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Simple model of microsegregation during solidification of steels

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Abstract

A simple analytical model of microsegregation for the solidification of multicomponent steel alloys is presented. This model is based on the Clyne-Kurz model and is extended to take into account the effects of multiple components, a columnar dendrite microstructure, coarsening, and the δ/γ transformation. A new empirical equation to predict secondary dendrite arm spacing as a function of cooling rate and carbon content is presented, based on experimental data measured by several different researchers. The simple microsegregation model is applied to predict phase fractions during solidification, microsegregation of solute elements, and the solidus temperature. The predictions agree well with a range of measured data and the results of a complete finite-difference model. The solidus temperature decreases with either increasing cooling rate or increasing secondary dendrite arm spacing. However, the secondary dendrite arm spacing during solidification decreases with increasing cooling rate. These two opposite effects partly cancel each other, so the solidus temperature does not change much during solidification of a real casting.

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References

  1. M.C. Flemings and G.E. Nereo: Trans. TMS-AIME, 1967, vol. 239, pp. 1449–61.

    CAS  Google Scholar 

  2. R. Mehrabian, M. Keane, and M.C. Flemings: Metall. Trans., 1970, vol. 1, pp. 1209–20.

    CAS  Google Scholar 

  3. T. Fuji, D.R. Poirier, and M.C. Flemings: Metall. Trans. B, 1979, vol. 10B, pp. 331–39.

    Google Scholar 

  4. H. Mizukami, M. Komatsu, T. Kitagawa, and K. Kawakami: Trans. Iron Steel Inst. Jpn. 1984, vol. 24, pp. 940–49.

    Google Scholar 

  5. K.S. Oh, I.R. Lee, Y.K. Shin, Y.S. Koo, I.J. Lee, and D.Y. Lee: Proc. 6th Int. Iron Steel Congr., ISIJ, Nagoya, 1990, pp. 256–63.

    Google Scholar 

  6. K. Ayata, S. Koyama, H. Nakata, S. Kawasaki, K. Ebina, and T. Hata: Proc. 6th Int. Iron Steel Congr., ISIJ, Nagoya, 1990, pp. 279–84.

    Google Scholar 

  7. M. El-Bealy: Scand. J. Metall., 1995, vol. 24, pp. 63–80.

    CAS  Google Scholar 

  8. V.R. Voller and C. Beckermann: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 2183–89.

    Article  CAS  Google Scholar 

  9. J. Miettinen: Metall. Trans. A, 1992, vol. 23A, pp. 1155–70.

    CAS  Google Scholar 

  10. C.Y. Wang and C. Beckermann: Mater. Sci. Eng., 1993, vol. 171, pp. 199–211.

    Article  Google Scholar 

  11. J.F. McCarthy: Acta Mater., 1997, vol. 45, pp. 4077–91.

    Article  CAS  Google Scholar 

  12. A. Karma and W.J. Rappel: Phys. Rev. D, 1998, vol. 57, pp. 4323–49.

    CAS  Google Scholar 

  13. J. Tiaden: J. Cryst. Growth, 1999, vol. 199, pp. 1275–80.

    Article  Google Scholar 

  14. J.S. Lee, S.G. Kim, W.T. Kim, and T. Suzuki: Iron Steel Inst. Jpn. Int., 1999, vol. 39, pp. 730–36.

    CAS  Google Scholar 

  15. B. Nestler and A.A. Wheeler: Physica D, 2000, vol. 138, pp. 114–33.

    Article  CAS  Google Scholar 

  16. J. Rappaz and J.F. Scheid: Math. Methods Appl. Sci., 2000, vol. 23, pp. 491–513.

    Article  Google Scholar 

  17. T. Matsumiya, H. Kajioka, S. Mizoguchi, Y. Ueshima, and H. Esaka: Trans. Iron Steel Inst. Jpn., 1984, vol. 24, pp. 873–82.

    Google Scholar 

  18. Y. Ueshima, S. Mizoguchi, T. Matsumiya, and H. Kajioka: Metall. Trans. B, 1986, vol. 17B, pp. 845–59.

    CAS  Google Scholar 

  19. K. Kim, T. Yeo, K.H. Oh, and D.N. Lee: Iron Steel Inst. Jpn. Int., 1996, vol. 36, pp. 284–89.

    CAS  Google Scholar 

  20. Y.M. Won, K.H. Kim, T. Yeo, and K.H. Oh: Iron Steel Inst. Jpn. Int., 1998, vol. 38, pp. 1093–99.

    CAS  Google Scholar 

  21. J.A. Sarreal and G.J. Abbaschian: Metall. Trans. A, 1984, vol. 17A, pp. 2063–73.

    Google Scholar 

  22. G. Shin, T. Kajitani, T. Suzuki, and T. Umeda: Tetsu-to-Hagané, 1992, vol. 78, pp. 587–93.

    CAS  Google Scholar 

  23. D.J. Seol, Y.M. Won, K.H. Oh, Y.C. Shin, and C.H. Yim: Iron Steel Inst. Jpn. Int., 2000, vol. 40, pp. 356–63.

    CAS  Google Scholar 

  24. E. Schmidtmann and F. Rakoski: Arch. Eisenhüttenwes., 1983, vol. 54, pp. 357–62.

    CAS  Google Scholar 

  25. H.G. Suzuki, S. Nishimura, and Y. Nakamura: Trans. Iron Steel Inst. Jpn., 1984, vol. 24, pp. 54–59.

    CAS  Google Scholar 

  26. T. Nakagawa, T. Umeda, J. Murata, Y. Kamimura, and N. Niwa: Iron Steel Inst. Jpn., 1995, vol. 35, pp. 723–29.

    CAS  Google Scholar 

  27. A Guide to the Solidification of Steels, Jernkontoret, Stockholm, 1977.

  28. L. Ericson: Scand. J. Metall., 1977, vol. 6, pp. 116–24.

    CAS  Google Scholar 

  29. S. Kobayashi: Trans. Iron Steel Inst. Jpn., 1988, vol. 28, pp. 535–42.

    CAS  Google Scholar 

  30. Y.C. Shin, J. Choi, and C.H. Yim: Technical Report, Iron & Steel Making Research Team, Technical Research Labs., POSCO, Korea, 1998.

