{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T10:53:54Z","timestamp":1791111234168,"version":"4.1.0"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation (RSF)","doi-asserted-by":"publisher","award":["22-79-00162"],"award-info":[{"award-number":["22-79-00162"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Material characterization at moderate strain rates is an important factor for improving the adequacy and accuracy of analysis of structures operating under extreme conditions. In this paper, the deformation and fracture of Ti-5Al-2.5Sn alloys were studied utilizing the punch test at strain rates up to several hundred per second. Loading velocities from 0.0003 to 15 m\/s were realized during the spherical body penetration through a thin titanium plate. To describe the plastic flow and fracture of the Ti-5Al-2.5Sn alloy at strain rates ranging from 0.001 to 103 s\u22121, a micromechanical damage model was coupled with a viscoplastic constitutive model based on the dislocation dynamics. Numerical simulations of the punch test at 15 and 2 m\/s were carried out to validate used constitutive relations. It was verified that the simulated fracture shape and deflections were similar to experimental ones. It was found that dynamic punch test is suitable for validation of damage kinetics under complex stress states.<\/jats:p>","DOI":"10.3390\/ma16010416","type":"journal-article","created":{"date-parts":[[2023,1,2]],"date-time":"2023-01-02T03:08:59Z","timestamp":1672628939000},"page":"416","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mechanical Behavior of Titanium Alloys at Moderate Strain Rates Characterized by the Punch Test Technique"],"prefix":"10.3390","volume":"16","author":[{"given":"Vladimir V.","family":"Skripnyak","sequence":"first","affiliation":[{"name":"Department of Mechanics of Deformed Solid Body, National Research Tomsk State University, 634050 Tomsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kristina V.","family":"Iohim","sequence":"additional","affiliation":[{"name":"Department of Mechanics of Deformed Solid Body, National Research Tomsk State University, 634050 Tomsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7162-3983","authenticated-orcid":false,"given":"Vladimir A.","family":"Skripnyak","sequence":"additional","affiliation":[{"name":"Department of Mechanics of Deformed Solid Body, National Research Tomsk State University, 634050 Tomsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.msea.2014.11.099","article-title":"Enhanced yielding strength of near-\u03b1 Ti\u2013Al\u2013Zr\u2013Sn high temperature alloys","volume":"625","author":"Jayaprakash","year":"2015","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"141380","DOI":"10.1016\/j.msea.2021.141380","article-title":"Investigation on the deformation mechanism of Ti\u20135Al-2.5Sn ELI titanium alloy at cryogenic and room temperatures","volume":"818","author":"Lu","year":"2021","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1016\/j.jmatprotec.2007.04.027","article-title":"High temperature deformation in Ti\u20135Al\u20132.5Sn alloy","volume":"192\u2013193","author":"Tan","year":"2007","journal-title":"J. Mater. Process. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1016\/j.proeng.2017.10.954","article-title":"Mechanism-based constitutive equations for superplastic forming of TA15 with equiaxed fine grain structure","volume":"207","author":"Zhao","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"153","DOI":"10.14429\/dsj.36.5969","article-title":"Superplastic forming and diffusion bonding of titanium alloys","volume":"36","author":"Ghosh","year":"1986","journal-title":"Def. Sci. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1108\/AEAT-04-2019-0086","article-title":"Mechanical properties of near alpha titanium alloys for high-temperature applications\u2014A review","volume":"92","author":"Tabie","year":"2020","journal-title":"Aircr. Eng. Aerosp. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.ijplas.2018.07.014","article-title":"On computing the evolution of temperature for materials under dynamic loading","volume":"111","author":"Luscher","year":"2018","journal-title":"Int. J. Plast."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1063\/5.0085338","article-title":"Hexagonal close packed (hcp) alloys under dynamic impacts","volume":"131","author":"Skripnyak","year":"2022","journal-title":"J. Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"\u00c7akan, B.G., Soyarslan, C., Bargmann, S., and H\u00e4hner, P. (2017). Experimental and computational study of ductile fracture in small punch tests. Materials, 10.","DOI":"10.3390\/ma10101185"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10707","DOI":"10.1007\/s10853-021-05929-8","article-title":"Mechanics of the small punch test: A review and qualification of additive manufacturing materials","volume":"56","author":"Torres","year":"2021","journal-title":"Int. J. Mater. