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A Phase Field Model for Grain Refinement in Deeply Undercooled Metallic Melts

Published online by Cambridge University Press:  21 March 2011

A.M. Mullis
Affiliation:
Department of Materials, University of Leeds, Leeds LS2 9JT, UK.
R.F. Cochrane
Affiliation:
Department of Materials, University of Leeds, Leeds LS2 9JT, UK.
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Abstract

We present the results of phase field simulations of dendritic growth into pure undercooled melts, at growth velocities up to 35 m s−1. We find that, at low growth velocities, dendrite morphologies are broadly self-similar with increasing growth velocity. However, above ≈ 15 m s−1 the initiation of side-branching moves closer to the dendrite tip with increasing growth velocity. This appears to be related to the level of kinetic undercooling at the tip. Once side- branch initiation begins to occur within 1-2 radii of the tip, profound morphological changes occur, leading to severe thinning of the dendrite trunk and ultimately repeated multiple tip- splitting. This process can be invoked to explain many of the observed features of spontaneous grain refinement in deeply undercooled metallic melts.

Type
Research Article
Copyright
Copyright © Materials Research Society 2001

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References

REFERENCES

1. Walker, J. L, in The Physical Chemistry of Process Metallurgy, part 2, ed. Pierre, G. R. St., Interscience (1959)Google Scholar
2. Powell, G. L. F., J. Aust. Inst. Met. 10, 223 (1965).Google Scholar
3. Mello, M. Costa Agra & Kiminami, C. S., J. Mater. Sci. Lett. 8, 1416 (1989).Google Scholar
4. Kattamis, T. Z. & Flemings, M. C., Trans. AIME 236, 1523 (1966).Google Scholar
5. Tarshis, L. A., Walker, J. L. & Rutter, J. W., Metall. Trans. 2, 2589 (1971).Google Scholar
6. Kobayashi, K. F. & Shingu, P. H., J. Mater. Sci. 23, 2157 (1988).Google Scholar
7. Willnecker, R., Herlach, D. M. & Feuerbacher, B., Phys. Rev. Lett. 62, 2707 (1989).Google Scholar
8. Bassler, B. T., Hofmeister, W. H., Carro, G. & Bayuzick, R. J., Metall. Mater. Trans. 25A, 1301 (1994).Google Scholar
9. Battersby, S.E., R.F Cochrane & Mullis, A.M., J. Mater. Sci. 34, 2049 (1999).Google Scholar
10. Battersby, S.E., Cochrane, R.F & Mullis, A.M., J. Mater. Sci. 35, 1365 (1999).Google Scholar
11. Matson, D., in: Solidification 1998, TMS, Warrendale, PA. pp. 233244, ISBN 0-87339-396-1.Google Scholar
12. Kattamis, T. Z. & Flemings, M. C., Mod. Casting 52, 97 (1967).Google Scholar
13. Schwarz, M., Karma, K., Eckler, K., Herlach, D. M., Phys. Rev. Lett. 73, 1380 (1994).Google Scholar
14. Karma, A., Int. J. Non-equilibrium Processing 11, 201 (1998).Google Scholar
15. Mullis, A. M & Cochrane, R. F., Int. J. Non-equilibrium Processing 11, 283 (2000).Google Scholar
16. Mullis, A. M., Mater. Sci. Eng. A226–228, 804 (1997).Google Scholar
17. Mullis, A. M. & Cochrane, R. F., J. Appl. Phys. 82, 3783 (1997).Google Scholar
18. Lipton, J., Kurz, W. & Trivedi, R., Acta Metall. 35, 957 (1987).Google Scholar
19. Mullis, A. M. & Cochrane, R. F., J. Appl. Phys. 84, 4905 (1998).Google Scholar
20. Tarshis, L. A., Walker, J. L. & Rutter, J. W., Metall. Trans. 2, 2589 (1971).Google Scholar
21. Norman, A. F., Eckler, K., Gartner, F., Moir, S. A., Greer, A. L., Ramous, E. & Herlach, D. M., Mater. Sci. Eng. A226–228, 48 (1997).Google Scholar
22. Warren, J. A. & Boettinger, W. J., Acta Metall. Mater. 43, 689 (1995).Google Scholar
23. Wheeler, A. A., Murray, B.T. & Schaefer, R.J., Physica D 66, 243 (1993).Google Scholar
24. Barber, M. N., Barbieri, A. & Langer, J. S., Phys Rev. A 36, 3340 (1987).Google Scholar
25. Langer, J. S., Phys. Rev. A 36, 3350 (1987).Google Scholar
26. Brener, E. & Temkin, D., Phys. Rev. E 51, 351 (1995).Google Scholar
27. Bisang, U. & Bilgram, J. H., Phys. Rev. E 54, 5309 (1996).Google Scholar
28. Turnbull, D., Acta Metall. 30, 2135 (1982).Google Scholar
29. Sawada, Y., Statphys. 16 (Ed. Stanley, H.E.), North Holland, Amsterdam, 1986.Google Scholar
30. Brener, E., Müller-Krumbhaar, H. & Tempkin, D., Europhys. Lett. 17, 535 (1992).Google Scholar