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Fracture behavior investigation on an arbitrarily oriented sub-interface Zener–Stroh crack

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Abstract

The general solution of an arbitrarily oriented sub-interface Zener–Stroh crack is derived with the aid of distributed dislocation methods. The crack problem is formulated as a set of singular integral equations and solved numerically so that the stress intensity factor can be evaluated for any orientation angle. To make the facture analysis more accurate, the plastic zone size (PZS) and the crack tip opening displacement (CTOD) are examined by the generalized Irwin model. The plastic zone area is assumed to follow the von Mises yielding criterion and can be related to the stress intensity factors at the crack tips. Numerical examples are given to demonstrate the influence of various parameters, such as material properties, crack–interface distance and loading ratios, on the normalized PZS and CTOD for vertical and parallel crack cases. It is found that the Zener–Stroh crack becomes easier to propagate when it is located in the “softer” phase of the bi-material structure and parallel to the material interface. If the crack is perpendicular to the interface, it would be much easier for the crack to propagate into the “softer” side of the structure.

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References

  1. Hutchinson J.W., Mear M., Rice J.R.: Crack paralleling an interface between dissimilar materials. J. Appl. Mech. 54, 828–832 (1987)

    Article  Google Scholar 

  2. Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. Math. Theory Dislocations. In: Mura, T. (ed.) ASME, pp. 70–115, New York (1969)

  3. Lu H., Lardner T.J.: Mechanics of subinterface cracks in layered material. Int. J. Solids Struct. 29, 669–688 (1992). doi:10.1016/0020-7683(92)90120-i

    Article  Google Scholar 

  4. Thouless M.D., Evans A.G., Ashby M.F., Hutchinson J.W.: The edge cracking and spalling of brittle plates. Acta Metall. 35, 1333–1341 (1987). doi:10.1016/0001-6160(87)90015-0

    Article  Google Scholar 

  5. Suo Z., Hutchinson J.W.: Steady-state cracking in brittle substrates beneath adherent films. Int. J. Solids Struct. 25, 1337–1353 (1989). doi:10.1016/0020-7683(89)90096-6

    Article  Google Scholar 

  6. Borliang C., Lardner T.J.: Two-dimensional cracks at an angle to an interface. Int. J. Solids Struct. 30, 1725–1735 (1993). doi:10.1016/0020-7683(93)90229-Z

    Article  MATH  Google Scholar 

  7. Fett T., Munz D., Tilscher M.: Weight functions for sub-interface cracks. Int. J. Solids Struct. 34, 393–400 (1997). doi:10.1016/s0020-7683(96)00010-8

    Article  MATH  Google Scholar 

  8. Xiao Z.M., Fan H.: On the contact zone and stress singularities of a subinterface crack. Eng. Fract. Mech. 68, 77–88 (2001). doi:10.1016/s0013-7944(00)00087-4

    Article  Google Scholar 

  9. Huang G.-Y., Wang Y.-S., Gross D.: Fracture analysis of functionally graded coatings: antiplane deformation. Eur. J. Mech. - A/Solids 21, 391–400 (2002). doi:10.1016/S0997-7538(02)01223-8

    Article  MATH  Google Scholar 

  10. Beom H.G., Jeong K.M., Kim Y.H.: Intensity factors for subinterface cracks in dissimilar anisotropic piezoelectric media. Arch. Appl. Mech. 73, 184–198 (2003). doi:10.1007/s00419-003-0280-y

    Article  MATH  Google Scholar 

  11. Tilbrook M.T., Rozenburg K., Steffler E.D., Rutgers L., Hoffman M.: Crack propagation paths in layered, graded composites. Compos. Part B: Eng. 37, 490–498 (2006). doi:10.1016/j.compositesb.2006.02.012

    Article  Google Scholar 

  12. Yang P.-S., Liou J., Sung J.-C.: Subinterface crack in an anisotropic piezoelectric bimaterial. Int. J. Solids Struct. 45, 4990–5014 (2008)

    Article  MATH  Google Scholar 

  13. Zhou K., Wu M.S.: Elastic fields due to an edge dislocation in an isotropic film-substrate by the image method. Acta Mech. 211, 271–292 (2010)

