Mathematical models of dynamic compaction and extrusion of incompact metallic materials are considered. According to the model of dynamic compaction, irreversible material volume changes occurring under the shock action are considered on the basis of the general equations of mass, momentum and energy conservation, which are written for the discontinuity surface.
A mathematical model of impact extrusion of incompact wire stock through a conical die1.Krupin A.V., Solovyev V.Ya., Popov G.S., Kr"stev M.R. Obrabotka metallov vzryvom [Explosion Processing of Metals]. Moscow, Metallurgiya Publ., 1991, 496 p. (In Russian).
2.Dmitriev A.M., Vorontsov A.L. Tekhnologiya kovki i obyemnoy shtampovki. Ch. 1. Obyemnaya shtampovka vydavlivaniem: ucheb. dlya vuzov [Technology of Forging and Bulk Stamping. Part 1. Bulk Stamping by Extrusion: Textbook for Colleges]. Moscow, Vysshaya Shkola Publ., 2002, 400 p. (In Russian).
3.Roman O.V., Gorobtsov V.G. Aktualnye problemy poroshkovoi metallurgii [Actual problems of powder metallurgy, eds., O.V. Roman, V.S. Arunachalam,]. Moscow, Metallurgiya Publ., 1990, pp. 78–99.
4.Belyakov G.V., Rodionov V.N., Samosadnyi V.P. Heating of porous material under impact compression. Combustion explosion and shock waves, 1977, vol. 13, iss. 4, pp. 524–528. DOI: 10.1007/BF00744803.
5.Gerasimov A.V., Krektuleva R.A. Numerical simulation of deformation and destruction of functionally gradient porous materials under explosive and impact loading. Mekhanika kompozitsionnykh materialov i konstruktsiy, 1999, vol. 5, no. 3, pp. 94–106. (In Russian).
6.Alekseev Yu.L., Ratnikov V.P., Rybakov A.P. Shock adiabats of porous metals. Journal of Applied Mechanics and Technical Physics, 1971, vol. 12, no. 2, pp. 257–262. DOI: 10.1007/BF00850698.
7.Anisichkin V.F. Shock compression of porous bodies. Combustion explosion and shock waves, 1979, vol. 15, no. 6, pp. 796–799. DOI: 10.1007/BF00739873.
8.Fomin V.M., Gulidov A.I., Sapozhnikov G.A., Shabalin I.I., Babakov V.A., Kuropatenko V.F., Kiselev A.B., Trishin Yu.A., Sadyrin A.I., Kiselev S.P.,Golovlev I.F. Vysokoskorostnoe vzaimodeistvie tel [High-speed interaction of bodies]. Novosibirsk, Siberian Branch of the Russian Academy of Sciences, 1999, 600 p. (In Russian).
9.Deribas A.A., Staver A.M. The shock compression of porous cylindrical bodies. Phizika Goreniya i Vzryva, 1974, vol. 10, no. 4, pp. 568–578. (In Russian).
10.Kuzmin G.E., Staver A.M. To the determination of flow parameters in shock-loaded powder materials. Fizika Goreniya i Vzryva, 1973, vol. 9, no. 6, pp. 898–905. (In Russian).
11.Yakovlev S.P., Kukhar V.D., Proskuryakov N.E., Seledkin E.M., Nechepurenko N.G. Magnito-impulsnaya shtampovka polykh tsilindricheskykh zagotovok [Magnetic Pulse Forming of Hollow Cylindrical Blanks]. Tula, Reproniks Ltd. Publ., 1998, 240 p. (In Russian).
12.Nesterenko V.F. Impul’snoe nagruzhenie geterogennykh materialov [Pulse loading of heterogeneous materials]. Novosibirsk, Nauka Publ., 1992, 200 p. (In Russian).
13.Roman O.V., Mirilenko A.P., Pikus I.M. Theory and technology of the component formation process - effect of high-speed loading conditions on the pressing mechanism. Soviet Powder Metallurgy and Metal Ceramics, 1989, vol. 28, no. 11, pp. 840–844. DOI: 10.1007/BF01198890.
14.Serdyuk G.G., Svistun L.I. Shock compaction of metal powders (theoretical research). In: Reologicheskie modeli i protsessy deformirovoniya poristykh i kompozitsionnykh materialov. Kiev, Naukova Dumka Publ., 1985, pp. 115–126. (In Russian).
