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Rolling and other Metal Forming Processes
ArticleName Analytical approximation of bending moment under repeated elastoplastic bending of steel sheet
ArticleAuthor V. N. Shinkin

National University of Science and Technology (Moscow, Russia):

V. N. Shinkin, Dr. Phys.-Math., Prof., e-mail:


At the up-to-date production of steel thick-walled pipes of large diameter for the main gas-and-oil pipelines, the steel sheet is bent sequentially several times during the technological transitions from one press to another. So, at the production of the steel large-diameter pipes by UOE-technology on TESA 1020, the steel sheet is bent sequentially on the flanging press, pre-shaping press (giving the sheet a U-shape) and final-shaping press (giving the sheet an O-shape). At the deformation of the steel sheet on the O-press, there is a hysteresis of the mechanical properties of the sheet: the excessively curved areas of the sheet are partially unbent by the press, and the insufficiently curved areas receive an additional bending in the original direction. At straightening of steel sheet on the multi-roller sheet-straightening machines (the sighn-alternating bending of the sheet between the working rollers of the machine) also observed a low-cycle hysteresis of the mechanical properties of the sheet. The calculation of the sheet’s curvature at the sighn-alternating bending causes the great difficulties for the metallurgical technologists because of the effect of the Bauschinger’s effect under bending. In this paper, we propose the analytical method for calculating of the final curvature of the thick steel sheet at hysteresis (at sighn-alternating bending). The results of the work can be applied in metallurgy at the production of the thick-walled largediameter steel pipes.

keywords Steel sheet, elastoplastic deformation, yield strength, bending moment, sheet’s curvature, steel large-diameter pipes

1. Bauschinger J. Die Veranderungen die elastizitatsgrenze. Mittheilungen aus dem mechanisch-technischen Laboratorium der Königlichen technischen Hochschule in München. 1886. Bd. 13. Heft 5. S. 1–31.
2. Moskvitin V. V. Plasticity under variable loads. Moscow : MGU, 1965. 263 p.
3. Lenard J. G. Metal Forming Science and Practice. Elsevier Science, 2002. 378 p.
4. Birger I. A. Residual stresses. Moscow : URSS, 2015. 231 p.
5. Rabotnov Yu. N. Mechanics of deformable solid. Moscow : Lenand, 2019. 712 p.
6. Klocke F. Manufacturing processes 1. Cutting. Springer, 2011. 506 p.
7. Wilko C. E. Formability. A review of parameters and processes that control, limit or enhance the formability of sheet metal. Springer, 2011. 112 p.
8. Shinkin V. N. Springback coefficient of round steel beam under elastoplastic torsion. CIS Iron and Steel Review. 2018. Vol. 15. pp. 23–27.
9. 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.
10. Banabic D. Sheet metal forming processes. Constitutive modelling and numerical simulation. Springer, 2010. 301 p.
11. Frank V. Lecture notes in production engineering. Springer, 2013. 211 p.
12. Calladine C. R. Plasticity for engineers. Theory and applications. Woodhead Publishing, 2000. 328 p.
13. Lin J., Balint D., Pietrzyk M. Microstructure evolution in metal forming processes. Woodhead Publishing, 2012. 416 p.
14. Chakrabarty J. Theory of plasticity. Butterworth-Heinemann, 2006. 896 p.

15. Predeleanu M., Gilormini P. Advanced methods in materials processing defects. Vol. 45. Elsevier Science, 1997. 422 p.
16. Rees D. Basic engineering plasticity. An introduction with engineering and manufacturing applications. Butterworth-Heinemann, 2006. 528 p.
17. Shinkin V. N. Elastoplastic flexure of round steel beams. 1. Springback coefficient. Steel in Translation. 2018. Vol. 48, No. 3. pp. 149–153.
18. Shinkin V. N. Elastoplastic flexure of round steel beams. 2. Residual Stress. Steel in Translation. 2018. Vol. 48, No. 11. pp. 718–723.
19. Hu J., Marciniak Z., Duncan J. Mechanics of Sheet Metal Forming. Butterworth-Heinemann, 2002. 211 p.
20. Predeleanu M., Ghosh S. K. Materials processing defects. Elsevier Science, 1995. Vol. 43. 434 p.
21. Bhattacharyya D. Composite sheet forming. Elsevier Science, 1997. Vol. 11. 530 p.
22. Kang S.-J. Sintering. Densification, grain growth and microstructure. Butterworth-Heinemann, 2004. 280 p.
23. Banabic D. Multiscale modelling in sheet metal forming. Springer, 2016. 405 p.
24. Chakrabarty J. Applied plasticity. Springer, 2010. 758 p.
25. Shinkin V. N. Preliminary straightening of steel strip. Chernye Metally. 2018. No. 5. pp. 34–40.
26. Shinkin V. N. Direct and inverse non-linear approximation of hardening zone of steel. Chernye Metally. 2019. No. 3. pp. 32–37.
27. Klocke F. Manufacturing processes 4. Forming. Springer, 2013. 516 p.
28. Gorshkov A. G., Starovoitov E. I., Tarlakovskij D. V. Theory of elasticity and plasticity. Moscow : Fizmatlit, 2002. 416 p.
29. Makhutov N. A. Structural strength, resource and technogenic safety. Part 1. Criteria of strength and resource. Novosibirsk : Nauka, 2005. 494 p.
30. Hingole R. S. Advances in metal forming. Expert system for metal forming. Springer, 2015. 116 p.
31. Lim Y., Venugopal R., Ulsoy A. G. Process control for sheet-metal stamping process modeling, controller design and stop-floor implementation. Springer, 2014. 140 p.
32. Qin Y. Micromanufacturing engineering and technology. William Andrew, 2015. 858 p.

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