Mathematical variational method for determining the effective yield strength of two-component composite materials
https://doi.org/10.22405/2226-8383-2021-22-1-370-377
Abstract
The paper proposes the development of the mathematical variational Hashin-Strickman method, which was previously used to determine the maximum possible values of effective elastic
characteristics. In this case, the effective plasticity characteristics of two-component composites are determined. In particular, the fork of possible values of the effective yield strength of such
composite materials is determined
About the Authors
Igor Konstantinovich Arkhipov
Tula State Pedagogical University L. N. Tolstoy
Russian Federation
Russian Federation
doctor of technical sciences, professor
Vlada Igorevna Abramova
Tula State Pedagogical University L. N. Tolstoy
Russian Federation
Russian Federation
candidate of technical sciences, associate professor
Olga Vladimirovna Kuzovleva
Russian State University of justice
Russian Federation
Russian Federation
candidate of technical sciences, docent
Alexandr Evgenyevich Gvozdev
Tula State Pedagogical University L.N. Tolstoy
Russian Federation
Russian Federation
doctor of engineering, professor
References
1. Hashin Z. 1964, «Theory of mechanical behavior of heterogeneous media», Appl. Mech. Rev., 17, №1.
2. Hashin Z., Shtrikman S. 1962, «On some variational principles in anisotropic and nonhomogeneous elasticity», J. Mech. Phys. Solids, 10, №4, p.335.
3. Arkhipov I.K. 1995, «Characteristics of the properties of elasticity and plasticity of composite materials», Dissertation for the degree of doctor of technical Sciences. Tula, 218 p.
4. Shermergor T.D. 1977, Theory of elasticity of micro-homogeneous media. Moscow. Nauka, 399 pp.
5. Zubchenko A.S. 2003. Vintage of steels and alloys. Moscow, Mashinostroenie, 715 p.
6. Shtanov E.N., Shtanova I.A. 2001. Non-ferrous metals and alloys. Directory. N. Novgorod, Venta-2, 277 p.
7. Gvozdev A.E., Golyshev I.V., Minayev I.V., Sergeyev A.N., Sergeyev N.N., Tikhonova I.V., Khonelidze D.M., Kolmakov A.G. 2015, «Multiparametric optimization of lasercutt in gofsteel
8. sheets», InorganikcMaterials: AppliedResearch, vol.6, No.1, pp. 305–310.
9. Gvozdev A.E., Sergeev N.N., Minaev I.V., Tikhonova I.V. 2015, «Role of nucleation in the development of first-order phase transformations», Inorganic Materials: Applied Research, vol.6, №4, pp. 283–288.
10. The patent for the invention 2014135667/02 (2590045) Russian Federation / Method for obtaining metal powder from high-speed steel waste in kerosene / / E. V. Ageev, E. A. Vorobyov, A. E. Gvozdev, E. V. Ageeva. Applicant and patent holder: Southwestern state University. No. 2014135667/02, publ. 10.07.2016. Byul. no. 19.
11. The patent for the invention 2014135539 (2597445) Russian Federation / Method for obtaining copper nanopowder from waste / / E. V. Ageev, N. M. Horyakova, A. E. Gvozdev, E. V.
12. Ageeva, V. S. Malyukhov. Applicant and patent holder: Southwestern state University. No. 2014135539/02, publ. 10.09.2016. Byul. 25.
13. The patent for invention 2014135563 (2599476) Russian Federation / Method of obtaining copper powder from the waste // E.V. Ageev, E.V. Ageeva, N.M. Horakova, A.E. Gvozdev.
14. Applicant and patent holder: Southwestern state University. No. 2014135563, publ. 10.10.2016.
15. Breki A.D., Gvozdev A.E., Kolmakov A.G. 2016, «Using the generalized Pascal triangle to describe vibrations of the friction force of materials», Materials science, No.11, pp. 3–8.
16. Shorshorov M.H., Gvozdev A.E., Afanaskin A.V., Gvozdev E.A. 2002, «The calculation of the cluster structure of the melt, its impact on education anamorph solid phases and their structural relaxation upon subsequent heating», The Metallography and heat treatment of metals, No. 6,
17. pp. 12–16.
18. Shorshorov M.Kh., Gvozdev A.E. 2004, «On mechanisms and kinetics of grain accommodation processes under superplastic deformation of metal alloys under uniaxial tension», Materials Science, No. 7 (88), pp. 13–17.
19. Gvozdev A.E., Sergeev N.N., Minaev I.V., Tikhonova I.V. 2015, «Role of nucleation in the development of first-order phase transformations», Inorganic Materials: Applied Research, vol.6, №4, pp. 283–288.