15.Hermann W. Constitutive equation for the dynamic compaction of ductile porous materials. Journal of Applied Physics, 1969, vol. 40, no. 6, pp. 2490–2499. DOI: 10.1063/1.1658021.
16.Shtertser A.A. Transmission of pressure in porous-media under explosive loading. Combustion explosion and shock waves, 1988, vol. 24, iss. 5, pp. 610–615.
17.Butcher B.M., Carroll M.M., Holt A.C. Shock wave compaction of porous aluminum. J. Appl. Phys., 1974, vol. 45, no. 9, pp. 3864–3875. DOI: 10.1063/1.1663877.
18.Carroll M.M., Holt A.C. Steady waves in ductile porous solids. J. Appl. Phys., 1973, vol. 44, no. 10, pp. 4388–4392. DOI: 10.1063/1.1661970.
19.Davison L. Shock-wave structure in porous solids. J. Appl. Phys., 1971, vol. 42, no. 13, pp. 5503–5512. DOI: 10.1063/1.1659971.
20.Hǿrlück S., Dimon P. Statistics of shock waves in a two-dimensional granular flow. Physical Review E, 1999, vol. 60, no. 1, pp. 671–686. DOI: 10.1103/PhysRevE.60.671.
21.Nunziato J.W., Walsh E.K. One-dimensional shock waves in uniformly distributed granular materials. International Journal of Solids and Structures, 1978, vol. 14, no. 8, pp. 681–689. DOI: 10.1016/0020-7683(78)90006-9.
22.Ayzenberg-Stepanenko М.V., Osharovich G.G., Sher Е.N., Yanovitskaya Z.Sh. Numerical Simulation of Shock-Wave Processes in Elastic Media and Structures. Part I: Solving Method and Algorithms. Journal of Mining Science, 2012, vol. 48, no. 1, pp. 76–95. DOI: 10.1134/S1062739148010091.
23.Afanas'eva S.A., Belov N.N., Burkin V.V., Dudarev E.F., Ishchenko A.N., Rogaev K.S., Tabachenko A.N., Khabibullin M.V., Yugov N. T. Simulation of the action of a shock wave on titanium alloy. Journal of Engineering Physics and Thermophysics, 2017, vol. 90, no. 1, pp. 24–34. DOI: 10.1007/s10891-017-1535-8.
24.Roman O.V., Shmuradko V.T., Tarasov G.D. Curve of the dynamic compressibility of powder media. Journal of Engineering Physics and Thermophysics, 2006, vol. 79, no. 4, pp. 817–823.
25.Chikova O.A., Shishkina E.V., Petrova A.N., Brodova I.G. Measuring the Nanohardness of Commercial Submicrocrystalline Aluminum Alloys Produced by Dynamic Pressing. The Physics of Metals and Metallography, 2014, vol. 115, no. 5, pp. 523–528. DOI: 10.1134/S0031918X14050044.
26.Shorokhov E.V., Zhgilev I.N., Gunderov D.V., Gurov A.A. Dynamic Pressing of Titanium for Producing an Ultrafine-Grained Structure. Russian Journal of Physical Chemistry B, 2008, vol. 2, no. 2, pp. 251–254. DOI: 10.1134/S1990793108020139.
27.Rogozin V.D. Vzryvnaya obrabotka poroshkovykh materialov [Explosive Processing of Powder Materials]. Volgograd, Polytekhnik Publ., 2002, 136 p. (In Russia).
28.Kinelovskii S.A., Maevskii K.K. Model of the behavior of the mixture with different properties of the species under high dynamic loads. Journal of Applied Mechanics and Technical Physics, 2013, vol. 54, no. 4, pp. 524–530. DOI: 10.1134/S0021894413040020.
29.Vogler T. Shock Wave Perturbation Decay in Granular Materials. J. dynamic behavior mater., 2015, vol. 1, pp. 370–387. DOI: 10.1007/s40870-015-0033-3.
30.Shtern M.B., Kartuzov E.V. Formation and propagation of shock waves in highly porous materials. Powder Metallurgy and Metal Ceramics, 2016, vol. 55, no. 3–4, pp. 134–140. DOI: 10.1007/s11106-016-9788-x.
