Research of mathematical model of the energy criterion for fracture of brittle materials

Authors

  • Dunaev V.I. Kuban State Technological University, Krasnodar, Russian Federation
  • Titov N.G. Kuban State University, Krasnodar, Russian Federation
  • Kesova E.F. Kuban State Technological University, Krasnodar, Russian Federation
  • Prikhodko M.G. Kuban State Technological University, Krasnodar, Russian Federation

UDC

539.375

EDN

ZARBWX

DOI:

10.31429/vestnik-16-1-21-25

Abstract

In this paper, we study a mathematical model of the criterion for the destruction of fragile materials at $\varepsilon \ll 1$ where $\varepsilon $ is the relative size of the resulting defect. Under the assumption that the crack does not "close" during development,

it is shown that the marginal curve represents an ellipse in the space of main stresses $P_{1}$, $P_{2}$. If we additionally assume that we have the physico-mechanical meaning of the determining parameter of the limiting curve, it is found that the relative size of the resulting defect $\varepsilon $ can be chosen significantly less than one. At the same time, the crack "opens" during development. An estimate of the relative size of the crack from the bottom was obtained from the condition of the non-closure of the crack faces.

Keywords:

destruction, brittle material, defect, cracks, mathematical model, stretching, compression

Authors info

  • Vladislav I. Dunaev

    д-р физ.-мат. наук, профессор кафедры оборудования нефтяных и газовых промыслов Института нефти, газа и энергетики Кубанского государственного технологического университета

  • Nikolay G. Titov

    преподаватель Института среднего профессионального образования Кубанского государственного университета

  • Elizveta F. Kesova

    преподаватель кафедры оборудования нефтяных и газовых промыслов Института нефти, газа и энергетики Кубанского государственного технологического университета

  • Marina G. Prikhodko

    магистрант кафедры оборудования нефтяных и газовых промыслов Института нефти, газа и энергетики Кубанского государственного технологического университета

References

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  2. Дунаев И.М., Дунаев В.И. Энергетическое условие разрушения твёрдых тел // Механика твёрдого тела. 2003. № 6. С. 69–81. [Dunaev, I.M., Dunaev, V.I. Energy condition for fracture of solids. Mechanics of solids, 2003, no. 6, pp. 69–81. (In Russian)]
  3. Дунаев В.И., Молдованов С.Ю., Лозовой С.Б, Георгияди В.Г. Хрупкое разрушение материалов при развитии "узких" изолированных дефектов // Экологический вестник научных центров черноморского экономического сотрудничества. 2015. №3. С. 26–37. [Dunaev, V.I., Moldavanov, S.Yu., Lozova, S.B., Georgiadi, V.G. Fragile destruction of materials in the development of "narrow" isolated defects. Ecological Bulletin of the scientific centers of the black sea economic cooperation, 2015, no. 3, pp. 26–37. (In Russian)]
  4. Dunaev I.M., Dunaev V.I. Macroscopic Criterion for Brittle Fructure of Solids // Proc. Of the 7-th EVROMECH. Solid Mechanics Conference 2009. Portugal, Lisbon. P. 117–118.
  5. Ильюшин А.А., Ленский Б.С. Сопротивление материалов. М.: Гос. из-во физ.-мат. лит., 1959. 371 с. [Ilyushin, A.A., Lenski, B.S. Mechanics of materials. GOS. iz-vo Fiz.-Mat. lit., Moscow, 1959. (In Russian)]
  6. Мусхелишвили Н.И. Некоторые основные задачи математической теории упругости. М.: Наука, 1966. 707 с. [Muskhelishvili, N.A. Some basic problems of mathematical theory of elasticity. Nauka, Moscow, 1966. (In Russian)]

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Issue

Vol. 16 (2019) No. 1

Pages

21-25

Section

Mechanics

Dates

Submitted

January 25, 2019

Accepted

February 23, 2019

Published

March 30, 2019

How to Cite

[1]
Dunaev, V.I., Titov, N.G., Kesova, E.F., Prikhodko, M.G., Research of mathematical model of the energy criterion for fracture of brittle materials. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2019, т. 16, № 1, pp. 21–25. DOI: 10.31429/vestnik-16-1-21-25

License

Copyright (c) 2019 Дунаев В.И., Титов Н.Г., Кесова Е.Ф., Приходько М.Г.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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