Incomplete contact between a coated elastic substrate and rigid foundation perturbed by a rigid disc

Abstract

This paper investigates an axisymmetric and frictionless contact problem of a coated elastic substrate pressed onto a rigid foundation with a rigid disc by remoted uniform compressive stress. Such an incomplete contact problem is formulated as a three-parts mixed boundary values problem (MBVP). By means of Hankel transform technique and a new solution derived for a multilayered elastic solid subjected to surface displacement (dislocation), the MBVP is converted to a system of triple integral equations. A series expansion method characterized by expressing the unknown surface displacement as Bessel function series is adopted to solve the triple integral equations. Explicit analytical expressions for contact stress, resultant contact force and Mode-I stress intensity factor are obtained. The accuracy of the present solutions is verified by comparing to the results available in the literatures for the simple cases of a single layer and a homogeneous half space. Numerical studies are also performed to investigate the contact mechanics of coated material under incomplete contact. Results from this study are valuable for the design of coating to protect engineering machine components against third-body abrasive particles or solid contaminants induced contact damage.