INHIBITION OF CURVILINEAR COHESIVE CRACK GROWTH IN A BENDING STRIP (BEAM) BY INDUCED HEAT STRESS FIELD
- Authors: MUSTAFAYEV AB1
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Affiliations:
- Institute of Mathematics and Mechanics of the Academy of Sciences of Azerbaijan
- Issue: No 3 (2017)
- Pages: 59-70
- Section: Articles
- URL: https://journals.rudn.ru/structural-mechanics/article/view/16309
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Abstract
We consider a temperature changes near end of curvilinear crack with end zones of mate- rial cohesive forces in bending strip (beam). The aim of the local temperature changes is a delay or inhibition of crack growth. Boundary value problem for equilibrium of curvilinear crack under the action of external bending loads, induced thermoelastic stress field and trac- tions in bonds, preventing its disclosure, is reduced to a system of nonlinear singular integro- differential equations with the kernel of Cauchy type. Condition of crack limit equilibrium is formulated on the basis of a two-parameter fracture criterion.
About the authors
A B MUSTAFAYEV
Institute of Mathematics and Mechanics of the Academy of Sciences of Azerbaijan
Author for correspondence.
Email: azer_bm@list.ru
к.ф.-м.н.
Азербайджан, AZ1141, Б. Вахабзаде, 9References
- Finkel VM. (1977) Physical Basis Of Fracture Retardation. Moscow: Metallurgiya. 360 p.
- Belen'kii VD. (1984) Closure of a central crack in a circular disk under the influence of a temperature field // Strength of Materials. Vol. 16. p. 806−810.
- Potthast B, Herrmann KP. (2000) Asymptotic analysis for temperature fields induced by dynamic crack growth in pressure-sensitive materials // Int. J. of Fracture. 106. p. 57–64
- Kadiev RI, Mirsalimov VM. (2001) Effect of heat source on the dynamics of crack growth, Vestnik Dagestanskogo universiteta. 2001. №4. p. 69–73.
- Fu Y-M, Bai X-Z, Qiao G-Y, Hu Y-D, Luan J-Y. (2001) Technique for producing crack arrest by electromagnetic heating // Materials Science and Technology. Vol. 17. p. 1653−1656.
- Kadiev RI. (2003) Коэффициенты интенсивности напряжений для пластины, ослабленной трещиной, при воздействии теплового источника // Вестник ДНЦ РАН. № 14. p. 15–18.
- Mirsalimov VM, Kadiev RI. (2004) Closing of a crack in the sheet element under action of local thermal field // J. of Machinery Manufacture and Reliability. Vol. 33, Issue 6. p. 69–75.
- Kovtunenko VA. (2005) Nonconvex problem for crack with nonpenetration // Z. Angew. Math. Mech.. Bd. 85. Fasz. 4. s. 242–251.
- 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. p. 120–136.
- Qin Z, Librescu L, Hasanyan D. (2007) Joule heating and its implications on crack detection/arrest in electrically conductive circular cylindrical shells // J. of Thermal Stresses. Vol. 30. p. 623−637
- Liu TJC. (2008) Thermo-electro-structural coupled analyses of crack arrest by Joule heating // Theoretical and Applied Fracture Mechanics. Vol. 49. p. 171–184.
- Mir-Salim-zada MV. (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. p. 269-279.
- Dimaki AV, Mel’nikov AG, Pleshanov VS, Sizova OV. (2010) Theoretical and experimental study of the healing of surface cracks using induction heating // Inorganic Materials: Applied Research. Vol. 1, Issue 4. p. 353–358.
- Liu TJC. (2011) Finite element modeling of melting crack tip under thermo-electric Joule heating // Engineering Fracture Mechanics. Vol. 78. p. 666–684.
- Liu TJC. (2011) Fracture mechanics of steel plate under Joule heating analyzed by energy density criterion // Theoretical and Applied Fracture Mechanics. Vol. 56. p. 154–161.
- Mirsalimov MV, Rustamov BE. (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, p. 1021–1029.
- Liu TJC. (2014) Compressive stresses near crack tip Induced by thermo-electric field // Int. J. of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering. Vol. 8. p. 1799–1802.
- Georgantzinos S.K., Anifantis N.K. (2014) Crack closure // Encyclopedia of Thermal Stresses (edit. R.B. Hetnarski). Springer Netherlands. p. 774−779.
- Mir-Salim-zade MV. (2014) Cracks with interfacial bonds in a perforated stringer plate // Structural Mechanics of Engineering Constructions and Buildings. Issue 5. p. 34−43.
- Itou S. (2014) Thermal stresses around two upper cracks placed symmetrically about a lower crack in an infinite orthotropic plane under uniform heat flux // J. of theoretical and applied mechanics. Vol. 52. p. 617–628.
- Mustafayev AB. (2014) Interaction of curved crack faces in bending strip (beam) under influence of temperature field // Structural Mechanics of Engineering Constructions and Buildings. Issue 4. p. 29−41.
- Mirsalimov VM, Mustafayev AB. (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. p. 96–103.
- Mirsalimov VM, Mustafayev AB. (2015) A contact problem on partial interaction of faces of a variable thickness slot under the influence of temperature field // Mechanika. Vol. 21. p. 19–22.
- Gadzhiev VD, Mirsalimov VM. (1999) Limit equilibrium state of the bushing-type component of a contact couple in the presence of cracks with bonds between the faces // Optimal Design of Mechanical Systems. Élm, Baku. p. 50–63.
- The special issue: Cohesive models // Eng. Fract. Mech. 2003. V.70, №14. P. 1741-1987.
- Panasyuk VV, Savruk MP, Datsyshyn AP. (1976) The stress distribution around cracks in plates and shells. Kiev: Naukova Dumka. 443 p. (in Russian)
- Muskhelishvili NI. (1977) Some basic problems of mathematical theory of elasticity. Amsterdam: Kluwer. 732 p.
- Mirsalimov VM. (1987) Non-one-dimensional elastoplastic problems. Moscow: Nauka. 256 p.
- Ladopoulos EG. (2000) Singular Integral Equations. Springer-Verlag, Berlin. 553 p.
- Il’yushin AA. (1948) Plasticity. Moscow and Leningrad: Gostexhizdat. 376 p. (in Russian)