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

E. S. Makarov ; A. E. Gvozdev ; G. M. Zhuravlev ; I. V. Minaev ; N. N. Dobrovol'sky ; S. V. Sapozhnikov ; A. A. Kalinin

Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 537-560.

Résumé

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.

Détail

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.

Bibliographie

[1] V. N. Nikolaevskii (ed.), Defining the laws of soil mechanics, Sat. articles, Mir, M., 1975, 230 pp.

[2] S. S. Vyalov, Rheological basis of soil mechanics, Higher School, M., 1978, 448 pp.

[3] G. A. Vinogradov, V. P. Katashinsky, The theory of sheet rolling of metal powders and granules, Metallurgy, M., 1979, 224 pp.

[4] V. E. Perelman, Forming powder materials, Metallurgy, M., 1979, 232 pp.

[5] E. S. Makarov, “To the theory of the formation of metal powders under conditions of plane deformation”, News of universities, Mashinostroenie, 1973, no. 10, 158–162

[6] V. A. Pavlov, S. S. Kiparisov, V. V. Shcherbina, Pressure treatment of non-ferrous metal powders, Metallurgy, M., 1977, 176 pp.

[7] A. P. Kolikov, P. I. Polukhin, A. V. Krupin et al., New deformation processes of metals and alloys, Higher School, M., 1986, 352 pp.

[8] Powder metallurgy, sprayed coatings, Metallurgy, M., 1987, 792 pp.

[9] K. N. Bogoyavlenskii, V. V. Ric (eds.), Economical methods of forming parts, Lenizdat, L., 1984, 144 pp.

[10] E. S. Makarov, A. E. Gvozdev, G. M. Zhuravlev, The theory of plasticity of dilating media, monograph, 2nd ed. reclaiming and add., ed. A. E. Gvozdev, Publishing House of TSU, Tula, 2015, 337 pp.

[11] Ya. A. Kaluzhsky, O. T. Batrakov, Seal roadbed, pavement, Transport, M., 1971, 158 pp.

[12] N. Ya. Kharkhut, Soil compaction machines, Mechanical Engineering, L., 1973, 176 pp.

[13] R. J. Green, “A plasticity theory for porous solids”, Int. J. Mech. Sci., 14 (1972), 215–224 | Zbl

[14] S. M. Doraivelu, H. L. Gegel, J. S. Gunasekera, J. C. Malas, J. T. Morgan, J. F. Tomas, “A new yield function for compressible P/M materials”, Int. J. Mech. Sci., 26 (1984), 527–535

[15] M. E. Harr, Fundamentals of theoretical soil mechanics, Stroiizdat, M., 1971, 320 pp.

[16] E. S. Makarov, L. A. Tolokonnikov, “Version of the theory of plasticity dilating medium”, Izv. USSR Academy of Sciences, Solid Mechanics, 1979, no. 1, 88–93

[17] L. M. Kachanov, Fundamentals of the theory of plasticity, Science, M., 1969, 420 pp.

[18] T. Thomas, Plastic flow and destruction in solids, Mir, M., 1964, 308 pp.

[19] I. V. Wide (ed.), Mechanics of granular media, Sat. articles, Mir, M., 1985, 280 pp.

[20] E. S. Makarov, L. A. Tolokonnikov, “Flat problems of the theory of plasticity of orthotropic dilating media”, Izv. USSR Academy of Sciences, Solid Mechanics, 1979, no. 5, 139–143

[21] E. S. Makarov, L. A. Tolokonnikov, “The theory of magnetoplasticity of dilating media”, V All-Union Congress on Theoretical and Applied Mechanics, annotated report, Science, Alma-Ata, 1981, 245

[22] E. S. Makarov, V. I. Kiselev, “Theory of electroplasticity of isotropic dilating media”, Issl. in the region plasticity and metal forming, ed. TulPI, Tula, 1982, 104–109

[23] E. S. Makarov, L. A. Tolokonnikov, “The equations of the theory of magnetoplasticity of an isotropic dilating medium”, Izv. USSR Academy of Sciences, Solid Mechanics, 1983, no. 5, 188–190

[24] E. S. Makarov, V. I. Kiselev, “Problems of the theory of plastic flow of dilating media in electric and magnetic fields”, General problems and methods for the study of plastic and viscoelastic materials and structures, Ed. UC AN SSSR, Sverdlovsk, 1986, 66–71

[25] E. S. Makarov, “Plastic deformation of dilating media in electrostatic and magnetostatic fields”, Essl. in the region theories, technologies and equipment of stamping production, Ed. TSU, Tula, 1998, 64–69

[26] E. S. Makarov, “A variant of construction and some flat problems of the theory of chemoplasticity”, Izv. USSR Academy of Sciences, Solid Mechanics, 1989, no. 5, 70–72

[27] E. S. Makarov, “The application of the theory of chemoplasticity to the calculation of the limiting states of corroding pipes”, Physico-chemical mechanics of materials, 1989, no. 2, 115–117

[28] B. A. Druyanov, Applied theory of plasticity of porous bodies, Mashinostroenie, M., 1989, 166 pp.

[29] L. A. Lyusternik, O. A. Chervonenkis, A. R. Yanpolsky, Mathematical analysis (calculation of elementary functions), Fizmatgiz, M., 1963, 248 pp.

[30] Pavlov V. A., Kiparisov S. S., Shcherbina V. V., Pressure treatment of non-ferrous metal powders, Metallurgy, M., 1977, 176 pp.

