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Fracture of dual crosslink gels with permanent and transient crosslinks

We have carried out systematic fracture experiments in a single edge notch geometry over a range of stretch rates on dual crosslink hydrogels made from polyvinyl alcohol chains chemically crosslinked with glutaraldehyde and physically crosslinked with borate ions. If the energy release rate necessary for crack propagation was calculated conventionally, by using the work done to deform the sample to the critical value of stretch $λ_c$ where the crack propagates, we found that the fracture energy $Γ$ peaks around $λ\sim 0.001 s^{-1}$ before decreasing sharply with increasing stretch rate, in contradiction with the measurements of crack velocity. Combining simulations and experimental observations, we propose therefore here a general method to separate the energy dissipated during loading before crack propagation, from that which is dissipated during crack propagation. For fast loading rates (with a characteristic strain rate only slightly lower than the inverse of the typical breaking time of physical bonds), this improved method to estimate a local energy release rate $g_{local}$ at the onset of crack propagation, gives a value of the local fracture energy $Γ_{local}$ which is constant, consistent with the constant value of the crack propagation velocity measured experimentally. Using this improved method we also obtain the very interesting result that the dual crosslink gels have a much higher value of fracture energy at low loading rates than at high loading rates, contrary to the situation in classical chemically crosslinked elastic networks.