A Three-phase Circular Inclusion With A SlidingInterface And A Radial Matrix Crack

Abstract

The solution for the elastic three-phase circular inclusion problem plays a fundamental role in many practical and theoretical applications. In particular, it offers the fundamental solution for the generalized self-consistent method in the mechanics of composites materials. In this paper, a general method is presented for evaluating the interaction between a pre-existing matrix crack and a threephase circular inclusion. The bonding at the inclusion-interphase interface is considered to be the sliding imperfect interface. Physically, this is important for modelling certain features of material behaviour (such as grain-boundary sliding and damage occurring in the circumferential direction at constituent interfaces). On the remaining boundary, that being the interphase-matrix interface, the bonding is considered to be perfect. Using complex variable techniques, we derive series representations for the corresponding stress functions inside the inclusion, in the interphase layer and in the surrounding matrix. The governing boundary value problem is then formulated in such a way that these stress distributions simultaneously satisfy the traction free condition along the crack face, the sliding imperfect interface condition and the prescribed asymptotic loading conditions. Stress intensity factor (SIF) calculations are performed at the crack tips for different material property combinations, interface imperfections and crack positions. The results illustrate convincingly the role of an interphase layer as well as the effects of a sliding interface on crack behaviour.