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Stress Field for a Coated Triangle-Like Hole Problem in Plane Elasticity

Published online by Cambridge University Press:  10 December 2019

S. C. Tseng ,
C. K. Chao Open the ORCID record for C. K. Chao [Opens in a new window]  and
F. M. Chen
S. C. Tseng
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan
C. K. Chao*
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan
F. M. Chen
Affiliation:
Department of Mechanical Engineering, Nan Kai University of Technology, Nantou County, Taiwan
*
*Corresponding author (ckchao@mail.ntust.edu.tw)
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Abstract

The stress field induced by an edge dislocation or a point force located near a coated triangle-like hole in an infinite plate is provided in this paper. Based on the method of analytical continuation and the technique of conformal mapping in conjunction with the alternation technique, a series solution for the displacement and stresses in the coating layer and the matrix is obtained analytically. Examples for the interaction between an edge dislocation and a coated triangle-like hole for various material constant combinations, coating thicknesses and shape factors are discussed. The analysis discovers that the so-called trapping mechanism of dislocations is more likely to exist near a coated triangle-like hole. The result shows that the dislocation will first be repelled by the coating layer and then attracted by a hole when the coating layer is slightly stiffer than the matrix. However, when the coating layer is sufficiently thin, the dislocation will always be attracted by a hole even the coating layer is stiffer than the matrix.

Keywords

Coating layerPlane elasticityShape factorsDislocations
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 1 , February 2020 , pp. 55 - 72
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics 

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References

REFERENCES

A. K., Head, “The interaction of dislocations and boundaries,” Philosophical Magazine, 44, pp. 92–44 (1953).Google Scholar
J., Dundurs and T., Mura, “Interaction between an edge dislocation and a circular inclusion,” Journal of the Mechanics and Physics of Solids, 12, pp. 177–189 (1964).CrossRefGoogle Scholar
L., Stagni and R., Lizzio, “Shape effects in the interaction between an edge dislocation and an elliptical inhomogeneity,” Applied Physics A, 30, pp. 217–221 (1983).CrossRefGoogle Scholar
W. E., Warren, “The edge dislocation inside an elliptical inclusion,” Mechanics of Materials, 2, pp. 319–330 (1983).CrossRefGoogle Scholar
M. H., Santare and L. M., Keer, “Interaction between an edge dislocation and a rigid elliptical inclusion,” Journal of Applied Mechanics, 53, pp. 382–385 (1986).CrossRefGoogle Scholar
N. I., Muskhelishivili, “Some Basic Problems of the Mathematical Theory of Elasticity,” Noordhoff, Groningen, (1953).Google Scholar
S. X., Gong and S. A., Meguid, “A screw dislocation interacting with an elastic elliptical inhomogeneity,” International Journal of Engineering Science, 32, pp. 1221–1228 (1994).CrossRefGoogle Scholar
R. M., Christensen and K. H., Lo, “Solution for effective shear properties in three phase sphere and cylinder models,” Journal of the Mechanics and Physics of Solids, 27, pp. 315–330 (1979).CrossRefGoogle Scholar
H. A., Luo and Y., Chen, “An edge dislocation in a three-Phase composite cylinder model,” Journal of Applied Mechanics, 58, pp. 75–86 (1991).CrossRefGoogle Scholar
Y. Z., Chen, “Elastic analysis of an infinite plate containing hole with cusps and applied by concentrated forces,” Engineering Fracture Mechanics, 20, pp. 573–582 (1984).Google Scholar
Y. Z., Chen, “A survey of new integral equations in plane elasticity crack problem,” Engineering Fracture Mechanics, 51, pp. 97–134 (1995).CrossRefGoogle Scholar
Y. Z., Chen, “Transfer matrix method for solution of multiple elliptic layers with different elastic properties Part I infinite matrix case,” Acta Mechanica, 226, pp. 191–209 (2015).CrossRefGoogle Scholar
Y. Z., Chen, “Transfer matrix method for solution of multiple elliptic layers with different elastic properties Part II exterior finite elliptic matrix case,” Acta Mechanica, 225, pp. 3617–3623 (2014).CrossRefGoogle Scholar
Z. M., Xiao and B. J., Chen, “On the interaction between an edge dislocation and a coated inclusion,” International Journal of Solids and Structure, 38, pp. 2533–2548 (2001).Google Scholar
F. M., Chen and C. K., Chao, “Stress analysis of an infinite plate with a coated elliptic hole under a remote uniform heat flow,” Journal of Thermal Stresses, 31, pp. 599–613 (2008).CrossRefGoogle Scholar
C. K., Chao, R. M., Lu, J. K., Chen and F. M., Chen, “Analytical solutions of a reinforcement layer bonded to an elliptic hole under a remote uniform load,” International Journal of Solids and Structure, 46, pp. 2959–2965 (2009).CrossRefGoogle Scholar
C. K., Chao, F. M., Chen and M. H., Shen, “Circularly cylindrical layered media in plane elasticity,” International Journal of Solids and Structure, 43, pp. 4739–4756 (2006).CrossRefGoogle Scholar
C. K., Chao, C. K., Chen, F. M., Chen and A. M., Korsunsky, “Green's function for a coated elliptic hole problem in plane elasticity,” International Journal of Theoretical and Applied Multiscale Mech, 1, pp. 281–305 (2010).CrossRefGoogle Scholar
F. M., Chen, C. K., Chao and C. K., Chen, “Interaction of an edge dislocation with a coated elliptic inclusion,” International Journal of Solids and Structure, 48, pp. 1451–1465 (2011).CrossRefGoogle Scholar
F. M., Chen, “Edge Dislocation interacting with a nonuniformly coated circular inclusion,” Archive of Applied Mechanics, 81, pp. 1117–1128 (2011).CrossRefGoogle Scholar
J. C., Luo and C. F., Gao, “Stress field of a coated arbitrary shape inclusion,” Meccanica, 46, pp. 1055–1071 (2011).CrossRefGoogle Scholar
C. K., Chao, S. C., Tseng and F. M., Chen, “Analytical solutions to a coated triangle hole embedded in an infinite plate under a remote uniform heat flow,” Journal of Thermal Stresses, 41, pp. 1259–1275 (2019).CrossRefGoogle Scholar
C. K., Chao, and F. M., Chen, “Revisit of an elliptic hole problem by using complex variable method,” Journal of Chinese Institute of Engineers, 39, pp. 121–130 (2016).CrossRefGoogle Scholar
T, Honein and G., Herrmann, “The involution correspondence in plane elastostatics for regions bounded by a circle,” Journal of Applied Mechanics, 55, pp. 566–573 (1988).CrossRefGoogle Scholar