PSI - Issue 75

Jan Papuga et al. / Procedia Structural Integrity 75 (2025) 289–298 Author name / Structural Integrity Procedia (2025)

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is more complicated. It asks for a non-linear regression to obtain all four its material parameters. However, it allows the curve to follow the trend including the transition to the conventional fatigue limit domain. The S-N curves are depicted in net nominal stress amplitudes. Some interesting trends might be noted. Both curves related to unnotched specimens lie the most upwards in both axial modes, with the full bar specimen reaching higher stress than the hollow specimen. This is quite expectable behaviour due to the probable differences in the crack growth phase proportion to the total life. The same mutual behaviour is observed also for torsion load mode, the distance between both curves is larger, however. Secondly these curves are not lying in the topmost position there – the mildest U-notch with root radius of 5 mm is consistently the highest-lying curve in torsion. If the fatigue lives of the unnotched hollow specimen in torque are compared, it can be found that below one million cycles, most other notch variants allow larger nominal stress to be reached for the same lifetime and only the sharpest notch configuration reaches similar nominal fatigue strengths below 1 million cycles. However, at lifetimes above one million cycles this configuration reaches nominal fatigue strengths superior to most other notched configurations except for U5.0. 4. Notch effect evaluations The RSG methods are based on the power law formulation of the S-N curve. Because some of the curves tend to bend to the horizontal direction below 1,000,000 cycles, this fatigue life was excluded from evaluation as it would result in extrapolation of the power law trend to unrealistically low values. For the other methods, the Kohout – V ěchet S -N curves were used, but the same limitation to applicable fatigue lives was applied. The comparison among various following solutions was made for the interpolated region of all experiments at lifetimes of 100,000, 200,000 and 500,000 cycles, while comparing the expectation and estimation results along stress axis. The relative error ERR  in estimating the fatigue strength compared to the experimental output is computed. 4.1. Relative stress gradient (RSG) solution The computational system used to evaluate the quality of various relative stress gradient solutions is described in [2]. In short, five different configurations of the solution are checked: 1. FKM-Guideline v. 6 [1] and later, either using the older approach proposed by Stieler to compute the fatigue factor or using the new solution defined in v.6 combining several different effects. 2. Solution used by Femfat fatigue solver [6] and using three different fatigue factors according to (a) Stieler, (b) Hück, and (c) Eichlseder. According to the scheme in Fig. 1, the available experimental data are used in these steps: 1. Relative stress gradient obtained from FE-analysis for a given configuration is integrated with the RSG solution to transform the material S-N curve (of the unnotched specimen) into a new component curve. 2. The maximum local stress at the notch root related to individual tested configurations is compared with the component S-N curve at chosen lifetimes. If the stress is below the component curve, this marks the non conservative prediction (and negative sign of the relative error). The overall results are provided in Table 2. It must be noted that they and the subsequent conclusion of the comparison somewhat differ from [2], likely both due to adding the new load mode of plane bending, and because of a more significant variation in the value of the relative stress gradient. The most surprising is the output of the Eichlseder method contradicting [2], where it was non-conservative in the average value to a substantial degree. On the other hand, the worse performance of the Hück and Eichlseder method remains also here, above all due to significantly increased scatter of data (though the average value of error delivered by the Hück method is close to zero).