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

In rolling/sliding contact fatigue, it is known that the crack propagates a t a characteristic angle theta=15-30 deg to the surface. To analyze the mec hanism, however, the body force method has been widely used assuming 3D cra ck models for theta=45-90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions an d polynomials. Then, a semi-elliptical crack model is analyzed for theta=15 -90 under compressive residual stresses and Hertzian contact loads. The str ess intensity factors K-II, K-III are calculated with varying the crack sha pe b/a, inclination crack angle theta, and crack face friction coefficient mu. The calculations show that the present method is useful for the analysi s for theta=15-30 deg with high accuracy. It is seen that the K-II-values w hen b/a --> 0 are larger than the ones when b/a=1 by 0-24% for both under c ompressive residual stress and Hertzian contact load. Regarding the maximum KII values under Hertzian contact load, the results of theta=15 deg are sm aller than the ones of theta=45 deg by 23-34%. Regarding the amplitude of ( K-II max - K-II min), the results of theta=15 deg are smaller than the ones of theta=45 deg by 4-24%. With increasing the value of friction coefficien t mu for crack faces the value of K-II decreases significantly. When the cr ack is short and the inclination angle theta is small, the value of frictio n coefficient f for Hertzian contact load largely affect the K-II value.