Fretting wear of elastic half-spaces with a groove in a frictional slip zone

A method for determining the limiting state after fretting wear of an elastic half-spaces with a groove in their complete contact under the action of alternating shear forces is developed. The limiting stress of bodies after the end of wear is given by the initial shape of the groove and the function of the thickness of the worn-out material in the slip zone. To determine the function of the thickness of the worn-out material, a singular integral equation with a Cauchy kernel is written and its analytical solution is obtained. The limiting shape of the groove and the contact pressure after wear for different values of shear loads, Poisson’s ratio, and width of wear zone are analyzed.