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Roughness Scaling of Fracture Surfaces in Polycrystalline Materials

Published online by Cambridge University Press:  15 March 2011

Eira T. Seppäaläa ,
Bryan W. Reed ,
Mukul Kumar ,
Roger W. Minich  and
Robert E. Rudd
Eira T. Seppäaläa
Affiliation:
Lawrence Livermore National Laboratory, L-415, Livermore, CA 94551, U.S.A.
Bryan W. Reed
Affiliation:
Lawrence Livermore National Laboratory, L-415, Livermore, CA 94551, U.S.A.
Mukul Kumar
Affiliation:
Lawrence Livermore National Laboratory, L-415, Livermore, CA 94551, U.S.A.
Roger W. Minich
Affiliation:
Lawrence Livermore National Laboratory, L-415, Livermore, CA 94551, U.S.A.
Robert E. Rudd
Affiliation:
Lawrence Livermore National Laboratory, L-415, Livermore, CA 94551, U.S.A.
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Abstract

The roughness scaling of fracture surfaces in two-dimensional grain boundary networks is stud- ied numerically. Grain boundary networks are created using a Metropolis method in order to mimic the triple junction distributions from experiments. Fracture surfaces through these grain boundary networks are predicted using a combinatorial optimization method of maximum flow — minimum cut type. We have preliminary results from system sizes up to N = 22500 grains suggesting that the roughness scaling of these surfaces follows a random elastic manifold scaling exponent ζ = 2/3. We propose a strong dependence between the energy needed to create a crack and the special boundary fraction. Also the special boundaries at the crack and elsewhere in the system can be tracked.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 819: Symposia N/P – Interfacial Engineering for Optimized Properties III , 2004 , N1.4
Copyright
Copyright © Materials Research Society 2004

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References

1. Statistical Models for the Fracture in Disordered Media, edited by Herrmann, H. J. and Roux, S., (North-Holland, Amsterdam, 1990).Google Scholar
2. Kertész, J., Horváth, V. K., and Weber, F., Fractals 1, 67 (1993).Google Scholar
3. Meinke, J. H., McGarry, E. S., Duxbury, P. M., and Holm, E. A., Phys. Rev. E 68, 066107 (2003).Google Scholar
4. Randomness in general includes correlated randomness, e.g. that arising under certain geometrical constraints of grain boundaries.Google Scholar
5. Minich, R. W., Schuh, C. A., and Kumar, M., Phys. Rev. B 66, 052101 (2002).Google Scholar
6. Schuh, C. A., Kumar, M., King, W. E., Acta Mater. 51, 687 (2003).Google Scholar
7. Räaisäanen, V. I., Seppäaläa, E. T., Alava, M. J., and Duxbury, P. M., Phys. Rev. Lett. 80, 329 (1998).Google Scholar
8. Seppäaläa, E. T., Räaisäanen, V. I., and Alava, M. J., Phys. Rev. E 61, 6312 (2000).Google Scholar
9. Alava, M., Duxbury, P., Moukarzel, C., and Rieger, H., Phase Transitions and Critical Phenomena, edited by Domb, C. and Lebowitz, J. L. (Academic Press, San Diego, 2001), vol 18.Google Scholar
10. Reed, B. W., Minich, R. W., Rudd, R. E., and Kumar, M., Acta Cryst. A 60, 263 (2004).Google Scholar
11. More details of maximum flow - minimum cut algorithms can be found from any basic data structure and algorithm book, see e.g., Sedgewick, R., Algorithms in C (Addison-Wesley, Reading, 1990).Google Scholar
12. Goldberg, A. V. and Tarjan, R. E., J. Assoc. Comput. Mach. 35, 921 (1988).Google Scholar
13. Seppäaläa, E. T., Reed, B. W., Minich, R. W., Kumar, M., and Rudd, R. E. (unpublished).Google Scholar