"Elasticity" Variables Parameters of Nonlinear Deformable Transversely-Isotropic Medium

Received 18 August 2017; Accepted 02 March 2018;
This paper is written in Russian
Citation: T. Karimbayev. "Elasticity" Variables Parameters of Nonlinear Deformable Transversely-Isotropic Medium. Lett. Mater., 2018, 8(2) 208-214
BibTex   https://doi.org/10.22226/2410-3535-2018-2-208-214

Abstract

A method for predicting nonlinear behavior of unidirectional reinforced composite is developed. It is based on nonlinear strain of matrix material described modified relations flow theory to account for the technological defects. The developed approach allows to build stress-strain curves of unidirectional-reinforced composite at tensile along the fibers, at tensile and shear in the reinforcement plane and explore resistance reinforced unidirectional composite complex loading.Composite materials based on metal and ceramic matrices appear in the design of parts and structures. The mechanical properties of the constituents of these com-posite materials are comparable. The design of parts made of polymer composite materials is usually based on the assumption of elastic deformations of constituents of the composite material, including the polymer matrix. This assumption does not always work for metal and ceramic composite materials, which makes it difficult to optimize products made of such materials. In addition, the assumption of the elas-ticity of the composites makes it impossible to estimate the ultimate deformation of the parts. In this connection, nonlinear properties of inhomogeneous, transversally anisotropic composite materials based on metallic or intermetallic matrices are dis-cussed here. It is assumed that the nonlinear properties of composite materials are formed by the nonlinear behavior of the matrix. Earlier, on the basis of the modi-fied theory of plastic flow, nonlinear dependences of the deformation of an anisot-ropic matrix were obtained. The modified theory of plastic flow makes it possible to take into account the nonlinear dependence not only between deviators of stresses and deformations, but also between the first invariants of stresses and de-formations. The nonlinearity in the dependence of the first invariants can be caused by particular manufacturing technology. Five independent strain curves for unidi-rectionally reinforced composite materials were obtained using the Maxwell and Feucht models. The obtained relations are used to find the stress-strain curves of an aluminum alloy unidirectionally reinforced with boron fibers.

References (22)

