PSI - Issue 75

Felix-Christian Reissner et al. / Procedia Structural Integrity 75 (2025) 382–391 Felix-Christian Reissner / Structural Integrity Procedia 00 (2025) 000–000

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5.4. Discussion

For linear models, such as the classical Basquin model, evaluation in the fatigue-life direction is both meaningful and physically appropriate. However, this study has shown that this evaluation strategy leads to highly biased esti mation results when applied to the bilinear Basquin model. The likely reason for this poor performance lies in the shape of the distribution near the knee point, which is not log-normal in the fatigue-life direction. Furthermore, the magnitudes of standard deviation di ff er in the HCF and LCF regimes. However, modeling in fatigue-life direction averages the standard deviations. This averaging leads to an overestimation of standard deviation in the HCF regime and an underestimation of standard deviation in the LCF regime. The evaluation in load direction , by contrast, is not a ff ected by this issue, as a constant standard deviation in the load direction is assumed throughout the analysis. Consequently, this approach provides precise estimates of the load amplitude at the knee point and the corresponding fatigue life. However, it struggles to accurately estimate the slope parameters due to the lack of consideration for truncation e ff ects in the upper left region of the S-N curve. In addition, the accuracy of the estimation decreases as the runout ratio increases. The piecewise evaluation is probably less a ff ected by this truncation issue. However, its main limitation lies in the region around the knee point. Specifically, the use of di ff erent slopes before and after the knee point introduces a discontinuity in the transformed scatter. The pointwise evaluation avoids this discontinuity by modeling a continuous transition from k 1 to k 2 . However, the assumption of a log-normal distribution close to the knee point is still violated. This probably leads to similar results to those obtained using the piecewise evaluation. In summary, the load-based evaluation provides the most balanced and robust performance across the investigated scenarios. The fatigue-life-based approach, although physically intuitive for linear models, proves unsuitable for bi linear models. The evaluation in load direction o ff ers precise knee point estimates but struggles with slope accuracy, while the pointwise and piecewise methods present a robust alternative for runout ratios above 10 %.

6. Conclusion

This study evaluates four strategies for statistical S-N modeling using the bilinear Basquin model and maximum likelihood estimation: (1) fatigue-life-based, (2) load-based, (3) piecewise transformation, and (4) pointwise transfor mation approaches. The fatigue-life-based method, though common for linear models, showed poor performance for bilinear S-N curves due to averaging e ff ects across regimes. Load-based evaluation identifies the load amplitude at the knee point most accurately, as well as the corresponding fatigue-life. It performs best at low runout ratios, though slope estimation can be biased. Piecewise and pointwise evaluation most accurately estimate the scatter and perform robustly as runout ratio increases. The fatigue-life-based approach performs the worst overall for bilinear S-N curves.

Author’s Note

This paper was edited with the assistance of ChatGPT-4o (OpenAI). The tool was used solely for language refine ment and formatting purposes; all content and analysis were developed by the authors.

References

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