Abstract
In this paper, the plane elasticity equations are used to investigate the in-plane normal (mode I) and shear (mode II) behavior of a crack perpendicular to and terminating at the interface in bonded media with a graded interfacial zone. The interfacial zone is treated as a nonhomogeneous interlayer with the continuously varying elastic modulus between the two dissimilar, homogeneous semi-infinite constituents. For each of the individual loading modes, based on the Fourier integral transform technique, a singular integral equation with a Cauchy kernel is derived in a separate but parallel manner. In the numerical results, the values of corresponding modes of stress intensity factors are illustrated for various combinations of material and geometric parameters of the bonded media in conjunction with the effect of the material nonhomogeneity within the graded interfacial zone.
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References
Abramowitz, M. and Stegun, I. A., 1972,Handbook of Mathematical Functions, Dover Publications, New York, pp. 771–802.
Anlas, G., Santare, M. H. and Lambros, J., 2000, “Numerical Calculation of Stress Intensity Factors in Functionally Graded Materials,”International Journal of Fracture, Vol. 104, pp. 131–143.
Bao, G. and Cai, H., 1997, “Delamination Cracking in Functionally Graded Coating/Metal Substrate Systems,”Acta Materialia, Vol. 45, pp. 1055–1066.
Chen, Y. F. and Erdogan, F., 1996, “The Interface Crack Problem for a Nonhomogeneous Coating Bonded to a Homogeneous Substrate,”Journal of the Mechanics and Physics of Solids, Vol. 44, pp. 771–787.
Choi, H. J., 1997, “Mode I Interaction of a Periodic Array of Parallel Cracks in a Functionally Graded Nonhomogeneous Plane,”KSME International Journal, Vol. 11, pp. 239–248.
Davis, P. J. and Rabinowitz, P., 1984,Method of Numerical Integration, 2nd Ed., Academic Press, New York, pp. 51–198.
Delale, F. and Erdogan, F., 1988, “Interface Crack in a Nonhomogeneous Elastic Medium,”International Journal of Engineering Science, Vol. 26, pp. 559–568.
Erdogan, F., 1995, “Fracture Mechanics of Functionally Graded Materials,”Composites Engineering, Vol. 5, pp. 753–770.
Erdogan, F., Kaya, A. C. and Joseph, P. F., 1991a, “The Crack Problem in Bonded Nonhomogeneous Materials,”ASME Journal of Applied Mechanics, Vol. 58, pp. 410–418.
Erdogan, F., Kaya, A. C. and Joseph, P. F. 1991b, “The Mode III Crack Problem in Bonded Materials With a Nonhomogeneous Interfacial Zone,”ASME Journal of Applied Mechanics, Vol. 58, pp. 419–427.
Friedman, B., 1969,Lectures on Application-Oriented Mathematics, Holden-Day, San Francisco, pp. 17–23.
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Choi, H.J. Mode I and mode II analyses of a crack normal to the graded interlayer in bonded materials. KSME International Journal 15, 1386–1397 (2001). https://doi.org/10.1007/BF03185680
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DOI: https://doi.org/10.1007/BF03185680