THE INTERFACE PENNY-SHAPED CRACK RECONSIDERED zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON L. M. KEERt and S. H. CHENS Department of Civil Engineering, Northwestern University, Evanston. IL 60201, U.S.A. and MARIA COMNINOUS Department of Applied Mechanics and Engineering Science, The University of Michigan, Ann Arbor, MI 48109. U.S.A. (Communicated by 1. N. SNEDDON) Ahstreet-The penny-shaped crack at the interface between two bonded dissimilar media is reconsidered on the basis of recent developments on the elimination of oscillatory singularities. This is accomplished by assuming an annular frictionless contact zone at the crack circumference and reducing the problem to a Fredholm integral equation. Expressions for the strain energy, crack opening force and bond stresses are obtained and numerical results given for specific material combinations. INTRODUCTION CONSIDERABLE attention has been recently directed to cracks between bonded dissimilar materi- als. The plane elasticity solution for a crack in the interface bond between dissimilar materials was given independently by England[l] and Erdogan[Z]. The solution, which was obtained by using standard complex analysis, displayed two undesirable features that are, apparently, inherent to the problem. (a) The stress distribution at the crack tip, in addition to the square root singularity, has an oscillatory multiplying factor of the kind sin(log r) or cos(log r). (b) The crack faces overlap very close to the crack tip. In a recent investigation by Comninou [3], which also provides an extensive literature survey on the in-plane problem, the oscillatory nature of the ‘singularities was removed by postulating a small region of frictionless contact near the crack tip. As a consequence of this postulate the singularities at the crack tip become of the square-root tyde, namely, a compressive singularity in the contact region and a shear singularity in the bond. The present investigation formulates and solves the analogous problem for a penny-shaped crack at the interface between bonded dissimilar half spaces. The conventional problem for a penny-shaped crack in an interface has been solved by Lowengrub and Sneddon[4], by using Hankel transform techniques to reduce the problem to a singular integral equation. Their conclusions are essentially the same as those of England and Erdogan for the plane elasticity problem. In the present paper techniques similar to Lowengrub and Sneddon are used to reduce the.Comninou-type contact-zone problem to a singular integral equation to determine the size of the contact zone. It should be noted that the nature of the solution given by Lowengrub and Sneddon does not allow for an easy determination of the field quantities such as bond stress and crack opening displacement, but they can obtain the strain energy release rate rather easily. FORMULATION OF PROBLEM We consider two homogeneous, isotropic, elastic half spaces, the upper half space having elastic constants fill uI and the lower half space having elastic constants p2, u2, where CL, v denote, respectively,‘the shear modulus and Poisson’s ratio. The two half spaces are joined together by a perfect bond everywhere, except in a region of radius L (see Fig. I) where the crack surfaces are perfectly smooth. The surface of this penny-shaped crack is subjected to a Wrofessor. Graduate Student. PAssistant Professor. 765