Consideration of spatial variation of the friction coefficient in contact mechanics analysis of laterally graded materials

Abstract

This paper presents a new analytical approach for sliding contact analysis of laterally graded materials, which allows taking into account the spatial variation of the friction coefficient. The method is developed by considering a sliding frictional contact problem between a laterally graded elastic medium and a rigid flat punch. Governing partial differential equations entailing the displacement components are derived in accordance with the theory of plane elasticity. General solutions are determined and boundary conditions are implemented by the use of Fourier transformation; and the problem is reduced to a singular integral equation of the second kind. Both the shear modulus and the coefficient of friction are assumed to be a functions of the lateral coordinate in the derivations. The singular integral equation is solved numerically by means of an expansion-collocation technique in which the primary unknown is represented as a series in terms of Jacobi polynomials. Outlined procedures yield the stresses at the half-plane surface and the tangential contact force required for sliding. Proposed techniques are verified by making comparisons to the contact stresses computed for constant-friction type sliding contact problems involving homogeneous and laterally graded materials. Parametric analyses are presented so as to demonstrate the influences of the variations in the friction coefficient and the shear modulus upon the contact stresses and the tangential contact force.