Numerical analysis of large elastoplastic deformations of bodies and continua and identification of their deformation diagrams under different types of loading

V.G. Bazhenov∗ , E.V. Nagornykh∗∗

National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603022 Russia

E-mail: ∗bazhenov@mech.unn.ru, ∗∗pavlyonkova@mech.unn.ru

Received September 19, 2022

 

ORIGINAL ARTICLE

Full text PDF

DOI: 10.26907/2541-7746.2022.4.316-328

For citation: Bazhenov V.G., Nagornykh E.V. Numerical analysis of large elastoplastic deformations of bodies and continua and identification of their deformation diagrams under different types of loading. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2022, vol. 164, no. 4, pp. 316–328. doi: 10.26907/2541-7746.2022.4.316-328. (In Russian)

 

Abstract

Based on the experimental-computational approach, a method for identifying deformation diagrams of elastoplastic materials by considering the inhomogeneity of the stress-strain state and large deformations was developed. Examples of the application of this method for various types of loading of the tested samples were presented: tension and torsion of cylindrical rods, kinetic indentation of a ball and a cylinder, dynamic compression of tablet samples, etc. A technique for interpolating the deformation diagram to take into account the type of stress state was proposed.

Keywords: experimental-computational approach, elastoplastic material, numerical technique, tension, torsion, compression, static and dynamic indentation, construction of true deformation diagrams, large plastic deformations

