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In the article, the pure bending problem for strip (beam) with straight, perpendicular to its axis crack located in the zone of tensile stresses is investigated on the assumption of narrow plastic strips near crack tips. Using methods of the theory of functions of a complex variable and complex potentials, the problem is reduced to the several linear conjunction problems. The solutions of latter problems are ob-tained in the class of functions confined in the edges of plastic strips. Formulas for the calculation of their lengths are derived. Expressions for the determination of crack tip opening values are written. Numerical analysis of the problem is performed.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
44--49
Opis fizyczny
Bibliogr. 18 poz., rys., wykr.
Twórcy
autor
- Department of Mechanics and Applied Computer Science Application, Faculty of Mechanical Engineering, Bialystok University of Technology, ul. Wiejska 45 C, 15-351 Bialystok, Poland
autor
- Faculty of Mechanics and Mathematics, Department of Mechanics, Ivan Franko National University of Lviv, Universytetska Street, 1, Lviv, 79000, Ukraine
autor
- Faculty of Mechanics and Mathematics, Department of Mechanics, Ivan Franko National University of Lviv, Universytetska Street, 1, Lviv, 79000, Ukraine
autor
- Faculty Training Specialists Battle (Operational) Software, Department of Engineering Mechanics, Hetman Petro Sahaidachnyi National Army Academy, Heroes of Maidan Street, 32, Lviv, Ukraine
Bibliografia
- 1. Bronshteyn I.N., Semendyaev K.A. (1967), Handbook of mathe-matics, Science, Moscow.
- 2. Fan M., Yi D.K., Xiao Z.M. (2014), A Zener–Stroh crack interacting with a coated inclusion with generalized Irwin plastic zone correction, International Journal of Solids and Structures, 51 (19–20), 3399-3409.
- 3. Kuz I., Kuz O., Sulym H. (2015) Stress-strain state of elastic plate with an arbitrary smooth notch, Acta Mechanica et Automatica, 9 (4), 241-244.
- 4. Kuz І.S., Моrоz О.І., Kuz О.N. (2019), Strength of elastoplastic plates containing square holes (inclusions) and cuts (thin inclusions) under uniaxial tension, Materials Science, 54 (4), 603–609.
- 5. Monfared M.M., Bagheri R., Yaghoubi R. (2018), The mixed mode analysis of arbitrary configuration of cracks in an orthotropic FGM strip using the distributed edge dislocations, International Journal of Solids and Structures, 130–131, 21-35.
- 6. Muskhelishvili N.I. (1966), Some basic problems of the mathemati-cal elasticity theory, Science, Moscow.
- 7. Nykolyshyn M.M., Opanasovych V.K., Kurotchyn L.R., Slobod-yan M.S. (2015), Biaxial tension of a piecewise homogeneous plate with two cracks on the interface of materials with regard for the plas-tic zones near their tips, Materials Science, 50 (6), 844-850.
- 8. Nykolyshyn M.M., Opanasovych V.K., Kurotchyn L.R., Slobod-yan M.S. (2010), Biaxial tension of a homogeneous isotropic plate with two equal coaxial cracks with regard for plastic zones near their tips, Journal of Mathematical Sciences, 168 (5), 643-652.
- 9. Ostash O.P., Chepil R.V., Vira V.V. (2017), The assessment of fatigue life of notched components at uniaxial pulsating loading using the fracture mechanics approach, International Journal of Fa-tigue,105, 305–311.
- 10. Panasyuk V.V. (1968), Limit equilibrium of brittle bodies with cracks, Naukova Dumka, Kyiv.
- 11. Panasyuk V.V., Lozovyy B.L. (1961), Bending of strips from a straight slit, Applied Mechanics, 7 (6), 627-634.
- 12. Pavazza R. (2000), An approximate solution for thin rectangular orthotropic/isotropic strips under tension by line loads, International Journal of Solids and Structures, 37 (32), 4353-4375.
- 13. Prawoto Y. (2012), How to compute plastic zones of heterogeneous materials: A simple approach using classical continuum and fracture mechanics, International Journal of Solids and Structures, 49 (15–16), 2195-2201.
- 14. Savruk M. P., Osyv P. N., Prokopchuk I. V. (1989), Numerical analysis in the plane problems of crack theory, Naukova dumka, Ky-iv.
- 15. Savyn G.V. (1968), Stress distribution near holes, Naukova dumka, Kyiv.
- 16. Shi P.P. (2015), On the plastic zone size of solids containing doubly periodic rectangular-shaped arrays of cracks under longitudinal shear, Mechanics Research Communications, 67, 39-46.
- 17. Sulym H., Opanasovych V., Slobodian M., Bilash O. (2018), Combined bending with tension of isotropic plate with crack consider-ing crack banks contact and plastic zones at its tops, Acta Mechanica et Automatica, 12 (2), 91-95.
- 18. Unger D.J. (2007), Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dug-dale plastic strip model, Mechanics Research Communications, 34 (4), 325-330.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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