Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/49615
Title: Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source
Authors: Zelenyak, Volodymyr
Kolyasa, Liubov
Affiliation: Lviv Polytechnic National University
Bibliographic description (Ukraine): Zelenyak V. Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source / Volodymyr Zelenyak, Liubov Kolyasa // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 5. — No 1. — P. 13–19.
Bibliographic description (International): Zelenyak V. Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source / Volodymyr Zelenyak, Liubov Kolyasa // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 5. — No 1. — P. 13–19.
Is part of: Український журнал із машинобудування і матеріалознавства, 1 (5), 2019
Ukrainian Journal of Mechanical Engineering and Materials Science, 1 (5), 2019
Journal/Collection: Український журнал із машинобудування і матеріалознавства
Issue: 1
Volume: 5
Issue Date: 20-Mar-2019
Publisher: Видавництво Львівської політехніки
Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
Keywords: crack
temperature stresses
heat source
stress intensity factor
singular integral equation
Number of pages: 7
Page range: 13-19
Start page: 13
End page: 19
Abstract: Purpose. To determine the two-dimensional thermoelastic state in a circular plate, weakened by an edge or internal crack induced by a stationary heat sourse. This paper proposes using singular integral equation (SIE) to investigate thermostressed intensity in the vicinity of the crack tip, depending on the local heat source placement and identify typical mechanical effects. Numerical results for the stress intensity factors (SIFs) can be potentially used to identify (with the limit equilibrium equations) critical values of the intensity of the local heat source at which crack begin to grow and the local destruction of the body. Methodology. The methods of studying two-dimensional thermoelastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of stationary thermoelasticity are reduced to a SIE of the first kind, a numerical solution which was obtained by the method of mechanical quadratures. Findings. In this paper graphic dependences of stress intensity factors at the crack tip on the relative position of crack and local heat source placement and on the length of crack are obtained. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of thermoelasticity for a circular plate containing a crack under the influence of local heating of heat source. Practical value. The practical value is the ability to more fully take into account the real situation in the thermoelastic elements of engineering structures with cracks that operate under conditions of heat stress in various industries, particularly in mechanical engineering. The results of specific values in the crack tip SIF in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.
URI: http://ena.lp.edu.ua:8080/handle/ntb/49615
Copyright owner: © Національний університет “Львівська політехніка”, 2019
© Zelenyak V., Kolyasa L., 2019
References (Ukraine): 1. I. F. Soltys, “Temperaturnyye napryazheniya v uprugoy ploskosti s krugovoy granitsey i termoizolirovannymi treshchinami zumovleni dzherelom tepla” [“The thermal elasticity of a circular plate with arc-shaped cracks due to the source of heat”], Fizico-khimicheskaia mekhanika materialov [Physicochemical mechanics of materials], no. 1, pp. 94–98, 1978. [in Russian].
2. N. A. Dorosh, and G. S. Kit, “Temperaturni napruzhennya v kruhliy plastyni z trishchynoyu, zumovleni dzherelom tepla” [“Temperature stresses in a plate with a crack due to a source of heat”], Visnyk Lvivskoho Politehnichnoho Instytutu [Bulletin of Lviv Polytechnic Institute], no. 31, pp. 58–64, 1969. [in Ukrainian].
3. N. A. Dorosh, “Termouprugost' krugloy plastiny s dugoobraznoy treshchinoy, obuslovlennaya istochnikom tepla” [“Thermoelasticity of a circular plate with an arched crack caused by a source of heat”], Vestnik Lvovskogo Politekhnicheskogo instituta [Bulletin of Lviv Polytechnic Institute], no. 25, pp. 200–204, 1968. [in Russian].
4. N. A. Dorosh,. “Termouprugost' krugloy plastiny s dugoobraznymi treshchinami, obuslovlennaya istochnikom tepla” [“The thermal elasticity of a circular plate with arc-shaped cracks due to the source of heat”], Vestnik L'vovskogo Politekhnicheskogo instituta [Bulletin of Lviv Polytechnic Institute], no. 47, pp. 176–180, 1970. [in Russian].
5. L. N. Karpenko, “O razvitii treshchiny v kruglom nagrevayemom diske” [“On the development of a crack in a circular heated disk”], Problemy prochnosti [Strength problems], no. 3, pp. 51–53, 1974. [in Russian].
