Заводская лаборатория. Диагностика материалов

Расширенный поиск
Доступ открыт Открытый доступ  Доступ закрыт Только для подписчиков

The stress-strain curve model in the form of an extremal of a non-integrable linear variation form

Полный текст:


The article develops an idea that the stress-strain curve for an arbitrary material is the extremum of some functional. However, for irreversible processes, the using of the principle of stationarity of some functional is incorrect, because due to the dissipation of the deformation process, the possible work of internal forces is non-integrable. Therefore, it is proposed to use the generalized variational principle of L. I. Sedov for modeling the stress-strain curve of elastoplastic materials. A concept of sequential inclusion of certain deformation mechanisms on different segment of the stress-strain curve is proposed. According to this concept, each section of the stress-strain curve must correspond either to the stationary value of the corresponding functional, or to the stationary value of the non-integrated form of variations of the corresponding stress derivatives. The combination of naturally obtained spectra of boundary conditions at the ends of each segment leads to a variation-consistent formulation of the system of boundary and contact conditions of solutions of different differential equations on each segment of stress-strain curve. As a result, it is possible to construct a differentiable stress-strain curve over the entire area of the stress-strain curve definition. The resulting solution, in contrast to the Ramberg - Osgood empirical law, has a strictly liner segment. The obtained mathematical model was tested on experimental data of materials for various industrial purposes. The achieved accuracy of the mathematical model is sufficient for engineering applications.

Об авторе

N. Y. Golovina
Tyumen Industrial University

Natalia Ya. Golovina

625000, Tyumen, Volodarskogo ul., 38

Список литературы

1. Ramberg W., Osgood W. R. Description of stress-strain curves by three parameters. National Advisory Committee For Aeronautics / Technical Note N 902. Washington, DC, 1943.

2. Mendelson A. Plasticity: Theory, and Application. — Malabar: Krieger, 1968. — 183 p. [in Russian].

3. Papirno R. Goodness-of-Fit of the Ramberg - Osgood Analytic Stress-Strain Curve to Tensile Test Data / J. Testing Eval. 1982. Vol. 6. N 10. E 263 - 268. DOI:10.1520/JTE10264J

4. Hollomon J. H. Tensile deformation / Trans. AIME. 1945. Vol. 162. E 268 - 290.

5. Ludwigson D. C. Modified stress — strain relation for FCC metals and alloys / Metall Trans. 1971. Vol. 2. N 10. E 2825 - 2828.

6. Ludwik P. Elemente der technologischen Mechanik. — Berlin: Springer, 1909. — 57 p. [in Russian].

7. Swift Pi. W. Plastic instability under plane stress / J. Mech. Phys. Solids. 1952. Vol. 1. N 1. E 1 - 18.

8. Voce E. The relationship between stress and strain for homogeneous deformation / J. Inst. Metals. 1948. N 74. E 537 - 562.

9. Gao Pi. S. Modeling Stress Strain Curves for Nonlinear Analysis / Materials Science Forum 2009. E 575 - 578, 539 - 544. DOI:10.4028/

10. Rasmussen K. Full-range stress-strain curves for stainless steel alloys / J. Constr. Steel Res. 2003. Vol. 59. N 1. E 47 - 61. DOI:10.1016/S0143-974X(02)00018-4

11. Belov P. A., Golovina N. Ya. Generalization of the Ramberg - Osgood Model for Elastoplastic Materials / J. Mater. Eng. Perform. 2019. Vol. 28. N 12. E 7342 - 7346. DOI:10.1007/sll665-019-04422-3

12. Belov P. A., Golovina N. Ya. Stress-strain curve as an extremal of some functional / Science and Business: Development Ways. 2019. Vol. 10. N 100. E 44 - 52.

13. Abdella K. Inversion of a full-range stress — strain relation for stainless steel alloys / Int. J. Non-Lin. Mech. 2006. N 41. E 456 - 463.

