The processes of complex loading structural steel for a five-link piecewise broken strain path

V. G. Zubchaninov ; A. A. Alekseev ; V. I. Gul'tyaev ; E. G. Alekseeva

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 61 (2019), pp. 32-44

Résumé

The paper proposes a mathematical model of the theory of elastoplastic processes for the variety of strain paths such as multi-link straight-line polygonal paths. The constitutive equations of the proposed mathematical model, as well as the methodology of experimental studies, are based on the vector representation of the strain and stress proposed by Ilyushin. In the mathematical model, the approximations of the functional are used, which depend on all parameters of the inner geometry of the strain path. The governing equations of the mathematical model are reduced to the Cauchy problem. A numerical solution to the latter and the calculated results are obtained using the fourth-order Runge-Kutta method. The experimental data on the complex loading (combined tension-compression and torsion) of a thin-walled tubular sample made of steel 45 according to a deformation program consisting of five straight sections with different break angles of the strain path are presented. The vector and scalar properties of the material are studied. A mathematical model of the theory of elastoplastic processes is verified by comparing the calculated results with the data of a physical experiment. It is shown that the applied mathematical model gives a qualitatively and quantitatively satisfactory description of the main effects of a complex plastic straining for the variety of strain paths such as multi-link polygonal strain paths.

Détail

Keywords: plasticity, theory of elastoplastic processes, complex loading, multi-link polygonal strain path, modeling of processes, experimental data.

Bibliographie

[1] V. G. Zubchaninov, Mechanics of the processes in plastic media, Fizmatlit, M., 2010

[2] V. G. Zubchaninov, Stability and plasticity, v. 2, Plasticity, Fizmatlit, M.

[3] A. A. Ilyushin, Plasticity. Fundamentals of general mathematical theory, Izdatel'stvo AN SSSR, M., 1963

[4] A. A. Ilyushin, Continuum mechanics, Izdatel'stvo MGU, M., 1990

[5] V. P. Degtyarev, Plasticity and creep of engineering structures, Mashinostroenie, M., 1967

[6] V. G. Zubchaninov, “The general mathematical theory of plasticity and the Il'yushin postulates of macroscopic definability and isotropy”, Moscow University Mechanics Bulletin, 73:5 (2018), 101–116 | DOI | Zbl

[7] V. A. Peleshko, “Applied and engineering versions of the theory of elastoplastic processes of active complex loading. Part 1: Conditions of mathematical well-posedness and methods for solving boundary value problems”, Mechanics of Solids, 50:6 (2015), 650–656 | DOI

[8] V. A. Peleshko, “Applied and engineering versions of the theory of elastoplastic processes of active complex loading part 2: Identification and verification”, Mechanics of Solids, 51:1 (2016), 91–113 | DOI

[9] I. A. Volkov, L. A. Igumnov, I. S. Tarasov, D. N. Shishulin, M. T. Markova, “Modeling complex plastic deformation of polycrystalline structural alloys along plane and spatial trajectories of arbitrary curvature”, Problemy prochnosti i plastichnosti Problems of Strength and Plasticity, 80:2 (2018), 194–208 | DOI

[10] F. M. Mitenkov, I. A. Volkov, L. A. Igumnov, A. V. Kaplienko, Yu. G. Korotkikh, V. A. Panov, Applied theory of plasticity, Fizmatlit, M., 2015

[11] V. G. Zubchaninov, A. A. Alekseev, E. G. Alekseeva, “Mathematical modeling of plastic deformation of materials on complex flat trajectories”, Materials Physics and Mechanics, 24:2 (2015), 107–118

[12] V. G. Zubchaninov, “Isotropy postulate and the law of complex unloading of continua”, Mechanics of Solids, 46:1 (2011), 21–29 | DOI

[13] A. V. Muravlev, “Experimental construction of plasticity functional for a two-link polygonal strain path in the experiments for cylindrical continuous areas”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 1996, no. 5, 74–80

[14] V. G. Zubchaninov, A. A. Alekseev, V. I. Gultiaev, “Modeling of elastic-plastic deformation of work material along multielement piecewise zig-zag linear trajectories”, Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Mekhanika PNRPU Mechanics Bulletin, 2017, no. 3, 203–215 | DOI

[15] V. G. Zubchaninov, A. A. Alekseev, V. I. Gultyaev, “On drawing the yield surface for steel 45 and verifying the postulate of isotropy on straight-line paths under repeated sign-variable loadings”, PNRPU Mechanics Bulletin, 2018, no. 1-2, 23–28 | DOI

[16] V. G. Zubchaninov, A. A. Alekseev, E. G. Alekseeva, V. I. Gultiaev, “Experimental verification of postulate of isotropy and mathematical modeling of elastoplastic deformation processes following the complex angled nonanalytic trajectories”, Materials Physics and Mechanics, 32:3 (2017), 298–304 | DOI

[17] V. S. Lenskiy, Experimental verification of the fundamental postulates of general theory of elastoplastic deformations, Izdatel'stvo AN SSSR, M., 1961

[18] V. G. Zubchaninov, A. A. Alekseev, V. I. Gultiaev, “Numerical simulation a processes of complex elastoplastic deformation steel on twolink broken trajectories”, Problems of Strength and Plasticity, 76:1 (2014), 18–25 | DOI