The equations of the plasticity theory properties of dilating materials in the concept of plastic gas
https://doi.org/10.22405/2226-8383-2018-19-2-163-171
Abstract
In paper investigate the properties of equations that are used in the calculation of the plastic deformation of dilatable materials (powder steels, pure metals, non-ferrous alloys) from the concept of plastic gas. A complete system of basic equations of the theory of the flow of rigid-plastic isotropic dilatation media is given. We consider a particular case of plane deformation, for a slow steady-state plastic flow, as a result of which the initial conditions for the solution of the problem are not formulated. Taking into account that the solid medium undergoes a change in its density under loading, the law of volume compressibility is given, and the plasticity condition is reciprocally satisfied. For equations of equilibrium, continuity and the ratio of the coaxiality of de-Viators, a system of equations is constructed, and its analytical solution is given. The boundary conditions for stresses, densities, and velocities are written out for the case of planar deformation of an isotropic dilatation medium endowed with the properties of a plastic gas.
About the Authors
Eduard Sergeevich Makarov
Tula State University.
Russian Federation
professor, doctor of technical sciences
Russian Federation
professor, doctor of technical sciences
Gennady Modestovich Zhuravlev
Tula State University.
Russian Federation
professor, doctor of technical sciences
Russian Federation
professor, doctor of technical sciences
Alexander Evgenievich Gvozdev
Tula State L. N. Tolstoy Pedagogical University.
Russian Federation
chief researcher of the department of technology and service, professor, doctor of technical sciences
Russian Federation
chief researcher of the department of technology and service, professor, doctor of technical sciences
Sergey Vladimirovich Sapozhnikov
LLC Tulachermet-Steel
Russian Federation
Chief specialist
Russian Federation
Chief specialist
Alexander Nikolaevich Sergeev
Tula L.N. Tolstoy State Pedagogical University.
Russian Federation
head of the department of technology and service, senior researcher of the department of technology and service, professor, doctor of technical sciences
Russian Federation
head of the department of technology and service, senior researcher of the department of technology and service, professor, doctor of technical sciences
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For citations:
Makarov E.S., Zhuravlev G.M., Gvozdev A.E., Sapozhnikov S.V., Sergeev A.N. The equations of the plasticity theory properties of dilating materials in the concept of plastic gas. Chebyshevskii Sbornik. 2018;19(2):163-171. (In Russ.) https://doi.org/10.22405/2226-8383-2018-19-2-163-171
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