31.Leitsin V.N. A model of reacting powder medium. In: Vestnik Tomskogo Gosudarstvennogo Universiteta. Byulleten Operativnoi Tekhnicheskoi Informatsii [Bulletin of Tomsk State University: technical newsletter]. Tomsk, TGU Publ., 2001, no. 5, 40 p. (In Russian).
32.Boltachev G.Sh., Kaygorodov A.S., Volkov N.B. Densification of the granular medium by the low amplitude shock waves. Acta Mechanica, 2009, vol. 207, pp. 223–234. DOI: 10.1007/s00707-008-0127-2.
33.Boltachev G.Sh., Volkov N.B., Ivanov V.V., Kaygorodov A.S. Shock-wave compaction of the granular medium initiated by magnetically pulsed accelerated striker. Acta Mechanica, 2009, vol. 204, pp. 37–50. DOI: 10.1007/s00707-008-0046-2.
34.Olevsky E.A., Bokov A.A., Boltachev G.Sh., Volkov N.B., Zayats S.V., Ilyina A.M., Nozdrin A.A., Paranin S.N. Modeling and optimization of uniaxial magnetic pulse compaction of nanopowders. Acta Mech., 2013, vol. 224, pp. 3177–3195. DOI 10.1007/s00707-013-0939-6
35.Boltachev G.Sh., Volkov N.B., Chingina E.A. Nanopowders in Dynamic Magnetic Pulse Compaction Processes. Nanotechnologies in Russia, 2014, vol. 9, no. 11–12, pp. 650–659. DOI: 10.1134/S1995078014060056.
36.Bokov A.A., Boltachev G.Sh., Volkov N.B., Zayats S.V., Il’ina A.M., Nozdrin A.A., Paranin S.N., Olevskii E.A. Uniaxial Compaction of Nanopowders on a Magnetic_Pulse Press. Technical Physics, 2013, vol. 58, no. 10, pp. 1459–1468. DOI: 10.1134/S106378421310006X.
37.Fedotov A.F., Amosov A.P., Radchenko V.P. Modelirivanie protsessa pressovaniya poroshkovykh materialov v uslovuyakh samorasprostranyayuschegosya vysokotemperaturnogo sinteza [Modeling the Powder Material Compaction in Conditions of the Self-Propagating High-Temperature Synthesis]. Moscow, Mashinostroenie-1 Publ., 2005, 282 p. (In Russian).
38.Kiselev A.B., Yumashev M.V Deformation and Failure under Impact Loading. Model of a Thermoelastoplastic Medium. Prikladnaya Mekhanika i Tekhnicheskaya Phizika, 1990, vol. 31, no. 5, pp. 116–123. (In Russian).
39.Godunov S.K., Romenskii E.I. Elementy mekhaniki sploshnykh sred i zakony sokhraneniya [Elements of continuum mechanics and conservation laws]. Novosibirsk, Nauchnaya Kniga Publ., 1998, 267 p. (In Russian).
40.Bardet J.P., Proubet J. Application of micromechanics to incrementally nonlinear constitutive equations for granular media. In: J. Biarez, R. Gourvès, eds. Powders and Grains, Int. Conf. on micromechanics of granular media, Clermont-Ferrand, 4–8 September, 1989: Proceedings., pp. 265–273.
41.Resnyansky A.D., Bourne N.K. Shock-wave compression of a porous material. J. Appl. Phys., 2004, vol. 95, no. 4, pp. 760–1769. DOI: 10.1063/1.1640460.
42.Boshoff-Mostert L., Viljoen H. J. Comparative study of analytical methods for Hugoniot curves of porous materials. J. Appl. Phys., 1999, vol. 86, no. 3, pp. 1245–1254. DOI: 10.1063/1.370878.
43.Fenton G., Grady D., Vogler T. Shock Compression Modeling of Distended Mixtures. Journal of Dynamic Behavior Materials, 2015, vol. 1, pp. 103–113. DOI: 10.1007/s40870-015-0021-7.
44.Shen A.H., Ahrens T.J., O’Keefe J.D. Shock wave induced vaporization of porous solids. J. Appl. Phys., 2003, vol. 93, pp. 5167–5174. DOI: 10.1063/1.1563035.
