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Heat flow parameters affecting dendrite spacings during unsteady-state solidification of Sn-Pb and Al-Cu alloys

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Abstract

Solidification thermal parameters and dendrite arm spacings have been measured in hypoeutectic Sn-Pb and Al-Cu alloys solidified under unsteady-state heat flow conditions. It was observed that both primary and secondary spacings decreased with increased solute content for Sn-Pb alloys. For Al-Cu alloys, the primary spacing was found to be independent of composition, and secondary spacings decrease as the solute content is increased. The predictive theoretical models for primary spacings existing in the literature did not generate the experimental observations concerning the Sn-Pb and Al-Cu alloys examined in the present study. The theoretical Bouchard-Kirkaldy’s (BK’s) equation relating secondary spacings with tip growth rate has generated adequately the experimental results for both metallic systems. The insertion of analytical expressions for tip growth rate and cooling rate into the predictive model, or into the resulting experimental equations in order to establish empirical formulas permitting primary and secondary dendritic spacings to be determined as functions of unsteady-state solidification parameters such as melt superheat, type of mold, and transient metal/mold heattransfer coefficient is proposed.

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References

  1. J.D. Hunt: Int. Conf. on Solidification and Casting of Metals, The Metals Society, London, 1979, pp. 3–9.

    Google Scholar 

  2. W. Kurz and J.D. Fisher: Acta Metall., 1981, vol. 29, pp. 11–20.

    Article  CAS  Google Scholar 

  3. W. Kurz and J.D. Fisher: Fundamentals of Solidification, Trans Tech Publications, Aedermannsdorf, Switzerland, 1992, pp. 85–90.

