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

DOI:

https://doi.org/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

Author Infos

Vladislav I. Dunaev

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

e-mail: dunaevatv@mail.ru

Nikolay G. Titov

преподаватель Института среднего профессионального образования Кубанского государственного университета

e-mail: titov_nik@mail.ru

Elizveta F. Kesova

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

e-mail: liza-kesova@mail.ru

Marina G. Prikhodko

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

e-mail: aniram-m03@mail.ru

References

  1. Dunaev, I.M., Dunaev, V.I. On the energy condition for fracture of solids. Proc. of Physics, 2000, vol. 372, no. 1, pp. 43–45. (In Russian)
  2. Dunaev, I.M., Dunaev, V.I. Energy condition for fracture of solids. Mechanics of solids, 2003, no. 6, pp. 69–81. (In Russian)
  3. 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 Fracture of Solids. Proc. Of the 7-th EVROMECH. Solid Mechanics Conference 2009. Portugal, Lisbon, pp. 117–118.
  5. Ilyushin, A.A., Lenski, B.S. Mechanics of materials. GOS. iz-vo Fiz.-Mat. lit., Moscow, 1959. (In Russian)
  6. Muskhelishvili, N.A. Some basic problems of mathematical theory of elasticity. Nauka, Moscow, 1966. (In Russian)

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Issue

2019. Vol. 16. No. 1

Section

Mechanics

Pages

21-25

Submitted

2019-01-25

Published

2019-03-30

How to Cite

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, vol. 16, no. 1, pp. 21-25. DOI: https://doi.org/10.31429/vestnik-16-1-21-25 (In Russian)

Copyright (c) 2019 Dunaev V.I., Titov N.G., Kesova E.F., Prikhodko M.G.

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