45.Nigmatulin R.I. Osnovy mekhaniki geterogennykh sred [Fundamentals of the Mechanics of Heterogeneous Media]. Moscow, Nauka Publ., 1978, 336 p. (In Russian).
46.Dunin S.Z., Surkov V.V. Dynamics of the closing of pores at the shock-wave front. PMM Journal of Applied Mathematics and Mechanics, 1979, vol. 43, iss. 3, pp. 550–558. DOI: 10.1016/0021-8928(79)90103-5.
47.Kraiko A.N., Miller L.G., Shirkovskii I.A. About gas flow in porous media with surfaces of porosity Discontinuity. Prikladnaya Mekhanika i Tekhnicheskaya Phizika, 1982, no. 1, pp. 111-118. (In Russian).
48.Zhdanovich G.M. Theory of Compaction of Metal Powders, transl. Teoriya Pressovaniya Metallicheskikh Poroshkov [Theory of Metal Powder Pressing, 1969, pp. 1–262]. Foreign Technology Division, Wright-Patterson Air Force Base, OH, 1971.
49.Ivanov V.V., Nozdrin A.A. Method of determining dynamic adiabatic compression curves of powders. Technical Physics Letters, 1997, vol. 23, pp. 527–528. DOI: 10.1134/1.1261734.
50.Nowacki W.K. Stress Waves in Non-Elastic Solids, Pergamon Press, Oxford, U.K, 1978, 182 p.
51.Proskuryakov N.E., Orlov S.Yu., Cherevatyi R.S. The effect of deformation velocity on dynamic yield stress. In: Mekhanika deformiruemogo tverdogo tela i obrabotka metallov davleniem, Tula, Tulskii Gosudarstvennyi Universitet Publ., 2001, pp. 134–138. (In Russian).
52.Carroll M.M., Kim K.T., Nesterenko V.F. The effect of temperature on viscoplastic pore collapse. J. Appl. Phys., 1986, vol. 59, no. 6, pp. 1962–1967. DOI: 10.1063/1.336426.
53.Polyakov A.P., Zalazinskaya E.A. Dynamic compaction of compacts of non-compacted metal stock. Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall., 2003, no. 1, pp. 30-34. (In Russian).
54.Green R.J. A plasticity theory for porous solids. Int. J. Mech. Sci., 1972, vol. 14, iss. 4, pp. 215–224. DOI: 10.1016/0020-7403(72)90063-X.
55.Zalazinskii A.G., Polyakov A.A., Polyakov A.P. On plastic compression of a porous body. Mechanics of Solids, 2003, vol. 38, no. 1, pp. 101–110.
56.Kolachev B.A., Livanov V.A., Bukhanova A.A. Mekhanicheskie svoistva titana i ego splavov [Mechanical Properties of Titanium and its Alloys]. Moscow, Metallurgiya Publ., 1974, 544 p. (In Russian).
57.Polyakov A.P., Mokrousova M.S. Mathematical modeling of the process of dynamic compaction of a powder material. Kuznechno-Shtampovochnoe Proizvodstvo. Obrabotka Materialov Davleniem, 2004, no. 2, pp. 20–22, 24–27. (In Russian).
58.Polyakov A.P. The effect of parameters of dynamic loading on the propagation character of shock waves in a powder. Russian Journal of Non-Ferrous Metals, 2009, vol. 50, no. 1, pp. 33–38. DOI: 10.3103/S106782120901009X.
59.Druyanov B.A. Prikladnaya teoriya plastichnosti poristykh tel [Applied Theory of Plasticity of Porous Bodies]. Moscow, Mashinostroenie Publ., 1989, 168 p. (In Russian).
60.Zalazinskii A.G., Plasticheskoe deformirovanie strukturno-neodnorodnykh materialov [Plastic Deformation of Structurally Nonuniform Materials]. Yekaterinburg, Ural. Otd. Ross. Akad. Nauk Publ., 2000, 492 p. (In Russian).
61.Polyakov A.P. Impact extrusion of rod stock through conical die. Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall., 2004, no. 4, pp. 50–54. (In Russian).
