Deformation of Cylindrical Shell Made of 9X2 Steel Under Complex Loading

Abstract

The development of the construction industry in terms of the design and manufacture of shell structures of non-standard architectural forms made of materials with complex mechanical properties requires using modern integrated computer-aided design systems with step-by-step modeling of deformation of structural elements under operating conditions, as well as taking into account their subsequent behavior after accumulation of residual strains during plastic deformation. The purpose of the study is to simulate the process of plastic deformation of a thin-walled cylindrical shell made of 9X2 GOST 5950-2000 (Interstate Standard) steel under compression and torsion with theoretical calculations based on the general theory of elastoplastic processes by A.A. Ilyushin. The constitutive equations of the theory of elastoplastic processes by A.A. Ilyushin for complex loading path and deformation of materials in the deviatoric strain space are presented. Based on the presented solutions, according to the strain path of the 9X2 steel shell implemented in the model, the graphs showing the relation of the vector and scalar properties of the material to the arc length of the strain path are constructed. A conclusion is made about the degree of hardening of the material in question and its dependence on the magnitude of the angle of convergence at the kink point of the complex path. The graphs of changes in the constitutive plasticity functions with respect to the increments of the arc length of the strain path are presented.

About the authors

Stepan V. Cheremnykh

Tver State Technical University

Author for correspondence.
Email: cheremnykh_s.v@mail.ru
ORCID iD: 0000-0002-4620-117X
SPIN-code: 9323-8370

