An analysis on statistical fatigue property of bearing steel in very high cycle regime under rotating bending

Abstract

In S-N diagrams for high strength steels, the duplex S-N curves for surface-initiated fracture and interior inclusion-initiated fracture were usually confirmed in the very high cycle regime. This trend is more distinct in the loading type of rotating bending due to the stress distribution. In the case of interior fracture mode, the fish-eye is usually observed on the fracture surface and an inclusion is also observed at the center of the fish-eye. In the present work, the authors have attempted to construct a probabilistic model on the statistical fatigue property of bearing steel in the interior fracture mode based on the distribution characteristics of the location and the size of the interior inclusion at the crack initiation site. The probability density functions of the radius of the largest inclusion among n of total inclusion, ρ_n and the inclusion depth, ξ were derived by connecting the concept of extremes distribution and Weibull distribution. The joint probability function for ρ_n and ξ is given by multiplication of the probability density functions of ρ_n and ξ. The distribution pattern of the fatigue strength at N=10⁹ derived from the joint probability function is well corresponding to the experimental aspect of the fatigue strength distribution for the bearing steel of SUJ2.