Crack surface roughness in three-dimensional random fuse networks

Using large system sizes with extensive statistical sampling, we analyze the scaling properties of crack roughness and damage profiles in the three-dimensional random fuse model. The analysis of damage profiles indicates that damage accumulates in a diffusive manner up to the peak load, and localization sets in abruptly at the peak load, starting from a uniform damage landscape. The global crack width scales as W approximately L(0.5) and is consistent with the scaling of localization length xi approximately L(0.5) used in the data collapse of damage profiles in the postpeak regime. This consistency between the global crack roughness exponent and the postpeak damage profile localization length supports the idea that the postpeak damage profile is predominantly due to the localization produced by the catastrophic failure, which at the same time results in the formation of the final crack. Finally, the crack width distributions can be collapsed for different system sizes and follow a log-normal distribution.