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ArticleName To calculation of stresses in drawing of anisotropic viscoplastic material
DOI 10.17580/tsm.2021.05.11
ArticleAuthor Chudin V. N., Chernyaev A. V., Tesakov D. M.

FSBEI HE Russian University of Transport (MIIT), Moscow, Russia:

V. N. Chudin, Professor of the Chair for Material Resistance and Structural Mechanics, Doctor of Technical Sciences


FSBEI HE Tula State University, Tula, Russia:

A. V. Chernyaev, Professor of the Chair for Mechanics of Plastic Shaping, Doctor of Technical Sciences, e-mail:


JSC KBP named after Academician A. Shipunov, Tula, Russia:

D. M. Tesakov, Design Engineer


Relations for calculation of stresses arising in the deformation zone during isothermal drawing without thinning the wall of cylindrical articles from a flat sheet blank are proposed. The stresses are determined by a joint solution of the equilibrium equations and plasticity condition for the plane stress state. The workpiece material is assumed to be transversely isotropic, the deformation is carried out under conditions of viscoplasticity. The deformation hardening and stress relaxation due to manifestation of viscosity of the material in the heating zone is taken into account. Tensile meridional stresses are defined as the sum of stresses in the workpiece flange, stresses caused by bending and straightening of the workpiece on the radial surface of the matrix, as well as friction on the planes of the clamp and the matrix. The received information on stresses in a flange allows to estimate power modes of drawing and damageability of workpiece material. On the basis of the obtained relations, the calculations of stresses and isothermal drawing forces for aluminum and titanium alloys at processing temperature of 450 and 930 оC, respectively, were performed. The dependences of the drawing force on the tool movement rate, which varied in the range from 1 to 10 mm/min, which corresponds to the viscoplasticity mode, are presented. It is established that in the given temperaturevelocity conditions the considered alloys show viscous properties that has considerable influence on the power mode of drawing. A comparison of the results of the force calculation with and without viscosity is performed. It is noted that the deformation degree, tool geometry and anisotropy of mechanical properties of the original material also have a significant effect on the drawing force. The obtained results can be used in design of processes for drawing workpieces from hard-to-deform aluminum and titanium alloys, which are used in aviation and space technology, the deformation of which is carried out under conditions of viscoplastic flow.
The work was performed within the framework of the grant for state support of the leading scientific schools of the Russian Federation NSh-2601.2020.8.

keywords Drawing, anisotropy, viscoplasticity, velocity, stress, force, aluminum and titanium alloys

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