62.Grigor'ev A.K., Rudskoi A.I. Deformatsiya i uplotnenie poroshkovykh materialov [Deformation and Compaction of Powder Materials]. Moscow, Metallurgiya Publ., 1992, 192 p. (In Russian).
63.Polyakov A.P. Impact extrusion process of billet production from low compressible material. Izv. VUZov. Chernaya Metallurgiya, 2006, no. 3, pp. 32–37. (In Russian).
64.Polyakov A.P. Power Parameters of the Impact Pressing Process of an Incompact Wire Stock. Russian Journal of Non-Ferrous Metals, 2007, vol. 48, no. 2, pp. 136–142. DOI: 10.3103/S1067821207020125.
Рассмотрены математические модели динамического прессования и выдавливания некомпактных металлических материалов. В соответствии с моделью динамического прессования, происходящие под действием ударных волн, необратимые изменения объема в материале рассматриваются на основе общих уравнений сохранения массы, количества движения и энергии, записанных для поверхности разрыва.
Построена математическая модель процесса ударного выдавливания некомпактной заготовки через коническую матрицу. Она основывается на суперпозиции решений задачи о прессовании порошкового материала в цилиндрической пресс-форме и задачи об ударном выдавливании несжимаемого материала. Модель позволяет определить минимальную скорость инструмента, позволяющую осуществить выдавливание заготовки.
1.Обработка металлов взрывом / А. В. Крупин, В. Я. Соловьев, Г. С. Попов, М. Р. Кръстев. – М. : Металлургия, 1991. – 496 с.
Дмитриев А. М., Воронцов А. Л. Технология ковки и объемной штамповки. Часть 1. Объемная штамповка выдавливанием : учебник для вузов с грифом Минобразования РФ. – М. : Высшая школа, 2002. – 400 с.
3.Роман О. В., Горобцов В. Г. Импульсное нагружение порошковых материалов // Актуальные проблемы порошковой металлургии / под ред. О. В. Романа, В. С. Аруначалама – М. : Металлургия, 1990. – С. 78–99.
4.Belyakov G. V., Rodionov V. N., Samosadnyi V. P. Heating of porous material under impact compression // Combustion explosion and shock waves. – 1977. – Vol. 13, iss. 4. – P. 524–528. – DOI: 10.1007/BF00744803.
5.Герасимов А. В., Кректулева Р. А. Численное моделирование деформирования и разрушения функционально градиентных пористых материалов при взрывном и ударном нагружении // Механика композиционных материалов и конструкций. – 1999. – Т. 5, № 3. – C. 94–106.
6.Alekseev Yu. L., Ratnikov V. P., Rybakov A. P. Shock adiabats of porous metals // Journal of Applied Mechanics and Technical Physics. – 1971. – Vol. 12, no. 2. – P. 257–262. – DOI: 10.1007/BF00850698.
7.Anisichkin V. F. Shock compression of porous bodies // Combustion explosion and shock waves. – 1979. – Vol. 15, iss. 6. – P. 796–799. – DOI: 10.1007/BF00739873.
8.Высокоскоростное взаимодействие тел / В. М. Фомин, А. И. Гулидов, Г. А. Сапожников, И. И. Шабалин, В. А. Бабаков, В. Ф. Куропатенко, А. Б. Киселев, Ю. А. Тришин, А. И. Садырин, С. П. Киселев, И. Ф. Головлев. – Новосибирск : СО РАН, 1999. – 600 с.
9.Дерибас А. А., Ставер А. М. Ударное сжатие цилиндрических пористых тел // ФГВ, 1974. – Т. 10, № 4. – С. 568–578.
10.Кузьмин Г. Е., Ставер А. М. К определению параметров течения при ударном нагружении порошкообразных материалов // ФГВ, 1973. – Т. 9, № 6. – С. 898–905.
11.Магнитно-импульсная штамповка полых цилиндрических заготовок / А. К. Талалаев, С. П. Яковлев, В. Д. Кухарь, Н. Е. Проскуряков, Е. М. Селедкин, Ю. Г. Нечепуренко. – Тула : Репроникс Лтд., 1998. – 238 с.
12.Нестеренко В. Ф. Импульсное нагружение гетерогенных материалов. – Новосибирск : Наука, 1992. – 200 с.
