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Examination of Dendritic Growth During Solidification of Ternary Alloys via a Novel Quantitative 3D Cellular Automaton Model

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Abstract

A three-dimensional (3D) quantitative cellular automaton (CA) model was developed to simulate dendritic growth during solidification processing of ternary alloys. A detailed method was proposed to solve solute diffusion and calculate the solid fraction for ternary alloys during solidification. The present model has been shown to accurately predict dendrite morphologies and solute distributions of both single equiaxed dendrite and columnar dendrites during solidification. The model was also used to study the influence of the concentration of a third component (Mg in the Al-Si-Mg system) on dendritic growth. With increasing Mg concentration, the steady-state dendrite tip growth velocity was shown to decrease, resulting in a shorter primary dendrite length. The 3D CA simulation results agree well with the prediction of the LGK theoretical model. Multi-columnar dendrite growth was simulated with different cooling rates. Primary and secondary dendrite morphology was shown to have little variation at low cooling rates (1.0 to 2.0 K/s) and a constant undercooling. The average secondary dendrite arm spacing was shown to decrease with the increase of cooling rate within this range. The 3D CA simulation results are in good agreement with the experimental directional solidification experiments of a commercial A356 (Al-7 wt pct Si-0.3 wt pct Mg).

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References

  1. 1 S.A. David, S.S. Babu, and J.M. Vitek: Trans. JWRI., 1996, vol. 25, pp. 127–43.

    Google Scholar 

  2. 2 W. Tan, S. Wen, N. Bailey, and Y.C. Shin: Metall. Mater. Trans. B, 2011, vol. 42, pp. 1306–18.

    Article  Google Scholar 

  3. 3 M.F. Zhu and C.P. Hong: Metall. Mater. Trans. A, 2004, vol. 35, pp. 1555–63.

    Article  Google Scholar 

  4. 4 D. Apelian: JOM, 2008, vol. 60, pp. 9–10.

    Article  Google Scholar 

  5. 5 M. Li: JOM, 2011, vol. 63, p. 14.

    Article  Google Scholar 

  6. 6 A.G. Murphy, D.J. Browne, W.U. Mirihanage, and R.H. Mathiesen: Acta Mater., 2013, vol. 61, pp. 4559–71.

    Article  Google Scholar 

  7. 7 G. Salloum-Abou-Jaoude, G. Reinhart, H. Combeau, M. Založnik, T.A. Lafford, and H. Nguyen-Thi: J. Cryst. Growth, 2015, vol. 411, pp. 88–95.

    Article  Google Scholar 

  8. 8 W. Wang, P.D. Lee, and M. McLean: Acta Mater., 2003, vol. 51, pp. 2971–87.

    Article  Google Scholar 

  9. 9 S. Luo and M.Y. Zhu: Comput. Mater. Sci., 2013, vol. 71, pp. 10–8.

    Article  Google Scholar 

  10. 10 M.F. Zhu and D.M. Stefanescu: Acta Mater., 2007, vol. 55, pp. 1741–55.

    Article  Google Scholar 

  11. 11 D. Tourret, Y. Song, A.J. Clarke, and A. Karma: Acta Mater., 2017, vol. 126, p. 576.

    Article  Google Scholar 

  12. 12 A. Choudhury, K. Reuther, E. Wesner, A. August, B. Nestler, and M. Rettenmayr: Comput. Mater. Sci., 2012, vol. 55, pp. 263–8.

    Article  Google Scholar 

  13. 13 A. Pineau, G. Guillemot, D. Tourret, A. Karma, and C.A. Gandin: Acta Mater., 2018, vol. 155, pp. 286–301.

    Article  Google Scholar 

  14. 14 M. Rappaz and C.A. Gandin: Acta Metall. Mater., 1993, vol. 41, pp. 345–60.

    Article  Google Scholar 

  15. 15 L. Nastac: Acta Mater., 1999, vol. 47, pp. 4253–62.

    Article  Google Scholar 

  16. 16 H.B. Dong and P.D. Lee: Acta Mater., 2005, vol. 53, pp. 659–68.

    Article  Google Scholar 

  17. 17 R. Han, S. Lu, W. Dong, D. Li, and Y. Li: J. Cryst. Growth, 2015, vol. 431, pp. 49–59.

    Article  Google Scholar 

  18. 18 W. Tan and Y.C. Shin: Comput. Mater. Sci., 2015, vol. 98, pp. 446–58.

    Article  Google Scholar 

  19. S Ghosh, L Ma, N Ofori-Opoku, JE Guyer: Model. Simul. Mater. Sci. Eng. 1:1–10. DOI: 10.1088/1361-651x/aa7369.

    Google Scholar 

  20. 20 S. Pan and M. Zhu: Acta Mater., 2010, vol. 58, pp. 340–52.

