I. V. Fedotov, A. S. Frolov, and B. A. Gurovich

FEATURES OF THE STRESS-STRAIN STATE IN THE NECK OF A RING SPECIMEN UNDER TENSION ON SEMICIRCULAR CYLINDRICAL MANDRELS

In this paper, the stress-strain state of a ring specimen under tension on semicircular cylindrical mandrels is analyzed by three-dimensional finite-element modeling. The material of unirradiated fuel cladding, namely cold-worked EK164-ID austenitic steel, is used as an example. The hardening curve of the material is determined by the iterative inverse method. The finite element model is validated by the variation of the geometrical parameters of the specimen gauge areas. The modeling results show that, before failure, the neck of the ring specimen experiences a triaxial stress state characterized by a pronounced non-uniform distribution of plastic strains and stresses along the neck cross-section. This limits the possibility of interpreting the stress-strain state in terms of plane-stress or plane-strain approximation. The analytical expressions proposed in the literature for interpreting the stress-strain state in the neck of a flat specimen with a rectangular cross-section under tension have limited applicability to similar areas of a ring specimen, and they may cause significant errors in the experimental determination of the hardening curve and the stress triaxiality factor. The effectiveness of applying 3D finite element modeling combined with the iteration procedure of plotting the hardening curve in order to analyze the stress-strain state in a ring specimen under tension on cylindrical semicircular mandrels is demonstrated. The critical values of equivalent stress, equivalent plastic strain, and the stress triaxiality factor in the neck of a ring specimen before failure are determined for the cold-worked EK164-ID austenitic steel.

References:

