Crack-cluster distributions in the random fuse model

Using large-scale numerical simulations and extensive sampling, we analyze the scaling properties of the crack-cluster distribution and the largest crack-cluster distribution at the peak load. The simulations are performed using both two-dimensional and three-dimensional random fuse models. The numerical results indicate that in contrast with the randomly diluted networks (percolation disorder), the crack-cluster distribution in the random fuse model at the peak load follows neither a power law nor an exponential distribution. The largest crack-cluster distribution at the peak load follows a lognormal distribution, and this is discussed in the context of whether there exists a relationship between the largest crack-cluster size distribution at peak load and the fracture strength distribution. Contrary to popular belief, we find that the fracture strength and the largest crack-cluster size at the peak load are uncorrelated. Indeed, quite often, the final spanning crack is formed not due to the propagation of the largest crack at the peak load, but instead due to coalescence of smaller cracks.