Partial closure of rectilinear bridged cracks in stringer plate with a hole
Keywords:
stringer plate, circular hole, cohesive forces in bonds, contact of crack faces, contact stressesAbstract
An elastic isotropic plate reinforced by stringers and having a circular hole has been considered. From the circular hole two symmetric rectilinear bridged cracks are originate. Size of the cracks end zones (zones with the interfacial bonds) is comparable with size of the cracks. The case of partial closure of the cracks is considered. Size of the zones of the crack faces contact is unknown in advance. Effect of the stringers is replaced by unknown equivalent concentrated forces applied at the points of the ribs and plate joining. For definition of the parameters characterizing the closure of cracks, a singular integral equation has been obtained. The singular integral equation has been reduced to a finite nonlinear algebraic system using the algebraization procedure. Solving the algebraic system by the method of successive approximations, the cohesive forces in the bonds, the contact stresses and the size of the contact zones of the cracks have been found.
References
Mirsalimov, V.M. (1977). Study of maximum stress field alongside cracks emerging from contours of openings in a perforated plate. J. of Applied Mechanics and Technical Physics. Vol. 18. pp. 263–269.
Mirsalimov, V.M. (1979). Uprugo-plasticheskoe ravnovesie plastiny, oslablennoj dvojakoperiodicheskoj sistemoj kruglyh otverstij i treshhinami, vyhodja-shhimi na kontury otverstij [Elastic-plastic equilibrium of the plate with the double-periodical system of the round orifices and cracks running to the orifices contour]. Izvestiya AN AzSSR, Seriya Fiz.-Tekh. i Mat. nauk. Issue 2. pp. 118–125.
Mirsalimov, V.M. (1980). Brittle fracture of a plate weakened by a periodic system of circular holes with cracks emanating from their contours. Int. Applied Mechanics. Vol. 16, Issue 11. pp. 992–997.
Mir-Salim-zadeh, M.V. (2003). Fracture of an elastic rib reinforced plate weakened by a circular cracked hole. Int. J. of Fracture. Vol. 122. pp. L113–L117.
Yan, Xiangqiao. (2006). Cracks emanating from circular hole or square hole in rectangular plate in tension. Engineering Fracture Mechanics. Vol. 73. pp. 1743–1754.
Mir-Salim-zade, M.V. (2007). Modelirovanie zarozhdenija treshhiny v podkreplennoj plastine s krugovym otverstiem [Modelling of nucleation of crack in strengthened plate with round hole]. Deformatsiya i Razrushenie materialov. Issue 8. pp. 40–47.
Mir-Salim-zade, M.V. (2008). Ultimate state of a plate with a regular system of stringers and cracks issuing from a circular hole. J. of Machinery Manufacture and Reliability. Vol. 37. pp. 352–358.
Mirsalimov, V.M., Shahbandaev E.G. (2008). Predel'noe ravnovesie teplovydeljajushhej sredy s periodicheskoj sistemoj otverstij i prjamolinejnyh treshhin [Limit equilibrium of heat-generating medium with a periodic system of holes and rectilinear cracks]. Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state. Issue 1. pp. 98–107.
Shahbandaev E.G. (2008). On partial closing of cracks in heat-releasing medium weakened by a periodic system of circular holes. Proceedings of IMM of NAS of Azerbaijan. Vol. XXIX, Issue XXXVII. pp. 215–224.
Chen Y.Z., Lin X.Y., Wang Z.X. (2009). A semi-analytic solution for multiple curved cracks emanating from circular hole using singular integral equation. Applied Mathematics and Computation. Vol. 213. pp. 389–404.
Mir-Salim-zade, M.V. (2012). Elastoplastic fracture of a perforated stringer plate. J. of Machinery Manufacture and Reliability. Vol. 41. pp. 218–222.
Mirsalimov, V.M., Iskenderov, R.A. (2013). Zarozhdenie treshhin pri odnorodnom izgibe izotropnoj plastiny, oslablennoj periodicheskoj sistemoj krugovyh otverstij [Crack nucleation at pure bending of isotropic plate weakened by periodic system of circular holes]. Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state. Issue 1. pp. 145–152.
Гасанов Ф.Ф. (2013). Modeling of shear crack nucleation in a body, weakening by periodic system of circular holes Моделирование зарождения трещин сдвига в теле, ослабленном периодической системой круглых отверстий. J. of mechanical engineering. Vol. 16, Issue 3. pp. 29–37.
Mirsalimov, V.M. (2017). Cracking in heat-releasing perforated material. Acta Mechanica. Vol. 228. pp. 201–214.
Mirsalimov, V.M. (1986). Some problems of structural arrest of cracks. Materials Science. Vol. 22. pp. 81–85.
Savruk M.P., Kravets V.S. (1995). Reinforcement of a thin cracked plate by a system of parallel stringers. Materials Science. Vol. 30. pp. 95–104.
Mir-Salim-zada, M.V. (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. pp. 269-279.
Mir-Salim-zada, M.V. (2014). [Contact problem for stringer plate weakened by variable width slit]. Fundamental and Applied Problems of Engineering and Technology. Issue 2. pp. 23–29.
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 I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state. Issue 1. pp. 78–89.
Muskhelishvili, N.I. (1977). Some Basic Problems of Mathematical Theory of Elasticity. Kluwer, Amsterdam.
Panasyuk, V.V., Savruk, M.P. and Datsyshin A.P. (1976). Raspredelenie naprjazhenij okolo treshhin v plastinah i obolochkah [Distribution of Stresses near Cracks in Plates and Shells]. Naukova Dumka, Kiev.
Mirsalimov, V.M. (1987). Neodnomernye uprugoplasticheskie zadachi [Non-one-dimensional Elastoplastic Problems]. Nauka, Moscow.
Downloads
Published
Issue
Section
License
Copyright (c) 2017 М. В. Мир-Салим-заде
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
All authors agree with the following conditions:
- The authors reserve the right to claim authorship of their work and transfer to the journal the right of first publication of the work under the license agreement (the agreement).
- Authors have a right to conclude independently additional agreement on non-exclusive spreading the work in the form in which it was published by the jpurnal (for example, to place the work in institution repository or to publish as a part of a monograph), providing a link to the first publication of the work in this journal.
- Journal policy allows authors to place the manuscript in the Internet (for example, in the institution repository or on a personal web sites) both before its submission to the editorial board and during its editorial processing, as this ensures the productive scientific discussion and impact positively on the efficiency and dynamics of citation of published work (see The Effect of Open Access).
