{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:20:51Z","timestamp":1760145651277,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,8,25]],"date-time":"2024-08-25T00:00:00Z","timestamp":1724544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Gansu Provincial Young Doctors Fund","award":["2023QB-046"],"award-info":[{"award-number":["2023QB-046"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The mechanical properties of local materials subjected to various stress triaxialities were investigated via self-designed small punch tests and corresponding simulations, which were tailored to the geometry and notch forms of the samples. The finite element model was developed on the basis of the actual test method. After verifying the accuracy of the simulation, the stress, strain, and void volume fraction distributions of the Ti6Al4V titanium alloy under different stress states were compared and analyzed. The results indicate that the mechanical properties of the local material significantly differ during downward pressing depending on the geometric shape. A three-dimensional tensile stress state was observed in the center area, where the void volume fraction was greater than the fracture void volume fraction. The fracture morphology of the samples further confirmed the presence of different stress states. Specifically, the fracture morphology of the globular head samples (with or without U-shaped notches) predominantly featured dimples. Modifying the specimen\u2019s geometry effectively increased stress triaxiality, facilitating the determination of the material\u2019s constitutive relationship under varying stress states.<\/jats:p>","DOI":"10.3390\/ma17174203","type":"journal-article","created":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T03:32:01Z","timestamp":1724643121000},"page":"4203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Small Punch Testing of a Ti6Al4V Titanium Alloy and Simulations under Different Stress Triaxialities"],"prefix":"10.3390","volume":"17","author":[{"given":"Kun","family":"Wang","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, 88 Anning West Road, Anning District, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xilong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Lanzhou Jiaotong University, 88 Anning West Road, Anning District, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeyu","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Lanzhou Jiaotong University, 88 Anning West Road, Anning District, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"80","DOI":"10.3901\/JME.2021.02.080","article-title":"Investigation on Small Punch Test with U-shaped Notch and Its Simulation","volume":"57","author":"Wang","year":"2021","journal-title":"J. Mech. Eng."},{"key":"ref_2","first-page":"557","article-title":"Fracture Behavior of Heat Affected Zone of Laser-welded Joint for Ti-6Al-4V titanium alloy: Experimental and Computational Study","volume":"92","author":"Zhao","year":"2013","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1179\/1743284713Y.0000000314","article-title":"Investigation on mechanical properties of laser welded joints for Ti-6AI-4V titanium alloy","volume":"29","author":"Zhao","year":"2013","journal-title":"Mater. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2957","DOI":"10.1177\/09544062211032988","article-title":"Investigation on the microstructure and mechanical properties of Ti6Al4V titanium alloy electron beam welding joint","volume":"236","author":"Zhao","year":"2022","journal-title":"Part C J. Mech. Eng. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6388","DOI":"10.1016\/j.ijhydene.2021.11.231","article-title":"Mechanical behavior of electrochemically hydrogenated electron beam melting (EBM) and wrought Ti\u20136Al\u20134V using small punch test","volume":"47","author":"Sabatani","year":"2022","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3182","DOI":"10.1007\/s11665-013-0614-z","article-title":"Small punch test of U-shaped notch of TC4 titanium alloy and its numerical simulation","volume":"22","author":"Zhao","year":"2013","journal-title":"J. Mater. Eng. Perform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"466","DOI":"10.3139\/146.111757","article-title":"Finite element simulation of the residual stress in Ti6Al4V titanium alloy laser welded joint","volume":"110","author":"Zhao","year":"2019","journal-title":"Int. J. Mater. Res."},{"key":"ref_8","first-page":"55","article-title":"Numerical calculation of fracture mechanics parameter J integral of narrow gap welded joint","volume":"35","author":"Tan","year":"2014","journal-title":"Trans. China Weld. Inst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106149","DOI":"10.1016\/j.engfailanal.2022.106149","article-title":"Characterization of creep deformation behavior of porous polymer membrane under Small-Punch test","volume":"135","author":"Kodaira","year":"2022","journal-title":"Eng. Fail. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"153263","DOI":"10.1016\/j.jnucmat.2021.153263","article-title":"Estimating damage parameters of a CuCrZr alloy subjected to two varying heat treatments using small punch test","volume":"557","author":"Vijayanand","year":"2021","journal-title":"J. Nucl. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103139","DOI":"10.1016\/j.tafmec.2021.103139","article-title":"Numerical analysis for characterizing hydrogen embrittlement behaviors induced in STS316L stainless steel using an in-situ small-punch test","volume":"116","author":"Shin","year":"2021","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"117332","DOI":"10.1016\/j.actamat.2021.117332","article-title":"Mechanism of brittle-to-ductile transition in tungsten under small-punch testing","volume":"220","author":"Zhang","year":"2021","journal-title":"Acta Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"142400","DOI":"10.1016\/j.msea.2021.142400","article-title":"Specimen size effect on evaluation of strength properties of 3Cr1MoV and Incoloy 800H using small punch test","volume":"832","author":"Wang","year":"2022","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.engfracmech.2011.08.011","article-title":"Investigation into plastic damage behavior of the CO2 laser deep penetration welded joint for Ti\u20136Al\u20134V alloy","volume":"83","author":"Zhang","year":"2012","journal-title":"Eng. Fract. Mech."