The wear contact problem with partial slippage

A method of analysing the variation in the stress state and shape of wearable bodies, subjected to the action of an oscillating shear load with partial slippage of the surface in the contact area is proposed. The method is based on the introduction of two time scales: the time of a single cycle of variation in the shear load and the time corresponding to a specified number of cycles. To estimate the shape variation of the surface due to wear a linear relation between the wear rate and the contact pressure and velocity of relative slippage is used. Cases of complete or partial removal of the wear particles from the friction zone are considered. As an example, the kinetics of the variation in the stress state in the contact of an elastic indentor, having a flat base and rounded edges, with an elastic half-space of the same material, is investigated. Analytical expressions for calculating the asymptotic values of the stresses and shape of the worn surface are obtained.