# Abstract

We give a mathematical description of calculation model for cracking in sheet structural element under a non-uniform stress field. The model of pre-fracture zones in state of plastic flow under constant stresses was accepted. The boundary value problem for interaction of zones of weakened interparticle material bonds in the sheet structural element under influence of the inhomogeneous stress field is reduced to a system of singular integral equations. The integral equations further reduce to a system of nonlinear algebraic equations for solution of which we use the method of successive approximations. Sizes of the prefracture zones and limit value of external loads at which in the sheet structural element the cracking occurs are found.

### Sh H HASANOV

Азербайджанский технический университет

Author for correspondence.
Email: iske@mail.ru
Azerbaijan Technical University, Azerbaijan, AZ1073, Baku, Pr. G. Javid, 25

# References

1. Panasyuk, V.V. (1991). Mechanics of Quasibrittle Fracture of Material. Kiev: Naukova Dumka, 416. (in Russian).
2. Levin, V.A., Morozov, E.M., Matvienko, Yu.G. (2004). Selected Non-Linear Problems of Fracture Mechanics. Moscow: FIZMATLIT, 408 (in Russian).
3. Mirsalimov, V.M. (2005). Initiation of crack type defect in bush of contact pair, Matematicheskoe modelirovanie, 17 (2), 35—45. (in Russian). .
4. Rusinko, A., Rusinko, K. (2011). Plasticity and Creep of Metals. Berlin: Springer Verlag, 434 p.
5. Mirsalimov, VM. (2007). The solution of a problem in contact fracture mechanics on the nucleation and development of a bridged crack in the hub of a friction pair, J. of Applied Mathematics and Mechanics, Vol. 71, Iss. 1, 120—136 (in Russian).
6. Mir-Salim-zade, M.V. (2006). Nucleation of crack type defect in riveted panel, J. of Machinery Manufacture and Reliability, (6), 45-51 (in Russian). .
7. Mirsalimov, V.M. (2007). Nucleation of a crack-type defect in a body with voids, J. of Machinery Manufacture and Reliability, Vol. 36, Iss. 4, 341—347 (in Russian). .
8. Mirsalimov, V.M. (2007). Nucleation of cracks in a perforated fuel cell, J. of Applied Mechanics and Technical Physics, Vol. 48, Iss. 5, 723—733 (in Russian). .
9. Shahbandaev, E.G. (2007). Cracks nucleation in heat-generating medium weakened by periodic system of circular holes. Mechanics. Machine Building, (4), 29—31 (in Russian). .
10. Mir-Salim-zade, M.V. (2007). Crack initiation in a stiffened plate, J. of Applied Mechanics and Technical Physics, Vol. 48, Iss. 4, 562—570 (in Russian). .
11. Mir-Salim-zade, M.V. (2007). Nucleation of crack in reinforced plate with circular hole, Izvestiya TulGU serija: Estestvennye nauki, Iss.1, 88—97 (in Russian). .
12. Hasanov, Sh.H. (2008). Pre-fracture zones on section boundary of road surface and elastic foundation, Structural Mechanics and Analysis of Constructions, (5), 49-54 (in Russian). .
13. Mir-Salim-zade, M.V. (2008). Generation of cracks in a perforated reinforced plate, J. of Applied Mechanics and Technical Physics, Vol. 49, Iss. 6, 1030—1039 (in Russian). .
14. Mir-Salim-zade, M.V. (2008). Nucleation of crack in an isotropic medium reinforced by regular system of stringers, Bulletin of the Yakovlev Chuvash State Pedagogical University. Series: Mechanics of Limit State, 5 (2), 115—128 (in Russian). .
15. Hasanov, Sh.H. (2008). Nucleation of crack on border section of the covering and the elastic basic, Strengthening Technologies and Coatings, (1), 20—24 (in Russian). .
16. Hasanov, Sh.H. (2008). Modelling of the deflected mode of the road covering with the curved interphase crack of stratification, Mathematical Modelling in Civil Engineering, (1), 13—21.
17. Mustafayev, A.B. (2009). Crack initiation in non-uniformly heated thick-walled cylinder, Proceedings of IMM of NAS of Azerbaijan, C. 30, N. 38, 143—150 (in Russian). .
18. Mustafayev, A.B. (2009). Modelling of nucleation of the crack in non-uniformly heated the cylinder, Fundamental and Applied Problems of Engineering and Technology, (4), 15—21 (in Russian). .
19. Mirsalimov, V.M., Mustafayev, A.B. (2010). Modeling cracking in thick-walled cylinder, Advances and Application in Mathematical Sciences, Vol. 2, Iss. 1, 1—8.
