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Chebyshevskii Sb., 2019, Volume 20, Issue 2, Pages 537–560 (Mi cheb789)  

HISTORY OF MATHEMATICS AND APPLICATIONS

Determination of material mathematical functions in the conditions of the duration of dilatating media from powder and ingot metal systems

E. S. Makarova, A. E. Gvozdevb, G. M. Zhuravleva, I. V. Minaevc, N. N. Dobrovol'skyab, S. V. Sapozhnikovd, A. A. Kalinina

a Tula State University (Tula)
b Tula State Lev Tolstoy Pedagogical University (Tula)
c NCE "Telar" (Tula)
d OTKRITIE Financial Corporation Bank (Tula)

Abstract: Irreversible changes in the volume of material, called dilatancy, occur in many technological processes. It manifests itself in powder and porous metals, soils and rocks, concretes, metal alloys of different chemical composition and other materials. In addition, under the conditions of plastic deformation, an irreversible change in the volume of the deformable material occurs — its plastic dilatancy, which is the main physical mechanism of damage to various metal systems (metals, steels, non-ferrous alloys) with their large plastic deformations. In this regard, it is necessary to take into account the irreversible changes in the volume of the material in the calculations of many technological processes, for example, pressing powder metal materials, pressure treatment and cutting of porous metals and metal alloys. In compiling the basic mathematical relationships, a theoretical description of the change in volume uses various mathematical models of plastic dilatancy: discrete models, continual models, including stochastic models, which describe the behavior of dilating materials, both subject to preferential compaction and loosening. For the construction of the conditions of fluidity used in the calculation of dilating media, it is necessary to define material mathematical functions for specific processes and materials. The paper discusses the main conditions of fluidity and methods of their construction, which are used in the calculations of the processes of plastic processing of powder and ingot metallic materials in various conditions and states.

Keywords: irreversible change in the volume of a material, plastic dilatancy, basic relations, mathematical models, compaction, loosening, yield conditions, material functions, methods of their construction, metal, powder material, metal alloy.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation RFMEF 157717X0271
The work was carried out within the framework of the Federal target program «Research and development in priority areas of development of the scientific and technological complex of Russia for 2014-2020» (unique identifier of the project RFMEF 157717X0271).


DOI: https://doi.org/10.22405/2226-8383-2018-20-2-537-560

Full text: PDF file (730 kB)
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UDC: 539.21:621.785
Received: 18.03.2019
Accepted:12.07.2019

Citation: E. S. Makarov, A. E. Gvozdev, G. M. Zhuravlev, I. V. Minaev, N. N. Dobrovol'sky, S. V. Sapozhnikov, A. A. Kalinin, “Determination of material mathematical functions in the conditions of the duration of dilatating media from powder and ingot metal systems”, Chebyshevskii Sb., 20:2 (2019), 537–560

Citation in format AMSBIB
\Bibitem{MakGvoZhu19}
\by E.~S.~Makarov, A.~E.~Gvozdev, G.~M.~Zhuravlev, I.~V.~Minaev, N.~N.~Dobrovol'sky, S.~V.~Sapozhnikov, A.~A.~Kalinin
\paper Determination of material mathematical functions in the conditions of the duration of dilatating media from powder and ingot metal systems
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 2
\pages 537--560
\mathnet{http://mi.mathnet.ru/cheb789}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-2-537-560}


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