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Mode-III Stress Intensity Factors of an Arbitrarily Oriented Crack Crossing Interface in a Layered Structure

Published online by Cambridge University Press:  07 August 2013

C. K. Chao  and
L. M. Lu
C. K. Chao*
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10607, R.O.C.
L. M. Lu
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10607, R.O.C.
*
*[email protected]
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Abstract

The problem of a layered structure containing an arbitrarily oriented crack crossing the interface in anti-plane elasticity is considered in this paper. The fundamental solution of displacements and stresses is obtained in a series form via the method of analytical continuation in conjunction with the alternating technique. A dislocation distribution along the prospective site of a crack is used to model a crack crossing the interface and the singular integral equations with logarithmic singular kernels for a line crack are then established. The crack is approximated by several line segments and the linear interpolation equation with undetermined coefficients was applied for the dislocation function along line segments. Once the undetermined dislocation coefficients are solved, the mode-III stress intensity factors KIII at two crack tips can be obtained for various crack inclinations with different material property combinations. All the numerical results are checked to achieve a good approximation that demonstrates the accuracy and the efficiency of the proposed method.

Keywords

Crack crossing interfacesLogarithmic singular integralStress intensity factors
Type
Research Article
Information
Journal of Mechanics , Volume 29 , Issue 4 , December 2013 , pp. 643 - 651
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

REFERENCES

1.Atkinson, C., “The Interaction Between a Crack and an Inclusion,” International Journal of Engineering Science, 10, pp. 127–136 (1972).Google Scholar
2.Erdogan, F.Gupta, G. D. and Ratwani, M., “Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack,” Journal of Applied Mechanics, 41, pp. 1007–1013 (1974).Google Scholar
3.Erdogan, F. and Gupta, G. D., “The Inclusion Problem with a Crack Crossing the Boundary,” International Journal of Fracture, 11, pp. 13–27 (1975).Google Scholar
4.Cheung, Y. K. and Chen, Y. Z., “Solutions of Branch Crack Problems in Plane Elasticity by Using a New Integral Equation Approach,” Engineering Fracture Mechanics, 28, pp. 31–41 (1987).Google Scholar
5.Chao, C. K. and Shen, M. H., “Solutions of Ther-moelastic Crack Problems in Bonded Dissimilar Media or Half-Plane Medium,” International Journal of Solids and Structures, 32, pp. 3537–3554 (1995).CrossRefGoogle Scholar
6.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).Google Scholar
7.Chao, C. K. and Kao, B., “A Thin Cracked Layer Bonded to an Elastic Half-Space Under an Antiplane Concentrated Load,” International Journal of Fracture, 83, pp. 223–241 (1997).CrossRefGoogle Scholar
8.Chen, Y. Z. and Chen, R. S., “Interaction Between Curved Crack and Elastic Inclusion in an Infinite Plate,” Archive of Applied Mechanics, 67, pp. 566–575 (1997).Google Scholar
9.Chao, C. K. and Wikarta, A., “Mode-III Stress Intensity Factors of a Three-Phase Composite with an Eccentric Circular Inclusion,” Computer Modeling in Engineering & Sciences, 84, pp. 439–458 (2012).Google Scholar
10.Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, pp. 105–175 (1953).Google Scholar