Analytical solution for sliding rounded-edge contact

Reliable analysis of the local stress fields in the vicinity of sliding frictional contacts of engineering components is a pre-requisite for the reliable assessment of structural integrity. In this paper we present the use of Muskhelishvili potentials to derive an analytical solution for a semi-infinite punch with a rounded edge pressed against a half-pane substrate, and a general numerical solution for a kind of Cauchy integral involved in the analytical contact solution. Using these solutions, the effect of the friction coefficient on the normal traction distribution is investigated. Numerical results show that the peak normal traction value is altered in comparison with the frictionless case solution, but this variation is mild (less than 5%), provided the friction coefficient does not exceed about 0.6. Finally, the adaptation of the analytical result to the solution of practical contact problems is addressed.