Cohesive element modeling of viscoelastic fracture: Application to peel testing of polymers

A computational modeling technique for fracture propagation in viscoelastic materials using cohesive elements for the zone ahead of the crack tip is presented. The computational technique is used to study the problem of increase in fracture energy with peel velocity in peel testing of polymers. A rate-independent phenomenological cohesive zone model is used to model the intrinsic fracture toughness of the interface between the polymer sheets. A dimensional analysis reveals that the macroscopic fracture energy scales with the intrinsic fracture toughness and is a function of peel velocity, and parameters such as the thickness, bulk properties of the polymer sheets, and other cohesive zone properties. The growth of fracture energy as a function of the peel velocity has been studied for polymer sheets characterized by a standard linear viscoelastic solid. Viscoelastic losses in the peel arm vanish in the limits of very slow and rapid peeling. Peak dissipation is obtained at an intermediate velocity, which is related to the characteristic relaxation time and thickness. This behavior is interpreted in terms of the size of elastic and viscous zones near the crack tip. It is found that the total energy dissipated is dependent upon both the intrinsic fracture toughness and the characteristic opening displacement of the cohesive zone model. The computational framework has been used to model experimental data on peeling of Butadiene rubbers. It is found that the usual interpretation of these data, that the macroscopic dissipation equals the rate-independent intrinsic toughness multiplied by a factor that depends on rate of loading, leads to a large quantitative discrepancy between theory and experiment. It is proposed that a model based on a rate-dependent cohesive law be used to model these peel tests.