The Crack Problem in Bonded Nonhomogeneous Materials

Abstract

In this paper the plane elasticity problem for two bonded half-planes containing a crack perpendicular to the interface is considered. The primary objective of the paper is to study the effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors. The two materials are, thus, assumed to have the shear moduli μ0 and μ0 exp(βx), x = 0 being the diffusion plane. Of particular interest is the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r −α , 0<α<1, in this problem the stresses have a standard square root singularity regardless of the location of the crack tip. The nonhomogeneity constant β has, however, considerable influence on the stress intensity factors.