{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T07:08:09Z","timestamp":1768288089970,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T00:00:00Z","timestamp":1631836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"US\/JUNTA\/FEDER_UE","award":["US-1263138"],"award-info":[{"award-number":["US-1263138"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e da Tecnologia of Portugal","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Metals"],"abstract":"<jats:p>In this paper, we revisit the formability of tube expansion by single point incremental forming to account for the material strain hardening and the non-proportional loading paths that were not taken into consideration in a previously published analytical model of the process built upon a rigid perfectly plastic material. The objective is to provide a new insight on the reason why the critical strains at failure of tube expansion by single point incremental forming are far superior to those of conventional tube expansion by rigid tapered conical punches. For this purpose, we replaced the stress triaxiality ratio that is responsible for the accumulation of damage and cracking by tension in monotonic, proportional loading paths, by integral forms of the stress triaxiality ratio that are more adequate for the non-proportional paths resulting from the loading and unloading cycles of incremental tube expansion. Experimental and numerical simulation results plotted in the effective strain vs. stress triaxiality space confirm the validity of the new damage accumulation approach for handling the non-proportional loading paths that oscillate cyclically from shearing to biaxial stretching, as the single point hemispherical tool approaches, contacts and moves away from a specific location of the incrementally expanded tube surface.<\/jats:p>","DOI":"10.3390\/met11091481","type":"journal-article","created":{"date-parts":[[2021,9,18]],"date-time":"2021-09-18T00:13:47Z","timestamp":1631924027000},"page":"1481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Tube Expansion by Single Point Incremental Forming: An Experimental and Numerical Investigation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5344-5845","authenticated-orcid":false,"given":"Carlos","family":"Suntaxi","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Facultad de Ingenier\u00eda Mec\u00e1nica, Escuela Polit\u00e9cnica Nacional, Ladr\u00f3n de Guevara E11-253, Quito P.O. Box 17-01-2759, Ecuador"},{"name":"Department of Mechanical and Manufacturing Engineering, School of Engineering, University of Seville, Camino de los Descubrimientos s\/n, 41092 Seville, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3684-2982","authenticated-orcid":false,"given":"Gabriel","family":"Centeno","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Manufacturing Engineering, School of Engineering, University of Seville, Camino de los Descubrimientos s\/n, 41092 Seville, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5284-8391","authenticated-orcid":false,"given":"M.","family":"Silva","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5903-1336","authenticated-orcid":false,"given":"Carp\u00f3foro","family":"Vallellano","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Manufacturing Engineering, School of Engineering, University of Seville, Camino de los Descubrimientos s\/n, 41092 Seville, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2630-4593","authenticated-orcid":false,"given":"Paulo","family":"Martins","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Keeler, S.P. (1968). Circular grid system\u2013A valuable aid for evaluating sheet metal formability. 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