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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Fig. 1. E ff ect of the number of S-N data pairs on parameter estimation accuracy.

The evaluation in load direction yields a precise estimate of the load amplitude at the knee point S a , k , the corre sponding fatigue life N k and the logarithmic standard deviation σ S , log . However, it tends to overestimate the slope k 1 . The piecewise evaluation leads to a biased estimation of the load amplitude at the knee point S a , k , the corresponding fatigue life N k and the slope k 1 across the investigated range. While the load amplitude at the knee point S a , k is under estimated, the knee point N k is overestimated. In addition, the slope k 1 and the logarithmic standard deviation σ S , log are overestimated. The pointwise evaluation shows a stronger tendency to underestimate the load amplitude at the knee point S a , k and to overestimate the corresponding fatigue life N k , relative to the reference, than the piecewise evaluation. Nonetheless, it yields good slope k 1 and standard deviation σ S , log estimates. In summary, the evaluation in load direction shows the best overall performance. The next investigation focuses on the e ff ect of a varying logarithmic standard deviation, as shown in Fig. 2. The logarithmic standard deviation σ S , log can be easily converted into the commonly used scatter parameter T S via the relation T S = 10 2 . 563 · σ S , log . Accordingly, the scatter is varied between T S = 1 . 06 and T S = 1 . 34. The evaluation in fatigue-life direction shows a very strong tendency to underestimate the load amplitude at the kneepoint S a , k and overestimate the corresponding fatigue life N k . It performs worse than the other approaches across all scatter levels. The evaluation in load direction provides very accurate estimates of the load amplitude at the knee point S a , k and the corresponding fatigue life N k , even at higher levels of scatter. However, in terms of standard deviation σ S , log and slope k 1 estimation, the reference value is increasingly biased as the standard deviation increases. The piecewise evaluation yields biased estimates of the load amplitude at the knee point S a , k , the corresponding fatigue life N k , the slope k 1 and the logarithmic standard deviation σ S , log . As the standard deviation increases, the bias in all parameters increases. The pointwise evaluation , while also underestimating the load amplitude at the knee point S a , k and overestimating the corresponding fatigue life N k , provides the best slope k 1 estimates. However, the logarithmic standard deviation σ S , log is increasingly overestimated as the reference value increases. In summary, all approaches perform well at low scatter levels. However, as the standard deviation increases, the evaluation in load direction continues to deliver the most robust and accurate results for the load amplitude at the knee point S a , k and the corresponding fatigue life N k , while the fatigue-life-based approach consistently performs the worst. The pointwise and piecewise evaluation o ff er competitive performance at low scatter levels and in estimating the slope k 1 . 5.2. Standard Deviation