{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T11:46:49Z","timestamp":1768564009630,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T00:00:00Z","timestamp":1711670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFB3400902"],"award-info":[{"award-number":["2021YFB3400902"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["52305372"],"award-info":[{"award-number":["52305372"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["51790175"],"award-info":[{"award-number":["51790175"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["52122509"],"award-info":[{"award-number":["52122509"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2030009401093"],"award-info":[{"award-number":["2030009401093"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["001027232090"],"award-info":[{"award-number":["001027232090"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021YFB3400902"],"award-info":[{"award-number":["2021YFB3400902"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52305372"],"award-info":[{"award-number":["52305372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51790175"],"award-info":[{"award-number":["51790175"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52122509"],"award-info":[{"award-number":["52122509"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2030009401093"],"award-info":[{"award-number":["2030009401093"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["001027232090"],"award-info":[{"award-number":["001027232090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Fund for Excellent Young Scholars","doi-asserted-by":"publisher","award":["2021YFB3400902"],"award-info":[{"award-number":["2021YFB3400902"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Fund for Excellent Young Scholars","doi-asserted-by":"publisher","award":["52305372"],"award-info":[{"award-number":["52305372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Fund for Excellent Young Scholars","doi-asserted-by":"publisher","award":["51790175"],"award-info":[{"award-number":["51790175"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Fund for Excellent Young Scholars","doi-asserted-by":"publisher","award":["52122509"],"award-info":[{"award-number":["52122509"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Fund for Excellent Young Scholars","doi-asserted-by":"publisher","award":["2030009401093"],"award-info":[{"award-number":["2030009401093"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Fund for Excellent Young Scholars","doi-asserted-by":"publisher","award":["001027232090"],"award-info":[{"award-number":["001027232090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009554","name":"Nanchang Hangkong University","doi-asserted-by":"publisher","award":["2021YFB3400902"],"award-info":[{"award-number":["2021YFB3400902"]}],"id":[{"id":"10.13039\/100009554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009554","name":"Nanchang Hangkong University","doi-asserted-by":"publisher","award":["52305372"],"award-info":[{"award-number":["52305372"]}],"id":[{"id":"10.13039\/100009554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009554","name":"Nanchang Hangkong University","doi-asserted-by":"publisher","award":["51790175"],"award-info":[{"award-number":["51790175"]}],"id":[{"id":"10.13039\/100009554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009554","name":"Nanchang Hangkong University","doi-asserted-by":"publisher","award":["52122509"],"award-info":[{"award-number":["52122509"]}],"id":[{"id":"10.13039\/100009554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009554","name":"Nanchang Hangkong University","doi-asserted-by":"publisher","award":["2030009401093"],"award-info":[{"award-number":["2030009401093"]}],"id":[{"id":"10.13039\/100009554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009554","name":"Nanchang Hangkong University","doi-asserted-by":"publisher","award":["001027232090"],"award-info":[{"award-number":["001027232090"]}],"id":[{"id":"10.13039\/100009554","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Double Thousand Plan of Jiang Xi Province","award":["2021YFB3400902"],"award-info":[{"award-number":["2021YFB3400902"]}]},{"name":"Double Thousand Plan of Jiang Xi Province","award":["52305372"],"award-info":[{"award-number":["52305372"]}]},{"name":"Double Thousand Plan of Jiang Xi Province","award":["51790175"],"award-info":[{"award-number":["51790175"]}]},{"name":"Double Thousand Plan of Jiang Xi Province","award":["52122509"],"award-info":[{"award-number":["52122509"]}]},{"name":"Double Thousand Plan of Jiang Xi Province","award":["2030009401093"],"award-info":[{"award-number":["2030009401093"]}]},{"name":"Double Thousand Plan of Jiang Xi Province","award":["001027232090"],"award-info":[{"award-number":["001027232090"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In order to study the multi-mode damage and fracture mechanisms of thin-walled tubular parts with cross inner ribs (longitudinal and transverse inner ribs, LTIRs), the Gurson\u2013Tvergaard\u2013Needleman (GTN) model was modified with a newly proposed stress state function. Thus, tension damage and shear damage were unified by the new stress state function, which was asymmetric with respect to stress triaxiality. Tension damage dominated the modification, which coupled with the shear damage variable, ensured the optimal prediction of fractures of thin-walled tubular parts with LTIRs by the modified GTN model. This included fractures occurring at the non-rib zone (NRZ), the longitudinal rib (LIR) and the interface between the transverse rib (TIR) and the NRZ. Among them, the stripping of material from the outer surface of the tubular part was mainly caused by the shearing of built-up material in front of the rollers under a large wall thickness reduction (\u0394T). Shear and tension deformation were the causes of fractures occurring at the NRZ, while axial tension under a large TIR interval (l) mainly resulted in fractures on LIRs. Fractures at the interface between the TIR and NRZ were due to the shearing applied by rib grooves and radial tension during the formation of ribs. This study can provide guidance for the manufacturing of high-performance aluminum alloy thin-walled tubular components with complex inner ribs.<\/jats:p>","DOI":"10.3390\/ma17071576","type":"journal-article","created":{"date-parts":[[2024,3,31]],"date-time":"2024-03-31T13:32:56Z","timestamp":1711891976000},"page":"1576","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi-Mode Damage and Fracture Mechanisms of Thin-Walled Tubular Parts with Cross Inner Ribs Manufactured via Flow Forming"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiang","family":"Zeng","sequence":"first","affiliation":[{"name":"School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China"},{"name":"Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leheng","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoguang","family":"Fan","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongwei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China"},{"name":"Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mei","family":"Zhan","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongbao","family":"Mi","sequence":"additional","affiliation":[{"name":"School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuefeng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yubin","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,29]]},"reference":[{"key":"ref_1","first-page":"285","article-title":"Flow forming: A review of research methodologies, prediction models and their applications","volume":"7","author":"Marini","year":"2016","journal-title":"Int. J. Mech. Eng. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1016\/S0890-6955(03)00172-X","article-title":"A review of spinning, shear forming and flow forming processes","volume":"43","author":"Wong","year":"2003","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.jmatprotec.2009.08.021","article-title":"A review of the mechanics of metal spinning","volume":"210","author":"Music","year":"2010","journal-title":"J. Mater. Process Technol."},{"key":"ref_4","unstructured":"Domack, M.S., and Wagner, J.A. (2014). NASA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/j.ijmecsci.2017.10.033","article-title":"An investigation into forming internally-spline sleeves by ball spinning","volume":"134","author":"Ahmed","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"117197","DOI":"10.1016\/j.jmatprotec.2021.117197","article-title":"Deformation mechanism of ZK61 magnesium alloy cylindrical parts with longitudinal inner ribs during hot backward flow forming","volume":"296","author":"Xia","year":"2021","journal-title":"J. Mater. Process Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1007\/s00170-018-2334-x","article-title":"Study on compound spinning technology of large thin-walled parts with ring inner ribs and curvilinear generatrix","volume":"98","author":"Luo","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.jmapro.2020.08.055","article-title":"Die filling mechanism in flow forming of thin-walled tubular parts with cross inner ribs","volume":"58","author":"Zeng","year":"2020","journal-title":"J. Manuf. Process"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.jmatprotec.2015.10.001","article-title":"Numerical simulation and experimental study on multi-pass stagger spinning of internally toothed gear using plate blank","volume":"229","author":"Xu","year":"2016","journal-title":"J. Mater. Process Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.jmatprotec.2016.03.007","article-title":"Damage minimised ball spinning process design","volume":"234","author":"Kuss","year":"2016","journal-title":"J. Mater. Process Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3509","DOI":"10.1016\/j.cja.2020.09.018","article-title":"A constitutive model coupling damage and material anisotropy for wide stress triaxiality","volume":"33","author":"Li","year":"2020","journal-title":"Chin. J. Aeronaut."