    Google Scholar 

  4. J.D. Hunt and S.Z. Lu: Metall. Mater. Trans. A, 1966, vol. 27A, pp. 611–23.

    Google Scholar 

  5. V. Laxmanan: Scripta Mater, 1998, vol. 38, pp. 1289–97.

    Article  CAS  Google Scholar 

  6. V. Laxmanan: Acta Metall., 1985, vol. 33, pp. 1023–35.

    Article  CAS  Google Scholar 

  7. V. Laxmanan: Acta Metall., 1985, vol. 33, pp. 1037–49.

    Article  CAS  Google Scholar 

  8. V. Laxmanan: J. Cryst. Growth, 1986, vol. 75, pp. 573–90.

    Article  CAS  Google Scholar 

  9. L. Nastac: Acta Mater., 1999, vol. 47, pp. 4253 to 62.

    Article  Google Scholar 

  10. J.S. Kirkaldy and D. Venugopalan: Scripta Metall., 1989, vol. 23, pp. 1603–08.

    Article  CAS  Google Scholar 

  11. J.S. Kirkaldy, L.X. Liu, and A. Kroupa: Acta Metall. Mater., 1995, vol. 43, pp. 2905–15.

    Article  CAS  Google Scholar 

  12. J. Li, G. Yang, and Y. Zhou: Mater. Res. Bull., 1998, vol. 33, pp. 141–48.

    Article  CAS  Google Scholar 

  13. M.H. Burden and J.D. Hunt: J. Cryst. Growth, 1974, vol. 22, pp. 99–111.

    Article  CAS  Google Scholar 

  14. R. Trivedi: Acta Metall., 1970, vol. 18, pp. 287–96.

    Article  CAS  Google Scholar 

  15. C.-A. Gandin, M. Eshelman, and R. Trivedi: Metall. Mater. Trans. A, 1996, vol. 27 A, pp. 2727–39.

    Google Scholar 

  16. J.A. Warren and J.S. Langer: Phys. Rev. A, 1990, vol. 42, pp. 3518–25.

    Article  Google Scholar 

  17. J.A. Warren and J.S. Langer: Phys. Rev. E, 1993, vol. 47, pp. 2702–12.

    Article  CAS  Google Scholar 

  18. Q. Li and C. Beckermann: Acta Mater., 1999, vol. 47, pp. 2345–56.

    Article  CAS  Google Scholar 

  19. Q. Han, and J.D. Hunt: Mater. Sci. Eng. A, 1997, vol. 238, pp. 192–95.

    Article  Google Scholar 

  20. B.J. Spencer and H.E. Huppert: J. Cryst. Growth, 1999, vol. 200, pp. 287–96.

    Article  CAS  Google Scholar 

  21. R. Trivedi: Metall. Mater. Trans. A, 1984, vol. 15A, pp. 977–82.

    CAS  Google Scholar 

  22. R. Trivedi and W. Kurz: Int. Mater. Rev., 1994, vol. 39, pp. 49–74.

    CAS  Google Scholar 

  23. T. Koseki and M.C. Flemings: Iron Steel Inst. Jpn. Int., 1995, vol. 35, pp. 611–17.

    CAS  Google Scholar 

  24. D. Bouchard and J.S. Kirkaldy: Metall. Mater. Trans. B, 1996, vol 27B, pp. 101–13.

    Article  CAS  Google Scholar 

  25. L. Makkonem: J. Cryst. Growth, 2000, vol. 208, pp. 772–78.

    Article  Google Scholar 

  26. J.A. Horwarth and L.F. Mondolfo: Acta Metall., 1962, vol. 10, pp. 1037–42.

    Article  Google Scholar 

  27. J.O. Coulthard and R. Elliott: J. Inst. Met., 1967, vol. 95, pp. 21–23.

    CAS  Google Scholar 

  28. T. Okamoto and K. Kishitake: J. Cryst. Growth, 1975, vol. 29, pp. 137–46.

    Article  CAS  Google Scholar 

  29. D. Bouchard and J.S. Kirkaldy: Metall. Mater. Trans. B, 1997, vol. 28B, pp. 651–63.

    CAS  Google Scholar 

  30. D.G. McCartney and J.D. Hunt: Acta Metall., 1981, vol. 29, pp. 1851–63.

    Article  CAS  Google Scholar 

  31. M. Chen and T.Z. Kattamis: Mater. Sci. Eng. A, 1998, vol. 247, pp. 239–47.

    Article  Google Scholar 

  32. B. Biblia, H. Jamgotchian, and L. Capella: Acta Metall., 1981, vol. 29, pp. 1785–89.

    Article  Google Scholar 

  33. C.T. Rios and R. Caram: J. Cryst. Growth, 1997, vol. 174, pp. 65–69.

    Article  CAS  Google Scholar 

  34. B. Drevet, H. Nguyen Thi, D. Camel, B. Biblia, and M.D. Dupouy: J. Cryst. Growth, 2000, vol. 218, pp. 419–33.

    Article  CAS  Google Scholar 

  35. J. Feng, W.D. Huang, X. Lin, Q.Y. Pan, T. Li, and Y.H. Zhou: J. Cryst. Growth, 1999, vol. 197, pp. 393–95.

    Article  CAS  Google Scholar 

  36. X. Lin, W.D. Huang, J. Feng, T. Li, and Y. Zhou: Acta Mater., 1999, vol. 47, pp. 3271–80.

    Article  CAS  Google Scholar 

  37. L. Yu, G.L. Ding, J. Reye, S.N. Ojha, and S.N. Tewari: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 2463–71.

    CAS  Google Scholar 

  38. E. Cadirli and M. Gündüz: J. Mater. Sci., 2000, vol. 35, pp. 3837–48.

    Article  CAS  Google Scholar 

  39. M. Gündüz and E. Çardili: Mater. Sci. Eng. A, 2002, vol. 327, pp. 167–85.

    Article  Google Scholar 

  40. J.M.V. Quaresma, C.A. Santos, and A. Garcia: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 3167–77.

    Article  CAS  Google Scholar 

  41. X. Wan, Q. Han, and J.D. Hunt: Acta Mater., 1997, vol. 45, pp. 3975–79.

    Article  CAS  Google Scholar 

  42. M.F. Lima and H. Goldenstein: J. Cryst. Growth, 2000, vol. 208, pp. 709–16.

    Article  CAS  Google Scholar 

  43. S. Yang, W. Huang, X. Lin, Y. Su, and Y. Zhou: Scripta Mater., 2000, vol. 42, pp. 543–48.

    Article  CAS  Google Scholar 

  44. R.M. Sharp and A. Hellawell: J. Cryst. Growth, 1969, vol. 5, pp. 155–61.

    Article  CAS  Google Scholar 

  45. G.L. Ding, W.D. Huang, X. Huang, X. Lin, and H. Zhou: Acta Mater., 1996, vol. 44, pp. 3705–09.

    Article  CAS  Google Scholar 

  46. J.A. Spittle and D.M. Floyd: Proc. Int. Conf. on Solidification and Casting of Metals, The Metals Society, London, 1979, pp. 15–20.

    Google Scholar 

  47. S.M. Lee, K.A.Q. O’Reilly, B. Cantor, and C.P. Hong: Mater. Sci. Eng. A, 1998, vol. 49, pp. 233–40.

    Google Scholar 

  48. J. Lapin, A. Klimová, R. Velisek, and M. Kursa: Scripta Mater., 1997, vol. 37, pp. 85–91.

    Article  CAS  Google Scholar 

  49. N. Tiedje, P.N. Hansen, and A.S. Pedersen: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 4085–93.

    Article  CAS  Google Scholar 

  50. M. Lin, T. Mori, and H. Iwasaki: Mater. Sci. Eng. A, 1999, vol. 265, pp. 217–23.

    Article  Google Scholar 

  51. S.P. O’Dell, G.L. Ding, and S.N. Tewari: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 2159–65.

    Article  CAS  Google Scholar 

  52. L.X. Liu and J.S. Kirkaldy: Acta Metall. Mater., 1995, vol. 43, pp. 2891–904.

    Article  CAS  Google Scholar 

  53. G. Ding, W. Huang, X. Lin, and Y. Zhou: J. Cryst. Growth, 1997, vol. 177, pp. 281–88.

    Article  CAS  Google Scholar 

  54. V.L. Voller and C.R. Swaminathan: Num. Heat Tranfer B, 1991, vol. 19, pp. 175–89.

    Google Scholar 

  55. W.R. Osório and A. Garcia: Mater. Sci. Eng. A, 2002, vol. 325, pp. 104–12.

    Google Scholar 

  56. C.A. Santos, J.M.V. Quaresma, and A. Garcia: J. Alloys Compounds, 2001, vol. 319, pp. 174–86.

    Article  CAS  Google Scholar 

  57. W.W. Mullins and R.F. Sekerka: J. Appl. Phys., 1965, vol. 35(1), pp. 264–68.

    Google Scholar 

  58. W.W. Mullins and R.F. Sekerka: J. Appl. Phys., 1965, vol. 36(2), pp. 444–51.

    Google Scholar 

  59. C.A. Siqueira, N. Cheung, and A. Garcia: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2107–2118.

    Article  CAS  Google Scholar 

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Rocha, O.L., Siqueira, C.A. & Garcia, A. Heat flow parameters affecting dendrite spacings during unsteady-state solidification of Sn-Pb and Al-Cu alloys. Metall Mater Trans A 34, 995–1006 (2003). https://doi.org/10.1007/s11661-003-0229-3

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