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Multiple crack propagation along the interface of a non-homogeneous composite subjected to anti-plane shear loading

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Abstract

The present work concerns with the multiple crack propagation along the interface of two bonded dissimilar strips. The crack faces are subjected to anti-plane shear traction. Galilean transformation is employed to reduce the problem to a quasi-static one. Then, using Fourier transforms and asymptotic analysis, the quasi-static problem is reduced to a pair of singular integral equations. That are solved numerically, using Gauss-Chebyshev integration formulae. The values of the dynamic stress intensity factors are obtained and compared with the previous similar works. Further, a parametric study is introduced to investigate the effect of crack growth rate, geometric and elastic characteristics of the composite on the values of dynamic stress intensity factors.

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References

  1. Kalthoff JF, Beinert J, Winkler S (1977) Fast fracture and crack arrest. ASTM STP 627:161–176

    Google Scholar 

  2. Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. J Appl Mech 32:412–432

    Google Scholar 

  3. Erdogan F, Gupta G (1971) Layered composites with an interface flaw. Int J Solids Struct 7:1089–1107

    Article  MATH  Google Scholar 

  4. Lowengrub M, Sneddon IN (1973) The stress field near a Griffith crack at the interface of two bonded dissimilar elastic have plane. Int J Eng Sci 11:1025–1034

    Article  MATH  Google Scholar 

  5. Dhaliwal RS, He W, Saxena HS (1992) A moving Griffith crack at the interface of two dissimilar elastic layers. Eng Fract Mech 43:923–939

    Article  ADS  Google Scholar 

  6. He W, Dhaliwal RS, Saxena HS (1992) Griffith crack at the interface of two orthotropic elastic layers. Eng Fract Mech 41:13–25

    Article  Google Scholar 

  7. Gupta V, Argon AS, Suo Z (1992) Crack deflection at the interface between two orthotropic media. J Appl Mech 59:S79–S87

    Article  Google Scholar 

  8. Debnath L, Das S (1999) Interaction of elastic waves by an interfacial Griffith crack. Comput Math Appl 38:151–158

    Article  MATH  MathSciNet  Google Scholar 

  9. Das S, Patra B, Debnath L (2000) Stress intensity factors around two co-planar Griffith cracks in an orthotropic layer sandwiched between two identical orthotropic half planes. Int J Eng Sci 38:121–133

    Article  Google Scholar 

  10. Das S, Debnath L (2001) Stress intensity factor around a Griffith cracks in an orthotropic punched layer. Math Comput Model 33:957–963

    Article  MATH  MathSciNet  Google Scholar 

  11. Matbuly MS (2004) Dynamic crack propagation between two bonded orthotropic plates. J Appl Math 1:55–68

    Article  MathSciNet  Google Scholar 

  12. Mukherjee S, Das S (2007) Interaction of three interfacial Griffith cracks between bonded dissimilar orthotropic half planes. Int J Solids Struct 44:5437–5446

    Article  MATH  Google Scholar 

  13. Li C, Weng GJ (2002) Yoffe-type moving crack in a functionally graded piezoelectric material. R Soc Proc Math Phys Eng Sci 458:381–399

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang YS, Huang GY, Dross D (2003) On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: anti-plane deformation. ASME J Appl Mech 70:676–680

    Article  MATH  Google Scholar 

  15. Wang YS, Huang GY, Gross D (2004) On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: plane deformation. Int J Fract 125:189–205

    Article  MATH  Google Scholar 

  16. Hu K, Zhong Z (2005) A moving mode-III crack in a functionally graded piezoelectric strip. Int J Mech Mater Des 2:61–79

    Article  ADS  Google Scholar 

  17. Zhou Z-G, Wang B (2006) Non-local theory solution for an anti-plane shear permeable crack in functionally graded piezoelectric materials. Appl Compos Mater 13:345–367

    Article  ADS  Google Scholar 

  18. Hu KQ, Kang YL, Li GQ (2006) Moving crack at the interface between two dis-similar magnetoelectroelastic materials. Acta Mech 182:1–16

    Article  MATH  Google Scholar 

  19. Feng WJ, Wang HJ, Xue Y, Li H (2006) Anti-plane shear impact of multiple coplanar Griffith cracks in an isotropic functionally graded strip. Compos Struct 73:354–359

    Article  Google Scholar 

  20. Zhou Z-G, Wu L-Z (2007) The non–local theory solution of a crack in the functionally graded piezoelectric materials subjected to the harmonic anti-plane shear stress waves. Trans Tech Publ Key Eng Mater 258–262

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

    Article  MATH  Google Scholar 

  22. Choi HJ (2006) 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

    Article  Google Scholar 

  23. Erdogan F, Gupta GD (1972) On the numerical solution of singular integral equations. Q Appl Math 525–531

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  26. Zhou Z-G, Ma L (1999) Two collinear Griffith cracks subjected to anti-plane shear in infinitely long strips. Mech Res Commun 26:437–444

    Article  MATH  Google Scholar 

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Correspondence to M. S. Matbuly.

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Matbuly, M.S. Multiple crack propagation along the interface of a non-homogeneous composite subjected to anti-plane shear loading. Meccanica 44, 547–554 (2009). https://doi.org/10.1007/s11012-009-9190-6

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  • DOI: https://doi.org/10.1007/s11012-009-9190-6

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