PSI - Issue 72

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ScienceDirect

Procedia Structural Integrity 72 (2025) 547–556

12th Annual Conference of Society for Structural Integrity and Life (DIVK12) A proposal for a probabilistic S-N prediction of components at variable amplitude loading based on the non-linear damage José A.F.O. Correia a, * a CONSTRUCT & Faculty of Engineering, University of Porto, Campus FEUP, 4200-465 Porto, Portugal Abstract In 1924, Palmgren introduced the concept of the linear damage rule (LDR) for fatigue verification, which was later mathematically formalised by Miner in 1945. Miner's model, widely utilised in engineering codes, estimates fatigue damage as the ratio of applied cycles to the cycles required for failure. However, this model does not adequately account for the effects of sequential loading, leading to the development of nonlinear damage theories. In 1954, Marco and Starkey proposed the first nonlinear damage theory. This was followed by Manson and Halford's introduction of the double linear damage rule (DLDR) in 1966 and 1981. More recently, in 2013, Huffman and Beckman developed a nonlinear fatigue damage model that calculates damage for each cycle based on the accumulated damage state. While all these approaches are deterministic, fatigue has an inherently probabilistic nature. Several probabilistic methodologies have been proposed, but many still rely on the linear damage accumulation assumption. This research presents a new approach for probabilistic S-N (stress-life) prediction under variable amplitude loading in components and connections. It combines nonlinear damage accumulation with probabilistic modelling based on fatigue fields derived from experimental material data. Numerical modelling further enhances this methodology to predict S-N fields based on the crack initiation and propagation phases under constant amplitude loading. © 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 Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia

Keywords: Fatigue; non-linear damage accumulation; constant and variable amplitudes; probabilistic modelling.

* Corresponding author. Tel.: +351-225081562. E-mail address: jacorreia@fe.up.pt

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 Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.137