Contact size and debris ejection in fretting: The inappropriate use of Archard-type analysis of wear data and the development of alternative wear equations for commonly employed non-conforming specimen pair geometries

Abstract

It has been long understood that fretting differs from sliding wear in that the relative displacement between the bodies is generally smaller than the size of the contact between them, with debris ejection from the contact thus playing an important role in the behaviour of the contact in fretting. Whilst these ideas were clearly articulated more than 30 years ago via Godet's third-body approach and Berthier's concept of the tribology circuit, calculation of wear rates in fretting have continued to employ Archard's wear equation (or approaches directly derived from it), despite this approach assuming that the rate of wear is controlled by the rate of generation of wear debris (as opposed to the rate of its ejection from the contact). It has been shown recently that when debris ejection is the rate-determining-process in fretting, the instantaneous rate of wear is inversely proportional to a characteristic dimension of the wear scar. When non-conforming specimen pair geometries (such as cylinder-on-flat) are employed in fretting testing, the wear scar size increases as wear proceeds, and thus the instantaneous rate of wear decreases. In this paper, wear equations have been derived for three commonly employed non-conforming pair specimen geometries, which all take the form Vw=KRn−1Edn (Vw is the wear scar volume, R is the radius of the non-plane specimen(s) in the pair and Ed is the frictional energy dissipated) where n varies between 0.67 and 0.8 depending upon the geometry and assumptions made regarding the governing equation. It is argued that the assumptions upon which the analysis is based are most valid for the cylinder-on-flat contact configuration with fretting perpendicular to the cylinder axis where the length of the line contact is large compared to the wear scar width. It is demonstrated that, despite the often apparently good fit of experimental data to an Archard-type equation, it is not appropriate to employ such Archard-type approaches to the analysis of fretting data in situations where debris ejection is the rate-determining-process. The equations derived in this paper relating wear scar size to some measure of the duration of the test should be used for such analysis instead of the linear relationships generally employed in previous work.