A closed-form solution for a crack approaching an interface

A closed-form solution is presented for the stress distribution in two perfectly bonded isotropic elastic half-planes, one of which includes a fully imbedded semi-infinite crack perpendicular to the interface.The solution is obtained in quadratures by means of the Wiener-Hopf-Jones method.It is based on the residue expansion of the contour integrals using the roots of the Zak-Williams characteristic equation.The closed-form solution offers a way to derive the Green's function expressions for the stresses and the SIF (stress intensity factor) in a form convenient for computation.A quantitative characterization of the SIF for various combinations of elastic properties is presented in the form of function the c(α, β), where α and β represent the Dundurs parameters.Together with tabulated c(α, β) the Green's function provides a practical tool for the solution of crack-interface interaction problems with arbitrarily distributed Mode I loading.Furthermore, in order to characterize the stability of a crack approaching the interface, a new interface parameter χ , is introduced, which is a simple combination of the shear moduli µ s and Poisson's ratios ν s (s = 1, 2) of materials on both sides of the interface.It is shown that χ uniquely determines the asymptotic behavior of the SIF and, consequently, the crack stability.An estimation of the interface parameter prior to detailed computations is proposed for a qualitative evaluation of the crack-interface interaction.The propagation of a stable crack towards the interface with a vanishing SIF is considered separately.Because in this case the fracture toughness approach to the material failure is unsuitable an analysis of the complete stress distribution is required.