  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 $\lambda_c$ where the crack
propagates, we found that the fracture energy $\Gamma$ peaks around
$\lambda\sim 0.001 s^{-1}$ 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 $\Gamma_{local}$ 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.