6. G. S. Kit, “Napryazhennoye sostoyaniye kruglogo diska s treshchinami, na beregakh kotorykh zadany temperatura ili teplovoy potok” [“The stressed state of a circular disk with cracks on which the temperature or heat flow is given”], Matematicheskiye metody i fiziko.-mekhanicheskiye polya [Mathematical methods and physicomechanical fields], no. 7, pp. 102–107, 1978. [in Russian].
7. V. M. Zelenyak, “Temperaturni napruzhennya u napivneskinchenniy plastyni z dovilʹno oriyentovanoyu krayovoyu trishchynoyu, zumovleni dzherelom tepla” [“Thermal stresses in a semi-infinite plate with an arbitrarily oriented edge cracks caused by a source of heat”], Prykladni problemy mekhaniky i matematyky [“Applied problems of mechanics and mathematics”], no. 13, pp. 117–121, 2015. [in Ukrainian].
8. S. Ya. Matusyak, A. A. Evtushenko, and V. M. Zelenyak, “Termouprugoye sostoyaniye polubeskonechnoy plastinki s krayevoy treshchinoy, obuslovlennoye istochnikom tepla” [“The thermoelastic state of a semi-infinite plate with an edge crack due to the source of heat.], Inzhenerno-fizicheskiy zhurnal [Journal of engineering physics and thermophisics], vol. 7, no. 2, pp. 134–137, 2003. [in Russian].
9. F. Delale, and S. P. Kolluri, “Fracture of thick-walled cylinders subjected to transient thermal stresses”, J. Therm. Stresses, vol. 8, issue 2, pp. 245–248, 1985.
10. V. M. Zelenyak, “Тermopruzhna vzayemodiya trishchyny ta vklyuchennya u kruhovomu dysku” [“Thermo-elastic interaction of a crack and inclusion in a circular disk”], Fizyko-matematychne modelyuvannya ta informatsiyni tekhnolohiyi [Phicico-mathematical modeling and informational technologies], no. 21, pp. 109–116, 2015. [in Ukrainian].
11. V. M. Zelenyak, and L. I. Kolyasa, “Thermoelastic state of a half plane with curvilinear crack under the conditions of local heating”, Materials Science, vol. 52, issue 3, pp. 315‒322, 2016.
12. V. M. Zelenyak, “Investigation of the thermoelastic state of two-dimensional composite bodies with cracks”, Materials Science, vol. 50, issue 1, pp. 14–19, 2014.
13. D. V. Grilytsky, and I. M. Osiv, Zadachi teploprovidnosti i termopruzhnosti dlya plastyn [Problems of thermal conductivity and thermoelasticity for plates]. Lviv, Ukraine: Vydavnytstvo Lvivskoho universytetu Publ., 1974. [in Ukrainian].
14. M. P. Savruk, Dvumernye zadachi uprugosti dlya tel s treshchinami [Two-dimensional elasticity problems for bodies with cracks]. Kyiv, Ukraine: Naukova dumka Publ., 1981. [in Russian].
15. V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin, Raspredelenie napryazheniy okolo treshchin v plastinah i obolochkah [Distribution of stresses near cracks in plates and shells]. Kyiv, Ukraine: Naukova dumka Publ., 1976. [in Russian].
References (International): 1. I. F. Soltys, "Temperaturnyye napryazheniya v uprugoy ploskosti s krugovoy granitsey i termoizolirovannymi treshchinami zumovleni dzherelom tepla" ["The thermal elasticity of a circular plate with arc-shaped cracks due to the source of heat"], Fizico-khimicheskaia mekhanika materialov [Physicochemical mechanics of materials], no. 1, pp. 94–98, 1978. [in Russian].
2. N. A. Dorosh, and G. S. Kit, "Temperaturni napruzhennya v kruhliy plastyni z trishchynoyu, zumovleni dzherelom tepla" ["Temperature stresses in a plate with a crack due to a source of heat"], Visnyk Lvivskoho Politehnichnoho Instytutu [Bulletin of Lviv Polytechnic Institute], no. 31, pp. 58–64, 1969. [in Ukrainian].
