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Three-dimensional cellular automaton models of microstructural evolution during solidification

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Abstract

The evolution of microstructural features during solidification involves complex interactions between several physical phenomena. Cellular automata (CA) models are often characterized as being simple in their construction and yet able to produce very complicated behaviour. This property of CA models has been exploited to produce computer simulations of various aspects of microstructural evolution occurring during solidification. Results of a series of three-dimensional simulations of non-isothermal “free” dendritic growth are presented and the changes in dendrite morphology for different conditions are quantified and discussed. A modification of this model was also developed to examine the effects of composition on microstructural evolution for a simple eutectic system. As the composition moves towards the eutectic the simulated microstructures change from combined dendritic/lamellar to completely lamellar.

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References

  1. B. Chalmers, “Principles of Solidification” (Wiley, New York, 1964) Ch. 4.

    Google Scholar 

  2. G. P. Ivantsov, Dokl. Acad. Nauk. 58 (1947) 567.

    Google Scholar 

  3. D. E. Temkin, ibid. 132 (1960) 1307.

    Google Scholar 

  4. G. Horvay and J. W. Cahn, Acta Metall. 9 (1961) 695.

    Article  CAS  Google Scholar 

  5. G. F. Bolling and W. A. Tiller, J. Appl. Phys. 32 (1961) 2587.

    Article  CAS  Google Scholar 

  6. M. E. Glicksman and R. J. Schaeffer, J. Crystal Growth 1 (1967) 297.

    Article  CAS  Google Scholar 

  7. L. A. Tarshis and G. R. Kotler, ibid. 2 (1968) 222.

    Article  CAS  Google Scholar 

  8. R. F. Sekerka, R. G. Seidensticker, D. R. Hamilton and J. D. Harrison, in “Investigation of Desalination by Freezing” (Westinghouse Research Laboratory Report, 1967).

  9. E. G. Holtzmann, J. Appl. Phys. 41 (1970) 1460.

    Article  Google Scholar 

  10. R. Trivedi, Acta Metall. 18 (1970) 287.

    Article  CAS  Google Scholar 

  11. G. E. Nash and M. E. Glicksman, ibid. 22 (1974) 1283.

    Article  CAS  Google Scholar 

  12. M. H. Burden and J. D. Hunt, J. Crystal Growth 22 (1974) 109.

    Article  CAS  Google Scholar 

  13. I. Jin and G. R. Purdy, ibid. 23 (1974) 29.

    Article  CAS  Google Scholar 

  14. J. S. Kircaldy, Scripta Metall. 14 (1980) 739.

    Article  Google Scholar 

  15. R. Trivedi, J. Crystal Growth 49 (1980) 219.

    Article  CAS  Google Scholar 

  16. W. Kurz and J. D. Fisher, Acta Metall. 29 (1981) 11.

    Article  CAS  Google Scholar 

  17. V. Laxmanan, ibid. 33 (1985) 1023.

    Article  CAS  Google Scholar 

  18. W. Oldfield, in “The Solidification of Metals” (The Iron and Steel Institute, London, 1968) p. 70.

    Google Scholar 

  19. W. Oldfield, Mater. Sci. Eng. 11 (1973) 211.

    Article  CAS  Google Scholar 

  20. J. D. Hunt, Acta Metall. Mater. 39 (1991) 2117.

    Article  CAS  Google Scholar 

  21. R. Kobayashi, Phys. D 63 (1993) 410.

    Article  Google Scholar 

  22. A. A. Wheeler, B. T. Murray and R. J. Schaeffer, ibid. 66 (1993) 243.

    Article  CAS  Google Scholar 

  23. S. L. Wang, R. G. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun and G. B. McFadden, ibid. 69 (1993) 189.

    Article  CAS  Google Scholar 

  24. W. J. Boettinger, A. A. Wheeler, B. T. Murray, G. B. McFadden and R. Kobayashi, in “Modeling of Casting, Welding and Advanced Solidification Processes—VI”, edited by T. S. Piwonka, V. Voller and L. Katgerman (TMS, Florida, 1993) p. 79.

    Google Scholar 

  25. M. Hillert, Jernkontorets Ann. 141 (1957) 757.

    CAS  Google Scholar 

  26. K. A. Tiller, “Liquid Metals and Solidification” (ASM, Cleveland, OH, 1958).

    Google Scholar 

  27. K. A. Jackson and J. D. Hunt, Trans. Metall. Soc. AIME 236 (1966) 1129.

    CAS  Google Scholar 

  28. J. P. Chilton and W. C. Winegard, J. Inst. Metals 89 (1961) 162.

    CAS  Google Scholar 

  29. J. D. Hunt and J. P. Chilton, ibid. 92 (1963) 21.

    CAS  Google Scholar 

  30. A. Moore and R. Elliot, in “The Solidification of Metals” (Iron and Steel Institute, London, 1968) p. 167.

    Google Scholar 

  31. J. Liu and R. Elliot, Mater. Sci. Eng. A173 (1993) 129.

    Article  CAS  Google Scholar 

  32. A. Karma, Phys. Rev. Lett. 59 (1987) 71.

    Article  CAS  Google Scholar 

  33. R. Xiao, J. Iwan, D. Alexander and F. Rosenberger, Phys. Rev. A 45 (1992) 571.

    Article  Google Scholar 

  34. S. G. R. Brown and J. A. Spittle, Scripta Metall. Mater. 27 (1992) 1599.

    Article  Google Scholar 

  35. S. G. R. Brown, T. Williams and J. A. Spittle, Acta Metall. Mater. 42 (1994) 2893.

    Article  CAS  Google Scholar 

  36. S. G. R. Brown, G. P. Clarke and A. J. Brooks, Mater. Sci. Technol. (1994) in press.

  37. J. A. Spittle and S. G. R. Brown, Acta Metall. Mater. (1994) to be published.

  38. M. E. Glicksman, R. J. Schaeffer and J. D. Ayers, Metall. Trans. A 7A (1976) 1747.

    Article  CAS  Google Scholar 

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Brown, S.G.R., Bruce, N.B. Three-dimensional cellular automaton models of microstructural evolution during solidification. JOURNAL OF MATERIALS SCIENCE 30, 1144–1150 (1995). https://doi.org/10.1007/BF00356112

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