We study a fracture on a quasistatic time scale in a three-dimensional (3D) fuse network model with “strong” and “weak” disorder. These two cases differ noticeably in the development of the fracture. For strong disorder the damage scaling is very close to volumelike [number of broken bonds Nb∼L3/(lnL)0.3] unlike for weak disorder [Nb∼L2.4/(lnL)0.3]. With strong disorder global load sharing is only approximately valid. The size distribution of “avalanches” of broken fuses in the failure follows roughly a power-law scaling. The power-law exponent τ has a value close to 2, close to but differing from the exponent −5/2 expected of global load sharing. For weak disorder τ is about 1.5 which means that the decay of the size distribution is much slower than expected. These exponent values that characterize the development of damage prior to catastrophic failure are comparable to experimental ones. For the final fracture surfaces we observe a roughness exponent ζ≈0.4 for weak disorder. For strong disorder, severe finite size effects are seen, but the exponent seems to converge to the same value as for weak disorder, which is close to the one for the 3D random bond Ising domain wall universality class.