  We investigate experimentally the adherence energy $\Gamma$ of model
polyacrylate Pressure Sensitive Adhesives (PSAs) with combined large strain
rheological measurements in uniaxial extension and an instrumented peel test.
We develop a nonlinear model for such peel test which captures the dependence
of $\Gamma(V)$ with peeling rate $V$ revealing the key role played by the
extensional rheology. Our model explains in particular why traditional linear
viscoelastic approaches correctly predict the slope of $\Gamma(V)$ curves for
sufficiently elastic PSAs characterized by a simple rate-independent debonding
criterion. However, for more viscoelastic adhesives, we identified a more
complex rate-dependent debonding criterion yielding a significant modification
of the $\Gamma(V)$ curves, an effect that has been largely overlooked so far.
This investigation opens the way towards the understanding of fibrils
debonding, which is the main missing block to predict the adherence of PSAs.
