Skip to main content
SpringerLink
Log in

Dynamic propagation of a weak-discontinuous interface crack between two dissimilar functionally graded layers under anti-plane shear

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The dynamic propagation of an interface crack between two functionally graded material (FGM) layers under anti-plane shear is analyzed using the integral transform method. The properties of the FGM layers vary continuously along their thicknesses. The properties of the two FGM layers vary and the two layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. The Fourier transform is used to reduce the problem to a dual integral equation, which is then expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGM to show the effect of the gradient of material properties, crack moving velocity, and thickness of FGM layers. The following are helpful to increase resistance to interface crack propagation in FGMs: a) increasing the gradient of material properties, b) an increase of shear modulus and density from the interface to the upper and lower free surface, and c) increasing the thickness of the FGM layer. The DERR increases or decreases with increase of the crack moving velocity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Delale and F. Erdogan, The crack problem for a nonhomgeneous plane, ASME J. Appl. Mech., 50 (1983) 609–614.

    Article  MATH  Google Scholar 

  2. F. Delale and F. Erdogan, On the mechanical modeling of the interfacial region in bonded half-planes, ASME J. Appl. Mech., 55 (1988) 317–324.

    Article  Google Scholar 

  3. F. Erdogan, The crack problem for bonded nonhomogeneous materials under antiplane shear loading, ASME J. Appl. Mech., 52 (1985) 823–828.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  5. P. Gu and R. J. Asaro, Cracks in functionally graded materials, Int. J. Solids Strut., 34 (1997) 1–17.

    Article  MATH  Google Scholar 

  6. Z. H. Jin and R. C. Batra, Some basic fracture mechanics concepts in functionally graded materials, J. Mech. Phys. Solids, 44 (1996a) 1221–1235.

    Article  Google Scholar 

  7. N. Konda and F. Erdogan, The mixed mode crack problem in a nonhomogeneous elastic plane, Eng. Fract. Mech., 47 (1994) 533–545.

    Article  Google Scholar 

  8. Y. D. Li and K. Y. Lee, Effects of the weak/microdiscontinuity of interface on the fracture behavior of a functionally graded coating with an inclined crack, Arch. Appl. Mech., 79 (2009) 779–791.

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. M. Ozturk and F. Erdogan, Mode I crack problem in an inhomogeneous orthotropic medium, Int. J. Eng. Sci., 35 (1997) 869–883.

    Article  MATH  Google Scholar 

  11. M. Ozturk and F. Erdogan, The mixed mode crack problem in an inhomogeneous orthotropic medium, Int. J. Fract., 98 (1998) 243–261.

    Article  Google Scholar 

  12. N. I. Shbeeb, W. K. Binenda and K. L. Kreider, 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 (2000) 23–50.

    Article  Google Scholar 

  13. W. Yang and C. F. Shih, Fracture along an interlayer, Int. J. Solids Strut., 31 (1994) 985–1002.

    Article  MATH  Google Scholar 

  14. R. Babaei and S. A. Lukasiexicz, Dynamic response of a crack in a functionally graded material between two dissimilar half planes under anti-plane impact load, Eng. Fract. Mech., 60 (1998) 479–487.

    Article  Google Scholar 

  15. B. L. Wang, J. C. Han and S. Y. Du, Crack problem for non-homogeneous composite materials subjected to dynamic loading, Int. J. Solids Strut., 37 (2000) 1251–1274.

    Article  MATH  Google Scholar 

  16. J. Chen, Z. Liu and Z. Zou, Transient internal crack problem for a nonhomogeneous orthotropic strip (mode I), Int. J. Eng. Sci., 40 (2002) 1761–1774.

    Article  Google Scholar 

  17. L. Ma, L. Z. Wu and L. C. Guo, Dynamic behavior of two collinear anti-plane cracks in a functionally graded layer bonded to dissimilar half planes, Mech. Res. Commun., 29 (2002) 270–215.

    Article  Google Scholar 

  18. Y. D. Li, K. Y. Lee and Y. Dai, Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface, Eur. J. Mech. A/Solids, 27 (2008) 808–823.

    Article  MathSciNet  MATH  Google Scholar 

  19. G. C. Sih and E. P. Chen, Moving cracks in layered composites, Int. J. Eng. Sci., 20 (1982) 1181–1192.

    Article  MATH  Google Scholar 

  20. X. D. Wang and S. A. Meguid, On the dynamic crack propagation in an interface with spatially varying elastic properties, Int. J. Fract., 69 (1994) 87–99.

    Article  Google Scholar 

  21. L. Y. Jiang and X. D. Wang, On the dynamic in and interphase with spatially varying elastic properties under inplane loading, Int. J. Fract., 114 (2002) 225–244.

