The fatigue limit of bearing steels – Part I: A pragmatic approach to predict very high cycle fatigue strength

► We model both surface and subsurface initiated fatigue of hardened steels. ► The model is based on small crack growth in air and in vacuum. ► The model provides a unified description of fatigue strength in LCF, HCF and VHCF. ► The model accounts for microstructure variability and stressed volume effect. ► The model predictions agree well with experiments. Bearing steels and other high strength steels exhibit complex fatigue behavior in excess of 10 7 cycles due to their sensitivity to defects like inclusions. Failure occurring in the very high cycle fatigue regime and the lack of an asymptote in the measured S–N data raise the questions as to the existence of fatigue limit and prediction of the fatigue strength of the high strength steel components. A series of two papers are written to discuss on the characteristics of the very high cycle fatigue and their implication for engineering applications. In the present paper (Part I) a deterministic defect model is developed to describe the fatigue crack growth from de-bonded hard inclusions. The model is shown to provide a unified prediction of fatigue behavior in different regimes, i.e. low cycle fatigue regime dictated by the tensile strength, high cycle fatigue regime obeying Basquin’s law and the very high cycle fatigue regime featured by the fish-eye and ODA (optically dark area) surrounding an interior fatigue-initiating inclusion on the fracture surface. The model predictions agree well with experiments. A combination of the deterministic model with a stochastic model that describes the inclusion size distribution allows prediction of fatigue strength and fatigue limit associated with certain reliability of a steel component. It is found that very high cycle fatigue, associated with interior inclusions, is attributed to the very slow crack propagation in vacuum condition, and that an asymptote for fatigue limit observed for mild steels also exists for high strength steels such as bearing steels, but extends beyond the very high cycle fatigue regime normally measured to-date. Monte Carlo simulation shows that such a fatigue limit asymptote becomes clearly visible in excess of 10 12 cycles, which is difficult to measure with today’s testing devices. Furthermore, the effects of steel cleanliness and specimen type and shape are studied by means of Monte Carlo simulations.