Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate
DOI:
https://doi.org/10.15587/1729-4061.2021.243990Keywords:
crack, inclusion, thermoelasticity, stress intensity coefficient, singular integral equationAbstract
A two-dimensional mathematical model of the thermoelastic state has been built for a circular plate containing a curvilinear inclusion and a crack, under the action of a uniformly distributed temperature across the entire piece-homogeneous plate. Using the apparatus of singular integral equations (SIEs), the problem was reduced to a system of two singular integral equations of the first and second kind on the contours of the crack and inclusion, respectively. Numerical solutions to the system of integral equations have been obtained for certain cases of the circular disk with an elliptical inclusion and a crack in the disk outside the inclusion, as well as within the inclusion. These solutions were applied to determine the stress intensity coefficients (SICs) at the tops of the crack.
Stress intensity coefficients could later be used to determine the critical temperature values in the disk at which a crack begins to grow. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of those engineering structures with cracks that are operated in the thermal power industry and, therefore, is relevant.
Graphic dependences of stress intensity coefficients on the shape of an inclusion have been built, as well as on its mechanical and thermal-physical characteristics, and a distance to the crack. This would make it possible to analyze the intensity of stresses in the neighborhood of the crack vertices, depending on geometric and mechanical factors.
The study's specific results, given in the form of plots, could prove useful in the development of rational modes of operation of structural elements in the form of circular plates with an inclusion hosting a crack.
The reported mathematical model builds on the earlier models of two-dimensional stationary problems of thermal conductivity and thermoelasticity for piece-homogeneous bodies with cracks.
References
- Choi, H. J. (2014). Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally graded interlayer. Acta Mechanica, 225 (7), 2111–2131. doi: https://doi.org/10.1007/s00707-013-1080-2
- Rashidova, E. V., Sobol, B. V. (2017). An equilibrium internal transverse crack in a composite elastic half-plane. Journal of Applied Mathematics and Mechanics, 81 (3), 236–247. doi: https://doi.org/10.1016/j.jappmathmech.2017.08.016
- Chen, H., Wang, Q., Liu, G. R., Wang, Y., Sun, J. (2016). Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method. International Journal of Mechanical Sciences, 115-116, 123–134. doi: https://doi.org/10.1016/j.ijmecsci.2016.06.012
- Sekine, H. (1978). Thermal stresses around a ribbon-like inclusion in a semi-infinite medium under uniform heat flow. Journal of Elasticity, 8 (1), 81–95. doi: https://doi.org/10.1007/bf00044511
- Tweed, J., Lowe, S. (1979). The thermoelastic problem for a half-plane with an internal line crack. International Journal of Engineering Science, 17 (4), 357–363. doi: https://doi.org/10.1016/0020-7225(79)90071-5
- Kryvyy, O. F. (2012). Interface circular inclusion under mixed conditions of interaction with a piecewise homogeneous transversally isotropic space. Journal of Mathematical Sciences, 184 (1), 101–119. doi: https://doi.org/10.1007/s10958-012-0856-6
- Zelenyak, B. M. (2016). Thermoelastic Equilibrium of a Three-Layer Circular Hollow Cylinder Weakened by a Crack. Materials Science, 52 (2), 253–260. doi: https://doi.org/10.1007/s11003-016-9952-y
- Zelenyak, V. M., Kolyasa, L. I. (2016). Thermoelastic State of a Half Plane with Curvilinear Crack Under the Conditions of Local Heating. Materials Science, 52 (3), 315–322. doi: https://doi.org/10.1007/s11003-016-9959-4
- Konechny, S., Evtushenko, A., Zelenyak, V. (2001). Heating of the semispace with edge cracks by friction. Trenie i Iznos, 22 (1), 39–45. Available at: http://www.scopus.com/inward/record.url?eid=2-s2.0-0035766285&partnerID=MN8TOARS
- Zelenyak, V. M. (2012). Thermoelastic interaction of a two-component circular inclusion with a crack in the plate. Materials Science, 48 (3), 301–307. doi: https://doi.org/10.1007/s11003-012-9506-x
- Hasebe, N., Wang, X., Saito, T., Sheng, W. (2007). Interaction between a rigid inclusion and a line crack under uniform heat flux. International Journal of Solids and Structures, 44 (7-8), 2426–2441. doi: https://doi.org/10.1016/j.ijsolstr.2006.07.016
- Kit, H. S., Chernyak, M. S. (2010). Stressed state of bodies with thermal cylindrical inclusions and cracks (plane deformation). Materials Science, 46 (3), 315–324. doi: https://doi.org/10.1007/s11003-010-9292-2
- Savruk, M. P. (1981). Dvumernye zadachi uprugosti dlya tel s treschinami. Kyiv: Naukova dumka, 324.
- Erdogan, F., Gupta, G. D., Cook, T. S. (1973). Numerical solution of singular integral equations. Methods of Analysis and Solutions of Crack Problems, 368–425. doi: https://doi.org/10.1007/978-94-017-2260-5_7
- Panasyuk, V. V., Savruk, M. P., Dacyshin, A. P. (1976). Raspredelenie napryazheniy okolo treschin v plastinah i obolochkah. Kyiv: Naukova Dumka, 442.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Volodymyr Zelenyak, Myroslava Klapchuk, Lubov Kolyasa, Oksana Oryshchyn, Svitlana Vozna
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