20. Gvozdev A.E., Kolmakov A.G., Kuzovleva O.V., Sergeev N.N., Tikhonova I.V. 2013, «Mechanical properties of structural and tool steels in the state of pre-rotation under thermomechanical action», Deformation and destruction of materials, No.11, pp. 39–43.
21. Gvozdev A.E., Kolmakov A.G., Provotorov D.A., Bogolyubova D.N., Sergeev N.N., Tikhonova I.V. 2015, «Features of Softening Processes of Aluminum, Copper, and Their Alloys under Hot Deformation», Inorganic Materials: Applied Research, vol.6, No.1, pp. 32–40.
22. Gvozdev A.E., Kolmakov A.G., Provotorov D.A., Minaev I.V., Sergeev N.N., Tikhonova I.V. 2015, «Grain size effect of austenite on the kinetics of pearlite transformation in low and medium carbon low alloy steels», Inorganic Materials: Applied Research, vol.6, No.1, pp. 41–44.
23. Zhuravlev G.M., Gvozdev A.E., Sergeev N.N., Provotorov D.A. 2016, «The calculation of maximum hardening of low carbon steels in plastic deformation processes», Production of rolled, No.7, pp. 9–13.
24. Gvozdev A.E., Zhuravlev G.M., Kolmakov A.G., Sergeev N.N. 2016, «Calculation of strain damage in the process of reverse extrusion of metal products», Technology of metals, No.1, pp. 23–32.
25. Breki A.D., Vasilyeva E.S., Tolochko O.V., Didenko A.L., Kudryavtsev V.V., Kolmakov A.G., Sergeev N.N., Gvozdev A.E., Starikov N.E., Provotorov D.A., Fadin Y.A. 2016, «Synthesisand
26. tribotechnical properties of composite coatings with PM-DAD PE polyimide matrix and fillers of tung stendich alcogenide nanoparticle supon dry sliding friction», Inorganic Materials:
27. Applied Research, T.7, №4, pp. 542–546.
28. Zhuravlev G.M., Gvozdev A.E. 2016. Processing of steels and alloys in the temperature range of phase transformations. Tula, Tula state University Publishing house, 320 p.
29. Kuzovleva O.V., Gvozdev A.E., Tikhonova I.V., Sergeev N.N., Breki A.D., Starikov N.E., Sergeev A.N., Kalinin A.A., Maliy D.V., Titova Yu.E., Aleksandrov S.E., Krylov N.A. 2016.
30. On the state of pre-conversion of metals and alloys. Tula: Tulsu Publishing house, 245 p.
31. Breki, A.D., Didenko, A.L., Kudryavtsev, V.V., Vasilyeva, E.S., Tolochko, O.V., Gvozdev, A.E., Sergeyev, N.N., Provotorov, D.A., Starikov, N.E., Fadin, Yu.A., Kolmakov, A.G. 2017,
32. «Composite coatings based on A-OOO polyimide and WS2 nanoparticles with enhanced dry sliding characteristics», Inorganic Materials: Applied Research, Т.8. №1. pp. 56–59.
33. Breki A.D., Gvozdev A.E., Kolmakov A.G. 2017, «Application of generalized pascal triangle for description of oscillations of friction forces», Inorganic Materials: Applied Research, Т.8, №4,
34. С. 509–514.
35. Gvozdev A. E. 2019. Extreme strength and ductility effects in high-alloy metal ingot and powder systems. 2nd ed., ISPR. and add. Tula: Publishing house of Tula state University, 476 p.
36. Gvozdev A.E., Sergeev N.N., Starikov N.E., Sapozhnikov S.V., Kutepov S.N., Malyarov A.V., Kalinin A.A. 2019. Low-waste technologies for obtaining tools from hot-rolled, powder and cast
37. billets of high-speed steels 2nd ed., ISPR. and add. Edited by Prof. N.N. Sergeev. Tula, Tula state University Publishing house, 282 p.
38. Minaev I.V., Tikhonova I.V., Gvozdev A.E., Kolmakov A.G., Arkhipova E.A. 2020, «Formation of the cutting surface and surface hardening during laser cutting with an asterisk for chains
39. made of St.3 and 30KHGSA steels», Deformation and destruction of materials, No.9, pp. 16–21.
40. Sergeev N.N., Minaev I.V., Tikhonova I.V., Gvozdev A.E., Kolmakov A.G., Sergeev A.N., Kutepov S.N., Malii D.V., 2020, «Selecting Laser Cutting Modes for Engineering Steel Sheets
41. Aiming at Provision of the Required Properties of Surface Quality», Inorganic Materials: Applied Research, v.11, №4, pp. 815–822.
Review
For citations:
Arkhipov I.K., Abramova V.I., Kuzovleva O.V., Gvozdev A.E. Mathematical variational method for determining the effective yield strength of two-component composite materials. Chebyshevskii Sbornik. 2021;22(1):370-377. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-1-370-377
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