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Elastic Green's function for a bimaterial composite solid containing a free surface normal to the interface

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

Elastic plane strain Green's function is calculated for an anisotropic bimaterial composite solid containing a free surface normal to the interface. An exact integral representation is obtained for the Green's function, which is evaluated numerically. The integral is also evaluated analytically, which gives a series representation for the Green's function. The singularities in the stress field associated with the presence of the free surface are identified and discussed. These singularities can be of the type r-δ, ln(r) as well as higher powers of ln(r), where δ is between 0 and 1 and r is the radial distance from the intersection of the free surface and the interface. The stress field may also contain an oscillatory factor of the type exp[ιg ln (r)] where g depends upon the material parameters of the two solids. For illustration, the formalism is applied to a cubic solid containing a Σ-5 grain boundary.

Type
Articles
Information
Journal of Materials Research , Volume 6 , Issue 12 , December 1991 , pp. 2592 - 2608
Copyright
Copyright © Materials Research Society 1991

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References

1.Pipes, R. B. and Pagano, N. J., J. Comp. Mater. 4, 538 (1970).CrossRefGoogle Scholar
2.Hsu, P. W. and Herakovich, C. T., J. Comp. Mater. 11, 422 (1977)CrossRefGoogle Scholar
3.Wang, A. S. D. and Crossman, F. W., J. Comp. Mater. 11, 92 (1977).CrossRefGoogle Scholar
4.Pagano, N. J., Int. J. Solids and Structures 14, 385 (1978).CrossRefGoogle Scholar
5.Wang, S. S. and Choi, I., “Modern Developments in Composite Materials and Structure”, edited by Vinson, J. L. (ASME Publication, 1979), p. 315.Google Scholar
6.Spilker, R. L. and Chou, S. C., J. Comp. Mater. 14, 2 (1980).Google Scholar
7.Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Elastic Body, translated by Fern, P. (HoldenDay, San Francisco, CA, 1963).Google Scholar
8.Dempsey, J. P. and Sinclair, G. B., J. Elasticity 9, 373 (1979).CrossRefGoogle Scholar
9.Ting, T. C. T. and Chou, S. C., Int. J. Solids and Structures, 17,1057 (1981).CrossRefGoogle Scholar
10.Zwiers, R. I., Ting, T. C. T., and Spilker, R. L., J. Appl. Mechanics 49, 561 (1982).CrossRefGoogle Scholar
11.England, A. H., J. Appl. Mechanics 32, 400 (1965).CrossRefGoogle Scholar
12.Rice, J. R. and Sih, G. C., J. Appl. Mechanics 32, 418 (1965).CrossRefGoogle Scholar
13.Tewary, V. K., Wagoner, R. H., and Hirth, J. P., J. Mater. Res. 4, 113 (1989).CrossRefGoogle Scholar
14.Tewary, V. K., Wagoner, R. H., and Hirth, J. P., J. Mater. Res. 4, 124 (1989).CrossRefGoogle Scholar
15.Stroh, A. N., J. Math. Phys. 41, 77 (1962).CrossRefGoogle Scholar
16.Tewary, V. K. and Kriz, R. D., J. Mater. Res. 6, 2609 (1991).CrossRefGoogle Scholar
17.Tewary, V. K. and Kriz, R. D., “Effect of a Free Surface on Stress Distribution in a Bimaterial Composite.” N. I. S. T. (United States Department of Commerce) Tech. Rep. SP 802 (1991).CrossRefGoogle Scholar
18.Tewary, V. K., J. Mater. Res. 6, 2585 (1991).CrossRefGoogle Scholar
19.Sinclair, J. E. and Hirth, J. P., J. Phys. F (Metal Physics) 5, 236 (1975).Google Scholar
20.Muskhelishvili, N. I., Singular Integral Equations (Noordhoff, Groningen, 1977).CrossRefGoogle Scholar
21.Vekua, N. P., Systems of Singular Integral Equations (Noordhoff, Groningen, 1977).Google Scholar
22.Bollman, W., Crystal Defects and Crystalline Interfaces (Springer Verlag, New York, 1970).Google Scholar
23.Tewary, V. K., Thomson, R. M., and Fuller, E. R., Jr., J. Mater. Res. 4, 309 (1989).CrossRefGoogle Scholar