    Article  Google Scholar 

  21. W. Wang, S. Luo, and M. Zhu (2016) Metall. Mater. Trans. A Phys. Metall. Mater. Sci., vol. 47, pp. 1355–66.

    Article  Google Scholar 

  22. W. Wang, S. Luo, and M. Zhu (2016) Metall. Mater. Trans. A Phys. Metall. Mater. Sci., vol. 47, pp. 1339–54.

    Article  Google Scholar 

  23. 23 S. Chen, G. Guillemot, and C.A. Gandin: Acta Mater., 2016, vol. 115, pp. 448–67.

    Article  Google Scholar 

  24. 24 M. Eshraghi, S.D. Felicelli, and B. Jelinek: J. Cryst. Growth, 2012, vol. 354, pp. 129–34.

    Article  Google Scholar 

  25. 25 M.F. Zhu, W. Cao, S.L. Chen, C.P. Hong, and Y.A. Chang: J. Phase Equilibria Diffus., 2007, vol. 28, pp. 130–8.

    Article  Google Scholar 

  26. 26 R. Chen, Q. Xu, and B. Liu: Comput. Mater. Sci., 2015, vol. 105, pp. 90–100.

    Article  Google Scholar 

  27. 27 S.C. Michelic, J.M. Thuswaldner, and C. Bernhard: Acta Mater., 2010, vol. 58, pp. 2738–51.

    Article  Google Scholar 

  28. 28 X. Zhang, J. Zhao, H. Jiang, and M. Zhu: Acta Mater., 2012, vol. 60, pp. 2249–57.

    Article  Google Scholar 

  29. 29 X.F. Zhang and J.Z. Zhao: J. Cryst. Growth, 2014, vol. 391, pp. 52–8.

    Article  Google Scholar 

  30. 30 C. Gu, Y. Wei, X. Zhan, and Y. Li: Sci. Technol. Weld. Join., 2017, vol. 22, pp. 47–58.

    Article  Google Scholar 

  31. K.C.H. Kumar, N. Chakraborti, H. Lukas, O. Bodak, and L. Rokhlin: Ternary Alloy Syst. - Phase Diagrams, Crystallogr. Thermodyn. Data Light Met. Syst. Part 3 Sel. Syst. from Al-Fe-V to Al-Ni-Zr, 2005, pp. 165–77.

  32. 32 M. Zhu, Z. Li, D. An, Q. Zhang, and T. Dai: ISIJ Int., 2014, vol. 54, pp. 384–91.

    Article  Google Scholar 

  33. 33 L. Beltran-Sanchez and D.M. Stefanescu: Metall. Mater. Trans. A, 2004, vol. 35, pp. 2471–85.

    Article  Google Scholar 

  34. 34 J. Lipton, M.E. Glicksman, and W. Kurz: Metall. Trans. A, 1987, vol. 18, pp. 341–5.

    Article  Google Scholar 

  35. 35 J. Lipton, M.E. Glicksman, and W. Kurz: Mater. Sci. Eng., 1984, vol. 65, pp. 57–63.

    Article  Google Scholar 

  36. 36 A. Karma and W.-J. Rappel: Phys. Rev. E, 1997, vol. 57, p. 4323.

    Article  Google Scholar 

  37. 37 A. Kermanpur, N. Varahraam, E. Engilehei, M. Mohammadzadeh, and P. Davami: Mater. Sci. Technol., 2000, vol. 16, pp. 579–86.

    Article  Google Scholar 

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Acknowledgment

The authors would like to acknowledge the National Science Foundation for supporting this work (Award CMMI-1432688).

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Authors and Affiliations

  1. Department of Materials Science and Engineering, The Ohio State University, Columbus, OH, 43210, USA

    Cheng Gu, Colin D. Ridgeway & Alan A. Luo

  2. Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH, 43210, USA

    Alan A. Luo

Authors
  1. Cheng Gu
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  2. Colin D. Ridgeway
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  3. Alan A. Luo
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Correspondence to Alan A. Luo.

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Manuscript submitted September 13, 2018.

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Gu, C., Ridgeway, C.D. & Luo, A.A. Examination of Dendritic Growth During Solidification of Ternary Alloys via a Novel Quantitative 3D Cellular Automaton Model. Metall Mater Trans B 50, 123–135 (2019). https://doi.org/10.1007/s11663-018-1480-8

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  • DOI: https://doi.org/10.1007/s11663-018-1480-8

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