13.Roman O. V., Mirilenko A. P., Pikus I. M. Theory and technology of the component formation process - effect of high-speed loading conditions on the pressing mechanism // Soviet Powder Metallurgy and Metal Ceramics. – 1989. – Vol. 28, iss. 11. – P. 840–844. – DOI: 10.1007/BF01198890.
14.Сердюк Г. Г., Свистун Л. И. Ударное прессование металлических порошков (теоретическое исследование). // Реологические модели и процессы деформирования пористых порошковых и композиционных материалов. – Киев : Наук. думка, 1985. – C. 115–126.
15.Hermann W. Constitutive equation for the dynamic compaction of ductile porous materials. // Journal of Applied Physics. – 1969. – Vol. 40, no. 6. – P. 2490–2499. – DOI: 10.1063/1.1658021.
16.Shtertser A. A. Transmission of pressure in porous-media under explosive loading // Combustion explosion and shock waves. – 1988. – Vol. 24, iss. 5. – P. 610–615.
17.Butcher B. M., Carroll M. M., Holt A. C. Shock wave compaction of porous aluminum // J. Appl. Phys. – 1974. – Vol. 45, no. 9. – P. 3864–3875. – DOI: 10.1063/1.1663877.
18.Carroll M. M., Holt A. C. Steady waves in ductile porous solids // J. Appl. Phys. – 1973. – Vol. 44, no. 10. – P. 4388–4392. – DOI: 10.1063/1.1661970.
19. Davison L. Shock-wave structure in porous solids // J. Appl. Phys. – 1971. – Vol. 42, no. 13. – P. 5503–5512. – DOI: 10.1063/1.1659971.
20.Hǿrlück S., Dimon P. Statistics of shock waves in a two-dimensional granular flow // Physical Review E. – 1999. – Vol. 60, no. 1. – P. 671–686. – DOI: 10.1103/PhysRevE.60.671.
21.Nunziato J. W., Walsh E. K. One-dimensional shock waves in uniformly distributed granular materials // Int. J. Solids and Struct. – 1978. – Vol. 14, no. 8. – P. 681–689. – DOI: 10.1016/0020-7683(78)90006-9.
22.Numerical Simulation of Shock-Wave Processes in Elastic Media and Structures. Part I: Solving Method and Algorithms / М. V. Ayzenberg-Stepanenko, G. G. Osharovich, Е. N. Sher, Z. Sh. Yanovitskaya // Journal of Mining Science. – 2012. – Vol. 48, no. 1. – P. 76–95. – DOI: 10.1134/S1062739148010091.
23.Simulation of the action of a shock wave on titanium alloy / S. A. Afanas'eva, N. N. Belov, V. V. Burkin, E. F. Dudarev, A. N. Ishchenko, K. S. Rogaev, A. N. Tabachenko, M. V. Khabibullin, N. T. Yugov // Journal of Engineering Physics and Thermophysics. – 2017. – Vol. 90, no. 1. – P. 24–34. – DOI: 10.1007/s10891-017-1535-8.
24.Roman O. V., Shmuradko V. T., Tarasov G. D. Curve of the dynamic compressibility of powder media // Journal of Engineering Physics and Thermophysics. – 2006. – Vol. 79, no. 4. – P. 817–823.
25.Measuring the Nanohardness of Commercial Submicrocrystalline Aluminum Alloys Produced by Dynamic Pressing / O. A. Chikova, E. V. Shishkina, A. N. Petrova, I. G. Brodova // The Physics of Metals and Metallography. – 2014. – Vol. 115, no. 5. – P. 523–528. – DOI: 10.1134/S0031918X14050044.
26.Dynamic Pressing of Titanium for Producing an Ultrafine-Grained Structure / E. V. Shorokhov, I. N. Zhgilev, D. V. Gunderov, A. A. Gurov // Russian Journal of Physical Chemistry B. – 2008. – Vol. 2, no. 2. – P. 251–254. – DOI: 10.1134/S1990793108020139.
27.Рогозин В. Д. Взрывная обработка порошковых материалов. – Волгоград : Политехник, 2002. – 136 с.
