Critical-distance fatigue analysis of limiting cases of ellipsoidal cavities

Abstract Closed-form stress distributions have been presented for limiting cases of an ellipsoidal cavity in a solid under uniform tension, such as a circular cylinder, a sphere, an elliptical cylinder, a through-crack or a circular crack. These stress distributions have been used with the point method of the theory of critical distances (TCD) to predict the influence of the size and shape of the cavity on the notch fatigue limit. Furthermore, the distributions of average stress for a circular cylinder, a sphere, a through-crack and a circular crack have been used to predict the influence of the cavity on the notch fatigue limit according to the TCD line method. TCD predictions of the fatigue limit of a solid with a through-crack or a circular crack are in good to excellent agreement with those of the imaginary crack method. An engineering estimate of the stress-concentration factor for a generic ellipsoid has been included.