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Thermoelastic state of a half-space having a thermally active crack parallel to its boundary

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Abstract

Using the boundary integral equation method, the problem of stationary heat conduction and thermoelasticity for a semi-infinite body with a crack parallel to its boundary is solved. Temperature or heat flow on the crack is prescribed. The body boundary is heat-insulated or is at zero temperature. The dependence of the stress intensity factor on the depth of occurrence of a circular crack at a constant temperature or under a constant heat flow is studied. In contrast to mechanical loading, thermal loading shows less SIF values than in an infinite body

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References

  1. N. M. Borodachev, “The thermoelastic problem for an infinite axisymmetrically cracked body,” Int. Appl. Mech., 2, No. 2, 54–58 (1966).

    Google Scholar 

  2. V. S. Kirilyuk, “Change in the stress intensity factors for plane cracks in a transversely isotropic medium due to thermal loads,” Int. Appl. Mech., 35, No. 9, 889–896 (1999).

    Article  Google Scholar 

  3. V. D. Kirilyuk, “Analogy between elastic and thermoelastic problems for symmetrically loaded isotropic and transverally isotropic media,” Int. Appl. Mech., 31, No. 12, 1004–1011 (1995).

    Article  MATH  Google Scholar 

  4. V. S. Kirilyuk, “Thermoelastic problems for an isotropic medium with plane mode I cracks,” Prikl. Mekh., 33, No. 1, 52–58 (1997).

    MATH  Google Scholar 

  5. V. S. Kirilyuk, “Equilibrium of a transversally isotropic body with an elliptic crack under thermal action,” Int. Appl. Mech., 37, No. 10, 1304–1310 (2001).

    Article  Google Scholar 

  6. V. S. Kirilyuk, “On relationship between the SIFs for plane cracks in isotropic and transversely isotropic media,” Teor. Prikl. Mekh., 29, 3–16 (1999).

    Google Scholar 

  7. V. S. Kirilyuk, “Using a comparison theorem for evaluating the stress for plane cracks in transversally isotropic media,” Int. Appl. Mech., 35, No. 7, 722–731 (1999).

    Article  Google Scholar 

  8. V. S. Kirilyuk, “The thermoelastic equilibrium of a transversally isotropic medium with an elliptic crack under symmetric loading,” Int. Appl. Mech., 36, No. 4, 509–517 (2000).

    Article  Google Scholar 

  9. G. S. Kit, B. S. Monastyrskii, and O. P. Sushko, “Thermoelastic state of a half-space with a plane surface crack subject to the action of a heat source,” Fiz.-Khim. Mekh. Mater., 4, 71–73 (2001).

    Google Scholar 

  10. G. S. Kit and M. V. Khai, “Integral equations of axisymmetric problems of thermoelasticity for cracked bodies,” Mat. Met. Fiz.-Mekh. Polya, 6, 3–7 (1977).

    MATH  Google Scholar 

  11. G. S. Kit and M. V. Khai, Method of Potentials in Three-Dimensional Problems of Thermoelasticity for Cracked Bodies [in Russian], Naukova Dumka, Kyiv (1989).

    Google Scholar 

  12. G. S. Kit and M. V. Khai, “Axisymmetric problem of thermoelasticity for an infinite body with two parallel circular cracks,” Tepl. Napryazh. Élem. Konstr., 12, 101–108 (1972).

    ADS  Google Scholar 

  13. M. P. Savruk, Stress Intensity Factors for Cracked Bodies, Vol. 2 of the four-volume Handbook of Fracture Mechanics and Strength of Materials [in Russian], Naukova Dumka, Kyiv (1988).

    Google Scholar 

  14. W. Nowacki, Issues of Thermoelasticity [Russian translation], Izd. AN SSSR, Moscow (1962).

    Google Scholar 

  15. Yu. N. Podil’chuk, “Mechanical and thermal strain states of transversely isotropic bodies with elliptic and parabolic cracks,” Int. Appl. Mech., 29, No. 10, 784–793 (1993).

    Article  Google Scholar 

  16. Yu. N. Podil’chuk, “Stress state of transversally isotropic body with elliptical crack in the presence of a uniform heat flux at its surface,” Int. Appl. Mech., 31, No. 3, 182–189 (1995).

    Article  MATH  Google Scholar 

  17. Yu. N. Podilchuk and Ya. I. Sokolovskii, “Thermostressed state of a transversely isotropic medium with an internal elliptic crack,” Prikl. Mekh., 33, No. 5, 3–12 (1997).

    MATH  Google Scholar 

  18. O. P. Sushko, “Thermoelastic state of a half-space with a spherical inclusion and a crack,” Prikl. Probl. Mekh. Mat., 1, 101–105 (2003).

