Roughness Scaling of Fracture Surfaces in Polycrystalline Materials


The roughness scaling of fracture surfaces in two-dimensional grain boundary networks is studied 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.

This is a preview of subscription content, access via your institution.


  1. 1.

    Statistical Models for the Fracture in Disordered Media, edited by H. J. Herrmann and S. Roux, (North-Holland, Amsterdam, 1990).

  2. 2.

    J. Kertesz, V. K. Horvöth, and F. Weber, Fractals 1, 67 (1993).

    Article  Google Scholar 

  3. 3.

    J. H. Meinke, E. S. McGarry, P. M. Duxbury, and E. A. Holm, Phys. Rev. E 68, 066107 (2003).

    CAS  Article  Google Scholar 

  4. 4.

    Randomness in general includes correlated randomness, e.g. that arising under certain geometrical constraints of grain boundaries.

  5. 5.

    R. W. Minich, C. A. Schuh, and M. Kumar, Phys. Rev. B 66, 052101 (2002).

    Article  Google Scholar 

  6. 6.

    C. A. Schuh, M. Kumar, W. E. King, Acta Mater. 51, 687 (2003).

    CAS  Article  Google Scholar 

  7. 7.

    V. I. Raisanen, E. T. Seppala, M. J. Alava, and P. M. Duxbury, Phys. Rev. Lett. 80, 329 (1998).

    CAS  Article  Google Scholar 

  8. 8.

    E. T. Seppala, V. I. Raisanen, and M. J. Alava, Phys. Rev. E 61, 6312 (2000).

    CAS  Article  Google Scholar 

  9. 9.

    M. Alava, P. Duxbury, C. Moukarzel, and H. Rieger, Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, San Diego, 2001), vol 18.

  10. 10.

    B. W. Reed, R. W. Minich, R. E. Rudd, and M. Kumar, Acta Cryst. A 60, 263 (2004).

    Article  Google Scholar 

  11. 11.

    More details of maximum flow - minimum cut algorithms can be found from any basic data structure and algorithm book, see e.g., R. Sedgewick, Algorithms in C (Addison-Wesley, Reading, 1990).

  12. 12.

    A. V. Goldberg and R. E. Tarjan, J. Assoc. Comput. Mach. 35, 921 (1988).

    Article  Google Scholar 

  13. 13.

    E. T. Seppala, B. W. Reed, R. W. Minich, M. Kumar, and R. E. Rudd (unpublished).

Download references


This work was performed under the auspices of the US Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.

Author information



Corresponding author

Correspondence to Eira T. Seppälä.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Seppälä, E.T., Reed, B.W., Kumar, M. et al. Roughness Scaling of Fracture Surfaces in Polycrystalline Materials. MRS Online Proceedings Library 819, 14 (2004).

Download citation