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Contact Problems of Plastic Flow in a Thin Layer: Theory, Analysis of Solutions, and Applications

  • RELIABILITY, STRENGTH, AND WEAR RESISTANCE OF MACHINES AND STRUCTURES
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Abstract

The high level of mechanical characteristics of the mechanical parts produced related to an increase in their operation lifetime is embedded at the stage of metal forming. In this paper the boundary value problems of the modern theory of plasticity are considered with application to a thin layer, the formulation of which is based on the composition of a statically determined system including the partial differential equations of quasi-static equilibrium, the full plasticity condition, and the Cauchy equation for strains. The assumptions and constraints are based on the consequences of the well-known Prandtl solution formulated by Il’yushin. The problem is supplemented by nonsymmetric boundary conditions at the face ends. By means of variation of the current formulation of plastic flow problem for a thin layer, solutions are found, including the contact pressure and force parameters, for various generalizations of the Prandtl problem about the free spreading of a band occupying the linear domain and upset by flat dies performing the opposite motion.

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Authors and Affiliations

  1. Russian Technological University MIREA, Moscow, Russia

    V. A. Kadymov

  2. Moscow State University of Technology STANKIN, Moscow, Russia

    E. N. Sosenushkin & E. A. Yanovskaya

Authors
  1. V. A. Kadymov
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  2. E. N. Sosenushkin
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  3. E. A. Yanovskaya
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Correspondence to V. A. Kadymov.

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Translated by E. Oborin

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Kadymov, V.A., Sosenushkin, E.N. & Yanovskaya, E.A. Contact Problems of Plastic Flow in a Thin Layer: Theory, Analysis of Solutions, and Applications. J. Mach. Manuf. Reliab. 51, 206–215 (2022). https://doi.org/10.3103/S1052618822030062

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  • DOI: https://doi.org/10.3103/S1052618822030062

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