An embedded crack in a functionally graded coating bonded to a homogeneous substrate under factional Hertzian contact

In an attempt to simulate nonuniform coating spalling, the elastostatic problem of an embedded crack in a functionally graded coating bonded to a homogeneous substrate subject to normal and tangential surface loading is considered. The coating is graded in the thickness direction and is orthogonal to the crack direction which is parallel with the free surface. The graded coating is modeled as a nonhomogeneous medium with an isotropic stress-strain law. Using integral transforms, the governing equations are converted into singular integral equations, which are solved numerically to yield the displacement field as well as the crack-tip stress intensity factors. Since the loading is compressive, a crack-closure algorithm is developed to avoid interpenetration assuming frictionless contact between the crack faces. The main objective of the paper is to study the influence of material nonhomogeneity on the ability of the coating to maintain its integrity with and without using the crack-closure algorithm.