Some notes on gradient, volumetric and weakest link concepts in fatigue

After pointing out possible higher-order effects of non-linear stress distributions in the vicinity of stress concentrators on fatigue stress predictions, a rigorous treatment of the effects of size and type of loading is given for the simple case of unnotched cylindrical specimens of different size loaded in tension/compression (TC), rotating bending (RB), and alternating axial bending (AB), comparing the predictive capabilities of gradient, volumetric (highly stressed volume), and weakest link (Weibull) concepts. It is shown that volumetric and weakest link concepts give qualitatively the same predictions; quantitative differences are highlighted. Also, an empirical modification of the volumetric concept is proposed to capture the experimentally observed saturation value of the fatigue strength for very large loaded volumes. Formulae for an easy determination of the model parameters as well as relations between the parameters of the different concepts are derived.