Empirical Stress Intensity Factors for Surface Cracks under Rolling Contact Fatigue

This article contains empirical equations for the K(I), K(II), and K(III) stress intensity factors (SIFs) for semi-elliptical surface cracks for brittle materials subjected to rolling contact fatigue (RCF) as a function of the contact patch diameter, angle of crack to the surface, max pressure, position along the crack front, and aspect ratio of the crack. The equations were developed from SIFs calculated by parametric three-dimensional (3D) finite element analysis (FEA) for a range of contact patch radii (1b, 2b, and 3b) and angles of the crack to the surface (0 degrees., 45 degrees, and 60 degrees). Calculating mixed-mode SIFs for surface cracks subject to RCF using 3D FEA is computationally complex because of extreme mesh refinement required at multiple levels to capture steep stress gradients. The comprehensive empirical curve fits presented are accurate to within 0.5% of FE simulations and are useful for component design where contact-initiated surface fatigue damage is important such as in gears, roller bearings, and railway wheels. The results are of particular relevance to hybrid silicon nitride ball bearings, which are susceptible to failure from fatigue spalls emanating from preexisting surface cracks, due to crack growth driven by RCF (G. Levesque and N. K. Arakere, An investigation of partial cone cracks in silicon nitride balls. International Journal of Solids and Structures, 2008, 45:6301-6315).