The penny-shaped crack at a bonded plane with localized elastic non-homogeneity

This paper examines the axisymmetric problem pertaining to a penny-shaped crack which is located at the bonded plane of two similar elastic halfspace regions which exhibit localized axial variations in the linear elastic shear modulus, which has the form G(z)=G1+G2e±ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The resulting mixed boundary value problem associated with the penny-shaped crack is reduced to a Fredholm integral equation of the second kind which is solved in a numerical fashion to generate the crack opening mode stress intensity factor at the tip.