A brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks

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dc.citation.epage70
dc.citation.issue3
dc.citation.journalTitleУкраїнський журнал із машинобудування і матеріалознавства
dc.citation.spage60
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorZelenyak, Volodymyr
dc.contributor.authorKolyasa, Liubov
dc.contributor.authorKlapchuk, Myroslava
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2024-04-03T07:37:01Z
dc.date.available2024-04-03T07:37:01Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractPurpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for the body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. Findings. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity factors at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. The influence of thermophysical and mechanical properties of inclusion on the SIF sat the crack types was investigated. The dependences of the stress intensity factor which characterizes the distribution of the intensity of stresses at the vertices of a crack have been built, as well as its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhoods of crack vertices depending on the geometrical and mechanical factors. As a result, this allows to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region due to the action of constant temperature as well as due to local heating by a heat flux were obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by the appropriate selection of composite components with appropriate mechanical characteristics.
dc.format.extent60-70
dc.format.pages11
dc.identifier.citationZelenyak V. A brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks / Volodymyr Zelenyak, Liubov Kolyasa, Myroslava Klapchuk // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 9. — No 3. — P. 60–70.
dc.identifier.citationenZelenyak V. A brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks / Volodymyr Zelenyak, Liubov Kolyasa, Myroslava Klapchuk // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 9. — No 3. — P. 60–70.
dc.identifier.doidoi.org/10.23939/ujmems2023.03.060
dc.identifier.issn2411-8001
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/61641
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofУкраїнський журнал із машинобудування і матеріалознавства, 3 (9), 2023
dc.relation.ispartofUkrainian Journal of Mechanical Engineering and Materials Science, 3 (9), 2023
dc.relation.references[1]. Choi, H. J. "Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally grade interlayer", Acta Mechanica, vol. 225, pp. 2111-2131, 2014. https://doi.org/10.1007/s00707-013-1080-2
dc.relation.references[2]. Brock, L. M. "Contours for planar cracks growing in three dimensions: Coupled thermoelastic solid (planar crack growth in 3D)", Journal of Thermal Stresses, vol.39, pp. 345-359, 2016. https://doi.org/10.1080/01495739.2015.1125656
dc.relation.references[3]. Elfakhakhre, N. R. F., Nik long, N. M. A. and Eshkuvatov, Z. K. "Stress intensity factor for multiple cracks in half plane elasticity", AIP Conference, 1795(1), 2017. https://doi.org/10.1063/1.4972154
dc.relation.references[4]. Rashidova, E. V. and Sobol, B. V. "An equilibrium internal transverse crack in a composite elastic half-plane", Journal of Applied Mathematics and Mechanics, vol.81, pp. 236-247, 2017. https://doi.org/10.1016/j.jappmathmech.2017.08.016
dc.relation.references[5]. Chen, H., Wang, Q., Liu, G.R., Wang, Y. and Sun, J. "Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method", International Journal of Mechanical Sciences, vol.115-116, pp. 123-134, 2016. https://doi.org/10.1016/j.ijmecsci.2016.06.012
dc.relation.references[6]. Tagliavia, G., Porfiri, M., Gupta, N. "Elastic interaction of interfacial spherical-cap cracks in hollow particle filled composites", International Journal of Solids and Structures, vol. 48, pp. 1141-1153, 2011. https://doi.org/10.1016/j.ijsolstr.2010.12.017
dc.relation.references[7]. Chu, S. N. G. "Elastic interaction between a screw dislocation and surface crack", Journal of Applied Physics, vol.53, pp. 8678-8685, 1982. https://doi.org/10.1063/1.330465
dc.relation.references[8]. Ming-huan, Z., Renji, T. "Interaction between crack and elastic inclusion", Applied Mathematics and Mechanics, Vol.16, pp. 307-318, 1982. https://doi.org/10.1007/BF02456943
dc.relation.references[9]. Bower A. F. "The effects of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks": Techn. Rep. No. CUED \C - Mech. I TR. 40. Univ. of Cambridge, pp. 22-25, 1987.