14. Golovina N. Ya. Comparative analysis of fatique models of plastic materials / XII All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics Collected Works. 2019. Vol. 4. E 611 - 613.

15. Gardner L., Yun X., Fieber A., Macorini L. Steel Design by Advanced Analysis: Material Modeling and Strain Limits / Engineering. 2019. N 5. E 243 - 249.

16. Golovina N. Ya., Krivosheeva S. Y. Research in area of longevity of sylphon scraies / IOP Conference Series: Earth and Environmental Science. Current Problems and Solutions. 2018. Vol. 12. N 3. E 012043.

17. Golovina N. Ya. The nonlinear stress-strain curve model as a solution of the fourth order differential equation / Int. J. Press. Vess. Piping. 2021. N 189. E 104258. DOI:10.1016/j.ijpvp.2020.104258

18. Golovina N. Ya. Modeling the Stress-Strain Curve of Elastic-Plastic Materials / Solid State Phenomena. 2021. N 316. E 936 - 941.

19. Quach W. M. Three-Stage Full-Range Stress-Strain Model for Stainless Steels / J. Struct. Eng. 2008. N 134. E 1518 - 1527.

20. Plertele S., De Waele W., Denys R. A generic stress — strain model for metallic materials with two-stage strain hardening behavior / Int. J. Non-Lin. Mech. 2011. Vol.46. N3 . E 519-531.

21. Li Т., Zheng J., Chen Z. Description of full-range strain hardening behavior of steels / Springer Plus. 2016. N 5. E 1316. DOI:10.1186/s40064-016-2998-3

22. Belov P. A., Gorshkov A. G, Lurie S. A. Variational model of nonholonomic 4D media / Rigid Body Mech. 2006. N 6. E 29 - 46.

23. Belov P. A., Lurie S. A. Variation model of non-holonomic media / Mech. Composite Mater. Designs. 2001. Vol. 7. N 2. P 266 - 276.

24. Golovina N. Ya. PhD thesis, Tyumen State Oil and Gas University, 2002. (accessed 2021-03-22).

25. Walport E, Gardner L., Real E., et al. Effects of material nonlinearity on the global analysis and stability of stainless steel frames / J. Constr. Steel Res. 2019. N 152. E 173 - 182. DOI:10.1016/j.jcsr.2018.04.019

26. Arrayago I., Real E., Gardner L. Description of stress-strain curves for stainless steel alloys / Materials and Design. 2015. N 87. E 540 - 552. DOI:10.1016/j.matdes.2015.08.001

27. Mirambell E., Real E. On the calculation of deflections in structural stainless steel beams: an experimental and numerical investigation / J. Constr. Steel Res. 2000. N 54. E 109 - 133.

28. Yun X., Gardner L. The continuous strength method for the design of cold-formed steel non-slender tubular cross-sections / Engineering Structures. 2018. N 175. E 549 - 564. DOI:10.1016/j.engstruct.2018.08.070

29. Golovina N. Ya. Stress-Strain Curve as Extremal of Some Functional / J. Mater. Eng. Perform. 2021. Vol. 30. N 6. E 4641-4650. DOI:10.1007/sll665-021-05768-3

30. Golovina N. Ya., Belov P. A. Analysis of empirical models of deformation curves of elastoplastic materials (review). Part 1 / Math. Model. Comput. Meth. 2022. N 1. E 63 - 96.


Для цитирования:

Golovina N.Y. The stress-strain curve model in the form of an extremal of a non-integrable linear variation form. Заводская лаборатория. Диагностика материалов. 2023;89(3):80-88.

For citation:

Golovina N.Y. The stress-strain curve model in the form of an extremal of a non-integrable linear variation form. Industrial laboratory. Diagnostics of materials. 2023;89(3):80-88.

Просмотров: 138

ISSN 1028-6861 (Print)
ISSN 2588-0187 (Online)