Auswertealgorithmus auf der Basis einer Modifikation des Goniometrischen Modells zur stetigen Beschreibung der Wöhlerkurve vom Low-Cycle-Fatigue- bis in den Ultra-High-Cycle-Fatigue-Bereich

A general problem with the structural durability calculation is the lack of clarity regarding the mathematical description of the Ultra High Cycle Fatigue (UHCF) region in the S-N diagram. Even taking into account that the fatigue strength still decreases beyond the standardized cycle limit, linear evaluation models lead to physically non-existing discontinuities. In the end, a non-linear and steady S-N curve has to be the basis for a suitable evaluation model containing the S-N field in its entity. In this work, a flexible algorithm based on the Modified Goniometric Model (MGM) is generated, tested and proven capable for practice. Not only the S-N curve itself but also the scatter is plausibly described. The distribution according to Müller and the tangent distribution developed here extend the spectrum of distribution functions. With a large sample size and an observable systematic error of the distribution, a transformation of the characteristic value via the tangent provides reliable extrapolations for quantiles with very high or low failure probability. The purely empirical MGM comprises steadily the continuous decrease of the S-N curve up to the UHCF region. In addition, a comprehensive transition from the LCF (Low Cycle Fatigue) to the HCF (High Cycle Fatigue) region is given. Therefore parts of the load spectrum beneath the so-called “endurance limit” and within the elastic-plastic region can be considered for the nominal stress concept. Extensive UHCF fatigue test data generated in this study on steel bolts of two material grades are successfully evaluated by means of the MGM. Furthermore it is shown that, independent of the material, the MGM permits plausible extrapolations of the fatigue strength beyond the standardized fatigue limit