Skip to main content
SpringerLink
Log in

Heating of a half space containing an inclusion and a crack

  • Published:
Materials Science Aims and scope

Abstract

Two-dimensional stationary problems of heat conduction and thermoelasticity for an elastic half space containing an elastic cylindrical macroinclusion and a thermally insulated crack are investigated. The problems are reduced to systems of two singular integral equations on closed (the boundary of the inclusion) and nonclosed (crack) contours. The numerical solutions of these systems are obtained by the method of mechanical quadratures for an inclusion in the form of an elliptic cylinder and a rectilinear crack in a half space heated by a friction heat flow uniformly distributed over a part of the surface of the half pace. For the problem posed for two cases of matrix-inclusion compositions (steel-aluminium and aluminium-steel), the numerical solutions are presented in the form of the plots of the stress intensity factors as functions of the dimensions of the inclusion and the distance between the inclusion and the crack.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. G. S. Kit and I. M. Zashkil’nyak, “Thermoelastic state of a plane containing a circular inclusion weakened by cracks,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 630–633 (1976).

  2. I. M. Zashkil’nyak, “Integral equations of the problems of heat conduction and thermoelasticity for a piecewise-homogeneous plane with curvilinear cracks,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 1001–1005 (1977).

  3. I. M. Zashkil’nyak, “Thermoelastic state of a half plane containing an inclusion and curvilinear cracks, ” Mat. Met. Fiz.-Mekh. Polya, No. 22, 60–65 (1985).

  4. V. V. Panasyuk and M. P. Savruk, “Two-dimensional problems of heat conduction and thermoelasticity for cracked bodies,” Uspekhi Mekh., 22, No.2, 75–115 (1984).

    Google Scholar 

  5. M. P. Savruk and V. M. Zelenyak, “Singular integral equations of two-dimensional problems of heat conduction and thermoelasticity for a piecewise-homogeneous plane with cracks,” Fiz.-Khim. Mekh. Mater., 22, No.3, 82–88 (1986).

    Google Scholar 

  6. M. P. Savruk and V. M. Zelenyak, “Two-dimensional problem of heat conduction and thermoelasticity for a piecewise-homogeneous body with cracks,” Fiz.-Khim. Mekh. Mater., 23, No.5, 70–78 (1987).

    Google Scholar 

  7. M. P. Savruk and V. M. Zelenyak, “Two-dimensional problem of heat conduction and thermoelasticity for two soldered half planes of different kinds with curvilinear inclusions and cracks,” Fiz.-Khim. Mekh. Mater., 24, No.2, 23–28 (1988).

    Google Scholar 

  8. V. M. Zelenyak and M. P. Savruk, “Periodic problem of thermoelasticity for a piecewise-homogeneous plane with curvilinear cuts,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1, 133–139 (1988).

  9. B. A. Cheeseman and M. H. Santare, “The interaction of a curved crack with a circular elastic inclusion, ” Int. J. Fract., 103, 259–277 (2000).

    Google Scholar 

  10. A. A. Evtushenko and V. M. Zelenyak, “Thermal problem of friction for a half space containing a crack, ” Inz.-Fiz. Zh., 72, No.1, 164–169 (1999).

    Google Scholar 

  11. S. Matysjak, A. Yevtushenko, and V. Zelenjak, “Frictional heating of a half space with cracks. I. Single or periodic system of subsurface cracks,” Trib. Internat., 32, No.5, 237–243 (1999).

    Google Scholar 

  12. S. Matysjak, A. Yevtushenko, and V. Zelenjak, “Frictional heating of a half space with an edge crack, ” Mat. Met. Fiz.-Khim. Polya, 43, No.2, 27–134 (2000).

    Google Scholar 

  13. S. Konechny, A. Evtushenko, and V. Zelenyak, “Frictional heating of a half space with edge cracks, ” Tren. Iznos, 22, No.1, 39–45 (2001).

    Google Scholar 

  14. S. Konechny, A. Evtushenko, and V. Zelenyak, “Influence of the type of distribution of a frictional heat flow on the stressed state of a half space containing a subsurface notch,” Tren. Iznos, 23, No.2, 115–119 (2002).

    Google Scholar 

  15. M. P. Savruk, Two-Dimensional Problems of Elasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  16. Ya. S. Pidstrygach, Ya. I. Burak, A. R. Gachkevich, and L. V. Chernyavskaya, Thermoelasticity of Conducting Bodies [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  17. Ya. S. Pidstrygach, V. A. Lomakin, and Yu. M. Kolyano, Thermoelasticity of Inhomogeneous Bodies [in Russian], Nauka, Moscow (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv

    S. I. Matysiak, O. O. Evtushenko & V. M. Zeleniak

  2. Bialystok University of Technology, Bialystok, Poland

    S. I. Matysiak, O. O. Evtushenko & V. M. Zeleniak

  3. “L’viv’ska Politekhnika” National University, Lviv

    S. I. Matysiak, O. O. Evtushenko & V. M. Zeleniak

Authors
  1. S. I. Matysiak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. O. Evtushenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. M. Zeleniak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 4, pp. 34–40, July–August, 2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matysiak, S.I., Evtushenko, O.O. & Zeleniak, V.M. Heating of a half space containing an inclusion and a crack. Mater Sci 40, 466–474 (2004). https://doi.org/10.1007/s11003-005-0063-4

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11003-005-0063-4

Keywords

Search

Navigation