Integro-Differential Equations for Stress Analysis in the Bridged Zone of Interface Cracks

Abstract

A mathematical model of joint of different materials with an interface crack and a bridged zone ahead of the crack tip is proposed. The bridged zone is considered as a part of the interface crack between two infinite half-planes and the sizes of these zones can be comparable to the whole length of the crack. It’s assumed that distributed spring-like quasilinear bonds link the crack surfaces along the bridged zone. Normal and shear bond tractions due to different properties of materials are occurred even under the action of the uniform external load normal to the interface with the bridged crack. Using the method of superposition the system of two singular integral-differential equations with Catchy-type kernel is derived for evaluation of the bond tractions in the bridged zone in the frame of the plane elasticity problem. The expressions for the interface crack opening and the stresses ahead of the crack tip, taking into account the presence of the bonds in the bridged zone, are obtained. The stress intensity factors at the crack tip are calculated taking into account both the external normal and shear loads and the compensating bond tractions in the bridged zones. Parametric numerical analysis of the proposed model under different loads cases and different properties of materials, bonds and bridged zone sizes is performed.