Abstract
A crack or a hole embedded in an anisotropic half-plane space subjected to a concentrated force at its surface is analyzed. Based on the Stroh formalism and the fundamental solutions to the half-plane solid due to point dislocations, the problem can be formulated by a system of boundary integral equations for the unknown dislocation densities defined on the crack or hole border. These integral equations are then reduced to algebraic equations by using the properties of the Chebyshev polynomials in conjunction with the appropriate transformations. Numerical results have been carried out for both crack problems and hole problems to elucidate the effect of geometric configurations on the stress intensity factors and the stress concentration.
Similar content being viewed by others
References
Barjansky, A. (1944). The distortion of the Boussinesq field due to a circular hole. Quarterly of Applied Mathematics 2, 16–30.
Bowie, O.L. and Freese, C.E. (1972). Central crack in plane orthotropic rectangular sheet. International Journal of Fracture Mechanics 8, 49–57.
Chadwick, P. and Smith, G.D. (1977). Foundations of the theory of surface waves in anisotropic elastic materials. Advances in Applied Mechanics 17, 303–376.
Chao, C.K. (1997). Boundary integral equations for notch problems in plane thermoelasticity. AIAA Journal 35, 1420–1422.
Chen, Y.Z. and Cheung, Y.K. (1990). New integral equation approach for crack problem in elastic half-plane. International Journal of Fracture 46, 57–69.
Gupta, G.D. and Erdogan, F. (1972). On the numerical solution of singular integral equations. Quarterly of Applied Mathematics 30, 525–534.
Heng, Z., McCammond, D. and Tabarrok, B. (1986). Stress determination in edge-cracked anisotropic plates by an extension of boundary-collocation method. Computer Methods in Applied Mechanics and Engineering 54, 187–195.
Kamel, M. and Liaw, B.M. (1991). Boundary element formulation with special kernels for an anisotropic plate containing an elliptical hole or a crack. Engineering Fracture Mechanics 39, 695–711.
Miller, G.R. (1989). Analysis of crack near interfaces between dissimilar anisotropic materials. International Journal of Engineering Science 27, 667–678.
Nisitani, H. (1968).Method of approximate calculation for interference of notch effects and its application. Journal of the Japan Society of Mechanical Engineers 71, 23–27.
Stroh, A.N. (1958). Dislocations and cracks in anisotropic elasticity. Philosophical Magazine 7, 625–646.
Sung, J.C. and Liou, J.Y. (1995). Analysis of a crack embedded in a linear elastic half-plane solid. Journal of Applied Mechanics ASME 62, 78–86.
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, 965–983.
Ting, T.C.T. (1996). Anisotropic Elasticity. Theory and Application, Oxford Science, New York.
Wang, Y.H. and Cheung, Y.K. (1994). Boundary collocation method for cracks emanating from a hole in an anisotropic plate. Engineering Fracture Mechanics 48, 53–62.
Wen, P. (1989). The solution of a displacement discontinuity for an anisotropic half-plane and its applications to fracture mechanics. Engineering Fracture Mechanics 34, 1145–1154.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chao, C., Hsiao, C. Boundary integral equations for notch problems in an anisotropic half-space. International Journal of Fracture 105, 137–159 (2000). https://doi.org/10.1023/A:1007640915101
Issue Date:
DOI: https://doi.org/10.1023/A:1007640915101