    Article  Google Scholar 

  22. S. A. Meguid, X. D. Wang and L. Y. Jiang, On the dynamic propagation of a finite crack in functionally graded materials, Eng. Fract. Mech., 69 (2002) 1753–1758.

    Article  Google Scholar 

  23. X. S. Bi, J. Cheng and X. L. Chen, Moving crack for functionally graded material in an infinite length strip under antiplane shear, Theoret. Appl. Fract. Mech., 39 (2003) 89–97.

    Article  Google Scholar 

  24. L. Ma, L. Z. Wu, Z. G. Zhou and T. Zeng, Crack propagating in a functionally graded strip under the plane loading, Int. J. Fract., 126 (2004) 39–55.

    Article  MATH  Google Scholar 

  25. L. Ma, L. Z. Wu, L. C. Guo and Z. G. Zhou, On the moving Griffith crack in a non-homogeneous orthotropic medium, Eur. J. Mech. A/Solids, 24 (2005) 393–405.

    Article  MATH  Google Scholar 

  26. Z. Cheng and Z. Zhong, Analysis of a moving crack in a functionally graded strip between two homogeneous layers, Int. J. Solids Strut., 49 (2007) 1038–1046.

    Google Scholar 

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

    Article  Google Scholar 

  28. Z. H. Jin and R. C. Batra, Interface cracking between functionally graded coatings and a substrate under antiplane shear, Int. J. Eng. Sci., 34 (1996b) 1705–1716.

    Article  MATH  Google Scholar 

  29. G. Y. Huang, Y. S. Wang and G. Dietmar, Fracture analysis of functionally graded coatings: antiplane deformation, Euro. J. Mech. A/Solids, 21 (2002) 391–400.

    Article  MATH  Google Scholar 

  30. G. Y. Huang, Y. S. Wang and D. Gross, Fracture analysis of functionally graded coatings: plane deformation, Euro. J. Mech. A/Solids, 22 (2003) 535–544.

    Article  MATH  Google Scholar 

  31. L. C. Guo, L. Z. Wu, T. Zeng and L. Ma, The dynamic fracture behavior of a functionally graded coating-substrate system, Compos. Strut., 64 (2004) 433–441.

    Article  Google Scholar 

  32. Y. D. Li, B. Jia, N. Zhang, L. Q. Tang and Y. Dai, Dynamic stress intensity factor of the weak/microdiscontinuous interface crack of a FGM coating, Int. J. Solids Strut., 43 (2006a) 4795–4809.

    Article  MATH  Google Scholar 

  33. Y. D. Li, E. Tan and H. Zhang, Anti-plane transient fracture analysis of the functionally gradient elastic bi-material weak/infinitesimal-discontinuous interface, Int. J. Fract., 142 (2006b) 163–171.

    MATH  Google Scholar 

  34. S. H. Ding and X. Li, Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure, Int. J. Fract., 153 (2008) 53–62.

    Article  Google Scholar 

  35. E. H. Yoffe, The moving Griffith crack, Philos. Magazine 7,42 (1951) 739–750.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Korea Aerospace Research Institute, 45 Eoeun-Dong, YouSeong, Daejeon, 305-333, Korea

    Jeong Woo Shin

  2. Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-Dong, YouSeong, Daejeon, 305-764, Korea

    Young-Shin Lee

Authors
  1. Jeong Woo Shin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Young-Shin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Young-Shin Lee.

Additional information

This paper was recommended for publication in revised form by Associate Editor

Jeong Woo Shin received a B.S. and Master’s degree in Mechanical Engineering from Yonsei University in Seoul, Korea in 1998 and 2000, respectively. A major field studied by Mr. Shin is fracture mechanics. He is currently working in the KARI (Korea Aerospace Research Institute) as a senior researcher. He conducted load analysis of fixed wing aircraft and full scale airframe static test at the KARI. He is now developing landing gear in the KHP (Korea Helicopter Program) as a performance and test engineer.

Young-Shin Lee received a B.S. degree in Mechanical Engineering from Yonsei University, Korea in 1972. He received Master’s and Ph.D degrees in Mechanical Engineering from Yonsei University, Korea in 1974 and 1980, respectively. He is currently professor in the Department of Mechanical Design Engineering at Chungnam National University, Korea. Prof. Lee’s research interests are in the areas of impact mechanics, optimal design, biomechanical analysis and shell structure analysis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shin, J.W., Lee, YS. Dynamic propagation of a weak-discontinuous interface crack between two dissimilar functionally graded layers under anti-plane shear. J Mech Sci Technol 25, 2551–2557 (2011). https://doi.org/10.1007/s12206-011-0723-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-011-0723-2

Keywords

Search

Navigation