  We study the fracture of reversible double transient networks, constituted of
water suspensions of entangled surfactant wormlike micelles reversibly linked
by various amounts of telechelic polymers. We provide a state diagram that
delineates the regime of fracture without necking of the filament from the
regime where no fracture or break-up has been observed. We show that filaments
fracture when stretched at a rate larger than the inverse of the slowest
relaxation time of the networks. We quantitatively demonstrate that dissipation
processes are not relevant in our experimental conditions and that, depending
on the density of nodes in the networks, fracture occurs in the linear
viscoelastic regime or in a non-linear regime. In addition, analysis of the
crack opening profiles indicates deviations from a parabolic shape close to the
crack tip for weakly connected networks. We demonstrate a direct correlation
between the amplitude of the deviation from the parabolic shape and the amount
of non linear viscoelasticity.
