Metallurgical and Materials Transactions A

, Volume 27, Issue 3, pp 611–623

Numerical modeling of cellular/dendritic array growth: spacing and structure predictions

  • J. D. Hunt
  • S. Z. Lu
Article

Abstract

A numerical model of cellular and dendritic growth has been developed that can predict cellular and dendritic spacings, undercoolings, and the transition between structures. Fully self-consistent solutions are produced for axisymmetric interface shapes. An important feature of the model is that the spacing selection mechanism has been treated. A small, stable range of spacings is predicted for both cells and dendrites, and these agree well with experiment at both low and high velocities. By suitable nondimensionalization, relatively simple analytic expressions can be used to fit the numerical results. These expressions provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.H. Burden and J.D. Hunt:J. Cryst. Growth, 1974, vol. 22, pp. 109–16.CrossRefGoogle Scholar
  2. 2.
    J.D. Hunt:Solidification and Casting of Metals, TMS, London, 1979, pp. 3–9.Google Scholar
  3. 3.
    W. Kurz and DJ. Fisher:J. Cryst. Growth, 1981, vol. 29, pp. 11–20.Google Scholar
  4. 4.
    J.D. Hunt:Acta Metall, 1991, vol. 39, pp. 2117–33.CrossRefGoogle Scholar
  5. 5.
    Shu-Zu Lu and J.D. Hunt:J. Cryst. Growth, 1992, vol. 123, pp. 17–34.CrossRefGoogle Scholar
  6. 6.
    Shu-Zu Lu, J.D. Hunt, P. Gilgien, and W. Kurz:Acta Metall. Mater., 1994, vol. 42 (5), pp. 1653–60.CrossRefGoogle Scholar
  7. 7.
    D.A. Kessler, J. Koplik, and H. Levine:Phys. Rev., 1986, vol. A33, p. 3352.Google Scholar
  8. 8.
    J.W. McLean and P.G. Saffman:J. Fluid Mech., 1981, vol. 102, pp. 455–69.CrossRefGoogle Scholar
  9. 9.
    G.P. Ivantsov:Dokl. Akad. Nauk. SSSR, 1947, vol. 59, p. 567.Google Scholar
  10. 10.
    W.A. Tiller, K.A. Jackson, J.W. Rutter, and B. Chalmers:Acta Metall, 1953, vol. 1, pp. 428–37.CrossRefGoogle Scholar
  11. 11.
    W.W. Mullins and R.F. Sekerka:J. Appl. Phys., 1964, vol. 34, pp. 444–52.CrossRefGoogle Scholar
  12. 12.
    J.S. Langer and H. Müller-KrumBhaar:Acta Metall., 1978, vol. 26, pp. 1681–95, 1697-1708.CrossRefGoogle Scholar
  13. 13.
    S.C. Huang and M.E. Glicksman:Acta Metall., 1981, vol. 29, pp. 701–15.CrossRefGoogle Scholar
  14. 14.
    R. Trivedi:J. Cryst. Growth, 1980, vol. 49, pp. 219–32.CrossRefGoogle Scholar
  15. 15.
    J.D. Hunt:Solidification Processing, Inst. Met., London, 1988, pp. 191–99.Google Scholar
  16. 16.
    S.H. Han and R. Trivedi:Acta Metall Mater., 1994, vol. 42 (1), pp. 25–41.CrossRefGoogle Scholar
  17. 17.
    Huang Weidong, Geng Xingguo, and Zhou Yaohe:J. Cryst. Growth, 1993, vol. 134, p. 101–15.CrossRefGoogle Scholar
  18. 18.
    J.A. Warren and J.S. Langer:Phys. Rev., 1990, vol. A42, pp. 3518- 25.Google Scholar
  19. 19.
    K. Somboonsuk, J.T. Mason, and R. Trivedi:Metall Trans. A, 1984, vol. 15, pp. 967–75.CrossRefGoogle Scholar
  20. 20.
    R. Trivedi and K. Somboonsuk:Mater. Sci. Eng., 1984, vol. 65, pp. 65–74.CrossRefGoogle Scholar
  21. 21.
    M.A. Eshelman, V. Seetharaman, and R. Trivedi:Acta Metall., 1988, vol. 36, pp. 1165–74.CrossRefGoogle Scholar
  22. 22.
    D.G. McCartney and J.D. Hunt:Acta Metall., 1981, vol. 29, pp. 1851- 63.CrossRefGoogle Scholar
  23. 23.
    M. Gremaud, M. Carrard, and W. Kurz:Acta Metall, 1990, vol. 38, pp. 2587–99.CrossRefGoogle Scholar
  24. 24.
    M. Gremaud, M. Carrard, and W. Kurz:Acta Metall., 1991, vol. 39, pp. 1431–43.CrossRefGoogle Scholar
  25. 25.
    M. Carrard, M. Gremaud, M. Zimmermann, and W. Kurz:Acta Metall., 1992, vol. 40, pp. 983–96.CrossRefGoogle Scholar
  26. 26.
    S.C. Gill, M. Zimmermann, and W. Kurz:Acta Metall, 1992, vol. 40, pp. 2895–2906.CrossRefGoogle Scholar
  27. 27.
    D.G. McCartney: D. Phil. Thesis, Oxford University, Oxford, 1981.Google Scholar
  28. 28.
    M.H. Burden and J.D. Hunt:J. Cryst. Growth, 1974, vol. 22, pp. 99- 108.CrossRefGoogle Scholar
  29. 29.
    E.F.J. Shelton: Part II Thesis, Oxford University, Oxford, 1994.Google Scholar

Copyright information

© The Minerals, Metals & Material Society 1996

Authors and Affiliations

  • J. D. Hunt
    • 1
  • S. Z. Lu
    • 2
  1. 1.Department of MaterialsOxford UniversityOxfordEngland
  2. 2.Michigan Technological UniversityHoughton

Personalised recommendations