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Green's function for generalized Hilbert problem for cracks and free surfaces in composite materials

Published online by Cambridge University Press:  31 January 2011

V.K. Tewary
V.K. Tewary
Affiliation:
Materials Reliability Division, National Institute of Standards and Technology, Boulder, Colorado 80303
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Abstract

Green's function for a generalized vector Hilbert problem is calculated which can be used to solve the Hilbert problem with any integrable inhomogeneity. The Green's function is obtained by using a complex transform defined by eigenfunctions of the homogeneous Hilbert problem. This method should be particularly convenient for the stress analysis of anisotropic composite materials containing cracks and free surfaces. The method is illustrated by applying it to calculate the stress field in an anisotropic bimaterial composite containing an interfacial crack. It is found that, in agreement with the earlier published work on isotropic composites, the stress field is oscillatory but, except very near the crack tip, the oscillations are negligible. Numerical results are presented for a stress field in a uniformly loaded (shear and compressive) Cu/Ni layered composite containing an interfacial crack as well as cracked homogeneous copper.

Type
Articles
Information
Journal of Materials Research , Volume 6 , Issue 12 , December 1991 , pp. 2585 - 2591
Copyright
Copyright © Materials Research Society 1991

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References

1.Tewary, V. K., Wagoner, R. H., and Hirth, J. P., J. Mater. Res. 4, 113 (1989).CrossRefGoogle Scholar
2.Tewary, V. K., Wagoner, R. H., and Hirth, J. P., J. Mater Res. 4, 124 (1989).CrossRefGoogle Scholar
3.Tewary, V. K., J. Mater. Res. 6, 2592 (1991).Google Scholar
4.Tewary, V. K. and Kriz, R. D., J. Mater. Res. 6, 2609 (1991).CrossRefGoogle Scholar
5.Muskhelishvili, N. I., Singular Integral Equations (Noordhoff, Groningen, 1977).CrossRefGoogle Scholar
6.Vekua, N. P., Systems of Singular Integral Equations (Noordhoff, Groningen, 1977).Google Scholar
7.England, A. H., J. Appl. Mech. 32, 400 (1965).CrossRefGoogle Scholar
8.Rice, J. R. and Sih, G. C., J. Appl. Mech. 32, 418 (1965).CrossRefGoogle Scholar
9.Sinclair, J. E. and Hirth, J. P., J. Phys. F (Metal Phys.) 5, 236 (1975).Google Scholar
10.Barbee, T. W., Jr., M.R.S. Bulletin XV, 17 (1990).CrossRefGoogle Scholar
11.Hirth, J. P. and Lothe, J., Theory of Dislocations 2nd ed. (Wiley Interscience, New York, 1982).Google Scholar
12.Tewary, V. K. and Kriz, R. D., “Effect of a Free Surface on Stress Distribution in a Bimaterial Composite”, NIST (United States Department of Commerce) Tech. Report SP 802 (1991).CrossRefGoogle Scholar