Rapid method of stress intensity factor calculation for semi-elliptical surface breaking cracks under three-dimensional contact loading

Fast methods of stress intensity factor calculation for inclined surface breaking cracks under contact loading are presented. Cracks are loaded in normal and tangential traction by a three-dimensional Hertzian elliptical contact patch, and friction between the crack faces is considered. Stress intensities are calculated from Green's functions originally developed for two-dimensional cracks through application of stresses on a plane below the three-dimensional contact patch, in place of those previously considered for a two-dimensional contact. This approach gives the method great speed advantages over fully three-dimensional methods. Both semi-circular and semi-elliptical cracks are examined. The validity of the approximations and the results are judged by validation with results from alternative fully three-dimensional cases. Very good agreement is found between trends in stress intensity factor with changes in crack size and applied tractions. Absolute values of stress intensity factor agree well for semicircular and shallow semi-elliptical cracks, but values were below those of the reference case for deep, narrow semi-elliptical cracks. Calibration of the model to overcome this under-prediction is discussed. A case of special value in railway rail-wheel contact modelling is that of a contact offset to the side of a crack, representing the wheel running alongside rather than directly across an existing crack. This configuration results from the common procedure of grinding the rail to change or maintain its cross-sectional profile. The three-dimensional contact patch methods presented here enable this case to be modelled while retaining very fast running times for the calculations.