A generalized Rivlin–Thomas theory for nucleation of cracks in viscoelastic materials

Abstract

Recent fracture experiments using the Rivlin–Thomas pure-shear geometry in rubbery viscoelastic materials have suggested nucleation of cracks at a critical stretch, independent on loading rate. For linear material using the rate-independent cohesive model theory, the critical elongation between grips (in a quite general testing geometry) at nucleation is instead monotonically decreasing with rate of up to the square root of the ratio between the instantaneous and relaxed elastic modulus of the material. Shrimali & Lopez-Pamies have made the assumption of a constant critical stretch to develop a theory which contrasts therefore with classical models. However, we further generalize the Rivlin–Thomas theory by assuming an arbitrary relation between nucleation stretch and loading rate, which therefore includes both models as limit cases. We present a simple case of a Double Cantilever Beam (DCB) geometry with linear standard materials, to show an analytical example.