Anti-Plane Shear Behavior of an Arbitrarily Oriented Crack in Bonded Materials with a Nonhomogeneous Interfacial Zone

  • Chung, Yong-Moon (School of Mechanical and Automotive Engineering, Kookmin University) ;
  • Kim, Chul (School of Mechanical and Automotive Engineering, Kookmin University) ;
  • Park, Hyung-Jip (School of Mechanical and Automotive Engineering, Kookmin University)
  • Published : 2003.02.01

Abstract

The anti-plane shear problem of bonded elastic materials containing a crack at an arbitrary angle to the graded interfacial zone is investigated in this paper The interfacial zone is modeled as a nonhomogeneous interlayer of finite thickness with the continuously varying shear modulus between the two dissimilar, homogeneous half-planes. Formulation of the crack problem is based upon the use of the Fourier integral transform method and the coordinate transformations of basic field variables. The resulting Cauchy-type singular integral equation is solved numerically to provide the values of mode 111 stress intensity factors. A comprehensive parametric study is then presented of the influence of crack obliquity on the stress intensity factors for different crack size and locations and for different material combinations, in conjunction with the material nonhomogeneity within the graded interfacial zone.

Keywords

References

  1. Abramowitz, M. and Stegun, I. A., 1972, Handbook of Mathematical Functions, Dover Publications, New York, pp. 771-802
  2. Bassani, J. L. and Erdogan, F., 1979, 'Stress Intensity Factors in Bonded Half-Planes Containing Inclined Cracks and Subjected to Antiplane Shear Loading,' International Journal of Fracture, Vol. 15, pp. 145-158 https://doi.org/10.1007/BF00037830
  3. Choi, H. J., 2001, 'The Problem for Bonded Half-Planes Containing a Crack at an Arbitrary Angle to the Graded Interfacial Zone,' International Journal of Solids and Structures, Vol. 38, pp. 6559-6588 https://doi.org/10.1016/S0020-7683(01)00090-7
  4. Davis, P. J. and Rabinowitz, P., 1984, Methods of Numerical Integration, 2nd Ed. Academic Press, New York, pp. 51-198
  5. Delale, F. and Erdogan, F., 1983, 'The Crack Problem for a Nonhomogeneous Plane,' ASME Journal of Applied Mechanics, Vol. 50, pp. 609-614 https://doi.org/10.1115/1.3167098
  6. Eischen, J. W., 1987, 'Fracture of Nonhomogeneous Materials,' International Journal of Fracture, Vol. 34, pp. 3-22 https://doi.org/10.1007/BF00042121
  7. Erdogan, F., 1995, 'Fracture Mechanics of Functionally Graded Materials,' Composites Engineering, Vol. 5, pp. 753-770 https://doi.org/10.1016/0961-9526(95)00029-M
  8. Erdogan, F., Kaya, A. C. and Joseph, P. F., 1991, 'The Mode III Crack Problem in Bonded Materials With a Nonhomogeneous Interfacial Zone,' ASME Journal of Applied Mechanics, Vol. 58, pp. 419-427 https://doi.org/10.1115/1.2897202
  9. Hwang, E. H., Choi, S. R. and Earmme, Y. Y., 1992, 'Inclined Edge Crack in Two Bonded Elastic Quarter Planes Under Out-of-Plane Loading,' International Journal of Fracture, Vol. 56, pp. R39-R49 https://doi.org/10.1007/BF00012333
  10. Jin, Z.-H. and Noda, N., 1994, 'Crack-Tip Singular Fields in Nonhomogeneous Materials,' ASME Journal of Applied Mechanics, Vol. 61, pp. 738-740 https://doi.org/10.1115/1.2901529
  11. Kondo, T., 1992, 'Singular Stresses at the Tips of a Crack Terminating at the Interface of Two Bonded Anisotropic Media Subjected to Longitudinal Shear Loading,' Engineering Fracture Mechanics, Vol. 42, pp. 445-451 https://doi.org/10.1016/0013-7944(92)90166-C
  12. Lee, Y. -D. and Erdogan, F., 1995, 'Residual/Thermal Stresses in FGM and Laminated Thermal Barrier Coatings,' International Journal of Fracture, Vol. 69, pp. 145-165 https://doi.org/10.1007/BF00035027
  13. Martin, P. A., 1992, 'Tip Behaviour for Cracks in Bonded Inhomogeneous Materials,' Journal of Engineering Mathematics, Vol. 26, pp. 467-480 https://doi.org/10.1007/BF00042764
  14. Muskhelishvili, N. I., 1953, Singular Integral Equations, Noordhoff, Groningen, the Netherlands, pp. 113-162
  15. Ozturk, M. and Erdogan, F., 1993, 'Antiplane Shear Crack Problem in Bonded Materials with a Graded Interfacial Zone,' International Journal of Engineering Science, Vol. 31, pp. 1641-1657 https://doi.org/10.1016/0020-7225(93)90080-E
  16. Rice, J. R., 1988, 'Elastic Fracture Mechanics Concepts for Interfacial Cracks,' ASME Journal of Applied Mechanics, Vol. 55, pp. 98-103 https://doi.org/10.1115/1.3173668
  17. Romeo, A. and Ballarini, R., 1995, 'A Crack Very Close to a Bimaterial Interface,' ASME Journal of Applied Mechanics, Vol. 62, pp. 614-619 https://doi.org/10.1115/1.2895990
  18. Schovanec, L. and Walton, J. R., 1988, 'On the Order of the Stress Singularity for an Antiplane Shear Crack at the Interface of Two Bonded Inhomogeneous Elastic Materials,' ASME Journal of Applied Mechanics, Vol. 55, pp. 234-236 https://doi.org/10.1115/1.3173638
  19. Suresh, S. and Mortensen, A., 1997, 'Functionally Graded Metals and Metal-Ceramic Composites : Part 2 Thermomechanical Behaviour,' International Materials Reviews, Vol. 42, pp. 85-116 https://doi.org/10.1179/095066097790093217
  20. Wang, X. D. and Meguid, S. A., 1996, 'On the General Treatment of an Oblique Crack Near a Bimaterial Interface Under Antiplane Loading,' International Journal of Solids and Structure, Vol. 33, pp. 2485-2500 https://doi.org/10.1016/0020-7683(95)00162-X