Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T01:08:53.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic Green's function for a composite solid with a planar interface

Published online by Cambridge University Press:  31 January 2011

V. K. Tewary ,
R. H. Wagoner  and
J. P. Hirth
V. K. Tewary
Affiliation:
Department of Materials Science and Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, Ohio 43210
R. H. Wagoner
Affiliation:
Department of Materials Science and Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, Ohio 43210
J. P. Hirth
Affiliation:
Department of Materials Science and Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, Ohio 43210
Get access

Abstract

The elastic plane-strain Green's function is calculated for a general anisotropic composite solid with a plane interface and a line load parallel to the composite interface. The interface may be between two different solids or between different orientations of the same solid such as a grain boundary. The equations of elastic equilibrium are solved by the Fourier transform method. Analytical expressions are obtained for the Green's function in real as well as Fourier space. These expressions should be useful for calculations of elastic properties of a composite solid containing defects. Two sum rules are also derived for matrices which constitute the Green's function and the stress tensor. These sum rules can serve as numerical checks in detailed computer simulation calculations.

Type
Articles
Information
Journal of Materials Research , Volume 4 , Issue 1 , February 1989 , pp. 113 - 123
Copyright
Copyright © Materials Research Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Morse, P.M. and Feshbach, H., Methods of Mathematical Physics (McGraw-Hill, New York, 1953), Part 1.Google Scholar
2Eshelby, J. D., Solid State Phys., edited by Seitz, F. and Thornbull, D. (Academic Press, New York, 1956), Vol. 3, p. 79.Google Scholar
3Willis, J.R., Phil. Mag. 21, 931 (1970).CrossRefGoogle Scholar
4Barnett, D. M., Phys. Stat. Sol. 49b, 741 (1972).CrossRefGoogle Scholar
5Hirth, J. P. and Lothe, J., Theory of Dislocations, 2nd ed. (Wiley Interscience, New York), 1982.Google Scholar
6Tewary, V. K., Adv. in Phys. 22, 757 (1973).CrossRefGoogle Scholar
7Sinclair, J. E. and Hirth, J. P., J. Phys. F (Metal Phys.) 5, 236 (1975).Google Scholar
8Kirchner, H.O.K. and Lothe, J., Phil. Mag. (in press).Google Scholar
9Tucker, M.O., Phil. Mag. 19, 1141 (1969).Google Scholar
10Barnett, D. M. and Lothe, J., Phys. Norvegica 7, 13 (1973).Google Scholar
11Hirth, J. P., Barnett, D. M., and Lothe, I., Phil. Mag. 40, 39 (1979).CrossRefGoogle Scholar
12Wagoner, R. H., Metall. Trans. A (American Society for Metals) 12A, 2015 (1981).Google Scholar
13Eshelby, J.D., Read, W. T., and Shockley, W., Acta Metall. 1, 251 (1953).CrossRefGoogle Scholar
14Stroh, A.N., Phil. Mag. 3, 625 (1958).Google Scholar
15Stroh, A.N., J. Math. Phys. 41, 77 (1962).Google Scholar
16Hirth, J.P. and Wagoner, R. H., Int. J. Solids Struct. 12, 117 (1976).CrossRefGoogle Scholar