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11","DOI":"10.5334\/uproc.11","article-title":"European standard on small punch testing of metallic materials","volume":"Volume 1","author":"Bruchhausen","year":"2018","journal-title":"Ubiquity Proceedings"},{"key":"ref_12","first-page":"1282","article-title":"Modeling of ductile fracture using the dynamic punch test","volume":"47","author":"Dabboussi","year":"2005","journal-title":"Int. J. Mater. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF02323188","article-title":"Experimental investigation of dynamic punch tests on isotropic and composite materials","volume":"41","author":"Mason","year":"2001","journal-title":"Exp. Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"439","DOI":"10.4028\/www.scientific.net\/AMR.123-125.439","article-title":"Small punch test of LC4\/SiC metal matrix composites","volume":"123\u2013125","author":"Mak","year":"2010","journal-title":"Adv. Mater. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3957","DOI":"10.1177\/00219983221127007","article-title":"Small punch testing of Al-TiB2 composites fabricated by spark plasma sintering: A computational and experimental study","volume":"56","author":"Priel","year":"2022","journal-title":"J. Compos. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s11182-015-0552-3","article-title":"The features of fracture behavior of an aluminum-magnesium alloy AMg6 under high-rate straining","volume":"58","author":"Skripnyak","year":"2015","journal-title":"Russ. Phys. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.matdes.2013.09.069","article-title":"Constitutive modeling and the effects of strain-rate and temperature on the formability of Ti\u20136Al\u20134V alloy sheet","volume":"55","author":"Li","year":"2014","journal-title":"Mater. Des."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Li, H., Chen, S.-F., Zhang, S.-H., Xu, Y., and Song, H.-W. (2022). Deformation characteristics, formability and springback control of Titanium alloy sheet at room temperature: A review. Materials, 15.","DOI":"10.3390\/ma15165586"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.jmapro.2018.12.010","article-title":"Mechanical behaviour modelling and finite element simulation of simple part of Ti-6Al-4V sheet under hot\/warm stamping conditions","volume":"38","author":"Sirvin","year":"2019","journal-title":"J. Manuf. Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Skripnyak, V.V., Skripnyak, E.G., and Skripnyak, V.A. (2020). Fracture of titanium alloys at high strain rates and under stress triaxiality. Metals, 10.","DOI":"10.3390\/met10030305"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Skripnyak, V.V., and Skripnyak, V.A. (2021). Localization of Plastic Deformation in Ti-6Al-4V Alloy. Metals, 11.","DOI":"10.3390\/met11111745"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"267","DOI":"10.22226\/2410-3535-2021-3-267-272","article-title":"Plastic deformation of titanium alloy Ti-6Al-4V in a complex stressed state under tension at high-strain rates","volume":"11","author":"Skripnyak","year":"2021","journal-title":"Lett. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Skripnyak, V.V., and Skripnyak, V.A. (2022). Mechanical behavior of alpha titanium alloys at high strain rates, elevated temperature, and under stress triaxiality. Metals, 12.","DOI":"10.3390\/met12081300"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.jallcom.2013.08.009","article-title":"Estimation of the mechanical properties of metallic materials by means of the small punch test","volume":"582","author":"Belzunce","year":"2014","journal-title":"J. Alloys Compd."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5625427","DOI":"10.1155\/2022\/5625427","article-title":"Post-surface processing and virtual simulation analysis of ball-punch test on CP-Ti material","volume":"2022","author":"Vemula","year":"2022","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1080\/02670836.2016.1230168","article-title":"Modelling the small punch tensile behaviour of an aerospace alloy","volume":"33","author":"Lancaster","year":"2016","journal-title":"Mater. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107974","DOI":"10.1016\/j.matdes.2019.107974","article-title":"Determining tensile yield stresses from small punch tests: A numerical-based scheme","volume":"182","author":"Soyarslan","year":"2019","journal-title":"Mater. Des."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"110473","DOI":"10.1016\/j.matdes.2022.110473","article-title":"Derivation of material properties using small punch and shear punch test methods","volume":"215","author":"Lancaster","year":"2022","journal-title":"Mater. Des."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.commatsci.2003.08.031","article-title":"Determination of deformation and failure properties of ductile materials by means of the small punch test and neural networks","volume":"28","author":"Abendroth","year":"2003","journal-title":"Comput. Mater. