic Vibration. Metall Mater Trans B 50, 2319–2333 (2019).

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