dc.relation.references[10]. Bryant H. D., Miller G. R., Keer I. M. "Line contact between a rigid indenter and damaged elastic body", Quart. J. Mech. Appl. Math., vol. 37, no. 3, pp. 467-478, 1984. https://doi.org/10.1093/qjmam/37.3.467
dc.relation.references[11]. Goshima Т., Kamishirna Y. "Mutual interference of multiple surface cracks due to rolling-sliding contact with frictional heating", JSME Int. J., Ser. 1, vol 37, no. 3, pp. 216-223, 1994. https://doi.org/10.1299/jsmea1993.37.3_216
dc.relation.references[12]. Goshima Т., Kamishirna Y. "Mutual interference of two surface cracks in a semi-infinite body due to rolling contact with frictional heating by a rigid roller", JSME Int. J., Ser. 1, vol. 39, no. 1, pp. 26-33, 1994. https://doi.org/10.1299/jsmea1993.39.1_26
dc.relation.references[13]. Hills D. A., Barber J. R. "Steady motion an insulating rigid flat-ended punch over a thermally conducting half-plane", Wear, vol.102, no. 1, pp. 15-22, 1985. https://doi.org/10.1016/0043-1648(85)90087-0
dc.relation.references[14]. Hills D. A., Nowell D., Sackfield A. "The state stress induced by circular sliding contacts with frictional heating", Int. J. Mech. Sci., vol. 32, no. 9, pp.767-778, 1990. https://doi.org/10.1016/0020-7403(90)90027-G
dc.relation.references[15]. Korovchinski M. V. "Plane contact problem of thermos-elasticity during quasi-stationary heat, generation on the contact surfaces", Trans. ASME. J. Basic Eng., vol.87, no. 3, pp. 811-817, 1965. https://doi.org/10.1115/1.3650823
dc.relation.references[16]. Bryant H. D., Miller G. R., Keer I. M. "Line contact between a rigid indenter and damaged elastic body", Quart. J. Mech. Appl. Math., vol. 37, no. 3, pp. 467-478, 1984. https://doi.org/10.1093/qjmam/37.3.467
dc.relation.references[17]. Miller, Gregory R., L. M. Keer, and H. S. Cheng. "On the mechanics of fatigue crack growth due to contact loading", Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, pp. 197-209, 1985. https://doi.org/10.1098/rspa.1985.0011
dc.relation.references[18]. Fan H., Keer I. M., Myra T. Tribology Transactions, vol.15, no 1, pp.121-127, 1992. https://doi.org/10.1080/10402009208982098
dc.relation.references[19]. Fujimoto, Koji, Hironobu Ito, and Takashi Yamamoto. "Effect of cracks on the contact pressure distribution", Tribology transactions, vol.35, no 4, pp. 684-695, 1992. https://doi.org/10.1080/10402009208982173
dc.relation.references[20]. Evtushenko A.A., Zelenyak V.M. "A thermal problem of friction for a half-space with a crack", Journal of Engineering Physics and Thermophysics, vol.72, no 1, pp. 170-175, 1999. https://doi.org/10.1007/BF02699085
dc.relation.references[21]. Goshima T., Keer I. M. J. Tribology., vol.112, no. 2, pp. 382-391, 1990. https://doi.org/10.1115/1.2920268
dc.relation.references[22]. Goshima, Takahito, and Toshimichi Soda. "Stress intensity factors of a subsurface crack in a semi-infinite body due to rolling/sliding contact and heat generation", JSME International Journal Series A Solid Mechanics and Material Engineering, vol.40, no2, pp.263-270. 1997. https://doi.org/10.1299/jsmea.40.263
dc.relation.references[23]. Sekine H. "Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow", Eng. Fract. Mech., vol.7, no4, pp.713-729 ,1975. https://doi.org/10.1016/0013-7944(75)90027-2
dc.relation.references[24]. Sekine H. "Thermal stresses near tips of an insulated line crack in a semi-infinite medium under uniform heat flow", Eng. Fract. Mech., vol.9, no2, pp.499-507 ,1977. https://doi.org/10.1016/0013-7944(77)90041-8
dc.relation.references[25]. Tweed I., Lowe S. "The thermoelastic problem for a half-plane with an internal line crack", Int. J. Eng. Sci., vol.17, no4, pp.357-363 ,1979. https://doi.org/10.1016/0020-7225(79)90071-5
dc.relation.references[26]. Kit H. S., Chernyak M. S. "Stressed state of bodies with thermal cylindrical inclusions and cracks (plane deformation)", Mater Sci., vol. 46, pp. 315-324, 2010.https://doi.org/10.1007/s11003-010-9292-2
dc.relation.references[27]. Cheesman B. A., Santare M.H. "The interaction of a curved crack with a circular elastic inclusion. Int. J. Fract., vol.103, pp. 259-278, 2000.
