{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T16:11:48Z","timestamp":1787069508970,"version":"build-2736575974"},"reference-count":40,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T00:00:00Z","timestamp":1685491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Centre for Industrial Technological Development (CDTI), Ministry of Science, Innovation, and Universities of Spain","award":["IDI-20170068"],"award-info":[{"award-number":["IDI-20170068"]}]},{"DOI":"10.13039\/501100001872","name":"company CIE-Galfor S.A.","doi-asserted-by":"publisher","award":["IDI-20170068"],"award-info":[{"award-number":["IDI-20170068"]}],"id":[{"id":"10.13039\/501100001872","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In this work, we present an efficient numerical tool for the prediction of the final microstructure, mechanical properties, and distortions of automotive steel spindles subjected to quenching processes by immersion in liquid tanks. The complete model, which consists of a two-way coupled thermal\u2013metallurgical model and a subsequent (one-way coupled) mechanical model, was numerically implemented using finite element methods. The thermal model includes a novel generalized solid-to-liquid heat transfer model that depends explicitly on the piece\u2019s characteristic size, the physical properties of the quenching fluid, and quenching process parameters. The resulting numerical tool is experimentally validated by comparison with the final microstructure and hardness distributions obtained on automotive spindles subjected to two different industrial quenching processes: (i) a batch-type quenching process with a soaking air-furnace stage prior to the quenching, and (ii) a direct quenching process where the pieces are submerged directly in the liquid just after forging. The complete model retains accurately, at a reduced computational cost, the main features of the different heat transfer mechanisms, with deviations in the temperature evolution and final microstructure lower than 7.5% and 12%, respectively. In the framework of the increasing relevance of digital twins in industry, this model is a useful tool not only to predict the final properties of quenched industrial pieces but also to redesign and optimize the quenching process.<\/jats:p>","DOI":"10.3390\/ma16114111","type":"journal-article","created":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T02:12:45Z","timestamp":1685585565000},"page":"4111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Numerical Modeling for the Prediction of Microstructure and Mechanical Properties of Quenched Automotive Steel Pieces"],"prefix":"10.3390","volume":"16","author":[{"given":"Carlos","family":"Coroas","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II, Escuela de Ingenier\u00eda de Telecomunicaci\u00f3n, Campus Marcosende, Universidade de Vigo, 36310 Vigo, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0645-0611","authenticated-orcid":false,"given":"Iv\u00e1n","family":"Vi\u00e9itez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II, Escuela de Ingenier\u00eda de Telecomunicaci\u00f3n, Campus Marcosende, Universidade de Vigo, 36310 Vigo, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3333-9970","authenticated-orcid":false,"given":"Elena","family":"Mart\u00edn","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica y Ciencias Aeroespaciales, Campus Ourense IFCAE, Universidade de Vigo, 32004 Ourense, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6907-1964","authenticated-orcid":false,"given":"Manuel","family":"Rom\u00e1n","sequence":"additional","affiliation":[{"name":"CIE\u2014Galfor Company, P.I. San Cibrao das Vi\u00f1as, Calle 2, 3, 32901 Ourense, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Totten, G. (2007). Steel Heat Treatment. Metallurgy and Technologies, CRC Press Taylor & Francis.","DOI":"10.1201\/NOF0849384523"},{"key":"ref_2","first-page":"1","article-title":"Simulation of Quenching: A Review","volume":"1","year":"2012","journal-title":"Mater. Perform. Charact."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/0749-6419(89)90002-8","article-title":"Mathematical modeling of transformation plasticity in steels II: Coupling with strain hardening phenomena","volume":"5","author":"Leblond","year":"1989","journal-title":"Int. J. 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