AXISYMMETRICAL CRACK PROBLEM IN BONDED MATERIALS WITH A GRADED INTERFACIAL REGION

The problem of a penny-shaped crack in homogeneous dissimilar material s bonded through an interfacial region with graded mechanical properti es is considered. The applied loads are assumed to be axisymmetric but otherwise arbitrary. The shear modulus of the interfacial region is a ssumed to be mu(2)(z) = mu(1)exp (alpha z) and that of the adherents m u(1) and mu(3) = mu(1)exp(alpha h), h being the thickness of the regio n. A crack of radius a is located at the z = 0 plane. The axisymmetric mode III torsion problem is separated and treated elsewhere. Because of material nonhomogeneity, the deformation modes I and II considered in this study are always coupled. The related mixed boundary value pro blem is reduced to a system of singular integral equations. The asympt otic behavior of the stress state near the crack tip is examined, and the influence of the thickness ratio h/a and the material nonhomogenei ty parameter alpha on the stress intensity factors and the strain ener gy release rate is investigated. The results show that the stress stat e near the crack tip would always have standard square-root singularit y provided h > 0 or the material properties are continuous but not nec essarily differentiable functions of z.