dc.relation.references[28]. Zelenyak V. M. "Temperature stresses in a circular center-cracked plate induced by head source", Mater Sci., vol. 30, pp. 272-275, 1995. https://doi.org/10.1007/BF00558586
dc.relation.references[29]. Chen H., Wang Q., Liu G., Sun J. "Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method", Int.J.of Mech. Sci., vol.115,116, pp.23-134, 2016. https://doi.org/10.1016/j.ijmecsci.2016.06.012
dc.relation.references[30]. Choi H. J. "Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally graded interlayer", Acta Mechanica, vol.225, no7, pp.2111-2131, 2014. https://doi.org/10.1007/s00707-013-1080-2
dc.relation.references[31]. Savruk M. P., Zelenyak V. M. "The plane problem of thermal conductivity and thermal elasticity for a finite piecewise uniform body with cracks", Mater Sci., vol. 23, pp.502 -510, 1987. https://doi.org/10.1007/BF01148677
dc.relation.references[32]. Savruk M. P., Zelenyak V. M. "Thermoelastic state of a two-component hollow cylinder with edge radial cracks", Mater Sci., vol. 30, pp. 470-474, 1995. https://doi.org/10.1007/BF00558841
dc.relation.references[33]. Savruk M. P., Zelenyak V. M. "Singular integral equations of plane problems of thermal conductivity and thermoelasticity for a piecewise-uniform plane with cracks", Mater Sci., vol. 22, pp. 294-307, 1986. https://doi.org/10.1007/BF00720495
dc.relation.references[34]. Savruk M. P., Zelenyak V. M. "Plane problem of thermal conductivity and thermal elasticity for two joined dissimilar half-planers with curved inclusions and cracks", Mater Sci., vol. 24, pp. 124-129, 1988. https://doi.org/10.1007/BF00736348
dc.relation.references[35]. 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", Tribology Transactions, vol. 32, pp. 237-243, 1999. https://doi.org/10.1016/S0301-679X(99)00042-0
dc.relation.references[36]. Konechnyj S., Evtushenko A., Zelenyak V. "The effect of the shape of distribution of the friction heat flow on the stress-strain of a semispace", Trenie i Iznos [Friction and Wear], vol. 23, pp. 115-119, 2002.
dc.relation.references[37]. Zelenyak V. M., Kolyasa L.I. "Thermoelastic state of a half plane with curvilinear crack under the conditions of local heating", Mater Sci., vol. 52, pp. 315-322, 2016. https://doi.org/10.1007/s11003-016-9959-4
dc.relation.references[38]. Konechnyj S., Evtushenko A., Zelenyak V. "Heating of the semi-space with edge cracks by friction", Trenie i Iznos [Friction and Wear], vol. 22, pp. 39-45, 2001.
