A Voronoi Finite Element Study of Fatigue Life Scatter in Rolling Contacts

Microlevel material failure has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearing. Therefore, microlevel features of materials will be of significant importance to RCF investigation. At the microlevel, materials consist of randomly shaped and sized grains, which cannot be properly analyzed using the classical and commercially available finite element method. Hence, in this investigation, a Voronoi finite element method (VFEM) was developed to simulate the microstructure of bearing materials. The VFEM was then used to investigate the effects of microstructure randomness on rolling contact fatigue. Here two different types of randomness are considered: (i) randomness in the microstructure due to random shapes and sizes of the material grains, and (ii) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus. In this investigation, in order to determine the fatigue life, the model proposed by Raje et al. (“A Numerical Model for Life Scatter in Rolling Element Bearings,” ASME J. Tribol., 130, pp. 011011-1–011011-10), which is based on the Lundberg–Palmgren theory (“Dynamic Capacity of Rolling Bearings,” Acta Polytech. Scand., Mech. Eng. Ser., 1(3), pp. 7–53), is used. This model relates fatigue life to a critical stress quantity and its corresponding depth, but instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. We consider the maximum range of orthogonal shear stress and the maximum shear stress as the critical stress quantities. Forty domains are considered to study the effects of microstructure on the fatigue life of bearings. It is observed that the Weibull slope calculated for the obtained fatigue lives is in good agreement with previous experimental studies and analytical results. Introduction of inhomogeneous elastic modulus and initial flaws within the material domain increases the average critical stresses and decreases the Weibull slope.