Abstract
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
$W \sim L^{0.5}$ and is consistent with the scaling of localization length $\xi \sim L^{0.5}$
used in the data collapse of damage profiles in the post-peak regime.
This consistency between the global crack roughness exponent and the post-peak damage
profile localization length supports the idea that
the post-peak 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.