dc.relation.references[39]. S.Ya.Matysyak, A.A.Evtushenko, V.M.Zelenyak, "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. https://doi.org/10.1023/A:1023621722039
dc.relation.references[40]. Matysiak S. I., 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. https://doi.org/10.1007/s11003-005-0063-4
dc.relation.references[41]. Zelenyak V. M. "Mathematical modeling of stationary thermoelastic state in a half plane containing an inclusion and a crack due to local heating by a heat flux", Mathematical modeling and computing, vol. 7, pp. 88-95, 2020. https://doi.org/10.23939/mmc2020.01.088
dc.relation.references[42]. Zelenyak. V. M. "Thermoelastic interaction of a two-component circular inclusion with a crack in the plate", Mater Sci., vol. 48, pp. 301-307, 2012. https://doi.org/10.1007/s11003-012-9506-x
dc.relation.references[43]. Zelenyak. V. M. "Integral equations of two-dimensional problems of thermoelasticity for a three-layer annual cracked domain", Mater Sci., vol. 51, pp. 290-299, 2015. https://doi.org/10.1007/s11003-015-9842-8
dc.relation.references[44]. Zelenyak. B. M. "Thermoelastic equilibrium of a three-layer circular hollow cylinder weakened by a crack", Mater Sci., vol. 52, pp. 253-260, 2016. https://doi.org/10.1007/s11003-016-9952-y
dc.relation.references[45]. Zelenyak. V. "Mathematical modeling of stationary thermoelastic state for a plate with periodic system inclusion and cracks", Acta mechanica et automatica, vol. 13, no.1, pp. 11-15, 2019. https://doi.org/10.2478/ama-2019-0002
dc.relation.referencesen[1]. Choi, H. J. "Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally grade interlayer", Acta Mechanica, vol. 225, pp. 2111-2131, 2014. https://doi.org/10.1007/s00707-013-1080-2
dc.relation.referencesen[2]. Brock, L. M. "Contours for planar cracks growing in three dimensions: Coupled thermoelastic solid (planar crack growth in 3D)", Journal of Thermal Stresses, vol.39, pp. 345-359, 2016. https://doi.org/10.1080/01495739.2015.1125656
dc.relation.referencesen[3]. Elfakhakhre, N. R. F., Nik long, N. M. A. and Eshkuvatov, Z. K. "Stress intensity factor for multiple cracks in half plane elasticity", AIP Conference, 1795(1), 2017. https://doi.org/10.1063/1.4972154
dc.relation.referencesen[4]. Rashidova, E. V. and Sobol, B. V. "An equilibrium internal transverse crack in a composite elastic half-plane", Journal of Applied Mathematics and Mechanics, vol.81, pp. 236-247, 2017. https://doi.org/10.1016/j.jappmathmech.2017.08.016
dc.relation.referencesen[5]. Chen, H., Wang, Q., Liu, G.R., Wang, Y. and Sun, J. "Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method", International Journal of Mechanical Sciences, vol.115-116, pp. 123-134, 2016. https://doi.org/10.1016/j.ijmecsci.2016.06.012
dc.relation.referencesen[6]. Tagliavia, G., Porfiri, M., Gupta, N. "Elastic interaction of interfacial spherical-cap cracks in hollow particle filled composites", International Journal of Solids and Structures, vol. 48, pp. 1141-1153, 2011. https://doi.org/10.1016/j.ijsolstr.2010.12.017
dc.relation.referencesen[7]. Chu, S. N. G. "Elastic interaction between a screw dislocation and surface crack", Journal of Applied Physics, vol.53, pp. 8678-8685, 1982. https://doi.org/10.1063/1.330465
dc.relation.referencesen[8]. Ming-huan, Z., Renji, T. "Interaction between crack and elastic inclusion", Applied Mathematics and Mechanics, Vol.16, pp. 307-318, 1982. https://doi.org/10.1007/BF02456943
dc.relation.referencesen[9]. Bower A. F. "The effects of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks": Techn. Rep. No. CUED \C - Mech. I TR. 40. Univ. of Cambridge, pp. 22-25, 1987.