20. Mir-Salim-zade, M.V. (2010). Modeling of crack formation in a perforated stringer panel, Mathematical Models and Computer Simulations, Vol. 2, Iss. 4, 533—541 (in Russian). .
21. Mir-Salim-zade, M.V. (2010). Crack formation in a perforated isotropic medium intensified by a regular system of stringers, Bulletin of he Yakovlev Chuvash State Pedagogical University. Series: Mechanics of Limit State, 7 (1), 79—91 (in Russian).
22. Mirsalimov, V.M., Zolgharnein, E. (2012). Nucleation of a crack under inner compression of cylindrical bodies, Acta Polytechnica Hungarica, 9 (2), 169—183.
23. Mirsalimov, V.M., Iskenderov, R.А. (2013). Crack nucleation at pure bending of isotropic plate weakened by periodic system of circular holes, Bulletin of the Yakovlev Chuvash State Pedagogical University. Series: Mechanics of Limit State, 15 (1), 145—152 (in Russian). .
24. Zulfugarov, E.I. (2013). Modeling of cracking in brake drum of wheel car, Mechanics and Mechanical Engineering, (3), 49—53 (in Russian). .
25. Iskenderov, R.А. (2013). The crack nucleation in the isotropic plate, weakened by a periodical system of circular holes under transverse bending, Structural Mechanics of Engineering Constructions and Buildings, (3), 18—28 (in Russian). .
26. Hasanov, F.F. (2013). Modeling of shear crack nucleation in a body, weakening by periodic system of circular holes, Problems of Mechanical Engineering, 16 (3), 29—37 (in Russian). .
27. Zulfugarov, E.I. (2014). Modelling of curved crack nucleation in automobile brake drum, Fundamental and Applied Problems of Engineering and Technology, (1), 24—30 (in Russian). .
28. Kalantarly, N.M. (2014). Influence of volume forces on crack nucleation in circular, Fundamental and Applied Problems of Engineering and Technology, (2), 17—22 (in Russian). .
29. Hasanov, F.F. (2014). Nucleation of the crack in a composite reinforced unidirectional orthotropous fibres at longitudinal shear, Mechanics of Machines, Mechanisms and Materials, 27 (2), 45—50.
30. Mirsalimov, V.M., Hasanov, Sh.G. (2014). Modeling of crack nucleation in covering on an elastic base, Int. J. of Damage Mechanics, 23(3), 430—450.
31. Hasanov, F.F. (2014). Nucleation of cracks in isotropic medium with periodic system of the circular holes filled with rigid inclusions, at longitudinal shear, Structural Mechanics of Engineering Constructions and Buildings, (3), 44—50 (in Russian). .
32. Hasanov, F.F. (2014). Modelling of crack nucleation in the fibre of composite reinforced with unidirectional fibres under shear, Problems of Mechanical Engineering, 17 (2), 17-25 (in Russian). .
33. Kalantarly, N.M. (2014). Cracking in circular disk under the influence of volume forces, Structural Mechanics of Engineering Constructions and Buildings, (6), 23—30 (in Russian). .
34. Mirsalimov, V.M., Hasanov, F.F. (2015). Nucleation of cracks in an isotropic medium with periodic system of rigid inclusions under transverse shear, Acta Mechanica, Vol. 226, Iss.2, 385—395.
35. Mirsalimov, V.M., Kalantarly, N.M. (2015). Modelling of cracking in circular disk loaded by concentrated forces, Saratov University News. New Series. Series Mathematics. Mechanics. Informatics, (1), 90—97 (in Russian). .
36. Mirsalimov, V.M., Kalantarly, N.M. (2015). Crack nucleation in circular disk under mixed boundary conditions, Archives of Mechanics, Vol. 67, Iss. 2, 115—136.
37. Mirsalimov, V.M., Kalantarly, N.M. (2015). Cracking in a circular disk under mixed boundary conditions, Acta Mechanica, Vol. 226, Iss. 6, 1897—1907.
38. Mirsalimov, V.M., Ismailova, R.I. (2016). Crack nucleation in rod fuel element, Tyazheloe mashinostroenie, (5). 10—16 (in Russian).
39. Mirsalimov, V.M.(1987). Non-One-Dimensional Elastoplastic Problems. Moscow: Nauka, 256 p.
40. Panasyuk, V.V., Savruk, M.P., Datsyshyn, A.P. (1976). The Stress Distribution around Cracks in Plates and Shells. Kiev: Naukova Dumka. 443. (in Russian).
41. Ladopoulos, E.G. (2000). Singular Integral Equations, Linear and Non-Linear Theory and its Applications in Science and Engineering. Berlin: Springer Verlag. 553.

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