    Google Scholar 

  19. V. M. Finkel’, Basic Physics of Fracture Arrest [in Russian], Metallurgiya, Moscow (1977).

    Google Scholar 

  20. M. V. Khai, Two-Dimensional Integral Equations of Newtonian Potential Type and Their Application [in Russian], Naukova Dumka, Kyiv (1993).

    Google Scholar 

  21. M. V. Khai and O. I. Stepanyuk, “Influence of the interface between media on the stress concentration around a crack,” Mat. Met. Fiz.-Mekh. Polya, 40, No. 2, 64–69 (1997).

    Google Scholar 

  22. M. V. Khai and O. I. Stepanyuk, “Interaction between cracks in a piecewise-homogeneous body,” Int. Appl. Mech., 28, No. 12, 815–824 (1992).

    Article  Google Scholar 

  23. B. R. Das, “A note on thermal stresses in a long circular cylinder containing a penny-shaped crack,” Int. J. Eng. Sci., 7, No. 7, 667–676 (1969).

    Article  MATH  Google Scholar 

  24. B. R. Das, “Thermal stresses in a long circular cylinder containing a penny-shaped crack,” Int. J. Eng. Sci., 6, No. 9, 497–516 (1968).

    Article  MATH  Google Scholar 

  25. E. Deutch, “The distribution of axisymmetric thermal stress in an infinite elastic medium containing a penny-shaped crack,” Int. J. Eng. Sci., 3, No. 5, 485–490 (1965).

    Article  Google Scholar 

  26. S. A. Kaloerov and O. I. Boronenko, “Magnetoelastic problem for a body with periodic elastic inclusions,” Int. Appl. Mech., 42, No. 9, 989–996 (2006).

    Article  Google Scholar 

  27. M. K. Kassir and A. Bregman, “Thermal stresses in a solid containing parallel circular cracks,” Appl. Sci. Res., 25, No. 3–4, 262–280 (1971).

    MATH  Google Scholar 

  28. V. S. Kirilyuk, “Stress state of an elastic orthotropic medium with an elliptic crack under tension and shear,” Int. Appl. Mech., 41, No. 4, 358–366 (2005).

    Article  Google Scholar 

  29. V. S. Kirilyuk, “Static equilibrium of an elastic orthotropic medium with an elliptic crack under bending,” Int. Appl. Mech., 41, No. 8, 895–903 (2005).

    Article  Google Scholar 

  30. V. S. Kirilyuk and O. I. Levchuk, “Stress state of an orthotropic material with an elliptic crack under linearly varying pressure,” Int. Appl. Mech., 42, No. 7, 790–796 (2006).

    Article  Google Scholar 

  31. Z. Olesiak and J. N. Sneddon, “Thermal stresses in an infinite elastic solid containing a penny-shaped crack,” Arch. Ration. Mech. Anal., 4, No. 3, 238–254 (1960).

    MATH  Google Scholar 

  32. R. Shail, “Some thermoelastic stress distributions in an infinite solid and a thick plate containing a penny-shaped crack,” Mathematica, 11, No. 2, 102–118 (1964).

    Google Scholar 

  33. K. N. Srivastava and J. P. Dwivedi, “Thermal stresses in an elastic sphere containing a penny-shaped crack,” Zeitschr. Angew. Math. Phys., 21, No. 6, 864–886 (1970).

    Article  MATH  Google Scholar 

  34. K. N. Srivastava and R. M. Palaiya, “The distribution of thermal stress in a semy-infinite elastic solid containing a penny-shaped crack,” Int. J. Eng. Sci., 7, No. 7, 647–666 (1969).

    Article  Google Scholar 

  35. K. N. Srivastava R. M. Palaiya, and A. Choudhary, “Thermal stresses in an elastic layer containing a penny-shaped crack and bonded to dissimilar half-space,” Int. J. Frac., 13, No. 1, 27–38 (1977).

    Article  Google Scholar 

  36. K. N. Srivastava and K. Singh, “The effect of penny-shaped crack on the distribution of stress in a semi-infinite solid,” Int. J. Eng. Sci., 7, No. 5, 469–490 (1969).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Ya. S. Podstrigach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv

    G. S. Kit & O. P. Sushko

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  1. G. S. Kit
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  2. O. P. Sushko
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__________

Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 46–54, April 2007.

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Kit, G.S., Sushko, O.P. Thermoelastic state of a half-space having a thermally active crack parallel to its boundary. Int Appl Mech 43, 395–402 (2007). https://doi.org/10.1007/s10778-007-0035-5

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  • DOI: https://doi.org/10.1007/s10778-007-0035-5

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