dc.relation.referencesen[10]. Bryant H. D., Miller G. R., Keer I. M. "Line contact between a rigid indenter and damaged elastic body", Quart. J. Mech. Appl. Math., vol. 37, no. 3, pp. 467-478, 1984. https://doi.org/10.1093/qjmam/37.3.467
dc.relation.referencesen[11]. Goshima T., Kamishirna Y. "Mutual interference of multiple surface cracks due to rolling-sliding contact with frictional heating", JSME Int. J., Ser. 1, vol 37, no. 3, pp. 216-223, 1994. https://doi.org/10.1299/jsmea1993.37.3_216
dc.relation.referencesen[12]. Goshima T., Kamishirna Y. "Mutual interference of two surface cracks in a semi-infinite body due to rolling contact with frictional heating by a rigid roller", JSME Int. J., Ser. 1, vol. 39, no. 1, pp. 26-33, 1994. https://doi.org/10.1299/jsmea1993.39.1_26
dc.relation.referencesen[13]. Hills D. A., Barber J. R. "Steady motion an insulating rigid flat-ended punch over a thermally conducting half-plane", Wear, vol.102, no. 1, pp. 15-22, 1985. https://doi.org/10.1016/0043-1648(85)90087-0
dc.relation.referencesen[14]. Hills D. A., Nowell D., Sackfield A. "The state stress induced by circular sliding contacts with frictional heating", Int. J. Mech. Sci., vol. 32, no. 9, pp.767-778, 1990. https://doi.org/10.1016/0020-7403(90)90027-G
dc.relation.referencesen[15]. Korovchinski M. V. "Plane contact problem of thermos-elasticity during quasi-stationary heat, generation on the contact surfaces", Trans. ASME. J. Basic Eng., vol.87, no. 3, pp. 811-817, 1965. https://doi.org/10.1115/1.3650823
dc.relation.referencesen[16]. Bryant H. D., Miller G. R., Keer I. M. "Line contact between a rigid indenter and damaged elastic body", Quart. J. Mech. Appl. Math., vol. 37, no. 3, pp. 467-478, 1984. https://doi.org/10.1093/qjmam/37.3.467
dc.relation.referencesen[17]. Miller, Gregory R., L. M. Keer, and H. S. Cheng. "On the mechanics of fatigue crack growth due to contact loading", Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, pp. 197-209, 1985. https://doi.org/10.1098/rspa.1985.0011
dc.relation.referencesen[18]. Fan H., Keer I. M., Myra T. Tribology Transactions, vol.15, no 1, pp.121-127, 1992. https://doi.org/10.1080/10402009208982098
dc.relation.referencesen[19]. Fujimoto, Koji, Hironobu Ito, and Takashi Yamamoto. "Effect of cracks on the contact pressure distribution", Tribology transactions, vol.35, no 4, pp. 684-695, 1992. https://doi.org/10.1080/10402009208982173
dc.relation.referencesen[20]. Evtushenko A.A., Zelenyak V.M. "A thermal problem of friction for a half-space with a crack", Journal of Engineering Physics and Thermophysics, vol.72, no 1, pp. 170-175, 1999. https://doi.org/10.1007/BF02699085
dc.relation.referencesen[21]. Goshima T., Keer I. M. J. Tribology., vol.112, no. 2, pp. 382-391, 1990. https://doi.org/10.1115/1.2920268
dc.relation.referencesen[22]. Goshima, Takahito, and Toshimichi Soda. "Stress intensity factors of a subsurface crack in a semi-infinite body due to rolling/sliding contact and heat generation", JSME International Journal Series A Solid Mechanics and Material Engineering, vol.40, no2, pp.263-270. 1997. https://doi.org/10.1299/jsmea.40.263
dc.relation.referencesen[23]. Sekine H. "Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow", Eng. Fract. Mech., vol.7, no4, pp.713-729 ,1975. https://doi.org/10.1016/0013-7944(75)90027-2
dc.relation.referencesen[24]. Sekine H. "Thermal stresses near tips of an insulated line crack in a semi-infinite medium under uniform heat flow", Eng. Fract. Mech., vol.9, no2, pp.499-507 ,1977. https://doi.org/10.1016/0013-7944(77)90041-8
dc.relation.referencesen[25]. Tweed I., Lowe S. "The thermoelastic problem for a half-plane with an internal line crack", Int. J. Eng. Sci., vol.17, no4, pp.357-363 ,1979. https://doi.org/10.1016/0020-7225(79)90071-5
dc.relation.referencesen[26]. Kit H. S., Chernyak M. S. "Stressed state of bodies with thermal cylindrical inclusions and cracks (plane deformation)", Mater Sci., vol. 46, pp. 315-324, 2010.https://doi.org/10.1007/s11003-010-9292-2
dc.relation.referencesen[27]. Cheesman B. A., Santare M.H. "The interaction of a curved crack with a circular elastic inclusion. Int. J. Fract., vol.103, pp. 259-278, 2000.
