  We investigate the role of disorder on the fracturing process of
heterogeneous materials by means of a two-dimensional fuse network model. Our
results in the extreme disorder limit reveal that the backbone of the fracture
at collapse, namely the subset of the largest fracture that effectively halts
the global current, has a fractal dimension of $1.22 \pm 0.01$. This exponent
value is compatible with the universality class of several other physical
models, including optimal paths under strong disorder, disordered polymers,
watersheds and optimal path cracks on uncorrelated substrates, hulls of
explosive percolation clusters, and strands of invasion percolation fronts.
Moreover, we find that the fractal dimension of the largest fracture under
extreme disorder, $d_f=1.86 \pm 0.01$, is outside the statistical error bar of
standard percolation. This discrepancy is due to the appearance of trapped
regions or cavities of all sizes that remain intact till the entire collapse of
the fuse network, but are always accessible in the case of standard
percolation. Finally, we quantify the role of disorder on the structure of the
largest cluster, as well as on the backbone of the fracture, in terms of a
distinctive transition from weak to strong disorder characterized by a new
crossover exponent.
