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- Category: Geotechnical and mining mechanical engineering, machine building
- Last Updated on 18 September 2018
- Published on 27 August 2018
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**Authors:**

**V. M. Zelenyak**, Cand. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0002-6653-4326, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

**L. I. Kolyasa**, Cand. Sc. (Phys.-Math.), orcid.org/0000-0002-9690-8042, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

**V. B. Loik**, Cand. Sc. (Tech.), orcid.org/0000-0002-3772-1640, Lviv State University of Life Safety, Lviv, Ukraine

**O.D. Synelnikov**, Cand. Sc. (Tech.), orcid.org/0000-0002-0429-147X, Lviv State University of Life Safety, Lviv, Ukraine

**Abstract:**

**Purpose. **To determine the two-dimensional thermoelastic state in semi-infinite solids (half-space), weakened by an edge crack by the actions of local heating. Heat flow due to frictional heating on the local area of the body, causes changes in temperature and stress 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 thermoelectromotive force intensity in the vicinity of the crack tip, depending on the local heat flux placement and orientation of cracks.

**Methodology. **The methods for studying two-dimensional thermoelastic state of a body with crack as stress concentrators are based on the method of complex variable function by which the problem of stationary heat conduction and thermoelasticity are reduced to singular integral equations (SIE) of the first kind, whose numerical solution was obtained by mechanical quadrature.

**Findings. **In this paper there are obtained graphic dependences of stress intensity factors (SIF) at the crack tip on the angle of orientation, the relative position of cracks and local region heating, the width of the region, that later on can be used 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. **It lies in the fact that the solutions of the new two-dimensional problems of heat conduction and thermoelasticity for half-space containing an arbitrary oriented boundary crack.

**Practical value. **The practical value is the ability to more fully take into account the real situation in the thermostatic elements of engineering structures with cracks that operate under conditions of heat stress (frictional heat) in various industries, particularly in mining. 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.

**References.**

**1**. Sushko, O. P., 2013. Thermoelastic state of a body with two coplanar thermally active circular cracks. Jou*rnal of Mathematical Sciences*, 190(5), pp. 725–739.

**2. **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), pp. 2111–2131.

**3. **Brock, L. M., 2016. Contours for planar cracks growing in three dimensions: Coupled thermoelastic solid (planar crack growth in 3D). J*ournal of Thermal Stresses*, 39(3), pp. 345–359. DOI: 10.1080/01495739.2015.1125656.

**4. **Elfakhakhre, N. R. F., Nik long*, *N. M. A. and Eshkuvatov, Z. K., 2017. Stress intensity factor for multiple cracks in half plane elasticity. *AIP Conference*, 1795(1). DOI: 10.1063/1.4972154.

**5. **Rashidova, E. V. and Sobol, B. V., 2017. An equilibrium internal transverse crack in a composite elastic half-plane. *Journal of Applied Mathematics and Mechanics*, 81(3), pp. 236‒247. DOI:10.1016/j.jappmathmech.2017.08.016.

**6. **Chen, H., Wang, Q., Liu, G.R., Wang, Y. and Sun, J., 2016. Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method. *International Journal of Mechanical Sciences*, 115–116, pp. 123‒134. DOI: 10.1016/j.ijmecsci.2016.06.012.

**7. **Kit, G. S. and Ivas’ko, N. M., 2013. Plane deformation of a semi-infinite body with a heat-active crack perpendicular to its boundary. *Teoret. I prikl. Mehanika*, 53(7), pp. 30–37.

**8. **Zelenyak, V. M. and Kolyasa, L. I., 2016. Thermoelastic state of a half plane with curvilinear crack under the conditions of local heating. *Materials Science*, 52(3), pp. 315‒322.

**9. **Zelenyak, V. M., 2014. Investigation of the thermoelastic state of two-dimensional composite bodies with cracks. *Materials Science*, 50(1), pp. 14–19.

**10. **Havrysh, V. I., 2017. Investigation of temperature fields in a heat-sensitive layer with through inclusion. *Materials Science*, 52(4), pp. 514–521.

**11. **Havrysh, V. I., 2015. Nonlinear boundary-value problem of heat conduction for a layred plate with inclusion. *Materials Science*, 51(3), pp. 331–339.

**12. **Savruk, M.P. and Zelenyak, V.M., 2009. Two-dimensional problems of thermoelasticity for piecewise- homogeneous bodies with cracks (monograph). Lviv: Rastr-7 [pdf]. Available at: <http://www.irbis-nbuv.gov.ua/cgi-bin/irbis64r_81/cgiirbis_64.exe?I21DBN=VFEIR&P21DBN=VFEIR&Z21ID=&S21REF=10&S21CNR=20&S21STN=1&S21FMT=fullwebr&C21COM=S&2_S21P03=A=&2_S21STR=%D0%97%D0%95%D0%9B%D0%95%D0%9D%D0%AF%D0%9A%20%D0%92%2E%20%D0%9C%2E> [Accessed 14 May 2017].

Tags: edge crack • heat flow • thermoelasticity • frictional heating • stress intensity factor • singular integral equation

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