1. Gurovich, B.A., Frolov, A.S., Kuleshova, E.A., and Fedotov, I.V. Long-term high-temperature exposure effects on mechanical properties and structure of the 42XNM alloy after neutron irradiation in the VVER-1000. Part 1. Mechanical tests. Voprosy Materialovedeniya, 2023, 113 (1),134–149. (In Russian). DOI: 10.22349/1994-6716-2023-113-1-134-149.
2. Frolov, A.S., Fedotov, I.V., and Gurovich, B.A. Evaluation of the true-strength characteristics for isotropic materials using ring tensile test. Nucl. Eng. Technol., 2021, 53 (7), 2323–2333. DOI: 10.1016/j.net.2021.01.033.
3. Karagergi, R.P., Konovalov, A.V., Evseev, M.V., and Kozlov, A.V. Construction of a strainhardening diagram to analyze the state of stress in the fuel-element cladding material. Russian Metallurgy, 2023, 1528–1534. DOI: 10.1134/S0036029523100117.
4. Karagergi, R.P., Kozlov, A.V., Yarkov, V.Yu., Pastukhov, V.I., and Barsanova, S.V. Microstructure of fracture surfaces after radial compression of annular specimens made of cladding austenitic steel exposed to damaging dose above 100 dpa. Physics of Metals and Metallography, 2024, 125 (6), 665–672. DOI: 10.1134/S0031918X2460043X.
5. Konovalov, A.V., Vichuzhanin, D.I., Partin, A.S., and Kozlov, A.V. Determination of true stress-strain (hardening) curve for the fuel rod material. Zavodskaya Laboratoriya. Diagnostika Materialov, 2017, 83 (7), 58–61. (In Russian).
6. Leontyeva-Smirnova, M.V., Izmalkov, I.N., Valitov, I.R., Loshmanov, L.P., Kostyukhina, A.V., Fedotov, P.V., Murzakhanov, G.H., and Baskakov, A.V. Determination of the yield strength of EK-181 steel during tensile testing of ring specimen. Zavodskaya Laboratoriya. Diagnostika Materialov, 2016, 82 (10), 56–61. (In Russian).
7. Kamaya, M., Kitsunai, Y., and Koshiishi, M. True stress-strain curve acquisition for irradiated stainless steel including the range exceeding necking strain. J. Nucl. Mater., 2015, 465, 316–325. DOI: 10.1016/j.jnucmat.2015.05.027.
8. Zouari, A., Bono, M., Le Boulch, D., Le Jolu, T., Crépin, J., and Besson, J. The effect of strain biaxiality on the fracture of zirconium alloy fuel cladding. J. Nucl. Mater., 2021, 554, 153070 (1–13). DOI: 10.1016/j.jnucmat.2021.153070.
9. Frolov, A.S. and Fedotov, I.V. Methodology of mechanical testing for fuel rod cladding materials of Russian nuclear reactors. Voprosy Atomnoy Nauki i Tekhniki. Seriya Fizika Yadernykh Reaktorov, 2024, 5, 75–97. (In Russian).
10. Leontieva-Smirnova, M.V., Kalin, B.A., Morozov, E.M., Kostyukhina, A.V., Fedotov, P.V., and Taktashev, R.N. Methodical features of tensile testing of ring samples. Inorg. Mater. Appl. Res., 2020, 11, 731–738. DOI: 10.1134/S2075113320030302.
11. Bridgman, P.W. Issledovanie bolshykh plasticheskikh deformatsiy i razryva [Studies in Large Plastic Flow and Fracture]. Librokom Publ., Moscow, 2010. 448 p. (In Russian).
12. Ostsemin, A.A. On the analysis of stress state in elliptical tensile neck. Strength of Materials, 2009, 41, 356–362. DOI: 10.1007/s11223-009-9147-y.
13. Tu, S., Ren, X., He, J., and Zhang, Z. Stress-strain curves of metallic materials and post-necking strain hardening characterization: a review. J. Nucl. Mater., 2020, 43 (1), 3–19. DOI: 10.1111/ffe.13134.
14. Bazhenov, V.G., Kazakov, D.A., Kukanov, S.S., Osetrov, D.L., and Ryabov, A.A. Analysis of methods for constructing true deformation diagrams of elastoplastic materials under large deformations. Vestnik PNIPU. Mekhanika, 2023, 4, 12–22. (In Russian). DOI: 10.15593/perm.mech/2023.4.02.
15. Wang, L. and Tong, W. Identification of post-necking strain hardening behavior of thin sheet metals from image-based surface strain data in uniaxial tension tests. Int. J. Solids Struct., 2015, 75–76, 12–31. DOI: 10.1016/j.ijsolstr.2015.04.038.
16. Gussev, M.N., Garrison, B., Massey, C., Le Coq, A., Linton, K., and Terrani, K.A. A correlation-based approach for evaluating mechanical properties of nuclear fuel cladding tubes. J. Nucl. Mater., 2023, 574, 154192 (1–12). DOI: 10.1016/j.jnucmat.2022.154192.
17. GOST 1497–2023 (ISO 6892–1). (In Russian).
18. Zhang, Z.L., Hauge, M., Ødegård, J., and Thaulow, C. Determining material true stress-strain curve from tensile specimens with rectangular cross-section. Int. J. Solids Struct., 1999, 36 (23), 3497–3516. DOI: 10.1016/S0020-7683(98)00153-X.
19. Choung, J.M. and Cho, S.R. Study on true stress correction from tensile tests. Journal of Mechanical Science and Technology, 2008, 22 (6), 1039–1051. DOI: 10.1007/s12206-008-0302-3.
20. De Wang, Y., Xu, S.H., Ren, S.B., and Wang, H. An experimental-numerical combined method to determine the true constitutive relation of tensile specimens after necking. Adv. Mater. Sci. Eng., 2016, 2016, 6015752 (1–12). DOI: 10.1155/2016/6015752.
21. Mu, Z., Zhao, J., Yu, G., Huang, X., Meng, Q., and Zhai, R. Hardening model of anisotropic sheet metal during the diffuse instability necking stage of uniaxial tension. Thin-Walled Structures, 2021, 159, 107198, 1–14. DOI: 10.1016/j.tws.2020.107198.
22. Korn, G. and Korn, T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [Mathematical Handbook for Scientists and Engineers]. Nauka Publ., Moscow, 1984, 833 p. (In Russian).
23. Joun, M., Choi, I., Eom, J., and Lee, M. Finite element analysis of tensile testing with emphasis on necking. Comput. Mater. Sci., 2007, 41 (1), 63–69. DOI: 10.1016/j.commatsci.2007.03.002.
24. Berezhnoi, D.V. and Paimushin, V.N. Two formulations of elastoplastic problems and the theoretical determination of the location of neck formation in samples under tension. Journal of Applied Mathematics and Mechanics, 2011, 75 (4), 635–659. DOI: 10.1016/j.jappmathmech.2011.09.009.
25. Kukudzhanov, V.N. and Levitin, A.L. Rheological instability and localization of strains in plane elastoplastic specimens under extension. Mechanics of Solids, 2005, 40 (6), 69–80.
26. Zhao, K., Wang, L., Chang, Y., and Yan, J. Identification of post-necking stress-strain curve for sheet metals by inverse method. Mech. Mater., 2016, 92, 107–118. DOI: 10.1016/j.mechmat.2015.09.004.
27. Wildemann, V.E., Mugatarov, A.I., and Khmelev, A.A. Computational-experimental method for stress-strain curve constructing under conditions of inhomogeneous stress fields. Vestnik PNIPU. Mekhanika, 2024, 2, 24–32. (In Russian). DOI: 10.15593/perm.mech/2024.2.03.
28. Kamaya, M. and Kawakubo, M. True stress-strain curves of cold worked stainless steel over a large range of strains. J. Nucl. Mater., 2014, 451 (1–3), 264–275. DOI: 10.1016/j.jnucmat.2014.04.006.
29. Marth, S., Häggblad, H.Å., Oldenburg, M., and Östlund, R. Post necking characterisation for sheet metal materials using full field measurement. J. Mater. Process. Technol., 2016, 238, 315–324. DOI: 10.1016/j.jmatprotec.2016.07.036.
30. Kim, J.S. and Kim, J.M. Prediction of the irradiation effect on the fracture toughness for stainless steel using a stress-modified fracture strain model. Int. J. Mech. Sci., 2024, 264, 108860, 1–16. DOI: 10.1016/j.ijmecsci.2023.108860.
31. Mase, G.E. Teoriya i zadachi mekhaniki sploshnykh sred [Theory and Problems of Continuum Mechanics]. LKI Publ., Moscow, 2007, 318 p. (In Russian).
32. Kolmogorov, V.L., Bogatov, A.A., Migachev, B.A., Zudov, E.G., Freydenzon, Yu.E., and Freydenzon, M.E. Plastichnost i razrushenie [Plasticity and Destruction]. Metallurgiya Publ., Moscow, 1977, 336 p. (In Russian).
33. Bai, Yu. Effect of Loading History on Necking and Fracture: Cand. Thesis, Massachusetts, USA, 2008, 262 p. Available at: https://www.researchgate.net/publication/38003378

Article reference