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

V. N. Shinkin, Dr. Sci. (Phys.-Math.), Prof., e-mail: shinkin-korolev@yandex.ru

After the elastoplastic deformation of the metal structures and the metal products (for example, after a torsion, a bending, a compression, a stretching, the complex types of deformations), these bodies change their shape and partially springback. At the same time, the residual stresses arise in the bodies. Under the appropriate external conditions (for example, when the temperature changes), these stresses can lead to a significant distortion of the bodies’ shape (adopted after deformation) and even destroy these bodies. To estimate the residual shape of the round steel beam, which it takes after the mechanical deformation (the forming), it is necessary to know the springback coefficient of the round beam at the torsion. At the torsion of a round steel beam, the torques (the torsional moments, the twisting moments) also appear in the beam. This moments are connected with the tangential stresses in its cross-section. The maximum of the tangential stresses occur on the surface of the round beam and can lead to the destruction of the metal beam. However, even at very strong elastoplastic torsion around the symmetry axis of the beam, the tangential stress in the center of the cross-section of the round beam is zero and the elastic zone in the beam’s cross-section exists. Therefore, the destruction of the round steel beam and the defects of its metal under the torsion always start at the beam’s surface. The magnitude of the tangential stresses and angular deformations, their distribution along the cross-section of the round beam are always associated with the torque of the external forces. The greater the torque, the greater the tangential stresses and angular deformations. In this paper we have obtained the springback coefficient and the torques of the straight round beam under a torsion for an elastoplastic medium with a linear hardening, depending on the beam’s radius, the shear modulus, the yield strength and the hardening modulus of beam’s material. The research results can be used in the metallurgical and machine-building factories.

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