Contact mechanics of two elastic spheres reinforced by functionally graded materials (FGM) thin coatings

Abstract

This paper examines the normal frictionless point contact between two dissimilar elastic spheres reinforced by FGM coatings with arbitrarily varied shear modulus and Poisson's ratio. Both the coating thicknesses and contact area are small compared to the radiuses of the two spheres. The material inhomogeneity of the FGM coating is only along the radial direction. The contact problem is formulated and reduced to a nonlinear Fredholm integral equation of the second kind. A multi-layer elastic half space model is used to develop the relationship between the contact stress and the vertical displacements of the FGM coated spheres. In this model, the FGM coating is divided into large number of perfectly bonded dissimilar thin sub-layers. Each sub-layer is homogeneous and has constant values of shear modulus and Poisson's ratio. Analytical solutions are derived for the contact force and stress. New numerical results are presented to show the effects of graded shear modulus and graded Poisson's ratio on the contact responses. It is shown that the contact force, stress and area can be significantly influenced by the graded shear modulus, and the effects of the graded Poisson's ratio are not negligible.