Fracture analysis of a functionally graded interfacial zone under plane deformation (original) (raw)

Abstract

A new multi-layered model for fracture analysis of functionally graded materials (FGMs) with the arbitrarily varying elastic modulus under plane deformation has been developed. The FGM is divided into several sub-layers and in each sub-layer the shear modulus is assumed to be a linear function while the PoissonÕs ratio is assumed to be a constant. With this new model, the problem of a crack in a functionally graded interfacial zone sandwiched between two homogeneous half-planes under normal and shear loading is investigated. Employment of the transfer matrix method and Fourier integral transform technique reduce the problem to a system of Cauchy singular integral equations. Stress intensity factors of the crack are calculated by solving the equations numerically. Comparison of the present new model with other existing models shows some of its advantages.

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References (25)

  1. Chen, Y.F., Erdogan, F., 1996. The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate. J. Mech. Phys. Solids 44, 771-787.
  2. Choi, H.J., 1997. A periodic array of cracks in a functionally graded nonhomogeneous medium loaded under in-plane normal and shear. Int. J. Fract. 88, 107-128.
  3. Choi, H.J., Lee, K.Y., Jin, T.E., 1998. Colinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone--Part I: Mechanical response. Int. J. Fract. 94, 103-122.
  4. Delale, F., Erdogan, F., 1983. The crack problem for a nonhomogeneous plane. ASME J. Appl. Mech. 50, 609-614.
  5. Delale, F., Erdogan, F., 1988. On the mechanical modeling of the interfacial region in bonded half-plane. ASME J. Appl. Mech. 55, 317-324.
  6. Eischen, J.W., 1987. Fracture of nonhomogeneous materials. Int. J. Fract. 34, 3-22.
  7. Erdogan, F., Gupta, G.D., 1972. On the numerical solution of singular integral equations. Q. Appl. Math. 29, 525-534.
  8. Erdogan, F., Kaya, A.C., Joseph, P.F., 1991. The mode-III crack problem in bonded materials with a nonhomogeneous interfacial zone. ASME J. Appl. Mech. 58, 419-427.
  9. Erg€ u uven, M.E., Gross, D., 1999. On the penny-shaped crack in inhomogeneous elastic materials under normal extension. Int. J. Solids Struct. 36, 1869-1882.
  10. Fildis, H., Yahsi, O.S., 1996. The axisymmetric crack problem in a nonhomogeneous interfacial region between homogeneous half- spaces. Int. J. Fract. 78, 139-164.
  11. Fildis, H., Yahsi, O.S., 1997. The mode III axisymmetric crack problem in a non-homogeneous interfacial region between homogeneous half-spaces. Int. J. Fract. 85, 35-45.
  12. Gao, H., 1991. Fracture analysis of nonhomogeneous materials via a moduli-perturbation approach. Int. J. Solids Struct. 27, 1663- 1682.
  13. Huang, G.Y., Wang, Y.S., Gross, D., 2002. Fracture analysis of functionally graded coatings: antiplane deformation. Eur. J. Mech. A/ Solids 21, 391-400.
  14. Itou, S., 2001. Transient dynamic stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes. Int. J. Solids Struct. 38, 3631-3645.
  15. Jin, Z.H., Noda, N., 1994. Crack tip singular fields in nonhomogeneous materials. J. Appl. Mech. 61, 738-740.
  16. Ozturk, M., Erdogan, F., 1993. Antiplane shear crack problem in bonded materials with a graded interfacial zone. Int. J. Eng. Sci. 31, 1641-1657.
  17. Ozturk, M., Erdogan, F., 1995. An axisymmetrical crack in bonded materials with a nonhomogeneous interfacial zone under torsion. ASME J. Appl. Mech. 62, 116-125.
  18. Ozturk, M., Erdogan, F., 1996. Axisymmetric crack problem in bonded materials with a graded interfacial region. Int. J. Solids Struct. 33, 193-219.
  19. Shbeeb, N.I., Binienda, W.K., 1999. Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Eng. Fract. Mech. 64, 693-720.
  20. Slater, L.J., 1960. Confluent Hypergeometric Functions. Cambridge University Press, Cambridge.
  21. Wang, B.L., Han, J.C., Du, S.Y., 2000. Cracks problem for nonhomogeneous composite material subjected to dynamic loading. Int. J. Solids Struct. 37, 1251-1274.
  22. Wang, X.Y., Wang, D., Zou, Z.Z., 1996. On the Griffith crack in a nonhomogeneous interlayer of adjoining two different elastic materials. Int. J. Fract. 79, R51-R56.
  23. Wang, Y.S., Gross, D., 2000. Analysis of a crack in a functionally gradient interface layer under static and dynamic loading. Key Engng. Mater. 183-187, 331-336.
  24. Wang, Y.S., Huang, G.Y., Gross, D., 2003. On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: anti-plane deformation. ASME J. Appl. Mech., in press.
  25. Wu, B.H., Erdogan, F., 1996. Crack problems in FGM layers under thermal stresses. J. Therm. Stresses 19, 237-265.