[31] N. N. Sergeev, A. E. Gvozdev, N. E. Starikov, V. I. Zolotukhin, A. N. Sergeev, A. D. Brecky, O. V. Kuzovlev, G. M. Zhuravlev, D. A. Provotorov, Technology of metals and alloys, textbook, ed. N. N. Sergeyev, TSU, Tula, 2017, 490 pp.

[32] A. E. Gvozdev, N. N. Sergeev, I. V. Minaev, I. V. Tikhonova, A. G. Kolmakov, “The role of the nucleation process in the development of some phase transitions of the first kind”, Material Science, 2015, no. 1, 15–21

[33] A. E. Gvozdev, I. V. Golyshev, I. V. Minayev, A. N. Sergeyev, N. N. Sergeyev, I. V. Tikhonova, D. M. Khonelidze, A. G. Kolmakov, “Multiparametric optimization of laser cutting of steel sheets”, Inorganic Materials: Applied Research, 6:4 (2015), 305–310 | MR

[34] A. E. Gvozdev, D. N. Bogolyubova, N. N. Sergeev, A. G. Kolmakov, D. A. Provotorov, I. V. Tikhonova, “Features of softening processes of aluminum, copper, and their alloys under hot deformation”, Inorganic Materials: Applied Research, 6:1 (2015), 32–40

[35] A. D. Breki, A. E. Gvozdev, A. G. Kolmakov, “Using the generalized Pascal triangle to describe the fluctuations of the friction force of materials”, Matherial Studies, 2016, no. 11, 3–8

[36] E. S. Makarov, A. E. Gvozdev, G. M. Zhuravlev, S. V. Sapozhnikov, A. N. Sergeev, A. G. Kolmakov, A. D. Breki, D. V. Maliy, N. N. Dobrovolsky, “Analysis of the equations of the theory of plasticity of powder metal systems”, Chebyshevsky collection, 19:1 (2018), 152–166 | DOI | MR | Zbl

[37] Makarov E. S., Zhuravlev G. M., Gvozdev A. E., Sapozhnikov S. V., Sergeev A. N., “Properties of equations of the theory of plasticity of dilating materials in the concept of plastic gas”, Chebyshevsky collection, 19:2 (2018), 163–171 | DOI | MR | Zbl

[38] G. M. Zhuravlev, A. E. Gvozdev, A. G. Kolmakov, A. N. Sergeev, D. V. Maliy, “The use of the mathematical method of local variations for solving the problems of plastic forming metal, powder and nanocomposite materials”, Chebyshevsky collection, 19:4 (2018), 43–54 | DOI | MR | Zbl

[39] E. S. Makarov, A. E. Gvozdev, G. M. Zhuravlev, A. N. Sergeev, I. V. Minaev, A. D. Breki, D. V. Maliy, “Application of the theory of plasticity of dilating media to the processes of compaction of powders of metal systems”, Chebyshevsky collection, 18:4 (2017), 268–284 | DOI | MR

[40] A. E. Gvozdev, G. M. Zhuravlev, S. V. Sapozhnikov, “To the theoretical analysis of the process of compacting powder materials by pressing”, Izvestiya Tula State University. Earth Sciences, 2017, no. 4, 273–283 | MR

[41] A. D. Breki, S. E. Aleksandrov, K. S. Tyurikov, A. G. Kolmakov, A. E. Gvozdev, A. A. Kalinin, “Antifriction properties of plasma-chemical coatings based on SiO${}_{2}$ with MoS${}_{2}$ nanoparticles under conditions of spinning friction on SHKH15 steel”, Inorganic Materials: Applied Research, 9:4 (2018), 714–718

[42] A. D. Breki, A. E. Gvozdev, A. G. Kolmakov, N. E. Starikov, D. A. Provotorov, N. N. Sergeyev, D. M. Khonelidze, “On friction of metallic materials with consideration for superplasticity phenomenon”, Inorganic Materials: Applied Research, 8:1 (2017), 126–129

[43] A. E. Gvozdev, N. N. Sergeyev, I. V. Minayev, I. V. Tikhonova, A. N. Sergeyev, D. M. Khonelidze, D. V. Maliy, I. V. Golyshev, A. G. Kolmakov, D. A. Provotorov, “Temperature distribution and structure in the heat-affected zone for steel sheets after laser cutting”, Inorganic Materials: Applied Research, 8:1 (2017), 148–152

[44] A. D. Breki, A. E. Gvozdev, A. G. Kolmakov, “Application of generalized pascal triangle for description of oscillations of friction forces”, Inorganic Materials: Applied Research, 8:4 (2017), 509–514 | MR

[45] A. E. Gvozdev, N. N. Sergeyev, I. V. Minayev, A. G. Kolmakov, I. V. Tikhonova, “Role of nucleation in the development of first-order phase transformations”, Inorganic Materials: Applied Research, 6:4 (2015), 283–288

[46] A. E. Gvozdev, D. N. Bogolyubova, N. N. Sergeev, A. G. Kolmakov, D. A. Provotorov, I. V. Tikhonova, “Features of softening processes of aluminum, copper, and their alloys under hot deformation”, Inorganic Materials: Applied Research, 6:1 (2015), 32–40

[47] A. E. Gvozdev, I. V. Minaev, N. N. Sergeev, A. G. Kolmakov, D. A. Provotorov, I. V. Tikhonova, “Grain size effect of austenite on the kinetics of pearlite transformation in low- and medium-carbon low-alloy steels”, Inorganic Materials: Applied Research, 6:1 (2015), 41–44