    Google Scholar 

  31. E. Scheil: Z. Metallkd., 1942, vol. 34, pp. 70–72.

    Google Scholar 

  32. H.D. Brody and M.C. Flemings: Trans. TMS-AIME, 1966, vol. 236, pp. 615–24.

    CAS  Google Scholar 

  33. I. Ohnaka: Trans. Iron Steel Inst. Jpn., 1986, vol. 26, pp. 1045–51.

    CAS  Google Scholar 

  34. T.W. Clyne and W. Kurz: Metall. Trans. A, 1981, vol. 12A, pp. 965–71.

    Google Scholar 

  35. S. Kobayashi: J. Cryst. Growth, 1988, vol. 88, pp. 87–96.

    Article  CAS  Google Scholar 

  36. T.P. Battle and R.D. Pehlke: Metall. Trans. B, 1990, vol. 21B, pp. 357–75.

    CAS  Google Scholar 

  37. J. Miettinen: Ironmaking and Steelmaking, 1996, vol. 23, pp. 346–56.

    CAS  Google Scholar 

  38. J. Miettinen: Metall. Mater. Trans. B, 1997, vol. 28B, pp. 281–97.

    CAS  Google Scholar 

  39. T. Kawawa: Tekko-no-Gyoko (Solidification of Steel), Solidification Communications of ISIJ, ISIJ, Tokyo, 1997, Appendix 13.

    Google Scholar 

  40. Y. Nakamura and H. Esaka: Tetsu-to-Hagané, 1981, vol. 67, p. S140.

  41. Tekko-no-Gyoko (Solidification of Steel), supplement, Solidification Communications of ISIJ, ISIJ, Tokyo, 1977, pp. S32–S50.

  42. Metals Handbook, 8th ed., T. Lyman, H.E. Boyer, W.J. Carnes, and M.W. Chevalier, eds., ASM, Metal Park, OH, 1973.

    Google Scholar 

  43. Tekko-Binran (Handbook for Steel), 3rd ed., ISIJ, Maruzen, Tokyo, 1981, vol. 1, pp. 193–94.

  44. W. Kurz and D.J. Fisher: Fundamentals of Solidification, Trans Techn Publications, Aedermannsdorf, 1989.

    Google Scholar 

  45. B. Sundman, B. Jansson and J.-O. Andersson: CALPHAD, 1985, vol. 9, pp. 153–90.

    Article  CAS  Google Scholar 

  46. E. Flender: MAGMASOFT, Magma Gmbh, Aachen, 2000.

    Google Scholar 

  47. H. Jacobi and K. Wünnenberg: Steel Res., 1999, vol. 70, pp. 362–67.

    CAS  Google Scholar 

  48. B. Weisgerber, M. Hecht, and K. Harste: Steel Res., 1999, vol. 70, pp. 403–11.

    CAS  Google Scholar 

  49. M. Imagumbai and T. Takeda: Iron Steel Inst. Jpn. Int., 1994, vol. 34, pp. 574–83.

    CAS  Google Scholar 

  50. D. Senk, B. Engl, O. Siemon, and G. Stebner: Steel Res., 1999, vol. 70, pp. 368–72.

    CAS  Google Scholar 

  51. A. Suzuki, T. Suzuki, Y. Nagaoka, and Y. Iwata: Nippon Kinzoku Gakkaishi, 1968, vol. 32, pp. 1301–05.

    CAS  Google Scholar 

  52. M. El-Bealy and B.G. Thomas: Metall. Mater. Trans. B, 1996, vol. 27B, pp. 689–93.

    Article  CAS  Google Scholar 

  53. D.J. Hurtuk and A.A. Tzavaras: Proc. Int. Conf. on Solidification, Solidification and Casting of Metals, University of Sheffield, Sheffield, 1977, pp. 21–28.

    Google Scholar 

  54. T.B. Massalski: Binary Alloy Phase Diagrams, ASM, Materials Park, 1986, vol. 1, p. 842.

    Google Scholar 

  55. V.R. Voller and S. Sundarraj: Mater. Sci. Technol., 1993, vol. 9, pp 478–81.

    Google Scholar 

  56. A.A. Howe: Ironmaking and Steelmaking, 1988, vol. 15, pp. 134–42.

    CAS  Google Scholar 

  57. R. Flesch and W. Bleck: Steel Res., 1998, vol. 69, pp. 292–99.

    CAS  Google Scholar 

  58. T.W. Clyne, M. Wolf, and W. Kurz: Metall. Trans. B, 1982, vol. 13B, pp. 259–66.

    CAS  Google Scholar 

  59. Y.M. Won, T. Yeo, D.J. Seol, and K.H. Oh: Metall. Mater. Trans. B, 2000, vol. 31B, pp. 779–94.

    CAS  Google Scholar 

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Won, YM., Thomas, B.G. Simple model of microsegregation during solidification of steels. Metall Mater Trans A 32, 1755–1767 (2001). https://doi.org/10.1007/s11661-001-0152-4

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