Geodesic
Determination of material mathematical functions in the conditions of the duration of dilatating media from powder and ingot metal systems
Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 537-560

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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. 
@article{CHEB_2019_20_2_a40,
     author = {E. S. Makarov and A. E. Gvozdev and G. M. Zhuravlev and I. V. Minaev and N. N. Dobrovol'sky and S. V. Sapozhnikov and A. A. Kalinin},
     title = {Determination of material mathematical functions in the conditions of the duration of dilatating media from powder and ingot metal systems},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {537--560},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a40/}
}
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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. Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 537-560. http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a40/