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

摘要

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle #theta# = 15-30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for #theta# = 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 #theta# = 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 #theta#, and crack face friction coefficient #mu#. The calculations show that the present method is useful for the analysis for #theta# = 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 percent for both under compressive residual stress and Hertzian contact load. Regarding the maximum K_(II) values under Hertzian contact load, the results of #theta#=15 deg are smaller than the ones of #theta# =45 deg by 23-34 percent. 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 percent. With increasing the value of friction coefficient #mu# for crack faces the value of K_(II) decreases significantly. When the crack is short and the inclination angle #theta# is small, the value of friction coefficient f for Hertzian contact load largely affect the K_(II) value.