1. P. G.Kiklyaev, Ya. B. Fridman. Anisotropy of mechanical properties of metals. Moscow, Metallurgy (1986) 223 p. (in Russian) [П. Г. Микляев, Я. Б. Фридман. Анизотропия механи­ческих свойств металлов. Москва, Металлургия (1986) 223 с.].
2. S. A. Berestova. Deformation anisotropy volume-isotropic structurally heterogeneous media: dissertacija na soiskanie stepeni doctora fiziko-matematicheskih nauk. Yekaterinburg (2006) 349 p. (in Russian) [С. А. Берестова. Деформационная анизотропия объёмно-изотропных структурно-неоднородных сред: диссертация на соискание ученой степени доктора физ-мат наук. Екатеринбург (2006) 349 с.].
3. A. I. Chanyshev. Applied Mechanics and Technical Physics. 2, 149 (1984). (in Russian) [А. И. Чанышев. Прикл. механика и техн. физика. 2, 149 (1984) .].
4. Ya. A. Erisov, F. V. Grechenkov, S. B. Surudin. Bulletin of MSTU G.I. Nosova. 14(4), 42 (2016). (in Russian) [Я. А. Ерисов, Ф. В. Греченков, С. В. Сурудин. Вестник МГТУ им. Г. И. Носова. 14(4), 42 (2016).].
5. L. L. Efimenko. Construction of elastoplastic models for anisotropic media: dissertacija na soiskanie stepeni kandidata fiziko-matematicheskih nauk. Novosibirsk (2007) 140 p. (in Russian) [Л. Л. Ефименко. Построение упругопластических моделей для анизотропных сред: диссертация на соискание ученой степени кандидата физ-мат наук. Новосибирск (2007) 140 с.].
6. O. V. Salov. Nonlinear deformation of two-matrix composite structures: aftoreferat dissertacii na soiskanie stepeni kandidata tehnicheskih nauk. Moscow (1999) 14 p. (in Russian) [О. В. Салов. Нелинейное деформирование двух­матричных композитных структур: автореферат диссертации на соискание ученой степени кандидата технических наук. Москва (1999) 14 с.].
7. L. Zawada, G. Ojard, E. Bouillon, P. Spriet, C. Legan. Evalution of Ceramic Matrix Composite Exhaust Nozzle Divergent Seals. Proceedings of the 43-th AIAA / ASME / SAE / ASEE Joint Conference and Exhibit. Cincinati (2007) pp. AIAA 2007 - 5082. Crossref
8. А. А. Ilyushin. Plasticity. Moscow, Gostekhizdat (1948) 348 p. (in Russian) [А. А. Ильюшин. Пластичность. Москва, Гостехиздат (1948) 348 с.].
9. L. M. Kachanov. Fundamentals of the Theory of Plasticity. Moscow, Nauka (1969) 420 p. (in Russian) [Л. М. Качанов. Основы теории пластичности. Москва, Наука (1969) 420 с.].
10. A. A. Ilyushin. Continuum mechanics. Moscow, MGU (1978) 287 p. (in Russian) [А. А. Ильюшин. Механика сплошной среды. Москва, МГУ (1978) 287 с.].
11. V. V. Novozhilov. Problems of Continuum Mechanics. Leningrad, Sudostroenie (1989) 400 p. (in Russian) [В. В. Новожилов. Вопросы механики сплошной среды. Ленинград, Судостроение (1989) 400 c.].
12. B. D. Annin, V. M. Zhigalkin. Behavior of materials under conditions of complex loading. Novosibirsk, Siberian Branch of the RAS (1999) 341 p. (in Russian) [Б. Д. Аннин, В. М. Жигалкин. Поведение материалов в условиях сложного нагружения. Новосибирск, СО РАН (1999) 341 с.].
13. T. D. Karimbaev. Trudy CIAM. 1109(3), 93 (1985). (in Russian) [Т. Д. Каримбаев. Труды ЦИАМ. 1109(3), 93 (1985).].
14. T. D. Karimbaev, B. Myktybekov, I. M. Panova. Trudy CIAM. 1334, 160 (2005). (in Russian) [Т. Д. Каримбаев, Б. Мыктыбеков, И. М. Панова. Труды ЦИАМ. 1334, 160 (2005).].
15. D. S. Abolinysh. Mechanics of polymers. 4, 52 (1965). (in Russian) [Д. С. Аболиньш. Механика полимеров. 4, 52 (1965).].
16. V. V. Bolotin. Calculations on the strength. 12, 3 (1966). (in Russian) [В. В. Болотин. Расчеты на прочность. 12, 3 (1966).].
17. S. W. Tsai. Aeronutronic Publication. U-1699 (1962).
18. R. Christensen. An Introduction to Composite Mechanics. Moscow, Mir (1982) 334 p. (in Russian) [Р. Кристенсен. Введение в механику композитов. Москва, Мир (1982) 334 с.].
19. B. E. Pobedrya. Applied Mathematics and Mechanics. 48 (4), 29 (1984). (in Russian) [Б. Е. Победря. Прикладная математика и механика. 48 (4), 29 (1984).].
20. Yu. N. Shevchenko. Thermoplasticity under variable loading. Kiev, Naukova Dumka (1979) 287 p. (in Russian) [Ю. Н. Шевченко. Термопластичность при переменных нагружениях. Киев, Наукова Думка (1979) 287 с.].
21. S. G. Lekhnitsky. Theory of Elasticity of an Anisotropic Body. Moscow, Nauka (1977) 415 p. (in Russian) [С. Г. Лехницкий. Теория упругости анизотропного тела. Москва, Наука (1977) 415 с.].
22. Ed. A. T. Tumanov. Aviation materials: Handbook in 9 volumes, V. 4, Part 1. Moscow, ONTI (1982) 625 p. (in Russian) [Под общ. ред. А. Т. Туманова. Авиационные материалы: Справочник в 9 томах, Том 4, Часть 1. Москва, ОНТИ (1982) 625 c.].

Similar papers