Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack
| dc.citation.epage | 52 | |
| dc.citation.issue | 1 | |
| dc.citation.journalTitle | Український журнал із машинобудування і матеріалознавства | |
| dc.citation.spage | 44 | |
| dc.citation.volume | 9 | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.author | Zelenyak, Volodymyr | |
| dc.contributor.author | Kolyasa, Liubov | |
| dc.contributor.author | Klapchuk, Myroslava | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2024-02-07T08:18:47Z | |
| dc.date.available | 2024-02-07T08:18:47Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | A mathematical model to determine the two-dimensional thermoelastic state in a semi-infinite solid weakened by an internal crack under conditions of local heating is examined. Heat flux due to frictional heating on the local area of the body causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the crack placement. The methods for studying the two-dimensional thermoelastic state of a body with cracks as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle orientation of the crack as well as forms of the intensity distribution of the local heat flux. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. The scientific novelty lies in the fact that the solutions to two-dimensional problems of heat conduction and thermoelasticity for a half-plane containing a crack due to local heating by a heat flux were obtained. This would make it possible to obtain a comparative analysis of the intensity of thermal stresses around the top of the crack, depending on the form of distribution of the intensity of the heat flow on the surface of the body. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with the crack that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks. | |
| dc.format.extent | 44-52 | |
| dc.format.pages | 9 | |
| dc.identifier.citation | Zelenyak V. Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack / Volodymyr Zelenyak, Liubov Kolyasa, Myroslava Klapchuk // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 9. — No 1. — P. 44–52. | |
| dc.identifier.citationen | Zelenyak V. Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack / Volodymyr Zelenyak, Liubov Kolyasa, Myroslava Klapchuk // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 9. — No 1. — P. 44–52. | |
| dc.identifier.doi | doi.org/10.23939/ujmems2023.01.044 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/61136 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Український журнал із машинобудування і матеріалознавства, 1 (9), 2023 | |
| dc.relation.ispartof | Ukrainian Journal of Mechanical Engineering and Materials Science, 1 (9), 2023 | |
| dc.relation.references | [1] Popov V. L., Heß M., Willert E. Handbook of Contact Mechanics, Exact Solutions of Axisymmetric Contact Problems; The Authors Translation from the German Language edition: Popov et al: Handbuch der Kontaktmechanik; Springer: Berlin/Heidelberg, Germany, 2018, p. 357. | |
| dc.relation.references | [2] Datsishin O. P., Marchenko G. P., and Panasyuk V. V. “Do teorії rozvitku trіshhin pri kontaktі kochennya” [“Theory of Crack Growth in Rolling Contact”], in Materials Science. 1993. 29, no. 4, рр. 373–383. | |
| dc.relation.references | [3] Popov V., Heß M. Method of Dimensionality Reduction in Contact Mechanics and Friction, Springer-Verlag Berlin Heidelberg, 2015. | |
| dc.relation.references | [4] Fan H., Keer L. M. & Mura T. “Near surface crack initiation under contact fatigue”. Tribology Trans., vol. 35, no. 1, pp. 121–127, 1992. | |
| dc.relation.references | [5] Fujimoto K., Ito H., Yamamoto T. “Effect of cracks on the contact pressure distribution”. Tribology Trans. vol. 35, no. 4, pp. 683–695, 1992. | |
| dc.relation.references | [6] Korovchinski M. V. “Plane contact problem of thermoelasticity during quasistationary heat generation on the contact surfaces|. Trans. ASME. J. Basic Eng., vol. D87, no. 3, pp. 811–817, 2003. | |
| dc.relation.references | [7] Evtushenko A. A., Zelenyak V. M. “A thermal problem of friction for a half-space with a crack”. J. Eng. Phys. Thermophys, vol. 72, pp. 170–175, 1999. | |
| dc.relation.references | [8] Matysiak S. J., Evtushenko O. O., Zeleniak V. M. “Heating of a half space containing an inclusion and a crack”, Mater Sci, vol. 40, pp. 466–474, 2004. | |
| dc.relation.references | [9] Matysyak S. Ya., Evtushenko A. A., Zelenyak V. M. “Heat-Source-Initiated Thermoelastic State of a Semiinfinite Plate with an Edge Crack”, Journal of Engineering Physics and Thermophysics, vol. 76, no. 2, pp. 392–396, 2003. | |
