We investigate the nucleation and propagation of cracks in self-assembled viscoelastic fluids, which are made of surfactant micelles reversibly linked by telechelic polymers. The morphology of the micelles can be continuously tuned, from spherical to rodlike to wormlike, thus producing transient double networks when the micelles are sufficiently long and entangled and transient single networks otherwise. For a single network, we show that cracks nucleate when the sample deformation rate involved is comparable to the relaxation time scale of the network. For a double network, by contrast, significant rearrangements of the micelles occur as a crack nucleates and propagates. We show that birefringence develops at the crack tip over a finite length, ξ, which corresponds to the length scale over which micelle alignment occurs. We find that ξ is larger for slower cracks, suggesting an increase of ductility.