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The collinear crack problem for an orthotropic functionally graded coating–substrate structure

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Abstract

A theoretical treatment of antiplane crack problem of two collinear cracks on the two sides of and perpendicular to the interface between a functionally graded orthotropic strip bonded to an orthotropic homogeneous substrate is put forward. Various internal cracks and crack terminating at the interface and crack crossing the interface configurations are investigated, respectively. The problem is formulated in terms of a singular integral equation with the crack face displacement as the unknown variable. The asymptotic stress field near the tip of a crack crossing the interface is examined, and it is shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case, the “kink” in material property at the interface does not introduce any singularity. Numerical calculations are carried out, and the influences of the orthotropy and nonhomogeneous parameters and crack interactions on the mode III stress intensity factors are investigated.

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References

  1. Ang W.T., Clements D.L.: On some crack problems for inhomogeneous elastic materials. Int. J. Solid Struct. 23, 1089–1104 (1987)

    Article  MATH  Google Scholar 

  2. Chen Y.F., Erdogan F.: The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate. J. Mech. Phys. Solids 44, 771–787 (1996)

    Article  Google Scholar 

  3. Li C.Y., Weng G.J.: Dynamic stress intensity factors of a cylindrical interface crack with a functionally graded interlayer. Mech. Mater. 33, 325–333 (2001)

    Article  Google Scholar 

  4. Noda N., Wang B.L.: The collinear cracks in an inhomogeneous medium subjected to transient load. Acta Mech. 153, 1–13 (2002)

    Article  MATH  Google Scholar 

  5. Huang G.Y., Wang Y.S., Yu S.W.: Fracture analysis of a functionally graded interfacial zone under plane deformation. Int. J. Solid Struct. 41, 731–743 (2004)

    Article  MATH  Google Scholar 

  6. Li Y.D., Jia B., Zhang N., Tang L.Q., Dai Y.: Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating. Int. J. Solids Struct. 43, 4795–4809 (2006)

    Article  MATH  Google Scholar 

  7. Li Y.D., Kang Y.L., Yao D.: Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to end on the two sides of bi-FGM weak–discontinuous interface. Eur. J. Mech. A/Solids 27, 808–823 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Yong H.D., Zhou Y.H.: Analysis of a mode III crack problem in a functionally graded coating–substrate system with finite thickness. Int. J. Fract. 141, 459–467 (2006)

    Article  MATH  Google Scholar 

  9. Ding S.H., Li X.: Periodic cracks in a functionally graded piezoelectric layer bonded to a piezoelectric half-plane. Theor. Appl. Fract. Mech. 49, 313–320 (2008)

    Article  Google Scholar 

  10. Li X., Ding S.H.: Periodically distributed parallel cracks in a functionally graded piezoelectric (FGP) strip bonded to a FGP substrate under static electromechanical load. Comput. Mater. Sci. 50, 1477–1484 (2011)

    Article  Google Scholar 

  11. Sampath S., Herman H., Shimoda N., Saito T.: Thermal spray processing of FGMs. Mrs Bull. 20, 27–31 (1995)

    Google Scholar 

  12. Kaysser W.A., Ilschner B.: FGM research activities in Europe. Mrs Bull. 20, 22–26 (1995)

    Google Scholar 

  13. Chen J., Liu Z.X.: Transient response of a mode III crack in an orthotropic functionally graded strip. Eur. J. Mech. A/Solids 24, 325–336 (2005)

    Article  MATH  Google Scholar 

  14. Wang B.L., Mai Y.-W.: Periodic antiplane cracks in graded coatings under static or transient loading. J. Appl. Mech. 73, 134–142 (2006)

    Article  MATH  Google Scholar 

  15. Guo L.C., Wu L.Z., Zeng T., Ma L.: Mode I crack problem for a functionally graded orthotropic strip. Eur. J. Mech. A-Solids 23, 219–234 (2004)

    Article  MATH  Google Scholar 

  16. Guo L.C., Wu L.Z., Zeng T.: The dynamic response of an edge crack in a functionally graded orthotropic strip. Mech. Res. Commun. 32, 385–400 (2005)

    Article  MATH  Google Scholar 

  17. Feng W.J., Zhang Z.G., Zou Z.Z.: Impact failure prediction of mode III crack in orthotropic functionally graded strip. Theor. Appl. Fract. Mech. 40, 97–104 (2003)

    Article  Google Scholar 

  18. Erdogan, F., Gupta, G.D., Cook, T.S.: Numerical solution of singular integral equations. In: Sih, G.C. (Ed.), Mechanics of Fracture 1: Method of Analysis and Solution of Crack Problem, Chap. 7. Noordhoff International Publishing, Leyden (1973)

  19. Erdogan F., Kaya A.C., Joseph P.F.: The mode III crack problem in bonded materials with a nonhomogeneous interfacial zone. J. Appl. Mech. 58, 419–427 (1991)

    Article  MATH  Google Scholar 

  20. Muskelishvili, I.N.: Singular Integral Equations. Noordhoff, Groningen (1953)

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  1. School of Mathematics and Computer Science, Ningxia University, Yinchuan, 750021, China

    Sheng-Hu Ding & Xing Li

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  1. Sheng-Hu Ding
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  2. Xing Li
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Correspondence to Sheng-Hu Ding.

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Ding, SH., Li, X. The collinear crack problem for an orthotropic functionally graded coating–substrate structure. Arch Appl Mech 84, 291–307 (2014). https://doi.org/10.1007/s00419-013-0800-3

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  • DOI: https://doi.org/10.1007/s00419-013-0800-3

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