dc.relation.referencesen[28]. Zelenyak V. M. "Temperature stresses in a circular center-cracked plate induced by head source", Mater Sci., vol. 30, pp. 272-275, 1995. https://doi.org/10.1007/BF00558586
dc.relation.referencesen[29]. Chen H., Wang Q., Liu G., Sun J. "Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method", Int.J.of Mech. Sci., vol.115,116, pp.23-134, 2016. https://doi.org/10.1016/j.ijmecsci.2016.06.012
dc.relation.referencesen[30]. Choi H. J. "Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally graded interlayer", Acta Mechanica, vol.225, no7, pp.2111-2131, 2014. https://doi.org/10.1007/s00707-013-1080-2
dc.relation.referencesen[31]. Savruk M. P., Zelenyak V. M. "The plane problem of thermal conductivity and thermal elasticity for a finite piecewise uniform body with cracks", Mater Sci., vol. 23, pp.502 -510, 1987. https://doi.org/10.1007/BF01148677
dc.relation.referencesen[32]. Savruk M. P., Zelenyak V. M. "Thermoelastic state of a two-component hollow cylinder with edge radial cracks", Mater Sci., vol. 30, pp. 470-474, 1995. https://doi.org/10.1007/BF00558841
dc.relation.referencesen[33]. Savruk M. P., Zelenyak V. M. "Singular integral equations of plane problems of thermal conductivity and thermoelasticity for a piecewise-uniform plane with cracks", Mater Sci., vol. 22, pp. 294-307, 1986. https://doi.org/10.1007/BF00720495
dc.relation.referencesen[34]. Savruk M. P., Zelenyak V. M. "Plane problem of thermal conductivity and thermal elasticity for two joined dissimilar half-planers with curved inclusions and cracks", Mater Sci., vol. 24, pp. 124-129, 1988. https://doi.org/10.1007/BF00736348
dc.relation.referencesen[35]. 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", Tribology Transactions, vol. 32, pp. 237-243, 1999. https://doi.org/10.1016/S0301-679X(99)00042-0
dc.relation.referencesen[36]. Konechnyj S., Evtushenko A., Zelenyak V. "The effect of the shape of distribution of the friction heat flow on the stress-strain of a semispace", Trenie i Iznos [Friction and Wear], vol. 23, pp. 115-119, 2002.
dc.relation.referencesen[37]. Zelenyak V. M., Kolyasa L.I. "Thermoelastic state of a half plane with curvilinear crack under the conditions of local heating", Mater Sci., vol. 52, pp. 315-322, 2016. https://doi.org/10.1007/s11003-016-9959-4
dc.relation.referencesen[38]. Konechnyj S., Evtushenko A., Zelenyak V. "Heating of the semi-space with edge cracks by friction", Trenie i Iznos [Friction and Wear], vol. 22, pp. 39-45, 2001.
dc.relation.referencesen[39]. S.Ya.Matysyak, A.A.Evtushenko, V.M.Zelenyak, "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. https://doi.org/10.1023/A:1023621722039
dc.relation.referencesen[40]. Matysiak S. I., 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. https://doi.org/10.1007/s11003-005-0063-4
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dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.rights.holder© Zelenyak V., Kolyasa L., Klapchuk M., 2023
dc.subjectstress intensity factor
dc.subjectsingular integral equation
dc.subjectinclusion
dc.subjectheat conduction
dc.subjectthermoselasticity
dc.subjectcrack
dc.subjectheat flux
dc.subjectheat source
dc.titleA brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks
dc.typeArticle

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Ukrainian Journal of Mechanical Engineering and Materials Science. – 2023. – Vol. 9, No. 3