Comparison of the logistic S-N model with the Stussi model for S-N curves description and its advantages over some other models

The regression function corresponding to the logistic S-N model is derived and presented in the form when all regression parameters directly describe the geometrical shape of S-N curve. The comparison with the Stussi model shows that both models lead to the same regression curve. A deeper mathematical analysis shows that both models are based on the logistic function and replacing x with logN. Unfortunately, usual equality between UTS (ultimate tensile strength) and the fatigue stress for one (or a half of the first) cycle to fracture is not fulfilled for the Stussi model, and its other parameters have no simple geometrical meaning. Compared with the Palmgren model and the Kohout-Vechet model, the logistic S-N model seems to be the most successful and most universally applicable. The strongest point of the logistic model is the ability to successfully describe the empirical S-N curves with extreme steepness, where most other models fail.