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Analysis of mode III crack perpendicular to the interface between two dissimilar strips

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Abstract

The present work is concerned with the problem of mode III crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss–Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.

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References

  1. Williams M.L.: The stress around a fault or crack in dissimilar media. Bull. Seismol. Soc. Am. 49, 199–204 (1959)

    Google Scholar 

  2. Sih G.C., Rice J.R.: The bending of plates of dissimilar materials with cracks. ASME J. Appl. Mech. 31, 477–482 (1964)

    Google Scholar 

  3. England A.H.: A crack between dissimilar media. ASME J. Appl. Mech. 32, 400–402 (1965)

    Google Scholar 

  4. Zak A.R., Williams M.L.: Crack point stress singularities at a biomaterial interface. ASME J. Appl. Mech. 30, 142–143 (1963)

    Google Scholar 

  5. Cook T.S., Erdogan F.: Stresses in bonded materials with a crack perpendicular to the interface. Int. J. Eng. Sci. 10, 677–697 (1972)

    Article  MATH  Google Scholar 

  6. Gupta G.D.: A layered composite with a broken laminate. Int. J. Solids Struct. 9, 1141–1154 (1973)

    Article  MATH  Google Scholar 

  7. Erdogan F.: Fracture mechanics of functionally graded materials. Composites Eng. 5, 753–770 (1995)

    Article  Google Scholar 

  8. Delale F., Erdogan F.: Interface crack in a nonhomogeneous elastic medium. Int. J. Eng. Sci. 26, 559–568 (1988)

    Article  MATH  Google Scholar 

  9. Erdogan F., Ozturk M.: Diffusion problems in bonded nonhomogeneous materials with an interface cut. Int. J. Eng. Sci. 30, 1507–1523 (1992)

    Article  MATH  Google Scholar 

  10. Ozturk M., Erdogan F.: Antiplane shear crack problem in bonded materials with a graded interfacial zone. Int. J. Eng. Sci. 31, 1641–1657 (1993)

    Article  MATH  Google Scholar 

  11. Shbeeb N.I., Binienda W.K.: Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Eng. Fract. Mech. 64, 693–720 (1999)

    Article  Google Scholar 

  12. Erdogan F., Kaya A.C., Joseph P.F.: The crack problem in bonded nonhomogeneous materials. ASME J. Appl. Mech. 58, 410–418 (1991)

    Article  MATH  Google Scholar 

  13. Choi H.J.: An analysis of cracking in a layered medium with a functionally graded nonhomogeneous interface. ASME J. Appl. Mech. 63, 479–486 (1996)

    MATH  Google Scholar 

  14. Choi H.J.: Bonded dissimilar strips with a crack perpendicular to the functionally graded interface. Int. J. Solids Struct. 33, 4101–4117 (1996)

    Article  MATH  Google Scholar 

  15. Guo L., Wu L., Zeng T., Ma L.: The dynamic fracture behavior of a functionally graded coating—substrate system. Composite Struct. 64, 433–441 (2004)

    Article  Google Scholar 

  16. Yue Z.Q., Xiao H.T., Tham L.G.: Elliptical crack normal to functionally graded interface of bonded Solids. Theor. Appl. Fract. Mech. 42, 227–248 (2004)

    Article  Google Scholar 

  17. Shbeeb N.I., Binienda W.K.: Analysis of the driving force for a generally oriented crack in a functionally graded strip sandwiched between two homogeneous half planes. Int. J. Fract. 104, 23–50 (2000)

    Article  Google Scholar 

  18. Choi H.J.: The problem for bonded half-planes containing a crack at an arbitrary angle to the graded interfacial zone. Int. J. Solids Struct. 38, 6559–6588 (2001)

    Article  MATH  Google Scholar 

  19. Choi H.J.: Elastodynamic analysis of a crack at an arbitrary angle to the graded interfacial zone in bonded half-planes under antiplane shear impact. Mech. Res. Commun. 33, 636–650 (2006)

    Article  Google Scholar 

  20. Choi H.J.: Stress intensity factors for an oblique edge crack in a coating/substrate system with a graded interfacial zone under anti-plane shear. Eur. J. Mech. A Solids 26, 337–347 (2007)

    Article  MATH  Google Scholar 

  21. Okawa T., Sumi Y.: Simulation-based fatigue crack management of ship structural details applied to longitudinal and transverse connections. Mar. Struct. 19, 217–240 (2006)

    Article  Google Scholar 

  22. Matbuly M.S.: Analytical solution for an interfacial crack subjected to dynamic anti-plane shear loading. Acta Mech. 184, 77–85 (2006)

    Article  MATH  Google Scholar 

  23. Kreyszig E.: Advanced Engineering Mathematics. Wiley, New York (1979)

    MATH  Google Scholar 

  24. Hills D.A., Kelly P.A., Dai D.N., KorsunsKy A.M.: Solution of Crack Problems: The Distributed Dislocation Technique. Kluwer, Dordrecht (1996)

    MATH  Google Scholar 

  25. Erdogan F., Gupta G.D.: On the numerical solution of singular integral equations. Q. Appl. Math. 29, 525–531 (1972)

    MATH  MathSciNet  Google Scholar 

  26. Kabir H., Madenci E., Ortega A.: Numerical solution of integral equations with logarithmic, Cauchy- and Hadamard- type singularities. Int. J. Num. Methods Eng. 41, 617–638 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  27. Parton V.Z., Morozov E.M.: Elastic-Plastic Fracture Mechanics. MIR Publications, Moscow (1978)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, Zagazig, Egypt

    M. S. Matbuly

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  1. M. S. Matbuly
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Correspondence to M. S. Matbuly.

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The English text was polished by Yunming Chen.

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Matbuly, M.S. Analysis of mode III crack perpendicular to the interface between two dissimilar strips. Acta Mech Sin 24, 433–438 (2008). https://doi.org/10.1007/s10409-008-0173-y

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  • DOI: https://doi.org/10.1007/s10409-008-0173-y

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