Two objective and independent fracture parameters for interface cracks and a paradox

TL;DR

This paper introduces two objective, independent fracture parameters for interface cracks that address non-objectivity issues and explain peculiar failure behaviors in interface fracture, improving characterization and comparison of experimental results.

Contribution

It proposes new fracture parameters that fully characterize the stress field near interface crack tips, resolving non-objectivity and paradox issues in existing models.

Findings

Two objective fracture parameters are proposed.

The parameters can characterize stress oscillation phase.

The failure criterion is free from arbitrary quantities.

Abstract

Due to the oscillatory singular stress field around a crack tip, interface fracture has some peculiar features. This paper is focused on two of them. One can be reflected by a proposed paradox that geometrically similar structures with interface cracks under similar loadings may have different failure behaviors. The other one is that the existing fracture parameters of the oscillatory singular stress field, such as a complex stress intensity factor, exhibit some non-objectivity because their phase angle depend on an arbitrarily chosen length. Two objective and independent fracture parameters are proposed which can fully characterize the stress field near the crack tip. One parameter represents the stress intensity with classical unit of stress intensity factors. It is interesting to find that the loading mode can be characterized by a length as the other parameter, which can properly reflect the phase of the stress oscillation with respect to the distance to the crack tip. This is quite different from other crack tip fields in which the loading mode is usually expressed by a phase angle. The corresponding failure criterion for interface cracks does not include any arbitrarily chosen quantity, and therefore is convenient for comparing and accumulating experimental results, even existing ones.