{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:24Z","timestamp":1760057844200,"version":"build-2065373602"},"reference-count":102,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T00:00:00Z","timestamp":1740614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Portuguese Foundation for Science and Technology, IP (FCT)","award":["PD\/BD\/143141\/2019","POCI-01-0247-FEDER-046111","C644940527-00000048","C645644454-00000065"],"award-info":[{"award-number":["PD\/BD\/143141\/2019","POCI-01-0247-FEDER-046111","C644940527-00000048","C645644454-00000065"]}]},{"name":"European Regional Development Fund (ERDF)","award":["PD\/BD\/143141\/2019","POCI-01-0247-FEDER-046111","C644940527-00000048","C645644454-00000065"],"award-info":[{"award-number":["PD\/BD\/143141\/2019","POCI-01-0247-FEDER-046111","C644940527-00000048","C645644454-00000065"]}]},{"name":"Recovery and Resilience Plan","award":["PD\/BD\/143141\/2019","POCI-01-0247-FEDER-046111","C644940527-00000048","C645644454-00000065"],"award-info":[{"award-number":["PD\/BD\/143141\/2019","POCI-01-0247-FEDER-046111","C644940527-00000048","C645644454-00000065"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>Parabolic leaf springs are components typically found in suspensions of freight railway rolling stock. These components are produced in high-strength alloyed steel, DIN 51CrV4, to resist severe loading and environmental conditions. Despite the material\u2019s good mechanical characteristics, the geometric notches and high surface roughness that features its leaves might raise local stress levels to values above the elastic limit, with cyclic elasto-plastic behaviour models being more appropriate. In this investigation, the parameters of the Chaboche model combining the kinematic and isotropic hardening models are determined using experimental data previously obtained in strain-controlled cyclic tests. Once the parameters of the cyclic hardening model are determined, they are validated using a finite element approach considering the Chaboche cyclic plasticity model. As a result, the material properties specified in this investigation can be used in the fatigue mechanical design of parabolic leaf springs made with 51CrV4 (local approaches to notches and at surface roughness level) or even in other components produced with the same steel.<\/jats:p>","DOI":"10.3390\/app15052549","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T05:13:58Z","timestamp":1740633238000},"page":"2549","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cyclic Elasto-Plastic Behaviour of 51CrV4 Steel for Railway Parabolic Leaf Spring Design"],"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\u2014Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1983-2451","authenticated-orcid":false,"given":"Rita","family":"Dantas","sequence":"additional","affiliation":[{"name":"FEUP\u2014Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"},{"name":"ICS\u2014Institute for Sustainable Construction, 4300-506 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\u2014Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"},{"name":"ICS\u2014Institute for Sustainable Construction, 4300-506 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\u2014Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,27]]},"reference":[{"key":"ref_1","first-page":"607272","article-title":"Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study","volume":"2014","author":"Kam","year":"2014","journal-title":"Sci. World J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"261926","DOI":"10.1155\/2013\/261926","article-title":"Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads","volume":"2013","author":"Kong","year":"2013","journal-title":"Sci. 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