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Anti-Plane Interaction between a Crack and an Elliptically Cylindrical Layered Media

Published online by Cambridge University Press:  08 February 2013

C.K. Chao  and
A. Wikarta
C.K. Chao*
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10607, R.O.C.
A. Wikarta
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10607, R.O.C.
*
*Corresponding author (ckchao@mail.ntust.edu.tw)
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Abstract

Anti-plane interaction of an elliptically cylindrical layered media with an arbitrarily oriented crack embedded in an infinite matrix, intermediate layer, or inner inclusion under a remote uniform shear load is considered in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation in the inclusions and the matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack can easily be obtained by using the screw dislocation solutions as the Green's function together with the principle superposition. The stress intensity factors, which can properly reflect the interaction between a crack and an elliptically cylindrical layered media, are then obtained numerically in terms of the values of the dislocation density functions of the integral equations. The effects of material property combinations and geometric parameters on the normalized mode-III stress intensity factors are discussed in detail and shown in graphic form.

Keywords

Elliptically cylindrical layered mediaArbitrarily oriented crackConformal mappingMode-III stress intensity factors
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 85 - 93
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1. Chao, C. K., Wikarta, A. and Korsunsky, A. M., “Anti-Plane Interaction of a Crack and Reinforced Elliptic Hole in an Infinite Matrix,” Theoretical and Applied Fracture Mechanics, 53, pp. 205–210 (2010).Google Scholar
2. Stagni, L. and Lizzio, R., “Shape Effects in the Interaction Between an Edge Dislocation and an Elliptical Inhomogeneity,” Applied Physics A: Materials Science & Processing, 30, pp. 217–221 (1983).Google Scholar
3. Ru, C. Q., “Effect of Interphase Layers on Thermal Stresses Within an Elliptical Inclusion,” Journal of Applied Physics, 84, pp. 4872–4879 (1998).CrossRefGoogle Scholar
4. Ru, C. Q., Schiavone, P. and Mioduchowski, A., “Uniformity of Stresses Within a Three-Phase Elliptic Inclusion in Anti-Plane Shear,” Journal of Elasticity, 52, pp. 121–128 (1999).Google Scholar
5. Shen, M. H., Chen, S. N. and Chen, F. M., “Antiplane Study on Confocally Elliptical Inhomogeneity Problem Using an Alternating Technique,” Archives of Applied Mechanics, 75, pp. 302–314 (2006).Google Scholar
6. Chao, C. K. and Shen, M. H., “Solutions of Thermoelastic Crack Problems in Bonded Dissimilar Media or Half-Plane Medium,” International Journal of Solids and Structures, 32, pp. 3537–3554 (1995).Google Scholar
7. Chao, C. K. and Lee, J. Y., “Interaction Between a Crack and a Circular Elastic Inclusion Under Remote Uniform Heat Flow,” International Journal of Solids and Structures, 33, pp. 3865–3880 (1996).CrossRefGoogle Scholar