PSI - Issue 77

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ScienceDirect

Procedia Structural Integrity 77 (2026) 440–446

© 2026 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 responsibility of ICSI organizers Keywords: Goodman; Gerber; Equivalent stress amplitude; DIN 34CrNiMo6 steel Abstract The objective of this research was to evaluate the applicability of mean stress correction models (Goodman, Gerber, Soderberg, and ASME) beyond their conventional validation boundaries (failures between 1 E 4–1 E 7 cycles) for predicting fatigue life in the very high cycle fatigue (VHCF) regime (failures after 1 E 7 cycles). Cyclic tests were performed on a high-strength structural steel under fully reversed and partially reversed loading conditions to compare experimental results with fatigue life predictions from these models. The material was tested under both fully reversed and mean stress loading conditions to determine fatigue life. Each model was employed to calculate the equivalent stress amplitude for fitting Basquin curves. Statistical tools were subsequently used to compare the Basquin curve derived from each model with the experimental curve obtained under fully reversed loading. The linear models (Goodman and Soderberg) demonstrated better agreement with experimental VHCF data, whereas the quadratic models exhibited greater inconsistency in the VHCF regime. International Conference on Structural Integrity On the applicability of mean stress correction models in the very high cycle fatigue regime (VHCF) J.A. Alves a , M.V. Pereira a, ∗ a Department of Chemical and Materials Engineering, Pontifical Catholic University of Rio de Janeiro – PUC-Rio, Rua Marqueˆs de Sa˜o Vicente, 225, Rio de Janeiro, 22451-900, RJ, Brazil

1. Introduction

Fatigue is estimated to be responsible for more than 80% of structural failures in industry (Volak and Mentl (2013)). Rotors, turbines, and other components are subjected to variable loading with non-zero mean stresses, which can lead to catastrophic fatigue failures resulting in significant economic and productive losses (Volak and Mentl (2013); Zhang et al. (2023)). In mechanical design, the S–N approach for life prediction is widely employed; however, S–N data are typically obtained under fully reversed loading, i.e., in the absence of mean stress (Meggiolaro et al. (2009); Schijve (2001)). In turbines, it is necessary to evaluate fatigue lives on the order of 10 10 cycles, entering the very-high cycle fatigue (VHCF) regime (Zhao et al. (2024)). To reach such high cycle numbers, ultrasonic testing equipment operating at 20 kHz, achieving 10 9 cycles in only 14 hours, allows the observation of fatigue failures within practical experimental times (Bathias (2006)). In this context, several approaches have been proposed to correlate fully reversed

∗ Corresponding author. Tel.: + 5521988003285. E-mail address: marcospe@puc-rio.br

2452-3216 © 2026 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 responsibility of ICSI organizers 10.1016/j.prostr.2026.01.056