A fully coupled partial slip contact problem in a graded half-plane

In this paper, we consider the two-dimensional nonlinear partial slip contact problem between a non-homogeneous isotropic graded half-plane and a rigid punch of an arbitrary profile subjected to a normal load. The graded medium is modeled as a non-homogeneous isotropic material with an exponentially varying shear modulus and a constant Poisson's ratio. The problem is formulated under plane strain conditions. Using standard Fourier transform, the problem is reduced to a set of two coupled singular integral equations in which the main unknowns are the normal and the tangential contact stresses and the stick zone size. An asymptotic analysis is performed to extract the proper singularities from the kernels. Using Gauss-Chebychev integration formulas, the two coupled equations are solved by sequential iterations. The objective of this paper is to study the effect of the graded medium non-homogeneity parameter and the friction coefficient on the size of the stick zone and the contact stresses for the cases of flat and circular stamp profiles. Particular attention is also paid to the effect of the coupling between the normal and the tangential contact stresses.