3. N. A. Dorosh, "Termouprugost' krugloy plastiny s dugoobraznoy treshchinoy, obuslovlennaya istochnikom tepla" ["Thermoelasticity of a circular plate with an arched crack caused by a source of heat"], Vestnik Lvovskogo Politekhnicheskogo instituta [Bulletin of Lviv Polytechnic Institute], no. 25, pp. 200–204, 1968. [in Russian].
4. N. A. Dorosh,. "Termouprugost' krugloy plastiny s dugoobraznymi treshchinami, obuslovlennaya istochnikom tepla" ["The thermal elasticity of a circular plate with arc-shaped cracks due to the source of heat"], Vestnik L'vovskogo Politekhnicheskogo instituta [Bulletin of Lviv Polytechnic Institute], no. 47, pp. 176–180, 1970. [in Russian].
5. L. N. Karpenko, "O razvitii treshchiny v kruglom nagrevayemom diske" ["On the development of a crack in a circular heated disk"], Problemy prochnosti [Strength problems], no. 3, pp. 51–53, 1974. [in Russian].
6. G. S. Kit, "Napryazhennoye sostoyaniye kruglogo diska s treshchinami, na beregakh kotorykh zadany temperatura ili teplovoy potok" ["The stressed state of a circular disk with cracks on which the temperature or heat flow is given"], Matematicheskiye metody i fiziko.-mekhanicheskiye polya [Mathematical methods and physicomechanical fields], no. 7, pp. 102–107, 1978. [in Russian].
7. V. M. Zelenyak, "Temperaturni napruzhennya u napivneskinchenniy plastyni z dovilʹno oriyentovanoyu krayovoyu trishchynoyu, zumovleni dzherelom tepla" ["Thermal stresses in a semi-infinite plate with an arbitrarily oriented edge cracks caused by a source of heat"], Prykladni problemy mekhaniky i matematyky ["Applied problems of mechanics and mathematics"], no. 13, pp. 117–121, 2015. [in Ukrainian].
8. S. Ya. Matusyak, A. A. Evtushenko, and V. M. Zelenyak, "Termouprugoye sostoyaniye polubeskonechnoy plastinki s krayevoy treshchinoy, obuslovlennoye istochnikom tepla" ["The thermoelastic state of a semi-infinite plate with an edge crack due to the source of heat.], Inzhenerno-fizicheskiy zhurnal [Journal of engineering physics and thermophisics], vol. 7, no. 2, pp. 134–137, 2003. [in Russian].
9. F. Delale, and S. P. Kolluri, "Fracture of thick-walled cylinders subjected to transient thermal stresses", J. Therm. Stresses, vol. 8, issue 2, pp. 245–248, 1985.
10. V. M. Zelenyak, "Termopruzhna vzayemodiya trishchyny ta vklyuchennya u kruhovomu dysku" ["Thermo-elastic interaction of a crack and inclusion in a circular disk"], Fizyko-matematychne modelyuvannya ta informatsiyni tekhnolohiyi [Phicico-mathematical modeling and informational technologies], no. 21, pp. 109–116, 2015. [in Ukrainian].
11. V. M. Zelenyak, and L. I. Kolyasa, "Thermoelastic state of a half plane with curvilinear crack under the conditions of local heating", Materials Science, vol. 52, issue 3, pp. 315‒322, 2016.
12. V. M. Zelenyak, "Investigation of the thermoelastic state of two-dimensional composite bodies with cracks", Materials Science, vol. 50, issue 1, pp. 14–19, 2014.
13. D. V. Grilytsky, and I. M. Osiv, Zadachi teploprovidnosti i termopruzhnosti dlya plastyn [Problems of thermal conductivity and thermoelasticity for plates]. Lviv, Ukraine: Vydavnytstvo Lvivskoho universytetu Publ., 1974. [in Ukrainian].
14. M. P. Savruk, Dvumernye zadachi uprugosti dlya tel s treshchinami [Two-dimensional elasticity problems for bodies with cracks]. Kyiv, Ukraine: Naukova dumka Publ., 1981. [in Russian].
15. V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin, Raspredelenie napryazheniy okolo treshchin v plastinah i obolochkah [Distribution of stresses near cracks in plates and shells]. Kyiv, Ukraine: Naukova dumka Publ., 1976. [in Russian].
Content type: Article
Appears in Collections:Ukrainian Journal of Mechanical Engineering And Materials Science. – 2019. – Vol. 5, No. 1



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