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Stochastic Modeling of Grain Structure Formation in Solidification Processes

Published online by Cambridge University Press:  29 November 2013

Michel Rappaz  and
Charles-André Gandin
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Besides the numerical tools which have been developed for solving the continuity equations in materials processing, the prediction of microstructures and defects in such processes is becoming an important step in assessing the quality, and ultimately the mechanical properties, of the final products. Because the typical length scales associated with the process and with the microstructure differ widely (typically a factor of 104), special techniques have to be used when coupling the macroscopic and microscopic levels. This contribution will briefly present some of the modeling tools recently developed for solidification. The trend is now to replace deterministic models used over the last 20 years by stochastic approaches which directly generate computed micrographs. Among those, Monte Carlo techniques originally developed for the grain growth in solids were adapted to the solidification of alloys, and cellular automata models specifically take into account the dendrite growth mechanisms.

Type
Mathematical Modeling of Materials Processing
Information
MRS Bulletin , Volume 19 , Issue 1 , January 1994 , pp. 20 - 24
Copyright
Copyright © Materials Research Society 1994

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References

1.Rappaz, M., Int. Mater. Rev. 34 (1989) p. 93.CrossRefGoogle Scholar
2.Kurz, W. and Fisher, D.J., Fundamentals of Solidification Processes (Trans Tech Publications, Aedermannsdorf, Switzerland, 1989).Google Scholar
3.Kurz, W., Giovanola, B., and Trivedi, R., Acta Metall. 34 (1986) p. 823.CrossRefGoogle Scholar
4.Zhu, P. and Smith, W., Acta Metall. 40 (1992) p. 683 and p. 3369.CrossRefGoogle Scholar
5.Hunt, J.D., Mater. Sci. Eng. 65 (1984) p. 75.CrossRefGoogle Scholar
6.Chalmers, B., Principles of Solidification (John Wiley & Sons, New York, 1964).Google Scholar
7.Esaka, H., PhD thesis, Ecole Polytechnique Fédérale de Lausanne, 1986.Google Scholar
8.Witzke, S., Riquet, J.P., and Durand, F., “Memoires Scientifiques,” Revue Métallurgie 701 (1979).Google Scholar
9.Blank, E. and Rappaz, M., J. Cryst. Growth 74 (1986) p. 67.Google Scholar
10.McLean, M., Directionally Solidified Materials for High Temperature Service (The Metals Society, London, 1983).Google Scholar
11.Anderson, M.P., Srolovitz, D.J., Crest, G.S., and Sahni, P.S., Acta Met. 32 (1984) p. 783, 793, and p. 1429; M.P. Anderson, D.J. Srolovitz, G.S. Crest, and P.S. Sahni, Acta Met.. 33 (1985) p. 509 and 2233.CrossRefGoogle Scholar
12.Spittle, J.A. and Brown, S.C.R., Acta Metall. 37 (1989) p. 1803; Mater. Sci. Technol. 5 (1989) p. 362.CrossRefGoogle Scholar
13.Ohsasa, K., private communication (Modeling for Welding Science Workshop, Florida, 1993).Google Scholar
14.Rappaz, M. and Gandin, Ch.-A., Acta Metall. 41 (1993) p. 345.CrossRefGoogle Scholar
15.Gandin, Ch.-A. and Rappaz, M., “A Coupled Finite Element—Cellular Automation Model for the Prediction of Dendritic Grain Structures in Solidification Processes,” Acta Metall. (submitted).Google Scholar
16.Thévoz, Ph., Desbiolles, J.L., and Rappaz, M., Met. Trans. 20A (1989) p. 311.CrossRefGoogle Scholar
17.Gandin, Ch.-A., Rappaz, M., and Tintillier, R., Met. Trans. 24A (1993) p. 467; Ch.-A. Gandin, M. Rappaz, and R. Tintillier, Met. Trans. 24A (1993) p. 467, (to appear, 1993).CrossRefGoogle Scholar