Crack propagation at the interface between viscoelastic and elastic materials

TL;DR

This paper investigates crack propagation at the interface between elastic and viscoelastic materials, revealing how viscoelastic properties influence crack speed and toughness, especially considering different material models and interface conditions.

Contribution

It extends cohesive zone models to bimaterial interfaces, analyzing the effects of viscoelasticity on crack propagation and toughness enhancement.

Findings

Crack speed depends on viscosity and stress intensity factor for Maxwell materials.

Maximum toughness enhancement is reduced at bimaterial interfaces compared to homogeneous materials.

Crack propagation behavior varies with viscoelastic model assumptions.

Abstract

Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970's. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the toughness increases between a value at very low speeds at a threshold toughness G0, to a very fast fracture value at Ginf, and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli. Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.