PSI - Issue 19

Jan Papuga et al. / Procedia Structural Integrity 19 (2019) 405–414 Author name / Structural Integrity Procedia 00 (2019) 000–000

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way to show perfect prediction for  FI =0%,  FI >0% for safe prediction and  FI <0% for unsafe prediction. In order not to extrapolate out of the experimentally proven domain, only the section cuts are used, at which the S-N curve regression curves can be used for interpolating FAD030 curve of the unnotched specimen (material), and for the evaluated S-N curves of the notched specimen. Due to the space limits, these tables describe only the overall  FI statistics of all predictions provided in maximum and minimum values, the complete range, the average value and the standard deviation. Depending on the analyst’s goals, the attitude to the output can differ. Some analyst can prefer the fact that the prediction is generally safe (i.e. the minimum  FI value is close to 0%), some other can prefer the quality proven by minimum range of results, or by the small value of the standard deviation and by the average  FI close to zero. In the latter case, the use of some safety coefficient would be necessary if using the selected method in a common practice. 5. Discussion of results The results of the nominal approaches are summarized in Tab. 5. All analyses were done based on Mises equivalent stress and the PS1 variant was not tested at all. It was found that the way the slope of the S-N curve of the notched specimen is defined has a tremendous effect on the prediction quality and thus three variants of setting the fatigue strength in the quasi-static domain were evaluated at last. Usually, the direct use of the tensile strength at the quasi static region led to too inclined S-N curves resulting in unsafe predictions at lower lifetimes, the use of the tensile strength divided by K t there was generally too safe on the other hand. The a =0.51 parameter of the Peterson formula Eq. (4) proposed by Schijve (2009) does not result in a good prediction for any of the analyzed variants. To achieve better results, optimization process of a parameter definition was run to obtain better results. The goal function was set to the sum of squares of  FI (called SRES hereafter), which thus affects the overall prediction output while keeping the prediction mean close to zero. The most interesting output can be further analyzed in a more details providing graph in Fig. 3. Because the notch sensitivity parameter depends on notch root radius, which is very different for the fillet notch (  = 0.4 mm) compared to others, the S-N curve of the fillet notch lies a bit apart from the other ones. Buch’s solution was analyzed while using within it the three variants of the S-N curve slope defined by the fatigue strengths  QS in the quasi-static regime, and the A parameter derived from the K t /K f ratio of the bluntest notches available. In this case, this condition concerns the specimens with the hole, where the notch root radius is quite far from being blunt (  = 2.0 mm). It was anyway found that even after the optimization, the final A values are very close from the starting values. The optimization showed that the best-balanced prediction according to the goal SRES function is obtained, when the h parameter of Buch’s function gets to zero. By achieving it, the effect of the notch root radius is completely erased, and the K t /K f ratio is set fixed for all notch types. The probable reason of this a bit unexpected conclusion is the fact that the notch radiuses are quite different for individual notch configurations, while the fatigue strengths do not differ accordingly. Thanks to this fitting ability, Buch’s solution provides much better results than the Peterson formula. The two distinct variants of the TCD approaches (the critical distance derived from  K th or from the calibration procedure) are analyzed, and the look into Tab. 6 shows how differing results of critical distances can be obtained from each scenario. The dispersion in the  K th -based variant is the outcome of the extensive range of possible values found for 2124-T851 material (see also Tab. 2). If the highest critical distance is approximately multiple of five of the lowest value at the shortest lifetime, the enormous multiple of about 35 can be found in the case of the typical high cycle fatigue life of 1 000 000 cycles. The dispersion of critical distances resulting from the calibration routines applied to individual notch types does not vary so extensively, but still the results the user can get differ in the order of one. The use of the 1 st principal stress (PS1) leads to higher critical distances than von Mises equivalent stress. The output of using these values in the prediction can be found in Tab. 7. In addition to the outmost values of the critical distances, the computation was also run for cases of their mean values (mean  K th or the geometrical mean of the calibrated critical distances). In the case of the calibration routine, comparatively better output was obtained if PS1 was used in conjunction with the geometrical mean of the calibrated critical distances. If the output is anyhow compared with the classic approaches given in Tab. 5, and the fact is taken into account that the user neither knows