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Powder Metallurgy and Additive Technologies
ArticleName Analytical description of metal plasticity at shift
DOI 10.17580/cisisr.2020.01.13
ArticleAuthor V. N. Shinkin

National Research University of Technology “MISiS” (Moscow, Russia):

V. N. Shinkin, Dr. Phys.-Math., Professor, E-mail:


The theory of elasticity, which is one of the departments of mechanics, is currently the basis for the design of all engineering structures in which elastic deformations have to be taken into account. It became the exact science only after the gradual development for more than two hundred years. Over the past few decades, the valuable information has been obtained about the non-elastic materials − the mechanical properties of plastic metals and the conditions under which the solid bodies are destroyed. However, the most satisfactory understanding of the plastic condition of materials and the report on the conditions, under which the destruction occurs, were achieved only after the crystal structure of metals and alloys, the mechanical and thermal history of the metal semi-finished products (rods and sheets) from the time of casting of ingots and ending with the annealing of finished products were alone with great care studied in the wide physical terms. The study of the plastic state of matter is currently of interest to many branches of science and technology. Thus, it is desirable for metallurgists to control more precisely the processes of deformation of metals at high temperatures. Since the rolling mills currently use huge amounts of energy, it is necessary to use the energy more economically. On the other hand, in order to choose the right materials for the different parts of machines, the designer must carefully consider the mechanical properties of these materials. He is not only interested in knowing as accurately as possible the ultimate stresses, at which the parts of machines should be expected to risk plastic deformation, destruction or cracking due to fatigue, but in many cases he wants to take into account the possible deformation of the parts of machines, that are subjected to the long-term forces. If the deformations are elastic, then the designer can base his calculations on the theory of elasticity, but he lacks such a reliable basis when moving from the elastic deformations to the plastic deformations or when figuring out the conditions, under which the fracture occurs.

keywords Shear stress, shift, thin-walled tube, tube torsion, Huber-Mises’s condition, Tresca-Saint-Venant’s condition, Nadai’s and Ludwik’s descriptions

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