Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T05:53:31.415Z Has data issue: false hasContentIssue false
  • English
  • Français

The Torsional Dislocation Loop and Mode III Cylindrical Crack

Published online by Cambridge University Press:  05 May 2011

I. Demir  and
T.A. Khraishi
I. Demir*
Affiliation:
School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99163–2920
T.A. Khraishi*
Affiliation:
Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131.
*
*Visiting Professor
**Assistant Professor, corresponding author
Get access

Abstract

The elastic fields of a torsional dislocation loop in a homogeneous material are first derived. The solution is based on torsional symmetry. The stress and displacement solutions are then extended to the case of a torsional loop in a bi-material. A main utility of basic dislocation solutions is in fracture mechanics. In particular, circular loop solutions can be used in the modeling of both cylindrical and penny-shaped cracks. In the present study we use them to model a Mode III cylindrical crack via the application of a “distributed-dislocation technique”. Stress intensity factors at the crack tips are presented. The influences of crack radius and material pair on the stress intensity factor of interfacial cracks are investigated.

Keywords

Distributed dislocationsSomigliana ring dislocation
Type
Articles
Information
Journal of Mechanics , Volume 21 , Issue 2 , June 2005 , pp. 109 - 116
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

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

1.Hills, D. A., Kelly, P. A., Dai, D. N. and Korsunsky, A. M., Solution of Crack Problems: The Distributed Dislocations Technique, Kluwer Academic Publisher, The Netherlands (1996).CrossRefGoogle Scholar
2.Khraishi, T. A. and Demir, I., “On Cauchy Singular Integrals and Stress Intensity Factors for 2D Mode I Cracks,” Mechanics Research Communications, 30(4), pp. 353–364 (2003).CrossRefGoogle Scholar
3.Farris, T. N., Kokini, K. and Demir, I., “The Cylindrical Crack,” Journal of Applied Mechanics, 56(4), pp. 981–983 (1989).CrossRefGoogle Scholar
4.Demir, I., Hirth, J. P. and Zbib, H. M., “Extended Stress Field around a Cylindrical Crack using the Theory of Dislocation Pile-ups,” International Journal of Engineering Science, 30(7), pp. 829–845 (1992).CrossRefGoogle Scholar
5.Ozbek, T. and Erdogan, F., “Some Elasticity Problems in Fiber-Reinforced Composites with Imperfect Bonds,” International Journal of Engineering Science, 7(9), pp. 931–946 (1969).CrossRefGoogle Scholar
6.Wang, W.-X., Takao, Y. and Suhara, T., “Fiber-Reinforced Matrix Containing a Penny-Shaped Crack Under Mode III Loading Condition,” International Journal of Engineering Science, 25(7), pp. 855–869 (1987).Google Scholar
7.Xie, Y. J., Zhang, X. and Wang, X. H., “An Exact Method on Penny-Shaped Cracked Homogeneous and Composite Cylinders,” International Journal of Solids and Structures, 38/39, pp. 6953–6963 (2001).CrossRefGoogle Scholar
8.Farris, T. N. and Liu, M., “Boundary-Element Crack Closure Calculation of 3-Dimensional Stress Intensity Factors,” International Journal of Fracture, 60(1), pp. 33–47 (1993).CrossRefGoogle Scholar
9.Ozturk, M. and Erdogan, F., “An Axisymmetric Crack in Bonded Materials with a Nonhomogeneous Interfacial Zone under Torsion,” Journal of Applied Mechanics, 62(1), pp. 116–125 (1995).CrossRefGoogle Scholar
10.Han, X.-L. and Duo, W., “The Crack Problem of a Fiber-Matrix Composite with a Nonhomogeneous Interfacial Zone Under Torsional Loading, I. A Cylindrical Crack in the Interfacial Zone,” Engineering Fracture Mechanics, 54(1), pp. 63–69 (1996).Google Scholar
11.Prasad, S. N. and Chatterjee, S. N., “Load Transfer in Torsion of Compound Cylinders with a Cylindrical Crack,” Journal of Applied Mechanics, 40(3), pp. 773–779 (1973).CrossRefGoogle Scholar
12.Demir, I., Hirth, J. P. and Zbib, H. M., “Somigliana Ring Dislocation,” Journal of Elasticity, 28(3), pp. 223–246 (1992).CrossRefGoogle Scholar
13.Khraishi, T. A., Hirth, J. P., Zbib, H. M. and Khaleel, M. A., “The Displacement and Strain-Stress Fields of a General Circular Volterra Dislocation Loop,” International Journal of Engineering Science, 38(3), pp. 251–266 (2000).CrossRefGoogle Scholar
14.Khraishi, T. A., Zbib, H. M., Hirth, J. P. and de la Rubia, T. D., “The Stress Field of a General Circular Volterra Dislocation Loop: Analytical and Numerical Approaches,” Philosophical Magazine Letters, 80(2), pp. 95–105 (2000).CrossRefGoogle Scholar
15.Freeman, N. J. and Keer, L. M., “Torsion of Cylindrical Rod Welded to Elastic Half Space,” Proceedings of the ASME Applied Mechanics Meeting, ApM-30, Paper No. 67 (1967).CrossRefGoogle Scholar
16.Keer, L. M. and Freeman, N. J., “Load Transfer Problem for an Embedded Shaft in Torsion,” Journal of Applied Mechanics, 37E(4), pp. 959–964 (1970).CrossRefGoogle Scholar
17.Keer, L. M. and Freeman, N. J., “Torsion of a Finite Elastic Cylindrical Rod Partially Bonded to an Elastic Half Space,” Quarterly of Applied Mathematics, 26(4), pp. 567–573 (1969).CrossRefGoogle Scholar
18.Luco, J. E., “Torsion of a Rigid Cylinder Embedded in an Elastic Half Space,” Journal of Applied Mechanics, 43(3), pp. 419–423 (1976).CrossRefGoogle Scholar
19.Mbanefo, U. and Westmann, R. A., “Axisymmetric Stress Analysis of a Broken, Debonded Fiber,” Journal of Applied Mechanics, 57(3), pp. 654–660 (1990).CrossRefGoogle Scholar
20.Keer, L. M., “Mixed Boundary Value Problems for a Penny-Shaped Cut,” Journal of Elasticity, 5(2), pp. 89–98 (1975).CrossRefGoogle Scholar