CURVILINEAR CRACK CLOSURE IN A SHEET ELEMENT UNDER THE INFLUENCE OF A TEMPERATURE FIELD

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DOI https://doi.org/10.15407/pmach2016.04.036
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 4, 2016 (December)
Pages 36-43
Cited by J. of Mech. Eng., 2016, vol. 19, no. 4, pp. 36-43

 

Authors

V. M. Mirsalimov, Azerbaijan Technical University, (25, H. Cavid Ave., Baku, AZ 1073, Azerbaijan), e-mail: mir-vagif@mail.ru, ORCID: 0000-0002-4551-6065

A. B. Mustafayev, Institute of Mathematics and Mechanics of Azerbaijan National Academy of Sciences (9, F. Agaev St., Baku, AZ1141, Azerbaijan), e-mail: azer_bm@list.ru

 

Abstract

This paper considers the change in the temperature field near the ends of a curved crack in a sheet element under the action of an inhomogeneous stress field. The solution to the boundary problem of equilibrium of a curvilinear crack with partially contacting faces under the action of an external inhomogeneous stress field  and induced thermoelastic field of stresses and forces on the crack contacting surfaces reduces to the problem of linear conjugation of analytical functions. It is accepted that on some part of the contact a cohesion of crack faces occurs, and on the rest of the contact, slippage is possible.

 

Keywords: curvilinear crack in a sheet element, inhomogeneous stress field, temperature field, contact stresses, contact zone, slippage zone

 

References

  1. Finkel, V. M. (1977). Fizicheskie osnovy tormozhenija razrushenija [Physical basis of fracture retardation]. Moscow: Metallurgiia, 360 p.
  2. Fan, H., Sun, Y. M., & Xiao, Z. M. (1998). Contact zone in an interfacial Zener–Stroh crack. Mechanics of Materials, vol. 30, pp. 151–159. https://doi.org/10.1016/S0167-6636(98)00044-1
  3. Kovtunenko, V. A. (2005). Nonconvex problem for crack with nonpenetration.  Z. Angew. Math. Mech., Bd. 85, pp. 242–251. https://doi.org/10.1002/zamm.200210176
  4. Mirsalimov, V.  M. (2009). Simulation of bridged crack closure in a contact pair bushing. Mechanics of Solids, vol. 44, pp. 232–243. https://doi.org/10.3103/S0025654409020083
  5. Mir-Salim-zada, M. V. (2010). Modeling of partial closure of cracks in a perfo­rated isotropic medium reinforced by a regular system of stringers. J. of Applied Mechanics and Technical Physics, vol. 51, pp. 269–279. https://doi.org/10.1007/s10808-010-0037-7
  6. Hasanov, Sh. H. (2012). Kogezionnaja treshhina s chastichno kontaktirujushhimi beregami v sechenii dorozhnogo pokrytija [Cohesive crack with partially contacting faces in section of the road covering]. Mehanika mashin, mehanizmov i materialov – Mechanics of machines, mechanisms and Materials, iss. 19, no. 2, pp. 58–64.
  7. Mirsalimov, V.  M. & Rustamov, B. E. (2013). Simulation of partial closure of a crack-like cavity with cohesion between the faces in an isotropic medium. J. of Applied Mechanics and Technical physics, vol. 54, pp. 1021–1029. https://doi.org/10.1134/S0021894413060175
  8. Mirsalimov, V. M. & Mustafayev, A. B. (2014). Tochnoe reshenie kontaktnoj zada-chi o chastichnom vzaimodejstvii beregov shheli peremennoj shiriny pri dejstvii temperaturnogo polja [Exact solution of contact problem for partial interaction of width variable slit faces at temperature field action]. Journal of Mechanical Engineering, vol. 17, no. 3, pp. 33–37.
  9. Belhouari, M., Amiri, A., Mehidi, A., Madani, K., & Bel Abbes Bachir, B. (2014). Elastic–plastic analysis of interaction between an interface and crack in bi-materials. Int. J. of Damage Mechanics, vol. 23, pp. 299–326. https://doi.org/10.1177/1056789513493646
  10. Mustafayev, A. B. (2014). Vzaimodejstvie beregov shheli peremennoj shiriny pri izgibe polosy (balki) pod vozdejstviem temperaturnogo polja [Interaction of variable width slit faces under strip (beams) bending and influence of temperature field]. Mehanika mashin, mehanizmov i materialov – Mechanics of machines, mechanisms and Materials, no. 3(28), pp. 30–36.
  11. Mirsalimov, V. M. & Mustafayev, A. B. (2015). Solution of the problem of partial contact between the faces of a slot of variable width under the action of temperature fields. Materials Science, vol. 51, pp. 96–103. https://doi.org/10.1007/s11003-015-9814-z
  12. Mirsalimov, V. M. & Mustafayev, A. B. (2015). A contact problem on partial interaction of faces of a variable thickness slot under the influence of temperature field. Mechanika, vol. 21, pp. 19–22. https://doi.org/10.5755/j01.mech.21.1.10132
  13. Mir-Salim-zada, M. V. (2015). Periodicheskaja kontaktnaja zadacha dlja stringernoj plastiny [Periodic contact problem for a stringer plate]. Tjazheloe mashino-stroenie – Heavy engineering, no. 6, pp. 37–42.
  14. Mir-Salim-zada, M. V. (2016). Zakrytie shheli, ishodjashhej iz kontura krugovogo otverstija v stringernoj plastine [Closing of a slit started from contour of circular hole in stringer plate]. Vestnik Chuvashskogo gosudarstvennogo pedagogiches-kogo universiteta imeni Ja. Jakovleva. Serija: Mehanika predel’nogo sostojanija – Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state, no. 1(27), pp. 78–89.
  15. Mirsalimov, V. M. (2016). Simulation of partial closure of a variable width slot with interfacial bonds in end zones in an isotropic medium. Int. J. Damage Mechanics, vol. 25, pp. 266–279. https://doi.org/10.1177/1056789515585178
  16. Mir-Salim-zadeh, M. V. (2016). Partial contact of faces of a variable width slit in a stringer plate. Materials Science, vol. 52, pp. 328–333. https://doi.org/10.1007/s11003-016-9960-y
  17. Mirsalimov, V. M. & Mustafayev, A. B. (2016). Inhibition of a curvilinear bridged crack by induced thermoelastic stress field. J. of Thermal Stresses, vol. 39, pp. 1301–1319. https://doi.org/10.1080/01495739.2016.1215742
  18. Muskhelishvili, N. I. (1977). Some basic problems of mathematical theory of elasticity. Amsterdam, 707 p. https://doi.org/10.1007/978-94-017-3034-1
  19. Gakhov, F. D. (1977). Kraevye zadachi [Boundary value problems]. Moscow:Nauka, 640 p.

 

Received 01 November 2016

Published 30 December 2016