ON THE ORDER OF THE STRESS SINGULARITY FOR AN ANTIPLANE SHEAR CRACK AT THE INTERFACE OF TWO BONDED INHOMOGENEOUS ELASTIC MATERIALS.

A number of investigations of crack problems in nonhomogeneous media have been undertaken in which the elastic moduli vary continuously with spatial coordinates. In all of these studies special forms of inhomogeneities have been assumed in order to insure a tractable problem for which the asymptotic form of the stress field near the crack tip could be calculated. One of the primary objectives of these works was to determine the effect of spatial inhomogeneity upon the known signular field quantities associated with the corresponding homogeneous problem. In the paper the nature of the stress singularity is investigated for a semi-infinite Mode III crack normally incident to the interface of two bonded nonhomogeneous elastic half-spaces. Without assuming any particular form for the shear modulus, only that it be continuous throughout the composite medium, symmetric about the crack plane and differentiasble everywhere except along the interface at which the crack tip terminates, it is shown that the crack tip stresses have a square root singularity, thus verifying. This paper does not consider the general question of existence of solutions for such a class of boundary value problems, which does not seem to be completely settled. Rather, the approach taken is to show that when there exists a physically meaningful solution, a notion to be made precise later, then that solution exhibits a square root singular stress field.