| dc.relation.references | [10] Matysiak S. J., Yevtushenko A. A., Zelenjak V. M. “Frictional heating of a half-space with cracks. I. Single or periodic system of subsurface cracks”, Tribol. Int., vol. 32, pp. 237–243, 1999. | |
| dc.relation.references | [11] Matysiak S. J., Yevtushenko A. A., Zelenjak V. M. “Heating of the semispace with edge cracks by friction”, Trenie i Iznos [Friction and Wear], vol. 22, no. 1, pp. 39–45, 2001. | |
| dc.relation.references | [12] Knothe K., Liebet S. K. ”Determination of temperature for sliding contact with applications for wheel–rail systems”, Wear, vol. 189, no. 10, pp. 91–99, 1995. | |
| dc.relation.references | [13] Evtushenko A., Konechny S. and Chapovska R. “Integration of the solution of the Ling heat problem using finite functions”, Inzh.-Fiz. Zh., vol. 74, no. 1, pp. 118–122, 2001. | |
| dc.relation.references | [14] Zozulya V. V. “Regularization of divergent integrals: A comparison of the classical and generalizedfunctions approaches”, Advances in Computational Mathematics, vol. 41, pp. 727–780, 2015. | |
| dc.relation.referencesen | [1] Popov V. L., Heß M., Willert E. Handbook of Contact Mechanics, Exact Solutions of Axisymmetric Contact Problems; The Authors Translation from the German Language edition: Popov et al: Handbuch der Kontaktmechanik; Springer: Berlin/Heidelberg, Germany, 2018, p. 357. | |
| dc.relation.referencesen | [2] Datsishin O. P., Marchenko G. P., and Panasyuk V. V. "Do teorii rozvitku trishhin pri kontakti kochennya" ["Theory of Crack Growth in Rolling Contact"], in Materials Science. 1993. 29, no. 4, rr. 373–383. | |
| dc.relation.referencesen | [3] Popov V., Heß M. Method of Dimensionality Reduction in Contact Mechanics and Friction, Springer-Verlag Berlin Heidelberg, 2015. | |
| dc.relation.referencesen | [4] Fan H., Keer L. M. & Mura T. "Near surface crack initiation under contact fatigue". Tribology Trans., vol. 35, no. 1, pp. 121–127, 1992. | |
| dc.relation.referencesen | [5] Fujimoto K., Ito H., Yamamoto T. "Effect of cracks on the contact pressure distribution". Tribology Trans. vol. 35, no. 4, pp. 683–695, 1992. | |
| dc.relation.referencesen | [6] Korovchinski M. V. "Plane contact problem of thermoelasticity during quasistationary heat generation on the contact surfaces|. Trans. ASME. J. Basic Eng., vol. D87, no. 3, pp. 811–817, 2003. | |
| dc.relation.referencesen | [7] Evtushenko A. A., Zelenyak V. M. "A thermal problem of friction for a half-space with a crack". J. Eng. Phys. Thermophys, vol. 72, pp. 170–175, 1999. | |
| dc.relation.referencesen | [8] Matysiak S. J., Evtushenko O. O., Zeleniak V. M. "Heating of a half space containing an inclusion and a crack", Mater Sci, vol. 40, pp. 466–474, 2004. | |
| dc.relation.referencesen | [9] Matysyak S. Ya., Evtushenko A. A., Zelenyak V. M. "Heat-Source-Initiated Thermoelastic State of a Semiinfinite Plate with an Edge Crack", Journal of Engineering Physics and Thermophysics, vol. 76, no. 2, pp. 392–396, 2003. | |
| dc.relation.referencesen | [10] Matysiak S. J., Yevtushenko A. A., Zelenjak V. M. "Frictional heating of a half-space with cracks. I. Single or periodic system of subsurface cracks", Tribol. Int., vol. 32, pp. 237–243, 1999. | |
| dc.relation.referencesen | [11] Matysiak S. J., Yevtushenko A. A., Zelenjak V. M. "Heating of the semispace with edge cracks by friction", Trenie i Iznos [Friction and Wear], vol. 22, no. 1, pp. 39–45, 2001. | |
| dc.relation.referencesen | [12] Knothe K., Liebet S. K. "Determination of temperature for sliding contact with applications for wheel–rail systems", Wear, vol. 189, no. 10, pp. 91–99, 1995. | |
| dc.relation.referencesen | [13] Evtushenko A., Konechny S. and Chapovska R. "Integration of the solution of the Ling heat problem using finite functions", Inzh.-Fiz. Zh., vol. 74, no. 1, pp. 118–122, 2001. | |
| dc.relation.referencesen | [14] Zozulya V. V. "Regularization of divergent integrals: A comparison of the classical and generalizedfunctions approaches", Advances in Computational Mathematics, vol. 41, pp. 727–780, 2015. | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.rights.holder | © Zelenyak V., Kolyasa L., Klapchuk M., 2023 | |
| dc.subject | crack | |
| dc.subject | heat flux | |
| dc.subject | heat condition | |
| dc.subject | thermoelasticity | |
| dc.subject | stress intensity factor | |
| dc.subject | singular integral equation | |
| dc.title | Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack | |
| dc.type | Article |
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