{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T02:47:25Z","timestamp":1762051645309,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T00:00:00Z","timestamp":1652227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Jiangsu Province","award":["BK20190869","BK20190873","21KJB130002","11972364"],"award-info":[{"award-number":["BK20190869","BK20190873","21KJB130002","11972364"]}]},{"name":"Natural Science Foundation of Jiangsu Higher Education Institutions of China","award":["BK20190869","BK20190873","21KJB130002","11972364"],"award-info":[{"award-number":["BK20190869","BK20190873","21KJB130002","11972364"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["BK20190869","BK20190873","21KJB130002","11972364"],"award-info":[{"award-number":["BK20190869","BK20190873","21KJB130002","11972364"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Uniaxial and notched tension samples are utilized to investigate the damage and failure of titanium alloy Ti6Al4V. The strain fields on the samples are obtained by the digital image correlation (DIC) method. Strain localization occurs before fracturing in all samples, and the width and size of the localized zone are characterized. Slant fractures are observed in uniaxial and notched tension specimen, which indicate that the initiation and propagation of cracks in thin sheet specimens are highly affected by the shear stress. Numerical simulations were performed for identification of hybrid hardening laws, and the results were compared with the experiments. The influence of the stress triaxiality on damage mechanism of Ti6Al4V was analyzed by observation of the specimen fracture surfaces using SEM. The results show that a higher stress triaxiality facilitates the formation and growth of micro-voids, which leads to a decrement of strain at failure.<\/jats:p>","DOI":"10.3390\/ma15103429","type":"journal-article","created":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T23:39:36Z","timestamp":1652225976000},"page":"3429","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Investigation on Strain Hardening and Failure in Notched Tension Specimens of Cold Rolled Ti6Al4V Titanium Alloy"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5170-4134","authenticated-orcid":false,"given":"Hao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2097-5740","authenticated-orcid":false,"given":"Jian","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xunpeng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haipeng","family":"Song","sequence":"additional","affiliation":[{"name":"Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ganyun","family":"Huang","sequence":"additional","affiliation":[{"name":"Tianjin Key Laboratory of Modern Engineering Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.actamat.2018.02.025","article-title":"Heterogeneous random medium plasticity and fracture model of additively-manufactured Ti-6Al-4V","volume":"148","author":"Gorji","year":"2018","journal-title":"Acta Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.ijsolstr.2015.08.025","article-title":"Constitutive modelling of high strength titanium alloy Ti-6Al-4 V for sheet forming applications at room temperature","volume":"80","author":"Badr","year":"2016","journal-title":"Int. J. Solids Struct."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Yi, S.-X., Yang, Z.-J., and Xie, H.-X. (2022). Hot Deformation and Constitutive Modeling of TC21 Titanium Alloy. Materials, 15.","DOI":"10.3390\/ma15051923"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.ijplas.2005.06.001","article-title":"Orthotropic yield criterion for hexagonal closed packed metals","volume":"22","author":"Cazacu","year":"2006","journal-title":"Int. J. Plast."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.ijmecsci.2018.10.045","article-title":"Modelling of fracture occurrence in Ti6Al4V sheets at elevated temperature ac-counting for anisotropic behaviour","volume":"150","author":"Wang","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.mechmat.2017.08.007","article-title":"High-strain-rate plastic deformation and fracture behaviour of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy at room temperature","volume":"116","author":"Ran","year":"2018","journal-title":"Mech. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.ijmecsci.2004.02.006","article-title":"On fracture locus in the equivalent strain and stress triaxiality space","volume":"46","author":"Bao","year":"2004","journal-title":"Int. J. Mech. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wilson-Heid, A., Furton, E., and Beese, A. (2021). Contrasting the Role of Pores on the Stress State Dependent Fracture Behavior of Additively Manufactured Low and High Ductility Metals. Materials, 14.","DOI":"10.3390\/ma14133657"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.engfracmech.2015.05.022","article-title":"Stress state dependence of ductile damage and fracture behavior: Experiments and numerical simulations","volume":"141","author":"Brenner","year":"2015","journal-title":"Eng. Fract. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1768","DOI":"10.1016\/j.ijsolstr.2006.09.031","article-title":"Rupture mechanisms in combined tension and shear\u2014Experiments","volume":"44","author":"Barsoum","year":"2007","journal-title":"Int. J. Solids Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2366","DOI":"10.1016\/j.ijplas.2009.03.006","article-title":"Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy","volume":"25","author":"Gao","year":"2009","journal-title":"Int. J. Plast."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"139295","DOI":"10.1016\/j.msea.2020.139295","article-title":"Influence of stress state on plastic flow and ductile fracture of three 6000-series aluminium alloys","volume":"783","author":"Thomesen","year":"2020","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1016\/j.ijplas.2007.09.004","article-title":"A new model of metal plasticity and fracture with pressure and Lode dependence","volume":"24","author":"Bai","year":"2008","journal-title":"Int. J. Plast."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1007\/s11340-011-9541-9","article-title":"Novel Technique for Static and Dynamic Shear Testing of Ti6Al4V Sheet","volume":"52","author":"Peirs","year":"2012","journal-title":"Exp. Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.jmatprotec.2005.09.003","article-title":"Simple shear tests: Experimental techniques and characterization of the plastic anisotropy of rolled sheets at large strains","volume":"172","author":"Bouvier","year":"2006","journal-title":"J. Mater. Process. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.ijsolstr.2015.03.032","article-title":"A grooved in-plane torsion test for the investigation of shear fracture in sheet materials","volume":"66","author":"Yin","year":"2015","journal-title":"Int. J. Solids Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1016\/j.engfracmech.2011.08.008","article-title":"Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading","volume":"78","author":"Dunand","year":"2011","journal-title":"Eng. Fract. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1016\/j.ijsolstr.2012.12.009","article-title":"Ductile failure under combined shear and tension","volume":"50","author":"Haltom","year":"2013","journal-title":"Int. J. Solids Struct."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ha, J., Baral, M., and Korkolis, Y.P. (2019). Ductile fracture of an aluminum sheet under proportional loading. J. Mech. Phys. Solids, 132.","DOI":"10.1016\/j.jmps.2019.103685"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s11340-015-9999-y","article-title":"Cruciform Specimen Design and Verification for Constitutive Identification of Anisotropic Sheets","volume":"55","author":"Deng","year":"2015","journal-title":"Exp. Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ijsolstr.2019.01.007","article-title":"Experiments with the X0-specimen on the effect of non-proportional loading paths on damage and fracture mechanisms in aluminum alloys","volume":"163","author":"Gerke","year":"2019","journal-title":"Int. J. Solids Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.commatsci.2004.02.004","article-title":"Computer-aided identification of the yield curve of a sheet metal after onset of necking","volume":"31","author":"Koc","year":"2004","journal-title":"Comput. Mater. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1746","DOI":"10.1016\/j.ijplas.2010.02.005","article-title":"A plastic constitutive equation incorporating strain, strain-rate, and temperature","volume":"26","author":"Sung","year":"2010","journal-title":"Int. J. Plast."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.matdes.2018.05.034","article-title":"Extrapolation based constitutive modeling of flow stress of titanium alloy sheet under hot-working condition","volume":"154","author":"Guo","year":"2018","journal-title":"Mater. Des."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"140206","DOI":"10.1016\/j.msea.2020.140206","article-title":"Experimental investigation on damage evolution in pre-corroded aluminum alloy 7075-T7651 under fatigue loading","volume":"799","author":"Song","year":"2021","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"082001","DOI":"10.1088\/1361-6501\/aac55b","article-title":"Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals","volume":"29","author":"Pan","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.engfracmech.2012.09.012","article-title":"Experimental investigation of deformation and failure mechanisms in rock under indentation by digital image correlation","volume":"96","author":"Zhang","year":"2012","journal-title":"Eng. Fract. Mech."},{"key":"ref_28","unstructured":"Sutton, M.A., Orteu, J.-J., and Schreier, H. (2009). Image Correlation for Shape, Motion and Deformation Measurements, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1007\/s00170-014-5670-5","article-title":"Evaluating the flow stress of aerospace alloys for tube hydroforming process by free expansion testing","volume":"72","author":"Saboori","year":"2014","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1007\/s11340-014-9900-4","article-title":"Identification of Post-Necking Hardening Phenomena in Ductile Sheet Metal","volume":"54","author":"Coppieters","year":"2014","journal-title":"Exp. Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.mechmat.2018.12.014","article-title":"Inverse identification of the post-necking work hardening behaviour of thick HSS through full-field strain measurements during diffuse necking","volume":"129","author":"Zhang","year":"2019","journal-title":"Mech. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Aliprandi, P., Giudice, F., Guglielmino, E., and Sili, A. (2019). Tensile and Creep Properties Improvement of Ti-6Al-4V Alloy Specimens Produced by Electron Beam Powder Bed Fusion Additive Manufacturing. Metals, 9.","DOI":"10.3390\/met9111207"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"161926","DOI":"10.1016\/j.jallcom.2021.161926","article-title":"An investigation of ductile fracture behavior of Ti6Al4V alloy fabricated by selective laser melting","volume":"890","author":"Yang","year":"2022","journal-title":"J. Alloys Compd."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ludwik, P. (1909). Elemente der Technologischen Mechanik, Springer.","DOI":"10.1007\/978-3-662-40293-1"},{"key":"ref_35","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_36","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1016\/0001-6160(77)90072-4","article-title":"Tensile instability and necking in materials with strain hardening and strain-rate hardening","volume":"25","author":"Ghosh","year":"1977","journal-title":"Acta Met."},{"key":"ref_37","first-page":"537","article-title":"The relationship between stress and strain for homogeneous deformation","volume":"74","author":"Voce","year":"1948","journal-title":"J. Inst. Met."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0022-5096(75)90018-6","article-title":"Large strain deformation of polycrystalline metals at low homologous temperatures","volume":"23","author":"Hockett","year":"1975","journal-title":"J. Mech. Phys. Solids"}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/10\/3429\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:09:02Z","timestamp":1760137742000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/10\/3429"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,11]]},"references-count":38,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["ma15103429"],"URL":"https:\/\/doi.org\/10.3390\/ma15103429","relation":{},"ISSN":["1996-1944"],"issn-type":[{"type":"electronic","value":"1996-1944"}],"subject":[],"published":{"date-parts":[[2022,5,11]]}}}