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.
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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.
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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). https://doi.org/10.1557/PROC-819-N1.4