A receding frictional contact problem between a graded layer and a homogeneous substrate pressed by a rigid punch

Abstract

This paper considers the plane problem of a receding frictional nonlinear contact between an elastic graded layer and a homogeneous half-space when they are pressed against each other by a rigid stamp. A non-homogenous isotropic stress-strain law was used to model the graded layer. The contact region is assumed to be under sliding contact conditions with Coulombs law relating the tangential traction to the normal component. Applying Fourier integral transform and the appropriate boundary conditions, the plane elasticity equations are converted analytically into a system of singular integral equations in which the unknowns are the pressures and receding contact lengths in the two contact zones. Ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the stamp and the layer are supplemented to solve the problem. The Gauss–Chebyshev quadrature-collocation method is used to convert the singular integral equations into a set of nonlinear equations which are solved with a newly developed iterative algorithm to yield the lengths of the receding contact zones and the associated contact pressures. The main focus of this paper is to investigate the effect of the non-homogeneity parameter of the graded layer, the friction coefficient in the contact zones and the radius of the stamp profile on the contact pressures and lengths of the receding contact zones.