Bauschinger Effect, Masing Principle and Hencky Theorem for Bending Moment at Repeated Alternating-Sign Bending of Steel Sheet

Abstract:

In the production of the large-diameter thick-walled steel pipes (with a diameter of 1020-1420 mm and with a wall thickness of up to 32-48 mm from the high-strength steels of the strength class K50-K65) under the SMS Meer technology for the main gas-and-oil pipelines, the steel sheet is bent several times sequentially during the technological transitions from one press to another. At the elastoplastic alternating-sign bends of the sheet, the yield strength of the bending moment of the sheet changes from one bend to another, which causes great difficulties for the metallurgical technologists when they calculate the curvature of the tube’s wall and the final diameter of the pipe. To solve this problem, we propose the new analytical method for calculating the bending moment and curvature of a steel sheet under the low-cycle alternating-sign bending.

• Periodical: Materials Science Forum (Volume 1052)
• Pages: 346-351
• DOI: https://doi.org/10.4028/p-ppsj83
• Online since: February 2022
• Authors: Vladimir N. Shinkin*
• Keywords: Alternating Bending, Bauschinger Effect, Hencky Theorem, Masing Principle

References

[1] V.N. Shinkin, Residual stresses in elastoplastic bending of round bar, Materials Science Forum 946 (2019) 862-867.

DOI: 10.4028/www.scientific.net/msf.946.862

[2] V.N. Shinkin, Tubes' rupture at the faulty fusion of welding seam, Materials Science Forum 946 (2019) 868-873.

DOI: 10.4028/www.scientific.net/msf.946.868

[3] V.N. Shinkin, Residual stresses of a round steel rod at the elastoplastic twisting, Materials Science Forum 989 (2020) 642-646.

DOI: 10.4028/www.scientific.net/msf.989.642

[4] J. Bauschinger, Die veranderungen die elastizitatsgrenze, Mittheilungen aus dem Mechanisch-Technischen Laboratorium der Koniglichen Technischen Hochschule in Munchen 13(5) (1886) 1-31.

DOI: 10.1007/bf02578721

[5] V.V. Moskvitin, Plasticity under Variable Loads, Moscow, (1965).

[6] I.A. Birger, Residual Stresses, Moscow, (2015).

[7] Ju.N. Rabotnov, Mechanics of Deformable Solid, Moscow, (2019).

[8] U. Muhin, S. Belskij, E. Makarov, T. Koynov, Simulation of accelerated strip cooling on the hot rolling mill run-out roller table, Frattura ed Integrita Strutturale. 10(37) (2016) 305-311.

DOI: 10.3221/igf-esis.37.40

[9] Bel¢skii S.M., Mukhin Y.A., Classification of regulation principles for strip flatness, Steel in Translation. 39(11) (2009) 1012-1015.

DOI: 10.3103/s0967091209110114

[10] S.M. Bel¢skii, Y.A. Mukhin, Hot strip rolling with local thickening, Steel in Translation. 39(5) (2009) 420-424.

DOI: 10.3103/s0967091209050143

[11] V.N. Shinkin, Springback coefficient of a round steel beam under elastoplastic torsion, CIS Iron and Steel Review. 15 (2018) 23-27.

DOI: 10.17580/cisisr.2018.01.05

[12] V.N. Shinkin, Simple analytical dependence of elastic modulus on high temperatures for some steels and alloys, CIS Iron and Steel Review. 15 (2018) 32-38.

DOI: 10.17580/cisisr.2018.01.07

[13] I.V. Ushakov, Method of mechanical testing of laser treated metallic glass by indenters with different geometry, Proceedings of SPIE - The International Society for Optical Engineering. 6597 (2007) 659714.

DOI: 10.1117/12.726773

[14] I.V. Ushakov, Yu.V. Simonov, Formation of surface properties of VT18u titanium alloy by laser pulse treatment, Materials Today: Proceedings. 19(5) (2019) 2051-2055.

DOI: 10.1016/j.matpr.2019.07.072

[15] I.V. Ushakov, V.A. Feodorov, I.J. Permyakova, Mechanical characteristics and crystallization of annealed metallic glass 82K3XCP, Proceedings of SPIE - The International Society for Optical Engineering. 5400 (2004) 261-264.

DOI: 10.1117/12.555528

[16] V.N. Skorokhodov, P.P. Chernov, Yu.A. Mukhin, S.M. Bel¢skij, Mathematical model of the process of free spreading during strip rolling, Stal¢. 3 (2001) 38-40.

[17] S.M. Bel¢skii, V.A. Tret¢yakov, V.V. Baryshev, S.V. Kudinov, Investigation of slab width formation in roughing group of broad strip mill, Steel in Translation. 28(1) (1998) 32-39.

[18] A.V. Kazak, M.A. Marchenkova, T.V. Dubinina, A.I. Smirnova, L.G. Tomilova, A.V. Rogachev, D.N. Chausov, A.A. Stsiapanau, N.V. Usol¢tseva, Self-organization of octa-phenyl-2,3-naphthalocyaninato zinc floating layers, New Journal of Chemistry. 44 (2020) 3833-3837.

DOI: 10.1039/c9nj06041c

[19] E.N. Vasilchikova, M.S. Konstantinov, V.I. Mashchenko, R.N. Kucherov, D.N. Chausov, A.K. Dadivanyan, Specific features of crystallization process of 4,4¢-azoxyanisole in the form of multiple coffee rings,, Liquid Crystals and Their Application. 20(1) (2020) 47-52.

DOI: 10.18083/lcappl.2020.1.47

[20] V.N. Shinkin, Elastoplastic flexure of round steel beams. 1. Springback coefficient, Steel in Translation. 48(3) (2018) 149-153.

DOI: 10.3103/s0967091218030117

[21] V.N. Shinkin, Elastoplastic flexure of round steel beams. 2. Residual stress, Steel in Translation. 48(11) (2018) 718-723.

DOI: 10.3103/s0967091218110098

[22] I.V. Ushakov, How a crack and the defect material in its neighborhood affect the radiation strength of transparent materials, Journal of Optical Technology 75(2) (2008) 128-131.

DOI: 10.1364/jot.75.000128

[23] I. Safronov, A. Ushakov, Effect of simultaneous improvement of plasticity and microhardness of an amorphous-nanocrystalline material based on Co, as a result of laser processing of nanosecond duration, Materials Today: Proceedings 38(4) (2021) 1516-1520.

DOI: 10.1016/j.matpr.2020.08.141

[24] V.N. Shinkin, Preliminary straightening of steel strip, Chernye Metally. 5 (2018) 34-40.

[25] V.N. Shinkin, Direct and inverse non-linear approximation of hardening zone of steel, Chernye Metally. 3 (2019) 32-37.

[26] D.N. Chausov, A.D. Kurilov, V.V. Belyaev, Liquid crystal nanocomposites doped with rare earth elements, Liquid Crystals and Their Application. 20(2) (2020) 6-22.

DOI: 10.18083/lcappl.2020.2.6

[27] V.V. Osipova, A.D. Kurilov, Y.G. Galyametdinov, A.A. Muravsky, S. Kumar, D.N. Chausov, Optical properties of nematic liquid crystal composites with semiconducting quantum dots, Liquid Crystals and Their Application. 20(4) (2020) 84-92.

DOI: 10.18083/lcappl.2020.4.84

[28] J. Hu, Z. Marciniak, J. Duncan, Mechanics of Sheet Metal Forming, Butterworth-Heinemann, (2002).