Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T01:42:21.042Z Has data issue: false hasContentIssue false
  • English
  • Français

An Arc-Shaped Debonding Crack Opened by Internal Pressure

Published online by Cambridge University Press:  05 May 2011

Ru-Min Chao
Ru-Min Chao*
Affiliation:
Department of Naval Architecture and Marine Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Associate Professor
Get access

Abstract

In this paper, the problem of a debonding crack at the interface between a circular fiber and an infinite matrix opened by internal pressure is discussed. We concentrated on the effect of contact near the crack tips within the content of linear elastic fracture mechanics. The Muskhelishvili complex variable method is used in this analysis. The frictionless contact crack tip condition is adopted in this study in order to avoid the oscillatory stress singularity at the crack tip as shown in the classical solution. By using the crack opening displacement gradient as the primary variable, the problem is then reduced to two coupled singular integral equations, and the final discretization of the equations employs the method given by Erdogan and Gupta (1972). The comprehensive numerical results of stress fields and the mode II SIF at the closed crack tip will be given in the paper. It is also found from the numerical evidences that the contact length at the crack tip is independent of one of the Dundurs parameters, α.

Keywords

Debonding crackContactComplex variable methodStress intensity factor.
Type
Articles
Information
Journal of Mechanics , Volume 14 , Issue 2 , June 1998 , pp. 83 - 89
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1998

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.England, A. H., “An Arc Crack Around a Circular Elastic Inclusion,” Journal of Applied Mechanics, Vol. 33, pp. 637–640(1966).CrossRefGoogle Scholar
2.Perlman, A. B. and Sih, G. C, “Elastostatic Problems of Curvilinear Cracks in Bonded Dissimilar Materials,” Int. J. Engrg. Sci., Vol. 5, pp. 856–867 (1967).CrossRefGoogle Scholar
3.Toya, M.“A Crack along the Interface of a Circular Inclusion Embedded in an Infinite Solid,” J. Mech. Phys. Solids, Vol. 22, pp. 325–348 (1974).CrossRefGoogle Scholar
4.Piva, A., “A Crack along a Circular Interface Between Dissimilar Media,” Mechanica, Vol. 17, pp. 85–90 (1982).CrossRefGoogle Scholar
5.Chao, R. and Laws, N., “Loss of Stiffness due to Microcracking in Uni-directional Ceramic Matrix Composites,” Damage Mechanics in Engineering Materials: edited by Lu, , Krajcinovic, and Schreyer, , pp. 55–62, ASME 1990 Annual Meeting (1990).Google Scholar
6.Rice, J. R., “Elastic Fracture Mechanics Concepts for Interfacial Cracks,” Journal of Applied Mechanics, Vol. 55, pp. 98–103 (1988).CrossRefGoogle Scholar
7.Suo, Z. and Hutchinson, J. W., “Sandwich Test Specimens for Measuring Interface Crack Toughness,” Material Science and Engineering, A107, pp. 135–143(1989).CrossRefGoogle Scholar
8.Comninou, M., “The Interfacial Crack,” Journal of Applied Mechanics, Vol. 44, pp. 631–636 (1977).CrossRefGoogle Scholar
9.Comninou., M. and Schmueser, D., “The Interfacial Crack in a Combined Tension-Compression and Shear Field,” Journal of Applied Mechanics, Vol. 46, pp. 345–348 (1979).CrossRefGoogle Scholar
10.Chao, R. and Laws, N., “Closure of an Arc Crack in an Isotropic Homogeneous Material due to Uni-axial Loading,” Quartly Journal of Mechanics and Applied Math., Vol. 45, Pt. 4, pp. 629–640 (1992).CrossRefGoogle Scholar
11.Chao, R. and Rau, M. Y., “Frictional Contact of an Arc Crack in an Isotropic Homogeneous Material Due to Uni-axial Loading,” Eng. Fracture Mechanics, Vol. 50, No. 1, pp. 121–130 (1995).CrossRefGoogle Scholar
12.Muskhelishvili, N. I., in Some Basic Problems of the Mathematical Theory of Elasticity, translated by Radok, J. R. M., Noordhoff, P. Ltd., Groningen (1963).Google Scholar
13.Erdogan, F. and Gupta, G. D., “On the Numerical Solution of Singular Integral Equations,” Quarterly of Applied Mathematics, 29, pp. 525–534 (1972).CrossRefGoogle Scholar
14.Williams, M. L., “The Stresses Around a Fault or Crack in Dissimilar Media,” Bulletin of the Seismological Society of America, Vol. 49, pp. 199–204(1959).CrossRefGoogle Scholar
15.Dundurs, J. and Comninou, M., “Some consequences of the inequality conditions in contact and crack problems,” Journal of Elasticity, Vol. 9, No. 1, pp. 71–82(1979).CrossRefGoogle Scholar
16.Dundurs, J., Discussion, Journal of Applied Mechanics, Vol. 36, pp. 650–652 (1969).CrossRefGoogle Scholar
17.Dundurs, J. and Mura, T., “Interaction Between an Edge Dislocation and a Circular Inclusion,” J. Mech. Phys. Solid, Vol. 12, pp. 637–640, (1964).CrossRefGoogle Scholar
18.Dundurs, J. and Sendeckyj, G. P., “Edge Dislocation Inside a Circular Inclusion,” J. Mech. Phys. Solids, Vol. 13, pp. 141–147(1965).CrossRefGoogle Scholar
19.Chao, R., “Potential Functions of an Edge Dislocation Associated with a Circular Inclusion,” Journal of Applied Mechanics, Vol. 61, pp. 217–219 (1994).CrossRefGoogle Scholar
20.Shield, R. T., “Uniqueness for Elastic Crack and Punch Problems,” Journal of Applied Mechanics, Vol. 49, pp. 516–518(1982).CrossRefGoogle Scholar
21.Chao, R., “Some Effects of Fiber-Matrix Debonding on the Response of Unidirectional Ceramic Matrix Composite Materials,” Ph.D. Thesis, University of Pittsburgh (1991).Google Scholar
22.Hutchinson, J. W. and Suo, Z., in Advances in Applied Mechanics, (edited by Hutchinson, J. W. and Wu, T. Y.), 29, Academic Press, New York, pp. 63– 191 (1991).Google Scholar
23.Chao, R. and Laws, N., “The Fiber-Matrix Interface Crack,” Journal of Applied Mechanics, Vol. 64, pp. 992–999 (1997).CrossRefGoogle Scholar