Effect of crack shape, inclination angle, and friction coefficient in crack surface contact problems

Abstract

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle θ=15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for θ=45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for θ=15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K _II, K _III are calculated with varying the crack shape b/a, inclination crack angle θ, and crack face friction coefficient μ. The calculations show that the present method is useful for the analysis for θ=15–30 deg with high accuracy. It is seen that the K _II-values when b/a→0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K _II values under Hertzian contact load, the results of θ=15 deg are smaller than the ones of θ=45 deg by 23–34%. Regarding the amplitude of (K _II max−K _II min), the results of θ=15 deg are smaller than the ones of θ=45 deg by 4–24%. With increasing the value of friction coefficient μ for crack faces the value of K _II decreases significantly. When the crack is short and the inclination angle θ is small, the value of friction coefficient f for Hertzian contact load largely affect the K _II value.