Numerical and experimental analysis of tension-torsion processes in cylindrical samples made of 09G2S steel under large deformations before destruction

V.G. Bazhenova*, E.V. Nagornykha**, D.L. Osetrovb***, A.A. Ryabovc

aResearch Institute of Mechanics, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950 Russia

bTupolev Kazan National Research Technical University, Kazan, 420111 Russia

E-mail: *bazhenov@mech.unn.ru, **pavlyonkova@mech.unn.ru, ***osetrovdmitry@mail.ru

Received February 22, 2018

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Abstract

The features of the mechanical behavior of materials under complex stress and large deformations preceding the failure is an urgent research problem. An experimental and numerical analysis of the features of the processes of elastoplastic deformation of solid cylindrical samples under proportional kinematic loading by torsion and tension up to failure has been carried out. With the joint torsion and tension action, a neck is formed. The radius of its cross section is greater and the length is smaller than in the case of pure tension. Destruction occurs along the helical surface with maximum shear deformations depending on the ratio of tension and torsion.

 A complete system of equations describing generalized axisymmetric torsion problems has been written in a cylindrical coordinate system. The kinematic relations have been formulated in velocities and constructed in the metric of the current state, which allows one to take into account the large deformations. The equation of continuous medium motion follows from the equation of the balance of virtual capacities. Since active loading processes close to proportional have been considered, the elastoplastic properties of materials have been described by the theory of flow with nonlinear isotropic hardening. The system of equations supplemented by the kinematic boundary and initial conditions has been solved by the finite element method in combination with an explicit integration scheme of the “cross” type. To study the effect of the stress state on the strain hardening of 09G2C steel, true deformation diagrams for tension and torsion before fracture have been constructed. Their essential difference has been revealed for deformations greater than 15%. Taking into account the dependence of the deformation diagram on the form of the stress state, a good coincidence of the results of the numerical simulation of deformation processes with the experimental data has been obtained. Neglecting the form of the stressed state leads to significant differences in the determination of the critical values of the forces and moments of the formation of the necks and the supercritical behavior of the rods.

Keywords: elastoplasticity, large deformations, deformation diagram, combined loading, tension-torsion, numerical simulation, experiment

Acknowledgments. The study was supported by the Russian Foundation for Basic Research (project no. 17-308-50006).

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For citation: Bazhenov V.G., Nagornykh E.V., Osetrov D.L., Ryabov A.A. Numerical and experimental analysis of tension-torsion processes in cylindrical samples made of 09G2S steel under large deformations before destruction. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 3, pp. 495–507. (In Russian)

 

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