Rupture of random fuse networks: ductile to brittle crossover

We study the rupture process of Random Fuse Networks (RFN's) with quenched disorder in the microscopic threshold voltages. If lattices are driven to breakdown in one blow by an externally applied voltage the RFN's are shown to be equivalent to the toughest percolation backbone. Critical path analysis holds exactly in this case for all disorder distributions. For gradual rupture, it is shown that the existence of a lower cutoff in the disorder distributions entails a crossover from ductile to brittle behavior. The crossover length is a function of microscopic disorder and diverges in the limit of infinite disorder.