Thermoelastic behavior of a bimaterial with interface crack filled with an incompressible fluid

Authors

  • Kh. I. Serednytska Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060, Lviv, Naukova str., 3-b https://orcid.org/0000-0003-2037-1223
  • R. M. Martynyak Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060, Lviv, Naukova str., 3-b https://orcid.org/0000-0001-7613-1427

DOI:

https://doi.org/10.17721/1812-5409.2019/1.48

Abstract

Thermo-stressed state of the bimaterial with the interfacial crack filled with an incompressible fluid is investigated. The bimaterial with zero Dundurs parameter is considered. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for a temperature jump between the cracks faces and an opening crack. The pressure of the fluid is determined from the equation of the incompressible fluid. Using the method of successive approximations a numerical solution of the problem is constructed. The opening crack and temperature jump are determined by the finite sum for Chebyshev polynomials of the second kind. The coefficients for Chebyshev polynomials are determined from the system of linear algebraic equations. Having made numerical calculations, the dependences of the pressure of the fluid and the opening crack from the mechanical loads and density and direction of the heat flow have been constructed. The influence of fluid pressure on the stress intensity factor mode I are analyzed.

Key words: bimaterial, interfacial crack, incompressible fluid, fluid pressure.

Pages of the article in the issue: 206-209

Language of the article: Ukrainian

References

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YEVTUSHENKO, А. and SULYM, H (1980) Koncentraciya napruzhen` poblyzu shhilyny, zapovnenoyi ridynoyu. Fizyko-khimichna mekhanika materialiv. 16 (6). p. 70-73.

SEREDNYTSKA, K., MARTYNYAK, R. M. and CHUMAK, K. (2019) The thermoelastic state of a bi-material with an open gas-filled interface crack. Journal of Theoretical and Applied Mechanics. 57(2). p. 331-341.

KACZYŃSKI, A. and MONASTYRSKYY, B. (2004) On the problem of some interface defect filled with a compressible fluid in a periodic stratified medium. Journal of Theoretical and Applied Mechanics. 42 (1). p. 41-57.

MARTYNYAK, R. M. and SEREDNYTSKA, K. I. (2017) Kontaktni zadachi termoprugnosti dlya migfaznyh trishchyn v bimetrialnyh tilah. Lviv : Rastr-7.

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How to Cite

Serednytska, K. I., & Martynyak, R. M. (2019). Thermoelastic behavior of a bimaterial with interface crack filled with an incompressible fluid. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 206–209. https://doi.org/10.17721/1812-5409.2019/1.48

Issue

Section

Differential equations, mathematical physics and mechanics