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Huang, T., Zhan, M., Wang, K., Chen, F., Guo, J., Li, Y., Song, Z., and Bai, L. (2019). Forming limit stress diagram prediction of pure titanium sheet based on GTN Model. Materials, 12.","DOI":"10.3390\/ma12111783"},{"key":"ref_31","first-page":"497","article-title":"Experimental and numerical analysis of forming limit diagram (FLD) and forming limit stress diagram (FLSD)","volume":"2","author":"Safari","year":"2011","journal-title":"Mater. Sci. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.tafmec.2016.09.012","article-title":"Recent developments in small punch testing: Tensile properties and DBTT","volume":"86","author":"Bruchhausen","year":"2016","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10704-020-00428-4","article-title":"Identification of material parameters of a shear modified GTN damage model by small punch test","volume":"222","author":"Sun","year":"2020","journal-title":"Int. J. Fract."},{"key":"ref_34","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_35","first-page":"55","article-title":"Development and validation of small punch testing at NIST National Institute of Standards and Technology Interagency or Internal Report 8303","volume":"8303","author":"Lucon","year":"2020","journal-title":"Natl. Inst. Stand. Technol. Interag. Intern."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5039","DOI":"10.1007\/s11665-021-05603-9","article-title":"Small punch testing to estimate the tensile and fracture properties of additively manufactured Ti-6Al-4V","volume":"30","author":"Lucon","year":"2021","journal-title":"J. Mater. Eng. Perform."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/0022-3115(87)90092-4","article-title":"Development of a further-miniaturized specimen of 3 mm diameter for TJZM disk (0.3 mm) small punch tests","volume":"150","author":"Mao","year":"1987","journal-title":"J. Nucl. Mater."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1111\/j.1460-2695.2008.01259.x","article-title":"Use of the small punch test to determine the ductile-to-brittle transition temperature of structural steels","volume":"31","author":"Contreras","year":"2008","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_39","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_40","doi-asserted-by":"crossref","first-page":"054119","DOI":"10.1103\/PhysRevB.78.054119","article-title":"Thermal equations of state for titanium obtained by high pressure\u2014temperature diffraction studies","volume":"78","author":"Zhang","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1063\/1.327799","article-title":"A constitutive model for metals applicable at high-strain rate","volume":"51","author":"Steinberg","year":"1980","journal-title":"J. Appl. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.commatsci.2004.09.010","article-title":"Identification of material parameters of the Gurson\u2013Tvergaard\u2013Needleman model by combined experimental and numerical techniques","volume":"32","author":"Springmann","year":"2005","journal-title":"Comput. Mater. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3399","DOI":"10.1111\/ffe.13568","article-title":"A novel method to uniquely determine the parameters in Gurson\u2013Tvergaard\u2013Needleman model","volume":"44","author":"Zhang","year":"2021","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3555","DOI":"10.1016\/S0020-7683(02)00170-1","article-title":"Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria","volume":"39","author":"Becker","year":"2002","journal-title":"Int. J. Solids Struct."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Dodd, B., and Bai, Y. (2012). Experimental Methods. Adiabatic Shear Locatization, Elsevier.","DOI":"10.1142\/p934"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Sharkeev, Y., Vavilov, V., Skripnyak, V.A., Belyavskaya, O., Legostaeva, E., Kozulin, A., Chulkov, A., Sorokoletov, A., Skripnyak, V.V., and Eroshenko, A. (2018). Analyzing the deformation and fracture of bioinert titanium, zirconium and niobium alloys in different structural states by the use of infrared thermography. Metals, 8.","DOI":"10.3390\/met8090703"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0749-6419(98)00069-2","article-title":"Adiabatic shear localization in the dynamic punch test, Part I: Experimental investigation","volume":"15","author":"Roessig","year":"1999","journal-title":"Int. J. Plast."},{"key":"ref_48","unstructured":"Bai, Y., and Dodd, B. (1992). Adiabatic Shear Localization: Occurrence, Theories and Applications, Pergamon Press. [1st ed.]."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.tafmec.2016.09.002","article-title":"Damage modeling in small punch test specimens","volume":"86","author":"Cuesta","year":"2016","journal-title":"Theor. Appl. Fract. Mech."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/16\/1\/416\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:55:54Z","timestamp":1760118954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/16\/1\/416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,1]]},"references-count":49,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["ma16010416"],"URL":"https:\/\/doi.org\/10.3390\/ma16010416","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,1]]}}}