Fitting fatigue test data with a novel S-N curve using frequentist and Bayesian inference

In design against fatigue, a lower bound stress range vs. endurance curve (S-N curve) is employed to characterize fatigue resistance of plain material and structural details. With respect to the inherent variability of the fatigue life, the S-N curve is related to a certain probability of exceedance, a percentile of the fatigue life. This paper is concerned with modelling and estimating uncertainties in fatigue resistance of welded joints under constant amplitude loading. A new S-N curve format is proposed and fitted to fatigue test data by using the Maximum Likelihood Method. The results have been compared with the Random Fatigue Limit Model and the Bilinear Random Fatigue Limit Model. The proposed S-N curve appears to be more accurate in describing the S-N relation in high-cycle fatigue: it presents a smooth transition from finite to infinite-life regions and, differently from previous non-linear S-N relations with fatigue limit, this transition is controlled by an independent model parameter. Thereby it provides more flexibility for statistical fitting. In addition, a Bayesian framework is defined to fit the proposed relation including informative and non-informative prior distributions.