Ural Federal University named after the first President of Russia B. N. Yeltsin, Yekaterinburg, Russia

D. A. Pavlov, Cand. Eng., Associate Prof., Dept. of Metal Forming, e-mail: d.a.pavlov@urfu.ru
M. V. Erpalov, Cand. Eng., Senior Researcher, Hydrogen Energy Research Laboratory

This article is devoted to the study of cylindrical specimens for tensile process. In the tensile testing practice, the Bridgman’s model, Davidenkov−Spiridonova’s model and Ostsemin’s model are used to calculate equivalent stresses. In this work, the effectiveness of the known methods for determining the equivalent stresses in the neck section was evaluated by reverse modeling in the Deform−2D program. In accordance with GOST 1497−84, a specimen diameter of 5 mm was adopted. Steel 09G2S was specified as the specimen material. Hardening curves for steel were obtained using an optical neck profile measurement system. The hardening curves were obtained taking into account of the neck curvature radius. The accuracy of determining the equivalent stresses was assessed by comparing the dependencies of the neck curvature radius on the strain obtained in the course of computer modeling and laboratory tests. A comparison was also made between the actual tensile force and the force obtained in the course of computer simulation.
The Research supported by Funding from the Ministry of Science and Higher Education of the Russian Federation, project FEUZ-2023-0015.

1. Bridgeman P. W. Studies in large plastic flow and fracture: with special emphasis on the effects of hydrostatic pressure. Translated from English. Moscow : Izdatelstvo inostrannoy literatury, 1955. 444 p.
2. Davidenkov N. N., Spiridonova N. I. Analysis of the state of stress in the neck of a tension test specimen. Proceedings ASTM. 1946. Vol. 46. pp. 1147–1158.
3. Ostsemin A. A. On the analysis of the stress state in the elliptical neck of a tensile sample. Problemy prochnosti. 2009. No. 4. pp. 19–28.
4. Gerbig D., Bower A., Savic V., Hector L. G. Coupling digital image correlation and finite element analysis to determine constitutive parameters in necking tensile specimens. International Journal of Solids and Structures. 2016. Vol. 97-98. pp. 496–509.
5. Vaz-Romero A., Rotbaum Y., Rodriguez-Martinez J. A., Rittel D. Necking evolution in dynamically stretched bars: New experimental and computational insights. Journal of the Mechanics and Physics of Solids. 2016. Vol. 91. pp. 216–239.
6. G’Sell C., Hiver J. M., Dahoun A., Souahi A. Video-controlled tensile testing of polymers and metals beyond the necking point. Journal of Materials Science. 1992. Vol. 27. pp. 5031–5039.
7. Vildeman V. E., Lomakin E. V., Tret’yakova T. V., Tret’yakov M. P. Development of inhomogeneous fields under postcritical deformation of steel specimens in extension. Mechanics of Solids. 2016. Vol. 51. pp. 612–618.
8. Sancho A., Cox M. J., Cartwright T., Davies C. M. et al. An experimental methodology to characterise post-necking behaviour and quantify ductile damage accumulation in isotropic materials. International Journal of Solids and Structures. 2019. Vol. 176-177. pp. 191–206.
9. Jones M., Hole M., Davies C. M. A comparison of stress triaxiality and strain distributions in notched bar geometries as determined by Bridgman expressions and finite element analysis. Procedia Structural Integrity. 2020. Vol. 28. pp. 2078–2085.
10. Lu F., Manik T., Andersen I. L., Holmedal B. A robust image processing algorithm for opticalbased stress-strain curve corrections after necking. Journal of Materials Engineering and Performance. 2021. Vol. 30. No. 6. pp. 4240–4253.
11. Shinkin V. N. Direct and inverse non-linear approximation of hardening zone of steel. Chernye Metally. 2019. No. 3. pp. 32–37.
12. Shinkin V. N. Influence of non-linearity of hardening curve on elasticoplastic bend of rectangular rod. CIS Iron and Steel Review. 2019. Vol. 17. pp. 39–42.
13. Kim J.-H., Serpantie A., Barlat F., Pierron F., Lee M.-G. Characterization of the post-necking strain hardening behavior using the virtual fields method. International Journal of Solids and Structures. 2013. Vol. 50 pp. 3829–3842.
14. Vorob’ev E. V. Peculiarities of neck formation under low-temperature discontinuous yield of metals. Part 1. Axisymmetric deformation. Strength of Materials. 2008. Vol. 40. pp. 350–355.
15. Erpalov M. V. A development of computer vision elements for processing the results of tensile tests of specimens and building diagrams of ultimate plasticity. IOP Conference Series: Materials Science and Engineering. 2020. Vol. 966. 012046.
16. Erpalov M. V. Evaluating the range of applicability of existing models of stress distribution in the neck forming on cylindrical specimens during tensile testing. IOP Conference Series: Materials Science and Engineering. 2020. Vol. 969. 012081.
17. Erpalov M. V., Khotinov V.A. Optical method to study post-necking material behavior. AIP Conference Proceedings. 2020. Vol. 2288. 030007.
18. GOST 1497–84. Metals. Methods of tension test. Introduced: 01.01.1986.