References

  1. Bazhenov V.G., Zefirov S.V., Kramarev L.N., Osetrov S.L., Pavlenkova E.V. A method for identification of the deformation and strength properties of materials under large deformations and inhomogeneous stress-strain state. Patent RF no. 2324162, 2008. (In Russian)
  2. Bazhenov V.G., Nagornykh E.V., Osetrov S.L., Osetrov D.L. Developing experimental-numerical methods for constructing true deformation diagrams of elastoplastic materials. In: Badriev I.B., Banderov V.V., Lapin S.A. (Eds.) Mesh Methods for Boundary-Value Problems and Applications. Lecture Notes in Computational Science and Engineering. Vol. 141. Springer, Cham, 2022, pp. 27–38. doi: 10.1007/978-3-030-87809-2 3.
  3. Bazhenov V.G., Kazakov D.A., Nagornykh E.V., Osetrov D.L., Ryabov A.A. Modeling the behavior of elastoplastic rods during tension-torsion deformation and plotting their strain diagram before rupture while taking into account the type of stress-strain state. Dokl. Phys., 2021, vol. 66, no. 11, pp. 311–315. doi: 10.1134/S102833582111001X.
  4. Bazhenov V.G., Lomunov V.K. Experimental and theoretical studying of neck formation under tension of a steel tubular sample to rupture. In: Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. Nizhny Novgorod, Izd. NNGU, 2001, no. 63, pp. 35–41. (In Russian)
  5. Bazhenov V.G., Zefirov S.V., Osetrov S.L. Experimental and computing method for identification of strain and strength properties of materials. Zavod. Lab. Diagn. Mater., 2006, vol. 72, no. 9, pp. 39–44. (In Russian)
  6. Bazhenov V.G., Zefirov S.V., Osetrov S.L. Method of identifying strain and strength properties of metals and alloys. Deform. Razrushenie Mater., 2007, no. 3, pp. 43–48. (In Russian)
  7. Bazhenov V.G., Osetrov S.L., Osetrov D.L. Analysis of stretching of elastoplastic samples and necking with edge effects. J. Appl. Mech. Tech. Phys., 2018, vol. 59, no. 4, pp. 693–698. doi: 10.1134/S0021894418040168.
  8. Bazhenov V.G., Kibets A.I., Laptev P.V., Osetrov S.L. Experimental and theoretical investigation of the limiting states of elastoplastic rods of different cross sections under tension. In: Problemy mekhaniki: Sb. st. k 90-letiyu so dnya rozhd. A.I. Ishlinskogo [Problems of Mechanics: A Collection of Articles Honoring the 90th Anniversary of A.I. Ishlinskii’s Birthday]. Klimov D.M. et al. (Eds.). Moscow, Fizmatlit, 2003, pp. 116–123. (In Russian)
  9. Bazhenov V.G., Kramarev L.N., Osetrov S.L. Experimental and theoretical studying of elastoplastic deformation and fracture of a steel ball when compressed between plates. In: Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. Nizhny Novgorod, Izd. NNGU, 2003, no. 65, pp. 85–91. (In Russian)
  10. Bazhenov V.G., Zefirov S.V., Kramarev L.N., Pavlenkova E.V. Modelling of the deformation processes and the localization of plastic deformations in the torsion-tension of solids of revolution. J. Appl. Math. Mech., 2008, vol. 72, no. 2, pp. 226–232. doi: 10.1016/j.jappmathmech.2008.04.001.
  11. Bazhenov V.G., Nagornykh E.V., Osetrov D.L., Ryabov A.A. Numerical and experimental analysis of tension-torsion processes in cylindrical samples made of 09g2s steel under large deformations before destruction. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 3, pp. 495–507. (In Russian)
  12. Bazhenov V.G., Kazakov D.A., Nagornykh E.V., Osetrov D.L., Ryabov A.A. The experimental and theoretical study of large deformations of cylindrical samples from steel 09G2S with stress concentrators under tension-torsion loading to failure. Vestn. Permsk. Nats. Issled. Politekh. Univ. Mekh., 2018, no. 4, pp. 69–81. doi: 10.15593/perm.mech/2018.4.06.
  13. Zubchaninov V.G. Mekhanika sploshnykh deformiruemykh sred [Mechanics of Continuous Deformable Media]. Tver, TGTU, ChuDo, 2000. 703 p. (In Russian)
  14. Ipatova A.V., Vildeman V.E. Construction of material functions of aluminum alloy D16T inelastic deformation based on the results of tests of tension and torsion. Vestn. Samar. Gos. Tekh. Univ. Ser. Fiz.-Mat. Nauki, 2012, no. 4, pp. 106–114. (In Russian)
  15. Malinin N.N. Prikladnaya teoriya plastichnosti i polzuchesti [Applied Theory of Plasticity and Creep]. Moscow, Mashinostroenie, 1975. 400 p. (In Russian)
  16. Lomakin E.V., Melnikov A.M. Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state. Mech. Solids, 2011, no. 1, pp. 77–89. doi: 10.3103/S0025654411010092.
  17. Kapustin S.A., Gorokhov V.A., Vilenskii O.Yu., Kaidalov V.B., Ruin A.A. Relations of the damaged medium model for materials subjected to thermal-radiation loading. Probl. Prochn. Plast., 2012, no. 74, pp. 5–15. (In Russian)
  18. Bondar V.S., Abashev D.R. Plastic deformation of materials sensitive to a type of stress state. Vestn. Permsk. Nats. Issled. Politekh. Univ. Mekh., 2018, no. 1, pp. 29–39. doi: 10.15593/perm.mech/2018.1.03.
  19. Vladimirov S.A., Trefilov S.I. Studying the process of deep deformation of samples with circular recess during stretching. Kosmonavt. Raketostr., 2017, no. 3, pp. 81–85. (In Russian)
  20. Kamaya M., Kawakubo M. A procedure for determining the true stress-strain curve over a large range of strains using digital image correlation and finite element analysis. Mech. Mater., 2011, vol. 43, no. 5, pp. 243–253. doi: 10.1016/j.mechmat.2011.02.007.
  21. Bazhenov V.G., Zefirov S.V., Osetrov S.L. Experimental and computing method for constructing true deformation diagrams at large strains on the basis of tests for hardness. Dokl. Phys., 2006, vol. 51, no. 3, pp. 118–121. doi: 10.1134/S1028335806030050.
  22. Bazhenov V.G., Osetrov D.L. Method of identification of dry and viscous friction forces and construction of dynamic deformation diagrams of metals in experiments with impact compression. Lobachevskii J. Math., 2019, vol. 40, no. 3, pp. 278–283. doi: 10.1134/S1995080219030065.
  23. Bazhenov V.G., Baranova M.S., Osetrov D.L., Ryabov A.A. Method for determining friction forces in experiments on shock compression and construction of dynamic stress-strain diagrams of metals and alloys. Dokl. Phys., 2018, vol. 63, no. 8, pp. 331–333. doi: 10.1134/S1028335818080049.
  24. Bazhenov V.G., Kotov V.L. Method for identifying elastoplastic properties of ground media by penetration of impactors. Mech. Solids, 2008, vol. 43, no. 4, pp. 678–684. doi: 10.3103/S002565440804016X.
  25. Bazhenov V.G., Kotov V.L. Determination of dynamic-compressibility parameters and of shear strength for a ground medium by the striker-penetration method. Dokl. Phys., 2006, vol. 51, no. 5, pp. 279–282. doi: 10.1134/S1028335806050120.

 

The content is available under the license Creative Commons Attribution 4.0 License.