    Article  MATH  Google Scholar 

  14. Thouless M., Li Z., Douville N., Takayama S.: Periodic cracking of films supported on compliant substrates. J. Mech. Phys. Solids 59, 1927–1937 (2011)

    Article  MATH  Google Scholar 

  15. Sharma K., Bui T., Zhang C., Bhargava R.: Analysis of a subinterface crack in piezoelectric bimaterials with the extended finite element method. Eng. Fract. Mech. 104, 114–139 (2013)

    Article  Google Scholar 

  16. Zhou K., Wei R.: Modeling cracks and inclusions near surfaces under contact loading. Int. J. Mech. Sci. 83, 163–171 (2014)

    Article  Google Scholar 

  17. Zener, C.: The micro-mechanism of Fracture. Fracturing of Metals, American Society of Metals, pp. 3–31, Cleveland (1948)

  18. Weertman J.: Zener–Stroh crack, Zener–Hollomon parameter, and other topics. J. Appl. Phys. 60, 1877–1887 (1986). doi:10.1063/1.337236

    Article  Google Scholar 

  19. Fan H., Sun Y.M., Xiao Z.M.: Contact zone in an interfacial Zener–Stroh crack. Mech. Mater. 30, 151–159 (1998). doi:10.1016/s0167-6636(98)00044-1

    Article  Google Scholar 

  20. Xiao Z.M., Chen B.J.: Stress analysis for a Zener–Stroh crack interacting with a coated inclusion. Int. J. Solids Struct. 38, 5007–5018 (2001). doi:10.1016/s0020-7683(00)00335-8

    Article  MATH  Google Scholar 

  21. Xiao Z.M., Fan H., Sun Y.M.: On the contact zone of a subinterfacial Zener–Stroh crack. Acta Mech. 142, 133–148 (2000). doi:10.1007/bf01190015

    Article  MATH  Google Scholar 

  22. Fan, M., Yi, D.K., Xiao, Z.M.: An interfacial arc-shaped Zener–Stroh crack due to inclusion–matrix debonding in composites. Acta Mech. 1–10 (2013). doi: 10.1007/s00707-013-1000-5

  23. Waszczak J.: Applicability of linear elastic fracture mechanics to 5.6-mil boron/6061 aluminum. J. Aircr. 13, 770–777 (1976)

    Article  Google Scholar 

  24. Sun C., Prewo K.: The fracture toughness of boron aluminum composites. J. Compos. Mater. 11, 164–175 (1977)

    Article  Google Scholar 

  25. Yi D., Xiao Z., Zhuang J., Sridhar I.: On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate. Philos. Mag. 91, 3456–3472 (2011)

    Article  Google Scholar 

  26. Hills, D.A.: Solution of crack problems: the distributed dislocation technique. In: Hills, D.A., et al. (eds.) Solid Mechanics and Its Applications, vol. 44. Kluwer, c1996 (1996)

  27. Erdogan F., Gupta G.D.: On the numerical solution of singular integral equations. Q. Appl. Math. 29, 525–534 (1972)

    MATH  MathSciNet  Google Scholar 

  28. Irwin, G.R.: Plastic zone near a crack and fracture toughness. IN: Paper Presented at the Sagamore Research Conference Proceedings

  29. Anderson T.L.: Fracture Mechanics: Fundamentals and Applications. CRC Press, Boca Raton (2005)

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore

    M. Fan & Z. M. Xiao

  2. College of Mechanics and Materials, Hohai University, Nanjing, China

    D. K. Yi

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  1. M. Fan
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  2. D. K. Yi
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  3. Z. M. Xiao
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Correspondence to Z. M. Xiao.

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Fan, M., Yi, D.K. & Xiao, Z.M. Fracture behavior investigation on an arbitrarily oriented sub-interface Zener–Stroh crack. Acta Mech 226, 1591–1603 (2015). https://doi.org/10.1007/s00707-014-1271-5

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  • DOI: https://doi.org/10.1007/s00707-014-1271-5

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