Journals →  Chernye Metally →  2022 →  #2 →  Back

Rolling and Tubemaking
ArticleName Moment at elastic-plastic bending of steel sheet. Part 2. Cubic approximation of steel's hardening zone
DOI 10.17580/chm.2022.02.03
ArticleAuthor V. N. Shinkin
ArticleAuthorData

National University of Science and Technology “MISiS”, Moscow, Russia:

V. N. Shinkin, Dr. Phys.-Math., Professor, Dept. of Physics, e- mail: shinkin-korolev@yandex.ru

Abstract

The classical approximations by P. Ludwik and A. Nadai of the steel hardening zone do not accurately describe the plastic deformation of steel. That often leads to the significant errors (defects) in the final form of metal products made from a steel sheet during its forming (based on the preliminary analytical and numerical calculations of the given model of metallurgical production) on the presses and dies. For example, the Nadai’s curve does not pass through the ultimate strength’s point of the experimental curve, signifi cantly exceeding the ultimate strength at this point, which is not permissible at calculating stresses and deformations. The Ludwik’s curve does not take into account the elastic deformation zone of the steel (immediately has a stress equal to the yield strength at zero relative deformation) and does not have the maximum (observed on the experimental curve) at the point of the ultimate strength. To eliminate the above-mentioned disadvantages, in the first published part of the paper, the author considered the parabolic approximations of the steel hardening zone in the form of the second-order polynomials, which satisfy three boundary conditions. The constructed parabolic approximations of the steel hardening zone turned out to be an order of magnitude more accurate than the classical approximations by Ludwik and Nadai. In this paper, the author considers even more exact cubic approximations of the steel hardening zone with the same supporting parameters of the experimental curve of the steel hardening zone. In this case, the cubic approximations already satisfy four boundary conditions. The constructed cubic approximations of the steel hardening zone are two orders of magnitude more accurate than the classical approximations by Ludwik and Nadai of the steel hardening zone.

keywords Steel sheet, bending, steel hardening, elasticity, plasticity, normal stress, bending moment, boundary conditions, cubic approximation
References

1. Shinkin V. N. Moment at elastic-plastic bending of steel sheet. Part 1. Parabolic approximation of steel`s hardening zone. Chernye metally. 2021. No. 3. pp. 22–27.
2. Fadeev V., Kondrushin A. Special aspects of determining parameters for continuous deformation of pipe billets for the specified pipes size range. Materials Today: Proceedings. 2021. Vol. 38. pp. 1322–1325.
3. Belskiy S. M., Pimenov V. A., Shkarin A. N. Mathematical model for evaluating the actual form of the profile’s contour of the hot-rolled strip’s cross section. Journal of Chemical Technology and Metallurgy. 2020. Vol. 56. No. 1. pp. 214–220.
4. Shinkin V. N. Simple analytical dependence of elastic modulus on high temperatures for some steels and alloys. CIS Iron and Steel Review. 2018. Vol. 15. pp. 32–38.
5. Shinkin V. N. Preliminary straightening of steel strip. Chernye metally. 2018. No. 5. pp. 34–40.
6. Ushakov I. V., Simonov Yu. V. Formation of surface properties of VT18u titanium alloy by laser pulse treatment. Materials Today: Proceedings. 2019. Vol. 19. No. 5. pp. 2051–2055.
7. Gurevich L. M., Novikov R. E., Bannikov A. I., Pronichev D. V., Frunkin D. B. Finite element simulation of the influence of the bending roll profi le on the stress-strain state of billets for longitudinal-welded rolled pipes. Communications in Computer and Information Science. 2021. Vol. 1437. pp. 284–299.
8. Belskiy S. M., Shopin I. I., Safronov A. A. Improving efficiency of rolling production by predicting negative technological events. Defect and Diffusion Forum. 2021. Vol. 410. pp. 96–101.
9. Yamnikov A. S., Matveev I. A., Rodionova E. N. Relationship of the method of obtaining the original billet with the accuracy of manufacturing of the extended axisymmetric bodies. CIS Iron and Steel Review. 2020. Vol. 20. pp. 25–28.
10. Ushakov I. V. How a crack and the defect material in its neighborhood affect the radiation strength of transparent materials. Journal of Optical Technology. 2008. Vol. 75. No. 2. pp. 128–131.
11. Goncharuk A. V., Fadeev V. A., Kadach M. V. Seamless pipes manufacturing process improvement using mandreling. Solid State Phenomena. 2021. Vol. 316. pp. 402–407.
12. Li S., Wei C., Long Y. Deformation analysis of engineering reinforcement straightening based on Bauschinger effect. International Journal of Steel Structures. 2020. Vol. 20. No. 1. pp. 1–12.

Language of full-text russian
Full content Buy
Back