Email this article Plane stress state of a uniformly piece-wise homogeneous plane with a periodic system of semi-infinite interphase cracks
- Authors: Hakobyan V.N.1, Grigoryan A.A.1
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Affiliations:
- Institute of Mechanics, National Academy of Sciences of the Republic of Armenia
- Issue: Vol 25, No 1 (2021)
- Pages: 67-82
- Section: Mechanics of Solids
- URL: https://journals.rcsi.science/1991-8615/article/view/59714
- DOI: https://doi.org/10.14498/vsgtu1816
- ID: 59714
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Abstract
The plane stress state of a uniformly piecewise-homogeneous plane obtained by alternately joining two dissimilar strips is considered, which along the lines of joints of dissimilar strips is weakened by a periodic system of two semi-infinite interfacial cracks and is deformed using normal loads applied to the crack banks. The basic cell of the problem in the form of a two-component strip is considered and, using the generalized Fourier transform, a governing system of equations for the problem is obtained in the form of one singular integral equation of the second kind for a complex combination of contact stresses in the junction zone of the strips.
As a special case, tending the height of the strips to infinity, the governing equation of the problem for a two-component plane of two dissimilar half-planes with two semi-infinite interfacial cracks is obtained and its exact solution is constructed. The governing equation for the stated problem is also obtained in the form of one singular integral equation of the first kind with respect to normal contact stresses in another particular case, when all strips are made of the same material, i.e. in the case of a homogeneous plane, a weakened periodic system of parallel, two semi-infinite cracks.
In the general case, the behavior of the unknown function at the end points of the integration interval is determined and the solution of the problem by the numerical-analytical method of mechanical quadratures is reduced to solving a system of algebraic equations. Simple formulas are obtained to determine the intensity factors, the Cherepanov–Rice integral and crack opening. A numerical calculation has been performed. Regularities of changes in contact stresses and the Cherepanov–Rice integral at the endpoints of cracks are revealed, depending on the elastic characteristics of heterogeneous strips and the geometric parameters of the problem.
About the authors
Vahram N. Hakobyan
Institute of Mechanics, National Academy of Sciences of the Republic of Armenia
Email: vhakobyan@sci.am
ORCID iD: 0000-0003-3684-9471
Scopus Author ID: 55914871100
http://www.mathnet.ru/rus/person141845
Dr. Phys. & Math. Sci., Professor; Chief Researcher; Dept. of Elasticity and Viscoelasticity
24B, Marshal Baghramyan ave., Yerevan, 0019, Republic of ArmeniaAram A. Grigoryan
Institute of Mechanics, National Academy of Sciences of the Republic of Armenia
Author for correspondence.
Email: grigoryan.aram.4@gmail.com
ORCID iD: 0000-0001-7582-1960
Scopus Author ID: 57216355950
http://www.mathnet.ru/rus/person158654
Postgraduate Student; Junior Researcher; Dept. of Elasticity and Viscoelasticity
24B, Marshal Baghramyan ave., Yerevan, 0019, Republic of ArmeniaReferences
- Panasyuk V. V., Savruk M. P., Datsyshin A. P. Raspredelenie napriazhenii okolo treshchin v plastinakh i obolochkakh [Stress Distribution Around Cracks in Plates and Shells]. Kiev, Naukova Dumka, 1976, 443 pp. (In Russian)
- Muskhelishvili N. I. Some Basic Problems of the Mathematical Theory of Elasticity. Netherlands, Springer, 1977, xxxi+732 pp. https://doi.org/10.1007/978-94-017-3034-1
- Razvitie teorii kontaktnykh zadach v SSSR [The Development of Theory of Contact Problems in USSR], ed. L. A. Galin. Moscow, Nauka, 1976, 493 pp. (In Russian)
- Popov G. Ya. Kontsentratsiia uprugikh napriazhenii vozle shtampov, razrezov, tonkikh vkliuchenii i podkreplenii [Concentration of Elastic Stress around Stamps, Cuts, Thin Inclusions, and Reinforcements]. Moscow, Nauka, 1982, 344 pp. (In Russian)
- Berezhnitskii L. T., Panasyuk V. V., Stashchuk N. G. Vzaimodeistvie zhestkikh lineinykh vkliuchenii i treshchin v deformiruemom tele [The Interaction of Rigid Linear Inclusions and Cracks in a Deformable Body]. Kiev, Naukova Dumka, 1983, 288 pp. (In Russian)
- Barzokas D. I., Fil'shtinskii L. A., Fil'shtinskii M. L. Aktual'nye problemy sviazannykh fizicheskikh polei v deformiruemykh telakh [Actual Problems of Coupled Physical Fields in Deformable Bodies], vol. 1. Moscow, Izhevsk, 2010, 864 pp. (In Russian)
- Hakobyan V. N. Smeshannye granichnye zadachi o vzaimodeistvii sploshnykh deformiruemykh tel s kontsentratorami napriazhenii razlichnykh tipov [Mixed Boundary-Value Problems on the Interaction of Continuous Deformable Bodies with Stress Concentrators of Various Types]. Yerevan, Gitutiun, 2014, 322 pp. (In Russian)
- Popov G. Ya. Izbrannye trudy [Selected Works]. In 2 volumes. Odessa, VMV, 2007 (In Russian).
- Hakobyan V. N., Dashtoyan L. L. Discontinuous solutions of a doubly periodic problem for a piecewise homogeneous plate with interphase defects, Mech. Compos. Mater., 2017, vol. 53, no. 5, pp. 601–612. https://doi.org/10.1007/s11029-017-9690-8.
- Hakobyan V. N., Sahakyan A. V., Aghayan K. L. Periodic problem for a plane composed of two-layer strips with a system of longitudinal internal inclusions and cracks, In: Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials, vol. 109. Cham, Springer, 2019, pp. 11–22. https://doi.org/10.1007/978-3-030-17470-5_2.
- Hakobyan V. N., Grigoryan A. H. Anti-plane stressed state uniformly piece-homogeneous space with a periodic system of parallel semi-infinite interfacial cracks, J. Phys.: Conf. Ser., 2020, vol. 1474, 012017. https://doi.org/10.1088/1742-6596/1474/1/012017.
- Brychkov Yu. A., Prudnikov A. P. Integral transforms of generalized functions, J. Soviet Math., 1986, vol. 34, no. 3, pp. 1630–1655. https://doi.org/10.1007/BF01262407.
- Stress Intensity Factors Handbook, vol. 1, ed. Y. Murakami. Oxford, Pergamon, 1987.
- Sahakyan A. V., Amirjanyan H. A. Method of mechanical quadratures for solving singular integral equations of various types, J. Phys.: Conf. Ser., 2018, vol. 991, 012070. https://doi.org/10.1088/1742-6596/991/1/012070.
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