INTRODUCTION: The current ISO standard [1] for the prediction of bearing fatigue life includes a term for the bearing fatigue limit i.e. a stress level below which a bearing will have infinite life. Although the current standard uses a universal value, it is generally considered to be dependent upon the steel used as well as material cleanliness. However, the experimental determination of the fatigue limit for bearing steels is an expensive and time consuming process and therefore an analytical method is preferred. It is well known that bearings that are properly installed, lubricated and kept free from the environmental contamination eventually fail due to material fatigue driven by Rolling Contact Fatigue (RCF) mechanism [3]. RCF damage nucleates in the subsurface of the material near microstructural inhomogeneities such as inclusions. These inclusions serve as stress raisers in the surrounding steel matrix, and thereby induce micro-plasticity even when the global stress is below the materials yield strength. As cyclic loading continues, this localized plasticity eventually leads to crack initiation, propagation, and ultimately bearing failure. Hence, the fatigue limit of a given bearing steel may be defined as the global stress level below which no local, micro-scale yielding occurs. In the present study, the authors have investigated the influence of inclusion geometry (size, shape, orientation), as well as the physical and mechanical properties of both the inclusion and the steel matrix (elastic modulus, yield strength) on the fatigue limit of bearing steel.
METHOD: In the absence of inclusion(s), no stress concentration in the material subsurface is expected and therefore the fatigue limit will be governed by the subsurface stress distribution and the material’s yield strength (τy). In this ideal case, the fatigue limit in shear is exactly equal to the material’s yield strength, because this is the highest stress that the material can sustain without deforming plastically. However, in the presence of inclusions, the stress concentration will increase the local stress in the steel matrix and thereby cause the material to yield at lower external loads. Therefore, the material fatigue limit (Tf) can be defined as the ratio between the yield strength of the material (τy) and the stress concentration factor (Kt). This stress concentration factor is defined as the ratio between the maximum subsurface stress in the vicinity of an inclusion (τ0) and far from any inclusion (T0). Throughout the study, the orthogonal shear stress is used for the calculation of Kt and Tf as it is known to be the most relevant stress measure for bearing failures and bearing life prediction [3, 4].
A simplified 2D plane strain FEA model consisting of two cylindrical rollers was developed which simulates the Hertzian contact stresses experienced in bearings as shown in Figure 1. A two-step finite element (FE) simulation process was then used to calculate Kt. In the first step, the model was ran without any inclusion and the maximum orthogonal shear stress (T0) max as well as its location were determined. In the second step, the simulation was reran with an inclusion at this critical location, and the maximum local orthogonal shear stress (τ0) max was determined. The results of these two simulations were then used to calculate the fatigue limit of the steel. This technique provides a way to cost effectively explore the effect of different inclusions as well as different matrix properties (due to variations in steel cleanliness and/or different steels) on the fatigue limit of bearing steels.