On fatigue limit in the presence of notches: classical vs. recent unified formulations

Classical formulations for the fatigue strength reduction factor of notched specimen, Kf, (such as those by Neuber, Peterson, Heywood) were developed long time ago and have found some success by introducing a material constant (dependent on the tensile strength only) in order to take into account the problem of notch sensitivity. However, being empirical fitting equations, they have serious limitations when their asymptotic behaviour is considered, or when the empirical constants are not directly calibrated with experiments. This is shown in this work by using example data taken from the literature for various steels and alloys, and various notch sizes and shapes. Furthermore, although the material constants can be modified to include fatigue threshold dependence (satisfying the requirements of fracture mechanics), only the Neuber formula has a correct functional form in the entire range of notch sizes and shapes, and indeed appears to be sufficiently conservative in the range of data considered. Improved accuracy is found with a more recent empirical criterion due to Atzori and Lazzarin based on the Smith and Miller classification of notches, and with a new criterion here obtained by making consistent the Atzori and Lazzarin with the Luka´sˇ– Klesnil, having a sound interpretation in terms of self-arrested cracks ahead of a rounded notch for which the Creager–Paris stress field is valid. A large number of experimental data are taken from the literature to compare the accuracies of the various criteria.