Abstract
In this paper, we studied the stress singularities near the tip of a two-dimension notch, which could be a crack tip, formed from several elastic materials, each of them may be generally anisotropic. By introducing the dual variables in the state space, the basic equations governing the posed problem equations were established. We also proposed a numerical method to solve the governing equations. It was shown that the mathematical formulations advanced are quite simple and the numerical method proposed is easy and highly accurate. Finally, a few examples of problems in this topic were solved and presented in order to demonstrate the accuracy and the potential possibilities of applications of the present method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Clements, D.L. (1971). A crack between dissimilar anisotropic media. International Journal of Engineering Science 9, 257–265.
Costabel, M. and Dauge, M. (1995). Computation of corner singularities in linear elasticity. Boundary value problems and integral equations in nonsmooth domains (Edited by Costabel, M. et al.), Marcel Dekker Inc., New York.
Delale, F. and Erdogan, F. (1979). Bonded orthotropic strips with cracks. International Journal of Fracture 15, 343–364.
Dundurs, J. (1969). Edge-bonded dissimilar orthogonal elastic wedges. ASME Journal of Applied Mechanics 29, 650–652.
Eshelby, J.D., Read, W.T. and Shockley, W. (1953). Anisotropic elasticity with applications to dislocation theory. Acta Metallurgica 1, 251–259.
Gotoh, M. (1967). Some problems of bonded anisotropic plates with cracks along the bond. International Journal of Fracture Mechanics 3, 253–265.
Gupta, V., Argon, A.S. and Suo, Z. (1992). Crack deflection at an interface between two orthotropic media. ASME Journal of Applied Mechanics 59, 79–87.
Hoenig, A. (1982). Near-tip Behavior of a crack in a plane anisotropic elastic body. Engineering Fracture Mechanics 16, 393–403.
Lekhnitskii, S.G. (1953) Theory of an anisotropic elastic body. Holden-Day, San Francisco.
Li, J., Zhang, X.B. and Recho, N. (1997). Investigation of an arbitrarily oriented crack meeting an interface between two elastic materials. European Journal of Mechanics, A/Solid, 16, 795–821.
Lin, Y.Y. and Sung, J.C. (1997). Singularities of an inclined crack terminating at an anisotropic bimaterial interface, International Journal of Solids and Structures 34, 3727–3754.
Mantic, V., Paris, and Canas. J. (1997). Stress singularities in 2D orthotropic corners. International Journal of Fracture 83, 67–90.
Qu, J. and Bassani, J.L. (1989). Cracks on bimaterial and bicrystal interfaces. Journal of Mechanics and Physics of Solids 37, 417–433.
Rice, J.R. (1988). Elastic fracture mechanics concepts for interfacial cracks. ASME Journal of Applied Mechanics 55, 98–103.
Sih, G.C., Paris, P.C. and Irwin, G.R. (1965). On cracks in rectilinearly anisotropic bodies. International Journal of Fracture Mechanics 1, 189–203.
Stroh, A.N. (1958). Dislocations and cracks in anisotropic elasticity. Philosophy Magazine 3, 625–646.
Sung, J.C. and Liou, J.Y. (1996). Singularities at the tip of a crack terminating normally at an interface between two orthotropic media. ASME Journal of Applied Mechanics 63, 264–270.
Suo, Z. (1990). Singularities, interfaces and cracks in dissimilar anisotropic media, Proceeding of the Royal Society of London A427, 331–358.
Ting, T.C.T. and Hoang, P.H. (1984). Singularities at the tip of a crack normal to the interface of an anisotropic layered composite. International Journal of Solids and Structures 20, 439–454.
Ting, T.C.T. (1986). Explicit solution and invariance of the singularities at an interface crack in anisotropic composites, International Journal of Solids and Structures 22, 965–763.
Ting, T.C.T. (1996). Anisotropic Elasticity. Oxford University Press, Oxford.
Willis, J.R. (1971). Fracture mechanics of interfacial cracks, Journal of Mechanics and Physics of Solids 19, 353–368.
Zak, A.K. and Williams, M.L. (1963). Crack point stress singularities at a bi-material interface. ASME Journal of Applied Mechanics 30, 142–143.
Zhong, W.X. (1997). New Systematical Methodology in Elasticity Theory Dalian Science & Technology University Press (in Chinese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, J., Zhang, XB. & Recho, N. Stress singularities near the tip of a two-dimensional notch formed from several elastic anisotropic materials. International Journal of Fracture 107, 379–395 (2001). https://doi.org/10.1023/A:1007620004700
Issue Date:
DOI: https://doi.org/10.1023/A:1007620004700