кандидат технических наук, доцент кафедры конструкций и сооружений

Tver, Russia

References

  1. Zubchaninov V.G. On the main hypotheses of the general mathematical theory of plasticity and the limits of theirapplicability. Proceedings of the Russian Academy of Sciences. Solid State Mechanics. 2020;6:73–81. (In Russ.) https://doi.org/10.31857/S0572329920060173
  2. Ilyushin A.A. Mechanics of a continuous medium. Moscow: Publishing House of Moscow State University, 1990. (In Russ.)
  3. Bondar V.S., Abashev D.R., Fomin D.Y. Comparative analysis of theories of plasticity under complex loading. Problems of strength and plasticity. 2022;84(4):493–510. (In Russ.) https://doi.org/10.32326/1814-9146-2022-84-4-493-510
  4. Bondar V.S., Abashev D.R., Petrov V.K. Construction of the Theory of Plasticity Irrelative of the Loading Surfaceand Associated Flow Law. Strength of Materials. 2021;53(4):550–558. https://doi.org/10.1007/s11223-021-00316-9
  5. Bondar V.S., Abashev D.R., Fomin D.Y. Theories of plasticity under complex loading along spatial trajectories ofdeformations. Bulletin of the Perm National Research Polytechnic University. Mechanics. 2021;4:41–48. (In Russ.) https://doi.org/10.15593/perm.mech/2021.4.05
  6. Bondar V.S., Abashev D.R., Fomin D.Y. Theories of plasticity under complex loading along flat deformationtrajectories. Bulletin of the Perm National Research Polytechnic University. Mechanics. 2021;3:35–47. (In Russ.) https://doi.org/10.15593/perm.mech/2021.3.04
  7. Gultyaev V.I., Bulgakov A.N. Experimental study of elastic-plastic deformation of structural materials on anautomated test complex of a CH-computer. Bulletin of the I.Ya. Yakovlev Chuvash State Pedagogical University. Series: Mechanics of the limit state. 2023;2(56):53–64. (In Russ.) https://doi.org/10.37972/chgpu.2023.56.2.006
  8. Zubchaninov V.G., Gultyaev V.I., Alekseev A.A., Savrasov I.A. Verification of the postulate of isotropy duringdeformation of alloy B95 along two-link polyline trajectories. Bulletin of the Moscow University. Series 1: Mathematics. Mechanics. 2023;5:47–52. (In Russ.) https://doi.org/10.55959/MSU0579-9368-1-64-5-7
  9. Zubchaninov V.G., Alekseev A.A., Gultyaev V.I., Alekseeva E.G. Processes of complex loading of structural steelalong a five-link piecewise polyline deformation trajectory. Bulletin of Tomsk State University. Mathematics and mechanics. 2019;61:32–44. (In Russ.) https://doi.org/10.17223/19988621/61/4
  10. Alekseev A., Zubchaninov V., Gultiaev V., Alekseeva E. Modeling of elastoplastic deformation of low-carbonsteel along multi-link plane strain trajectories. AIP Conference Proceedings. 2021;020001. https://doi.org/10.1063/5.0059630
  11. Zubchaninov V.G., Alekseev A.A., Gultiaev V.I., Alekseeva E.G. Modeling of elastoplastic deformation ofstructural steel by a trajectory containing three circles touching internally. Materials Physics and Mechanics. 2019;42(5): 528–534. https://doi.org/10.18720/MPM.4252019_6
  12. Bondar V.S., Abashev D.R. Refining the thermoplasticity theory for modeling of cyclic nonisothermic loadingprocesses. Journal of Mechanics of Materials and Structures. 2021;16(4):501–510. https://doi.org/10.2140/jomms.2021.16.501
  13. Bondar V.S., Abashev D.R. Mathematical Modeling of the Monotonic and Cyclic Loading Processes. Strength of Materials. 2020;52(3):366–373. https://doi.org/10.1007/s11223-020-00186-7
  14. Bondar V.S., Dansin V.V., Vu L.D., Duc N.D. Constitutive modeling of cyclic plasticity deformation and low– high-cycle fatigue of stainless steel 304 in uniaxial stress state. Mechanics of Advanced Materials and Structures. 2018;25(12):1009–1017. https://doi.org/10.1080/15376494.2017.1342882
  15. Temis Yu.M., Fakeev A.I. Model of the curve of non-isothermal cyclic deformation. Problems of strength and plasticity. 2013;75(1):5–10. (In Russ.)
  16. Bazhenov V.G., Zhestkov M.N. Numerical Modeling of Large Deformations for Porous Metals and Identificationof Carcass Deformation Diagrams. Mechanics of Composite Materials. 2021;56(6):747–754. https://doi.org/10.1007/ s11029-021-09920-x
  17. Bazhenov V.G., Zhestkov M.N. Computer Modeling Deformation of Porous Elastoplastic Materials and Identification their Characteristics Using the Principle of Three-dimensional Similarity. Journal of Siberian Federal Universit. Mathematics and Physics. 2021;14(6):746–755. https://doi.org/10.17516/1997-1397-2021-14-6-746-755
  18. Bazhenov V.G., Kazakov D.A., Nagornykh E.V. Modeling the behavior of elastic-plastic rods under tensiontorsion and constructing their diagrams of deformation to rupture, taking into account the type of stress-strain state. Reports of the Russian Academy of Sciences. Physics, technical sciences. 2021;501(1):23–28. (In Russ.) https://doi.org/10.31857/S268674002106002X
  19. Bazhenov V.G., Nagornykh E.V., Samsonova D.A. Modeling of elastoplastic buckling of a cylindrical shell withinitial shape imperfections and elastic filler under external pressure. AIP Conference Proceedings: 28th Russian Conference on Mathematical Modelling in Natural Sciences, 02–05 October 2019, Perm, Russia, 2020;2216:040001. https://doi.org/10.1063/5.0003598
  20. Cheremnykh S., Zubchaninov V., Gultyaev V. Deformation of cylindrical shells of steel 45 under complex loading. E3S Web of Conferences. 22nd International Scientific Conference on Construction the Formation of Living Environment, FORM 2019. 2019;04025. https://doi.org/10.1051/e3sconf/20199704025
  21. Cheremnykh S.V. Experimental study of elastic-plastic deformation of a cylindrical shell made of 45 steel. Construction mechanics of engineering structures and structures. 2021;17(5):519–527. (In Russ.) https://doi.org/10.22363/1815-5235-2021-17-5-519-527
  22. Cheremnykh S., Kuzhin M. Solution of the problem of stability of 40x steel shell. Journal of Physics: Conference Series. International Scientific Conference on Modelling and Methods of Structural Analysis, MMSA 2019. 2020;012191. https://doi.org/10.1088/1742-6596/1425/1/012191
  23. Bondar V.S., Abashev D.R. Constructing a memory surface for separating the processes of monotone and cyclicloads. Problems of strength and plasticity. 2022;84(3):364–375. (In Russ.) https://doi.org/10.32326/1814-9146-2022-84-3-364-375
  24. Bazhenov V.G., Nagornykh E.V. Numerical analysis of large elastoplastic deformations of bodies and media andidentification of their deformation diagrams under various types of loading. Scientific notes of Kazan University. Series: Physical and Mathematical Sciences. 2022;164(4):316–328. (In Russ.) https://doi.org/10.26907/2541-7746.2022.4.316-328
  25. Bazhenov V.G., Kazakov D.A., Osetrov S.L. Analysis of the limiting states of cylindrical elastoplastic shellsunder tension and combined loading by internal pressure and tension. Bulletin of the Perm National Research Polytechnic University. Mechanics. 2022;2:39–48. (In Russ.) https://doi.org/10.15593/perm.mech/2022.2.04
  26. Bazhenov V.G., Kazakov D.A., Kibets A.I. Formulation and numerical solution of the problem of loss of stabilityof elastoplastic shells of rotation with elastic filler under combined axisymmetric torsion loads. Bulletin of the Perm National Research Polytechnic University. Mechanics. 2022;3:95–106. (In Russ.) https://doi.org/10.15593/perm.mech/2022.3.10
  27. Abrosimov N.A., Elesin A.V., Igumnov L. Computer simulation of the process of loss of stability of compositecylindrical shells under combined quasi-static anddynamic loads. Advanced Structured Materials. 2021;137:125–137. https://doi.org/10.1007/978-3-030-53755-5_9

Copyright (c) 2024 Cheremnykh S.V.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies