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Stress intensity factors for bonded two half planes weakened by thermally insulated cracks

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Abstract

The thermally insulated inclined or circular arc cracks problems subjected to axial stress in the upper part of bonded two half planes are considered. The modified complex potential function method with the continuity conditions of the resultant force, displacement, and heat conduction functions is used to develop the new system of hypersingular integral equations (HSIEs) for the problems. The new system of HSIEs is solved numerically for the unknown crack opening displacement function and the known traction along the crack as the right-hand term using the appropriate quadrature formulas. Numerical results for the nondimensional stress intensity factors (SIFs) at all cracks tips are presented. A comparison between the nondimensional SIFs for cracks with and without thermal influence is also given

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References

  1. Chen, Y.Z., Hasebe, N.: Solution for a curvilinear crack in a thermoelastic medium. J. Therm. Stress. 26, 245–259 (2003)

    Article  Google Scholar 

  2. Hasebe, N., Wang, X.: Complex variable method for thermal stress problem. J. Therm. Stress. 28, 595–648 (2005)

    Article  MathSciNet  Google Scholar 

  3. Yu, C., Zou, D., Li, Y.H., Yang, H.B., Gao, C.F.: An arc-shaped crack in nonlinear fully coupled thermoelectric materials. Acta Mech. 229, 1989–2008 (2018)

    Article  MathSciNet  Google Scholar 

  4. Jafari, M.: Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method. Eur. J. Mech. A/Solids 73, 212–223 (2019)

    Article  MathSciNet  Google Scholar 

  5. Jin, Z.H., Noda, N.: An internal crack parallel to the boundary of a nonhomogeneous half plane under thermal loading. Int. J. Eng. Sci. 31(5), 793–806 (1993)

    Article  Google Scholar 

  6. Li, W., Li, J., Abdelmoula, R., Song, F., Jiang, C.P.: Inertia effect analysis of a half-plane with an induced crack under thermal loading using hyperbolic heat conduction. ZAMM J. Appl. Math. Mech. 96, 1–17 (2015)

    Google Scholar 

  7. Chen, Y.Z.: Solution for a crack embedded in thermal dissimilar elliptic inclusion. Eng. Fract. Mech. 160, 15–21 (2016)

    Article  Google Scholar 

  8. Weibgraeber, P., Felger, J., Geipel, D., Becker, W.: Cracks at elliptical holes: stress intensity factor and finite fracture mechanics solution. Eur. J. Mech. A/Solids 55, 192–198 (2016)

    Article  Google Scholar 

  9. Chen, Y.Z.: Numerical solution for thermal confocal elliptic dissimilar layers in plane elasticity. Acta Mech. 227, 2233–2244 (2016)

    Article  MathSciNet  Google Scholar 

  10. Bregman, A.M., Kassir, M.K.: Thermal fracture of bonded dissimilar media containing a penny-shaped crack. Int. J. Fract. 10(1), 87–98 (1974)

    Article  Google Scholar 

  11. Chao, C.K., Shen, M.H.: Solutions of thermoelastic crack problems in bonded dissimilar media or half-plane medium. Int. J. Solids Struct. 32(24), 3537–3554 (1995)

    Article  Google Scholar 

  12. Chao, C.K., Chen, S.J.: Stress intensity factors of two bonded half-plane problem with a point heat source. Nucl. Eng. Des. 160, 97–109 (1996)

    Article  Google Scholar 

  13. Petrova, V.E., Herrmann, K.P.: Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source. Int. J. Fract. 128, 49–63 (2004)

    Article  Google Scholar 

  14. Hasebe, N., Kato, S.: Solution of problem of two dissimilar materials bonded at one interface subjected to temperature. Arch. Appl. Mech. 84(6), 913–931 (2014)

    Article  Google Scholar 

  15. Choi, H.J.: Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally graded interlayer. Acta Mech. 225, 2111–2131 (2014)

    Article  MathSciNet  Google Scholar 

  16. Lee, K.Y., Shul, C.W.: Determination of thermal stress intensity factors for an interface crack under vertical uniform heat flow. Eng. Fract. Mech. 40(6), 1067–1074 (1991)

    Article  Google Scholar 

  17. Petrova, V., Schmauder, S.: Thermal fracture of a functionally graded/homogeneous bimaterial with system of cracks. Theor. Appl. Fract. Mech. 55, 148–157 (2011)

    Article  Google Scholar 

  18. Wang, B.L., Han, J.C., Du, S.Y.: Thermoelastic fracture mechanics for nonhomogeneous material subjected to unsteady thermal load. J. Appl. Mech. 67, 87–95 (2000)

    Article  Google Scholar 

  19. Wu, H., Li, L., Chai, G., Song, F., Kitamura, T.: Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading. J. Therm. Stress. 39(4), 371–385 (2016)

    Article  Google Scholar 

  20. Rizk, A.A.: Stress intensity factor for an edge crack in two bonded dissimilar materials under convective cooling. Theor. Appl. Fract. Mech. 49, 251–267 (2008)

    Article  Google Scholar 

  21. Hu, X.F., Gao, H.Y., Yao, W.A., Yang, S.T.: Study on steady-state thermal conduction with singularities in multi-material composites. Int. J. Heat Mass Transf. 104, 861–870 (2017)

    Article  Google Scholar 

  22. Weiss, N.A., Keer, L.M.: Periodic array of traction-free interface cracks subjected to far-field uniform heat flow. Mech. Res. Commun. 68, 95–97 (2015)

    Article  Google Scholar 

  23. Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff International Publishing, Leyden (1953)

    MATH  Google Scholar 

  24. Nik Long, N.M.A., Eshkuvatov, Z.K.: Hypersingular integral equation for multiple curved cracks problem in plane elasticity. Int. J. Solids Struct. 64, 2611–2617 (2009)

    Article  Google Scholar 

  25. Hamzah, K.B., Nik Long, N.M.A., Senu, N., Eshkuvatov, Z.K.: Stress intensity factor for multiple cracks in bonded dissimilar materials using hypersingular integral equations. Appl. Math. Model. 73, 95–108 (2019)

    Article  MathSciNet  Google Scholar 

  26. Chen, Y.Z., Hasebe, N., Lee, K.Y.: Multiple Crack Problems in Elasticity. WIT Press, Southampton (2003)

    MATH  Google Scholar 

  27. Wang, C.H.: Introduction to Fracture Mechanics. DSTO Aeronautical and Maritime Research Laboratory, Melbourne, Australia (1996)

  28. Chen, Y.Z., Lin, X.Y., Wang, X.Z.: Numerical solution for curved crack problem in elastic half-plane using hypersingular integral equation. Philos. Mag. 89(26), 2239–2253 (2009)

    Article  Google Scholar 

  29. Rafar, R.A., Nik Long, N.M.A., Senu, N., Noda, N.A.: Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity. ZAMM J. Appl. Math. Mech. 97(11), 1482–1494 (2017)

    MathSciNet  Google Scholar 

  30. Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. Chapman and Hall/CRC, Boca Raton (2003)

    MATH  Google Scholar 

  31. Kythe, P.K., Schaferkotter, M.R.: Handbook of Computational Methods for Integration. Chapman and Hall/CRC, Boca Raton (2004)

    Book  Google Scholar 

  32. Monegato, G.: Numerical evaluation of hypersingular integrals. J. Comput. Appl. Math. 50(1–3), 9–31 (1994)

    Article  MathSciNet  Google Scholar 

  33. Mayrhofer, K., Fischer, F.D.: Derivation of a new analytical solution for a general two-dimensional finite-part integral applicable in fracture mechanics. Int. J. Numer. Method Eng. 33, 1027–1047 (1992)

    Article  MathSciNet  Google Scholar 

  34. Elfakhakhre, N.R.F., Nik Long, N.M.A., Eshkuvatov, Z.K.: Stress intensity factor for an elastic half plane weakened by multiple curved cracks. Appl. Math. Model. 60, 540–551 (2018)

    Article  MathSciNet  Google Scholar 

  35. Elfakhakhre, N.R.F., Nik Long, N.M.A., Eshkuvatov, Z.K.: Stress intensity factor for multiple cracks in half plane elasticity. In: AIP Conference Proceedings, vol. 1795, pp. 1–8 (2017)

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The Universiti Teknikal Malaysia Melaka and Universiti Putra Malaysia are gratefully acknowledged.

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The N. M. A. Nik Long would like to thank the Ministry of Education Malaysia for financial support by the Fundamental Research Grant Scheme with Project Number 5540269.

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Hamzah, K.B., Nik Long, N.M.A., Senu, N. et al. Stress intensity factors for bonded two half planes weakened by thermally insulated cracks. Acta Mech 231, 4157–4183 (2020). https://doi.org/10.1007/s00707-020-02753-0

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  • DOI: https://doi.org/10.1007/s00707-020-02753-0

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