PSI - Issue 75

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ScienceDirect

Procedia Structural Integrity 75 (2025) 382–391 Structural Integrity Procedia 00 (2025) 000–000 Structural Integrity Procedia 00 (2025) 000–000

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© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under the responsibility of Dr Fabien Lefebvre with at least 2 reviewers per paper Abstract The statistical evaluation of S-N curves plays a central role in fatigue analysis, especially under the constraint of limited test data and the presence of runouts. While traditional approaches focus on modeling uncertainty in the fatigue-life direction, this study investigates four di ff erent evaluation strategies for the bilinear Basquin model using maximum likelihood estimation: (1) minimization in the fatigue-life direction, (2) minimization in the load direction, (3) a hybrid piecewise transformation approach, and (4) a novel hybrid pointwise transformation approach. All models are formulated within a consistent probabilistic framework based on a log-normal distribution. A systematic Monte Carlo study examines the performance of these strategies under variation of key parameters such as the number of data points, the logarithmic standard deviation, and the runout ratio. The results show that the commonly used evaluation in the fatigue-life direction yields the poorest parameter estimates. The load-based evaluation performs well in estimating the load amplitude at the knee point and the corresponding fatigue life, but struggles with slope accuracy due to truncation e ff ects. The newly introduced pointwise transformation and the piecewise transformation improve robustness for higher runout ratios. Overall, load-based evaluation performs best at low runout ratios, whereas piecewise and pointwise evaluations outperform under higher censoring. These findings contribute to a better understanding of the directional assumptions in statistical S-N modeling and support the development of more reliable fatigue assessment methods. © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the Fatigue Design 2025 organizers. Keywords: S-N curve; Maximum Likelihood; statistical evaluation Abstract The statistical evaluation of S-N curves plays a central role in fatigue analysis, especially under the constraint of limited test data and the presence of runouts. While traditional approaches focus on modeling uncertainty in the fatigue-life direction, this study investigates four di ff erent evaluation strategies for the bilinear Basquin model using maximum likelihood estimation: (1) minimization in the fatigue-life direction, (2) minimization in the load direction, (3) a hybrid piecewise transformation approach, and (4) a novel hybrid pointwise transformation approach. All models are formulated within a consistent probabilistic framework based on a log-normal distribution. A systematic Monte Carlo study examines the performance of these strategies under variation of key parameters such as the number of data points, the logarithmic standard deviation, and the runout ratio. The results show that the commonly used evaluation in the fatigue-life direction yields the poorest parameter estimates. The load-based evaluation performs well in estimating the load amplitude at the knee point and the corresponding fatigue life, but struggles with slope accuracy due to truncation e ff ects. The newly introduced pointwise transformation and the piecewise transformation improve robustness for higher runout ratios. Overall, load-based evaluation performs best at low runout ratios, whereas piecewise and pointwise evaluations outperform under higher censoring. These findings contribute to a better understanding of the directional assumptions in statistical S-N modeling and support the development of more reliable fatigue assessment methods. © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the Fatigue Design 2025 organizers. Keywords: S-N curve; Maximum Likelihood; statistical evaluation Fatigue Design 2025 (FatDes 2025) E ff ect of Scatter Direction on the Maximum Likelihood Evaluation of Bilinear S-N Curves Felix-Christian Reissner, Jo¨rg Baumgartner Fatigue Design 2025 (FatDes 2025) E ff ect of Scatter Direction on the Maximum Likelihood Evaluation of Bilinear S-N Curves Felix-Christian Reissner, Jo¨rg Baumgartner Fraunhofer Institute for Structural Durability and System Reliability LBF, Bartningstraße 47, 64289 Darmstadt, Germany Fraunhofer Institute for Structural Durability and System Reliability LBF, Bartningstraße 47, 64289 Darmstadt, Germany

1. Introduction 1. Introduction

S-N curves (or Wo¨hler curves) are essential tools in fatigue analysis, describing the relationship between cyclic load amplitude and fatigue-life. Despite their wide application in engineering standards and guidelines such as ASTM E739-10 ASTM International (2010) or DIN 50100 Deutsches Institut fu¨r Normung e.V. (2022), the statistical evalua- S-N curves (or Wo¨hler curves) are essential tools in fatigue analysis, describing the relationship between cyclic load amplitude and fatigue-life. Despite their wide application in engineering standards and guidelines such as ASTM E739-10 ASTM International (2010) or DIN 50100 Deutsches Institut fu¨r Normung e.V. (2022), the statistical evalua-

∗ Corresponding author E-mail address: felix-christian.reissner@lbf.fraunhofer.de ∗ Corresponding author E-mail address: felix-christian.reissner@lbf.fraunhofer.de

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under the responsibility of Dr Fabien Lefebvre with at least 2 reviewers per paper 10.1016/j.prostr.2025.11.039 2210-7843 © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the Fatigue Design 2025 organizers. 2210-7843 © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the Fatigue Design 2025 organizers.