A linear cohesive model of zero degree peeling of a viscoelastic tape from a substrate

Peeling in viscoelastic materials has been studied experimentally for many years mostly at 90 or 180 degrees angle, and typically the classical Rivlin energy balance equation is used to obtain a velocity-dependent work of fracture. The latter has been shown to be the product of an angular term and a velocity-dependent term, but there is no simple model to explain this behaviour: attempts have been made to generalize the Kendall elastic equation to viscoelasticity, but they lead to no velocity dependence (and infinite load) with frictional dissipation at zero angles, and in general at large angles. In the present model, we consider the original Kendall's "sticking conditions," for which a linear cohesive model is formulated for the viscoelastic tape as being on an elastic foundation, and peeling velocity is found to be proportional to the cubic power of the force for Maxwell material, or standard material with a large ratio between instantaneous and relaxed moduli. An explicit closed-form solution to this problem is first derived in this work. Experimental results on zero peel angle are scarce, and may be affected by the finite length of adhered and unadhered parts: hence, a complete picture of peeling behaviour at zero angles is elusive.