Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-19T00:11:54.319Z Has data issue: false hasContentIssue false
  • English
  • Français

The Stress Field Due to an Edge Dislocation Interacting With Two Circular Inclusions

Published online by Cambridge University Press:  14 July 2016

C.-K. Chao ,
F.-M. Chen  and
T.-H. Lin
C.-K. Chao*
Affiliation:
Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipei, Taiwan
F.-M. Chen
Affiliation:
Department of Mechanical EngineeringNan Kai University of TechnologyNantou, Taiwan
T.-H. Lin
Affiliation:
Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipei, Taiwan
*
*Corresponding author ([email protected])
Get access

Abstract

A general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.

Keywords

Interacting circular inclusionsAnalytical continuationAlternation technique
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 161 - 172
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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

1. Head, A. K., “The Interaction of Dislocations and Boundaries,” Philosophical Magazine, 44, pp. 92–94 (1953).Google Scholar
2. Dundurs, J. and Mura, T., “Interaction Between an Edge Dislocation and a Circular Inclusion,” Journal of Mechanics and Physics of Solids, 12, pp. 177–189 (1964).CrossRefGoogle Scholar
3. Warren, W. E., “The Edge Dislocation Inside an Elliptical Inclusion,” Mechanics of Materials, 2, pp. 319–330 (1983).Google Scholar
4. Stagni, L. and Lizzio, R., “Shape Effects in the Interaction Between an Edge Dislocation and An Elliptical Inhomogeneity,” Applied Physics, A30, pp. 217–221 (1983).Google Scholar
5. Muskhelishivili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1953).Google Scholar
6. Santare, M. H. and Keer, L. M., “Interaction Between an Edge Dislocation and a Rigid Elliptical Inclusion,” ASME Journal of Applied Mechanics, 53, pp. 382–385 (1986).Google Scholar
7. Christensen, R. M. and Lo, K. H., “Solution for Effective Shear Properties in Three Phase Sphere and Cylinder Models,” Journal of Mechanics and Physics of Solids, 27, pp. 315–330 (1979).CrossRefGoogle Scholar
8. Luo, H. A. and Chen, Y., “An Edge Dislocation in a Three-Phase Composite Cylinder Model,” ASME Journal of Applied Mechanics, 58, pp. 75–86 (1991).Google Scholar
9. Xiao, Z. M. and Chen, B. J., “On the Interaction Between an Edge Dislocation and a Coated Inclusion,” International Journal of Solids and Structures, 38, pp. 2533–2548 (2001).CrossRefGoogle Scholar
10. Chao, C. K., Chen, F. M. and Shen, M. H., “Circularly Cylindrical Layered Media in Plane Elasticity,” International Journal of Solids and Structures, 43, pp. 4739–4756 (2006).CrossRefGoogle Scholar
11. Chen, F. M., “Edge Dislocation Interacting with a Nonuniformly Coated Circular Inclusion,” Arch Applied Mechanics, 81, pp. 1117–1128 (2011).Google Scholar
12. Gong, S. X. and Meguid, S. A., “Interacting Circular Inhomogeneities in Plane Elastostatics,” Acta Mechanica, 99, pp. 49–60 (1993).CrossRefGoogle Scholar
13. Chao, C. K., Shen, M. H. and Fung, C. K., “On Multiple Circular Inclusions in Plane Thermoelasticity,” International Journal of Solids and Structures, 34, pp. 1873–1892 (1997).CrossRefGoogle Scholar
14. Wang, X. and Shen, Y. P., “Green's Function for the Two Circular Inclusion Problem in Plane Elastostatics,” Acta Mechanica Sinica, 33, pp. 639–654 (2001).Google Scholar
15. England, A. H., Complex Variable Methods in Elasticity, Wiley Interscience, London (1971).Google Scholar
16. Hirth, J. P. and Lothe, J., Theory of Dislocation, 2nd Ed., Wiley Interscience, New York (1982).Google Scholar