ّFracture Modes of an Annular Cracks in a Transversely Isotropic Solid

Document Type : Research Article


School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran


The existence and extension of the cracks in structural materials is one of the issues to be considered to prevent the devastating effects of cracks. Cracks can be subjected to different types of fracture modes that considering these modes help us to predict the behavior of cracks. This paper investigates the effects of the fracture modes (opening, shearing and tearing) on the annular crack in an infinite transversely isotropic solid. In each mode, by substituting the boundary conditions into governing equations of the medium, the problem reduced to triple integral equations. With the aid of Hankel and Abel integral transforms, the triple integral equations reduced to two Fredholms integral equations which are amenable to numerical solutions. The inner and outer stress intensity factors of the annular crack are obtained for different ratios of inner-outer radius of the annular crack. Some limiting cases such as the penny-shaped crack and external crack are considered. From the results, it can be concluded that the stress intensity factors (SIFs) are independent of material properties; additionally, loads play major role in the variation of SIFs which may lead to change in the direction of crack extension.


Main Subjects

[1] O.V. Menshykov, V.A. Menshykov, I.A. Guz, The contact problem for an open penny-shaped crack under normally incident tension-compression wave, Engineering Fracture Mechanics, 75(5) (2008) 1114-1126.
[2] F. Erdogan, Stress distribution in bonded dissimilar materials with cracks, Journal of Applied Mechanics, 32(2) (1965) 403-410.
[3] B. Smetanin, Problem of extension of an elastic space containing a plane annular slit PMM vol. 32, no. 3, 1968, pp. 458-462, Journal of Applied Mathematics Mechanics, 32 (1968) 461-466.
[4] T. Shibuya, I. Nakahara, T. Koizumi, The axisymmetric distribution of stresses in an infinite elastic solid containing a flat annular crack under internal pressure, ZAMM-Journal of Applied Mathematics Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 55(7-8) (1975) 395-402.
[5] L. Moss, A. Kobayashi, Approximate analysis of axisymmetric problems in fracture mechanics with application to a flat toroidal crack, International Journal of Fracture Mechanics, 7(1) (1971) 89-99.
[6] E. Mastrojanni, T. Kermanidis, An approximate solution of the annular crack problem, International Journal for Numerical Methods in Engineering, 17(11) (1981) 1605-1611.
[7] I. Choi, R. Shield, Structures, A note on a flat toroidal crack in an elastic isotropic body, International Journal of Solids, 18(6) (1982) 479-486.
[8] A. Selvadurai, B. Singh, The annular crack problem for an isotropic elastic solid, The Quarterly Journal of Mechanics Applied Mathematics, 38(2) (1985) 233-243.
[9] H. Danyluk, B. Singh, Problem of an infinite solid containing a flat annular crack under torsion, Engineering Fracture Mechanics, 24(1) (1986) 33-38.
[10] H.M. Shodja, S.S. Moeini-Ardakani, M. Eskandari, Axisymmetric Problem of Energetically Consistent Interacting Annular and Penny-Shaped Cracks in Piezoelectric Materials, Journal of Applied Mechanics, 78(2) (2010) 021010.
[11] M. Eskandari-Ghadi, A. Ardeshir-Behrestaghi, B.N. Neya, Mathematical analysis for an axissymmetric disc-shaped crack in transversely isotropic half-space, International Journal of Mechanical Sciences, 68 (2013) 171-179.
[12] S. Moeini-Ardakani, M. Kamali, H. Shodja, Eccentric annular crack under general nonuniform internal pressure, Journal of the Mechanical Behavior of Materials, 25(3-4) (2016) 69-76.
[13] S. Lekhnitskii, P. Fern, J.J. Brandstatter, E. Dill, Theory of elasticity of an anisotropic elastic body, Physics Today, 17 (1964) 84.
[14] M. Rahimian, M. Eskandari-Ghadi, R.Y. Pak, A. Khojasteh, Elastodynamic potential method for transversely isotropic solid, Journal of Engineering Mechanics, 133(10) (2007) 1134-1145.
[15] J. Cooke, Triple integral equations, The Quarterly Journal of Mechanics Applied Mathematics, 16(2) (1963) 193-203.
[16] M. Kassir, G.C. Sih, Three-dimensional crack problems: A new selection of crack solutions in three-dimensional elasticity(Book), Leiden, Noordhoff International Publishing, 2 (1975).