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

2023;
: 44-52
https://doi.org/10.23939/ujmems2023.01.044
Received: November 22, 2022
Revised: March 16, 2023
Accepted: March 17, 2023
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University, Mathematics Department
3
Lviv Polytechnic National University

Purpose. 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.
Methodology. 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.
Findings. 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.
Originality. 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.
Practical value. 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.

[1]. K. Dzhonson Mexanika kontaktnogo vzaimodejstviya. M.: Nauka, 1989, 510 s. [in Russian].
[2]. A. P. Dacishin, G. P. Marchennko, V. V. Panasyuk Do teorії rozvitku trіshhin pri kontaktі kochennya. Fіz.-xіm. mexanіka materіalіv. 29, № 4. s. 49-61, 1993.
[3]. Н. D. Bryant, G. R. Miller, L. M. Keer Line contact between a rigid indenter and damaged elastic body. Quart. J. Mech. and Appl. Math. 37, № 3. pp. 467-478, 1984.
https://doi.org/10.1093/qjmam/37.3.467
[4]. H. Fan, L. M. Keer, T. Mura Near surface crack initiation under contact fatigue. Tribology Trans. 35, №1. pp.121-127, 1992.
https://doi.org/10.1080/10402009208982098
[5]. K. Fujimoto, H. Ito, T. Yamamoto Effect of cracks on the contact pressure distribution. Tribology Trans. 35, № 4 P. 683-695, 1992.
https://doi.org/10.1080/10402009208982173
[6]. M. V. Korovchinski Plane contact problem of thermoelasticity during quasistationary heat generation on the contact surfaces. Trans. ASME. J. Basic Eng. D87, №3. pp. 811-817, 2003.
https://doi.org/10.1115/1.3650823
[7]. M. V. Korovchinskij Osnovy' teorii termicheskogo kontakta pri lokal'nom trenii. Ch. ІІ. Voprosy' treniya i problemy' smazki. M.: Nauka, 1968, s. 5-72.
[8]. M. P. Savruk Dvumernye zadachi uprugosti dlya tel s treshchinami [Two-dimensional elasticity problems for bodies with cracks], Kyiv: Naukova dumka, 1981, 324 p. [in Russian].
[9]. A. A. Evtushenko, V. M. Zelenyak Teplovaya zadacha treniya dlya poluprostranstva s treshhinoj. Inzh.-fiz. zhurnal. 72, №1. s. 164-169, 1999.
https://doi.org/10.1007/BF02699085
[10]. S. J. Matysiak, A. A. Yevtushenko, V. M. Zelenjak Frictional heating of a half-space with cracks. I. Single or periodic system of subsurface cracks. Tribol. Int. 32. P.237-243, 1999.
https://doi.org/10.1016/S0301-679X(99)00042-0
[11]. S. Matysiak, A. Yevtushenko, V. Zelenjak Frictional heating of a half-space with an edge crack. Mat. metodi ta fіz.-mex. polya. 43, № 2. pp. 127-130, 2000.
[12]. S. Konechny', A. Evtushenko, V. Zelenyak Frikcionny'j nagrev poluprostranstva s kraevy'mi treshhinami. Trenie i iznos. 22, № 1. s. 39-45, 2001.
[13]. V. S. Shhedrov Temperatura na skol'zyashhem kontakte. Trenie i iznos v mashinax. M.: Izd-vo AN SSSR. № 10. s. 155-296, 1955.
[14]. M. A. Korotkov Vliyanie sheroxovatosti na formirovanie edinichnoj konturnoj ploshhadki kontakta. Trudy' Kalinin. politex. in-ta. 15, № 13. 1972, s. 173.
[15]. K. Knothe, S. K. Liebet Determination of temperature for sliding contact with applications for wheel-rail systems. Wear. 189, № 10. pp. 91-99, 1995.
https://doi.org/10.1016/0043-1648(95)06666-7
[16]. A. Evtushenko, S. Konechny', R. Chapovska Integrirovanie resheniya teplovoj zadachi Linga s pomoshh'yu finitny'x funkcij . Inzh.-fiz. zhurnal. 2001. 74, № 1. S. 118-122.
https://doi.org/10.1023/A:1012716521496
[17] F. Erdogan, G. D. Gupta, T. S. Cook The numerical solutions of singular integral equations. Methods of analysis and solutions of crack problems. Leyden: Noordhoff Intern. Publ., Mechanics of fracture, pp. 368-425, 1973.
https://doi.org/10.1007/978-94-017-2260-5_7