A fractional rate-dependent cohesive-zone model

Abstract

This paper presents a novel formulation of a hereditary cohesive zone model able to effectively capture ratedependent crack propagation along a defined interface, over a wide range of applied loading rates and with a single set of seven input parameters only, as testified by the remarkable agreement with experimental results in the case of a double cantilever beam made of steel adherends bonded along a rubber interface. The formulation relies on the assumption that the measured fracture energy is the sum of a rate-independent ‘rupture’ energy, related to the rupture of primary bonds at the atomic or molecular level, and of additional dissipation caused by other rate-dependent dissipative mechanisms present in the material and occurring simultaneously to rupture. The first contribution is accounted for by introducing a damage-type internal variable, whose evolution follows a rate-independent law for consistency with the assumption of rate independence of the rupture energy. To account for the additional dissipation, a fractional-calculus-based linear viscoelastic model is used, because for many polymers, it is known to capture the material response within an extremely wide range of strain rates much more effectively than classic models based on an exponential kernel. To the authors’ knowledge, this is the first application of fractional viscoelasticity to the simulation of fracture.