28.Kinelovskii S. A., Maevskii K. K. Model of the behavior of the mixture with different properties of the species under high dynamic loads // Journal of Applied Mechanics and Technical Physics. – 2013. – Vol. 54, no. 4. – P. 524–530. – DOI: 10.1134/S0021894413040020.
29.Vogler T. Shock Wave Perturbation Decay in Granular Materials // J. dynamic behavior mater. – 2015. – Vol. 1. – P. 370–387. – DOI 10.1007/s40870-015-0033-3.
30.Shtern M. B., Kartuzov E. V. Formation and propagation of shock waves in highly porous materials // Powder Metallurgy and Metal Ceramics. – 2016. – Vol. 55, no. 3–4. – P. 134–140. – DOI: 10.1007/s11106-016-9788-x.
31.Лейцин В. Н. Модель реагирующей порошковой среды // Вестник Томск. гос. ун-та : общенаучный периодический журнал : бюллетень оперативной технической информации. – Томск : ТГУ, 2001. – № 5. – 40 с.
32.Boltachev G. Sh., Kaygorodov A. S., Volkov N. B. Densification of the granular medium by the low amplitude shock waves // Acta Mechanica. – 2009. – Vol. 207. – P. 223–234. – DOI: 10.1007/s00707-008-0127-2.
33.Shock-wave compaction of the granular medium initiated by magnetically pulsed accelerated striker / G. Sh. Boltachev, N. B. Volkov, V. V. Ivanov, A. S. Kaygorodov // Acta Mechanica. – 2009. – Vol. 204. – P. 37–50. – DOI: 10.1007/s00707-008-0046-2.
34.Modeling and optimization of uniaxial magnetic pulse compaction of nanopowders / E. A. Olevsky, A. A. Bokov, G. Sh. Boltachev, N. B. Volkov, S. V. Zayats, A. M. Ilyina, A. A. Nozdrin, S. N. Paranin // Acta Mech. – 2013. – Vol. 224. – P. 3177–3195. – DOI: 10.1007/s00707-013-0939-6.
35.Boltachev G. Sh., Volkov N. B., Chingina E. A. Nanopowders in Dynamic Magnetic Pulse Compaction Processes // Nanotechnologies in Russia. – 2014. – Vol. 9, no. 11–12. – P. 650–659. – DOI: 10.1134/S1995078014060056.
36.Uniaxial Compaction of Nanopowders on a Magnetic Pulse Press / A. A. Bokov, G. Sh. Boltachev, N. B. Volkov, S. V. Zayats, A. M. Il’ina, A. A. Nozdrin, S. N. Paranin, E. A. Olevskii // Technical Physics. – 2013. – Vol. 58, no. 10. – P. 1459–1468. – DOI: 10.1134/S106378421310006X.
37.Федотов А. Ф., Амосов А. П., Радченко В. П. Моделирование процесса прессования порошковых материалов в условиях самораспространяющегося высокотемпературного синтеза. – М. : Машиностроение-1, 2005. – 282 с.
38.Киселев А. Б., Юмашев М. В. Деформирование и разрушение при ударном нагружении. Модель повреждаемой термоупругопластической среды // ПМТФ. – 1990. – Т. 31, № 5. – С. 116–123.
39.Годунов С. К., Роменский Е. И. Элементы механики сплошных сред и законы сохранения. – Новосибирск : Научная книга, 1998. – 267 с.
40.Bardet J. P., Proubet J. Application of micromechanics to incrementally nonlinear constitutive equations for granular media // Int. Conf. on micromechanics of granular media “Powders and Grains”, Clermont-Ferrand, 4-8 September 1989 : proceedings / ed. by J. Biarez, R. Gouvrès. – 1989. – P. 265–273.
41.Resnyansky D., Bourne N. K. Shock-wave compression of a porous material // J. Appl. Phys. – 2004. – Vol. 95, no. 4. – P. 760–1769. – DOI: 10.1063/1.1640460.
42.Boshoff-Mostert L., Viljoen H.J. Comparative study of analytical methods for Hugoniot curves of porous materials // J. Appl. Phys. – 1999. – Vol. 86, no. 3. – P. 1245–1254. – DOI: 10.1063/1.370878.
43.Fenton G., Grady D., Vogler T. Shock Compression Modeling of Distended Mixtures // J. dynamic behavior mater. – 2015. – Vol. 1. – P. 103–113. – DOI: 10.1007/s40870-015-0021-7.
