On Ratchetting-Based Models of Wear and Rolling Contact Fatigue (RCF)
Authors: Ciavarella M. , Afferrante L. 
Published: January 2009

Recent efforts to develop simple unified models of both wear and RCF (Kapoor & Franklin, 2000, Franklin et al., 2001) are discussed, in view of previous theoretical and experimental results on ratchetting in rolling contact. At sufficiently high contact pressures, surfaces deform plastically with unidirectional cumulation of “ratchetting” strains (Johnson, 1985, Ch.9). However, the modelling of ratchetting strains as a function of plastic material properties has turned out more complicated than what originally suggested by the first attempts (Merwin & Johnson, 1963), as recently discussed by Ponter et al. (2003). Wear due to surface ratchetting occurs for sufficiently high friction, whereas RCF is mainly due to ratchetting subsurface. It appears that experimental data on ratchetting strains in the literature unfortunately do not show a clear and unique trend, and various proposed fitting equations differ significantly in quantitative and qualitative terms, particularly at large number of cycles. It is shown that ratchetting in rolling contact is a combination of “structural ratchetting” (that modelled with the perfect plasticity model) and “material ratchetting”, and the latter is very sensitive to the hardening behaviour of the material. Also, the surface and subsurface flow regimes are very different: in pure rolling, a simplified model of the stress cycle condition is a fully reversed cycle of shear superposed to an out-of-phase pulsating compression in a extended region below the surface (neglecting other two components also of pulsating compression); increasing the friction coefficient, a mean shear stress is induced as well as a tensile component in the direct stress, and for friction f &gt; 0.3 the maximum moves at the surface, but the highly stressed zone becomes a thin surface layer which suffers uniquely of “material ratchetting”. In the limit of very high friction, we have the critical condition on the surface which obviously gives a pulsating shear stress cycle in phase with a pulsating compression, but in addition we have a nearly fully reversed cycle of tension-compression (although the tensile peak is very localized also in the longitudinal direction). Such multiaxial stress fields and their largely different features introduced cause a response of the material which has not been studied enough, perhaps both in terms of ratchetting rates and in terms of the failure condition. In particular, the ductility for ratchetting surface flow as used in wear models seems apparently much higher than that for RCF ratchetting models. Also, RCF at large number of cycles in the C&S experiments (Clayton & Su, 1996, Su & Clayton, 1997) seems not well correlated with shakedown theory, and accordingly, simple ratchetting equations based on excess of shakedown such as that of Tyfoor et al (1996), do not seem well suited a Wohler SN life curve. However, these conclusions are only very qualitative as the materials in the two tests are different, and at present empirical separate models for wear and RCF based on hardness of materials and a posteriori data fitting seem the only quantitative way forward for engineering purposes.