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, X.X., Zhan, M., Guo, J., and Zhao, B. (2016). Evaluating the Applicability of GTN Damage Model in Forward Tube Spinning of Aluminum Alloy. Metals, 6.","DOI":"10.3390\/met6060136"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jmatprotec.2018.07.032","article-title":"An extended GTN model for low stress triaxiality and application in spinning forming","volume":"263","author":"Wu","year":"2019","journal-title":"J. Mater. Process Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1115\/1.3443401","article-title":"Continuum theory of ductile rupture by void nucleation and growth: Part I-yield criteria and flow rules for porous ductile media","volume":"99","author":"Gurson","year":"1977","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0001-6160(84)90213-X","article-title":"Analysis of the cup-cone fracture in a round tensile bar","volume":"32","author":"Tvergaard","year":"1984","journal-title":"Acta Metall."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.euromechsol.2016.10.014","article-title":"Prediction of shear-dominated ductile fracture in a butterfly specimen using a model of plastic porous solids including void shape effects","volume":"61","author":"Morin","year":"2017","journal-title":"Eur. J. Mech. A-Solid."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105153","DOI":"10.1016\/j.jmps.2022.105153","article-title":"A shear modified enhanced Gurson constitutive relation and implications for localization","volume":"171","author":"Khan","year":"2023","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.euromechsol.2007.08.002","article-title":"Modification of the Gurson model for shear failure","volume":"27","author":"Nahshon","year":"2008","journal-title":"Eur. J. Mech. A-Solid."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3343","DOI":"10.1016\/j.engfracmech.2007.07.022","article-title":"Constitutive modeling of void shearing effect in ductile fracture of porous materials","volume":"75","author":"Xue","year":"2008","journal-title":"Eng. Fract. Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.ijplas.2013.08.015","article-title":"An extended GTN model for ductile fracture under high and low stress triaxiality","volume":"54","author":"Malcher","year":"2014","journal-title":"Int. J. Plast."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.euromechsol.2015.12.009","article-title":"Modified GTN model for a broad range of stress states and application to ductile fracture","volume":"57","author":"Jiang","year":"2016","journal-title":"Eur. J. Mech. A-Solid."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s12541-017-0009-4","article-title":"Deformation behavior of haynes230 superalloy during backward flow forming","volume":"18","author":"Wang","year":"2017","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.jmatprotec.2009.09.028","article-title":"Experimental study and FEM analysis of redundant strains in flow forming of tubes","volume":"210","author":"Mohebbi","year":"2010","journal-title":"J. Mater. Process Technol."},{"key":"ref_24","first-page":"582","article-title":"Mechanik der festen K\u00f6rper im plastisch deformablen Zustand","volume":"1","year":"1913","journal-title":"G\u00f6ttin Nachr. Math. Phys."},{"key":"ref_25","unstructured":"R\u00f6sler, J., Harders, H., and B\u00e4ker, M. (2007). Mechanical Behavior of Engineering Materials, Springer. [1st ed.]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-5096(52)90002-1","article-title":"Plastic instability under plane stress","volume":"1","author":"Swift","year":"1952","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"116687","DOI":"10.1016\/j.jmatprotec.2020.116687","article-title":"Investigations on failure-to-fracture mechanism and prediction of forming limit for aluminum alloy incremental forming process","volume":"282","author":"Zhan","year":"2020","journal-title":"J. Mater. Process Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.ijmecsci.2018.11.006","article-title":"Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF","volume":"151","author":"Borrego","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2840","DOI":"10.1016\/j.ijsolstr.2014.04.007","article-title":"Suppression of necking in incremental sheet forming","volume":"51","author":"Seong","year":"2014","journal-title":"Int. J. Solids Struct."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/7\/1576\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:21:02Z","timestamp":1760106062000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/7\/1576"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,29]]},"references-count":29,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["ma17071576"],"URL":"https:\/\/doi.org\/10.3390\/ma17071576","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,29]]}}}