Critical Manifolds in Polycrystalline Grain Structures


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With the development of new, fully three-dimensional metallographic techniques, there is considerable interest in characterizing three-dimensional microstructures in ways that go beyond twodimensional stereology. One characteristic of grain structures is the surface of lowest energy across the microstructure, termed the critical manifold (CM). When the grain boundaries are sufficiently weak, the CM lies entirely on grain boundaries, while when the grain boundaries are strong, cleavage occurs. A scaling theory for the cleavage to intergranular transition of CMs is developed. We find that a critical length scale exists, so that on short length scales cleavage is observed, while at long length scales the CM is rough. CMs for realistic polycrystalline grain structures, determined by a network optimization algorithm, are used to verify the analysis.



Materials Science Forum (Volumes 467-470)

Edited by:

B. Bacroix, J.H. Driver, R. Le Gall, Cl. Maurice, R. Penelle, H. Réglé and L. Tabourot




E. A. Holm et al., "Critical Manifolds in Polycrystalline Grain Structures", Materials Science Forum, Vols. 467-470, pp. 1039-1044, 2004

Online since:

October 2004




[1] G. Palumbo, E.M. Lehockey, and P. Lin, JOM 50 40 (1998).

[2] R. Haslinger and R. Joynt, Phys. Rev. B 61 4206 (2000).

[3] T. Watanabe and S. Tsurekawa, Acta Mater. 47 4171 (1999).

[4] S.F. Nielsen, E.M. Lauridsen, Juul Jensen D., and H.F. Poulsen, Mater. Sci. Eng. A 319-321 179 (2001).

[5] M. P. Anderson, G. S. Grest, D. J. Srolovitz, Phil. Mag. B 59 293 (1989).

[6] L. R. Ford Jr., D. R. Fulkerson, Flows in Networks (Princeton Press, Princeton, NJ, 1962).

[7] J. Edmonds, R. M. Karp, JACM 19 248 (1972).

[8] A. V. Goldberg and R. E. Trajan, J. Assoc. Comput. Mach. 35 921 (1988).

[9] M. J. Alava, P. M. Duxbury, C. F. Moukarzel, and H. Rieger, Phase Transitions and Critical Phenomena, ed. By C. Domb and J. Lebowitz (Academic Press, New York, 2001), vol. 18.

[10] J. H. Meinke, E. S. McGarrity, P. M. Duxbury, E. A. Holm, Phys. Rev. E 68 066107 (2003).

[11] D. A. Huse and C. L. Henley, Phys. Rev. Lett. 54 2708 (1985).

[12] D. S. Fisher, Phys. Rev. Lett. 56 1964 (1986).

[13] A. A. Middleton, Phys. Rev. E 52 R3337 (1995).

[14] M. J. Alava and P. M. Duxbury, Phys. Rev. B 54 14 990 (1996).