Closure of a curvilinear crack in sheet element under influence of temperature field

Authors

  • В. М. Мирсалимов Azerbaijan technical University, Baku, Azerbaijan
  • А. Б. Мустафаев Institute of Mathematics and Mechanics of NAS of Azerbaijan, Azerbaijan

Keywords:

curvilinear crack in sheet element, non-uniform stress field, temperature field, contact stresses, contact zone, slippage zone

Abstract

We consider a change of temperature field near ends of a curvilinear crack in structure sheet element under influence of an inhomogeneous strength field. Solution of the boundary value problem for equilibrium of a curvilinear crack with partially contacting faces under the influence of an external inhomogeneous stress field, an in­duced thermoelastic field and tractions on contacting crack faces is reduced in each approximation to the problem of analytic functions linear conjugation. It is assumed that in some part of the contact zone a stick of crack faces occurs, and in the rest part of the contact zone a crack faces slippage is possible. The goal of the local tempera­ture changes is deceleration or braking of curvilinear crack growth.  From the solu­tion of the problem of analytic functions linear conjugation the normal and tangential contact stresses are found. The sizes of contact zones also are found

Author Biographies

В. М. Мирсалимов, Azerbaijan technical University, Baku

Doctor of Physical and Mathematical Sciences

А. Б. Мустафаев, Institute of Mathematics and Mechanics of NAS of Azerbaijan

PhD

References

1. Finkel, V.M. (1977). Fizicheskie osnovy tormozhenija razrushenija [Physical basis of fracture retardation]. Moscow: 360.

2. Fan, H., Sun, Y.M., Xiao, Z.M. (1998). Contact zone in an interfacial Zener–Stroh crack. Mechanics of Materials. 30: 151–159.

3. Kovtunenko, V.A. (2005). Nonconvex problem for crack with nonpenetration. Z. Angew. Math. Mech. 85: 242–251.

4. Mirsalimov, V.M. (2009). Simulation of bridged crack closure in a contact pair bushing. Mechanics of Solids. 44: 232–243.

5. Mir-Salim-zada, M.V. (2010). Modeling of partial closure of cracks in a perfo¬rated isotropic medium reinforced by a regular system of stringers. J. of Applied Mechanics and Technical Physics. 51: 269-279.

6. Hasanov, Sh.H. (2012). Kogezionnaja treshhina s chastichno kontaktirujushhi-mi 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]. Issue 2(19): 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. 54: 1021–1029.

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]. Problemy mashinostroenija [J. of mechani¬cal engineering]. Issue 3: 33–37.

9. Belhouari, M., Amiri, A., Mehidi, A., Madani, K., Bel Abbes Bachir, B. (2014). Elastic–plas¬tic analysis of interaction between an interface and crack in bi-materials. Int. J. of Damage Mechanics. 23: 299–326.

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) bend¬ing and influence of temperature field]. Mehanika mashin, mehanizmov i materialov [Mechanics of machines, mechanisms and Materials]. Issue 3(28): 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. 51: 96–103.

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. 21: 19–22.

13. Mir-Salim-zada, M.V. (2015). Periodicheskaja kontaktnaja zadacha dlja stringer-noj plastiny [Periodic contact problem for a stringer plate]. Tjazheloe mashino-stroenie [Heavy engineering]. Issue 6: 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 I.Ja. Jakovleva. Serija: Mehanika predel'nogo sostojanija [Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state]. Issue 1(27): 78-89.

15. Mirsalimov, V.M. (2016). Simulation of partial closure of a variable width slot with interfa¬cial bonds in end zones in an isotropic medium. Int. J. Damage Mechan¬ics. 25: 266–279.

16. Mir-Salim-zadeh, M.V. (2016). Partial contact of faces of a variable width slit in a stringer plate. Materials Science. 52: 328–333.

17. Mirsalimov, V.M., Mustafayev, A.B. (2016). Inhibition of a curvilinear bridged crack by induced thermoelastic stress field. J. of Thermal Stresses. 39: 1301–1319.

18. Muskhelishvili, N.I. (1977). Some basic problems of mathematical theory of elasticity. Amsterdam: 707.

19. Gakhov, F.D. (1977). Kraevye zadachi [Boundary value problems]. Moscow: 640.

Published

2016-12-20

Issue

Section

Dynamics and Strength of Machines