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Because fatigue is a significant factor that impacts the longevity of railway components, it is imperative that the fatigue resistance properties of crucial components, like leaf springs, be thoroughly investigated. This research investigates the fatigue resistance of 51CrV4 steel under bending and axial tension, considering different stress ratios across low-cycle fatigue (LCF), high-cycle fatigue (HCF), and very-high-cycle fatigue (VHCF) regimes, using experimental data collected from this work and prior research. Data included fractographic analyses aiming to help in understanding some of failures for different loads. The presence of geometric discontinuities, such as notches, amplifies stress concentrations, requiring a probabilistic approach to fatigue assessment. To address notch effects, the theory of critical distances (TCD) was employed to evaluate fatigue strength. TCD model was integrated in fatigue statistical models, such as the Walker model (WSN) and the Castillo\u2013Fern\u00e1ndez-Cantelli model adapted for mean stress effects (ACFC). Extending the application of the TCD theory, this research provides an improved probabilistic fatigue model that integrates notch sensitivity, mean stress effects, and fatigue regimes, contributing to more reliable design approaches of railway leaf springs or other components produced in 51CrV4 steel.<\/jats:p>","DOI":"10.3390\/app15179739","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T09:51:21Z","timestamp":1757065881000},"page":"9739","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fatigue Probabilistic Approach of Notch Sensitivity of 51CrV4 Leaf Spring Steel Based on the Theory of Critical Distances"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3982-6913","authenticated-orcid":false,"given":"V\u00edtor M. G.","family":"Gomes","sequence":"first","affiliation":[{"name":"FEUP\u2014 Faculty of Engineering, University of Porto, 4150-564 Porto, Portugal"},{"name":"INEGI\u2014 Institute of Science and Innovation in Mechanical and Industrial Engineering, 4150-564 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6425-4339","authenticated-orcid":false,"given":"Miguel A. V.","family":"de Figueiredo","sequence":"additional","affiliation":[{"name":"FEUP\u2014 Faculty of Engineering, University of Porto, 4150-564 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4148-9426","authenticated-orcid":false,"given":"Jos\u00e9 A. F. O.","family":"Correia","sequence":"additional","affiliation":[{"name":"FEUP\u2014 Faculty of Engineering, University of Porto, 4150-564 Porto, Portugal"},{"name":"INEGI\u2014 Institute of Science and Innovation in Mechanical and Industrial Engineering, 4150-564 Porto, Portugal"},{"name":"ICS\u2014 Institute for Sustainable Construction, 4150-564 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1059-715X","authenticated-orcid":false,"given":"Ab\u00edlio M. P.","family":"de Jesus","sequence":"additional","affiliation":[{"name":"FEUP\u2014 Faculty of Engineering, University of Porto, 4150-564 Porto, Portugal"},{"name":"INEGI\u2014 Institute of Science and Innovation in Mechanical and Industrial Engineering, 4150-564 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.engfracmech.2012.09.029","article-title":"Safe life and damage tolerance aspects of railway axles \u2013 A review","volume":"98","author":"Zerbst","year":"2013","journal-title":"Eng. Fract. Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1550","DOI":"10.1016\/j.ijfatigue.2009.04.016","article-title":"Probabilistic fatigue S\u2013N curves including the super-long life regime of a railway axle steel","volume":"31","author":"Zhao","year":"2009","journal-title":"Int. J. 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