},{"key":"ref_15","first-page":"299","article-title":"A systematic FEM analysis of the influence of mechanical properties in the reliability of the correlation methods in the small punch test","volume":"153","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111580","DOI":"10.1016\/j.matchar.2021.111580","article-title":"Effects of long-term thermal aging on elevated temperature deformation behaviors of wrought 316LN stainless steel by small punch test","volume":"182","author":"Fan","year":"2021","journal-title":"Mater. Charact."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"116501","DOI":"10.1016\/j.actamat.2020.116501","article-title":"Correlation of measured load-displacement curves in small punch tests with tensile stress-strain curves","volume":"204","author":"Leclerc","year":"2021","journal-title":"Acta Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102442","DOI":"10.1016\/j.tafmec.2019.102442","article-title":"Use of notched small punch test specimens for the determination of fracture properties in structural steels","volume":"106","author":"Belzunce","year":"2020","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104211","DOI":"10.1016\/j.euromechsol.2021.104211","article-title":"Predicting ductile fracture of cracked pipes using small punch test data","volume":"87","author":"Lee","year":"2021","journal-title":"Eur. J. Mech.-A\/Solids"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102627","DOI":"10.1016\/j.tafmec.2020.102627","article-title":"Study of estimation of ductile-brittle transition temperature using U-notched small punch test specimens","volume":"108","author":"Wang","year":"2020","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107906","DOI":"10.1016\/j.engfracmech.2021.107906","article-title":"Hydrogen embrittlement testing procedure for the analysis of structural steels with Small Punch Tests using notched specimens","volume":"253","author":"Zafra","year":"2021","journal-title":"Eng. Fract. Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.nucengdes.2012.03.023","article-title":"Comparison of mechanical properties in conventional and small punch tests of fractured anisotropic A350 alloy forging flange","volume":"247","author":"Song","year":"2012","journal-title":"Nucl. Eng. Des."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/j.prostr.2019.05.063","article-title":"Determination of J-initiation toughness using pre-cracked small punch test specimens","volume":"14","author":"Shikalgar","year":"2019","journal-title":"Procedia Struct. Integr."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"104482","DOI":"10.1016\/j.tafmec.2024.104482","article-title":"Exploring stress states of notched small punch test specimens with different notch types","volume":"132","author":"Ding","year":"2024","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_25","first-page":"357","article-title":"Porous rigid-plastic materials containing rigid inclusions: Yield function, plastic potential, and void nucleation","volume":"3","author":"Gurson","year":"1978","journal-title":"Phys. Metall. Fract. March"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1115\/1.3443401","article-title":"Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I\u2014Yield Criteria and Flow Rules for Porous Ductile Media","volume":"99","author":"Gurson","year":"1977","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF00015686","article-title":"On localization in ductile materials containing spherical voids","volume":"18","author":"Tvergaard","year":"1982","journal-title":"Int. J. Fract."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF00036191","article-title":"Influence of voids on shear band instabilities under plane strain conditions","volume":"17","author":"Tvergaard","year":"1981","journal-title":"Int. J. Fract."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"112947","DOI":"10.1016\/j.ijsolstr.2024.112947","article-title":"Numerical analysis of ductile fracture in stretch bending of AA6061-T6 aluminum alloy sheet using GTN damage model","volume":"301","author":"Maziar","year":"2024","journal-title":"Int. J. Solids Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.tafmec.2019.01.013","article-title":"Experimental and numerical analysis of creep and damage behavior of P92 steel by small punch tests","volume":"100","author":"Song","year":"2019","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.ijmecsci.2016.09.008","article-title":"Experimental and numerical study on shear-punch test of 6060 T6 extruded aluminum profile","volume":"118","author":"Qian","year":"2016","journal-title":"Int. J. Mech. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"152260","DOI":"10.1016\/j.jnucmat.2020.152260","article-title":"A novel methodology for estimating tensile properties in a small punch test employing in-situ DIC based deflection mapping","volume":"538","author":"Vijayanand","year":"2020","journal-title":"J. Nucl. Mater."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/17\/4203\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:42:27Z","timestamp":1760110947000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/17\/4203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,25]]},"references-count":32,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["ma17174203"],"URL":"https:\/\/doi.org\/10.3390\/ma17174203","relation":{},"ISSN":["1996-1944"],"issn-type":[{"type":"electronic","value":"1996-1944"}],"subject":[],"published":{"date-parts":[[2024,8,25]]}}}