44.Shen H., Ahrens T. J., O’Keefe J. D. Shock wave induced vaporization of porous solids // J. Appl. Phys. – 2003. – Vol. 93. – P. 5167–5174. – DOI: 10.1063/1.1563035.
45.Нигматулин Р. И. Основы механики гетерогенных сред. – М. : Наука, 1978. – 336 с.
46.Dunin S. Z., Surkov V. V. Dynamics of the closing of pores at the shock-wave front // Journal of Applied Mathematics and Mechanics. – 1979. – Vol. 43, iss. 3. – P. 550–558.
47.Крайко А. Н., Миллер Л. Г., Ширковский И. А. О течении газа в пористой среде с поверхностями разрыва пористости // ПМТФ. – 1982. – № 1. – С. 111–118.
48.Жданович Г. М. Теория прессования металлических порошков. – М. : Металлургия, 1969. − 264 с.
49.Ivanov V. V., Nozdrin A. A. Method of determining dynamic adiabatic compression curves of powders // Technical Physics Letters. – 1997. – Vol. 23. – P. 527–528. – DOI: 10.1134/1.1261734.
50.Nowacki W. K. Stress Waves in Non-Elastic Solids. – Oxford : Pergamon Press, 1978. – 182 p.
51.Проскуряков Н. Е., Орлов С. Ю., Череватый Р. С. Влияние скорости деформирования на динамический предел текучести // Механика деформируемого твердого тела и обработка металлов давлением : сб. науч. тр. – Тула : ТулГУ, 2001. – Ч. 1. – С. 134–138.
52.Carroll M. M., Kim K. T., Nesterenko V. F. The effect of temperature on viscoplastic pore collapse // J. Appl. Phys. – 1986. – Vol. 59, no. 6. – P. 1962–1967. – DOI: 10.1063/1.336426.
53.Поляков А. П., Залазинская Е. А. Ударное прессование заготовки из некомпактного металлического сырья // Изв. ВУЗов. Цветная металлургия. – 2003. – № 1. – С. 30–35.
54.Green R. J. A plasticity theory for porous solids // Int. J. Mech. Sci. – 1972. – Vol. 14. – P. 215–224. – DOI: 10.1016/0020-7403(72)90063-X.
55.Zalazinskii A. G., Polyakov A. A., Polyakov A. P. On plastic compression of a porous body // Mechanics of Solids. – 2003. – Vol. 38, no. 1. – P. 101–110.
56.Колачев Б. А., Ливанов В. А., Буханова А. А. Механические свойства титана и его сплавов. – М. : Металлургия, 1974. – 544 с.
57.Поляков А. П., Мокроусова М. С. Математическое моделирование процесса динамического прессования порошкового материала // КШП. ОМД. – 2004. – № 2. – С. 20–22. – C. 27–30.
58.Polyakov P. The Effect of parameters of dynamic loading on the propagation character of shock waves in a powder // Russian Journal of Non-Ferrous Metals. – 2009. – Vol. 50, no. 1. – P. 33–38. – DOI: 10.3103/S106782120901009X.
59.Друянов Б. А. Прикладная теория пластичности пористых тел. – М. : Машиностроение, 1989. – 168 с.
60.Залазинский А. Г. Пластическое деформирование структурно-неоднородных материалов. – Екатеринбург : УрО РАН, 2000. – 492 с.
61.Поляков А. П. Ударное выдавливание прутковой заготовки через коническую матрицу // Изв. ВУЗов. Цветная металлургия. – 2004. – № 4. – C. 50–54.
62.Григорьев А. К., Рудской А. И. Деформация и уплотнение порошковых материалов. – М. : Металлургия, 1992. – 192 с.
63.Поляков А. П. Ударное выдавливание заготовки с учетом малой сжимаемости материала // Изв. ВУЗов. Черная металлургия. – 2006. – № 3. – С. 32–37.
64Polyakov A. P. Power Parameters of the Impact Pressing Process of an Incompact Wire Stock // Russian Journal of Non-Ferrous Metals. – 2007. – Vol. 48, no. 2. – P. 136–142. – DOI: 10.3103/S1067821207020125.
