A self-similar model for fretting wear contact with the third body in gross slip

Abstract

A continuum mechanics approach is applied to model fretting wear in gross-slip regime with accounting for the third-body layer, which is formed by wear debris trapped within contact interface. The developed modeling framework employs the known concept of a third-body conversion factor and utilizes it in a self-similar form. A two-dimensional Hertzian type contact geometry (cylinder on a plate of relatively large thickness) is assumed, though a major part of the presented analysis is curried out for an arbitrary initial gap function. A Winkler foundation model is used to describe the contact deformation of the third-body layer. The effect of elasticity is neglected in describing the self-similar evolution of the contact pressure profile in the advanced stage of fretting wear. A comparison with the FEM-based simulations available in the literature is given. The fact that the elasticity effect plays a minor role has been verified a posteriori in the considered example. Simple formulas are derived to estimate the continuous variation of the third body layer profile, thickness, and volume.