Abstract
Stress investigation for the interaction problem between a coated circular inclusion and a near-by line crack has been carried out. The crack and the coated inclusion (a coated fiber) are embedded in an infinitely extended isotropic matrix, with the crack being along the radial direction of the inclusion. Two loading conditions, namely, the tensile and shear loading ones are considered. During the solution procedure, the crack is treated as a continuous distribution of edge dislocations. By using the solution of an edge dislocation near a coated fiber as the Green's function, the problem is formulated into a set of singular integral equations which are solved by Erdogan and Gupta (1972) method. The expressions for the stress intensity factors of the crack are then obtained in terms of the asymptotic values of the dislocation density functions evaluated from the integral equations. Several numerical examples are given for various material and geometric parameters. The solutions obtained from the integral equations have been checked and confirmed by the finite element analysis results.
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References
ANSYS analysis guides release 5.4 (1997). Canonsburg, PA: ANSYS, Inc.
Erdogan, F. and Gupta, G.D. (1972). On the numerical solution of singular integral equations. Quarterly of Applied Mathematics 34, 525-534.
Erdogan, F., Gupta, G.D. and Ratwani, M (1974). Interaction between a circular inclusion and an arbitrarily oriented crack. ASME Journal of Applied Mechanics 41, 1007-1013.
Hashin, Z. (1962). The elastic moduli of heterogeneous materials. ASME Journal of Applied Mechanics 29, 143-150.
Hashin, Z. and Rosen, B.W. (1964). The elastic moduli of fiber-reinforced materials. ASME Journal of Applied Mechanics 31, 223-232.
Hsu, Y.C. and Shivakumar, V. (1976). Interaction between an elastic circular inclusion and two symmetrically placed collinear cracks. International Journal of Fracture Mechanics 12, 619-630.
Mikata, Y. and Taya, M. (1985a). Stress field in and around a coated short fiber in infinite matrix subjected to uniaxial and biaxial loadings. ASME Journal of Applied Mechanics 52, 19-24.
Mikata, Y. and Taya, M. (1985b). Stress field in a coated continuous fiber composite subjected to thermalmechanical loadings. Journal of Composite Materials 19, 554-578.
Nisitani, H., Chen, D.H. and Saimoto, A. (1996). Interaction between an elliptic inclusion and a crack. Proceedings of the International Conference on Computer-Aided Assessment and Control, Computational Mechanics Inc, MA, USA, Vol.4, 325-332.
Qiu, Y.P. and Weng, G.J. (1991). Elastic moduli of thickly coated particle and fiber-reinforced composite. ASME Journal of Applied Mechanics 58, 388-398.
Savin, G.N. (1961). Stress Concentration Around Holes. Pergamon, Oxford.
Sendeckyj, G. P. (1974). Interaction of cracks with rigid inclusions in longitudinal shear deformation. International Journal of Fracture Mechanics 101, 45-52.
Tamate, O. (1968). The effect of a circular inclusion on the stresses around a line crack in a sheet under tension. International Journal of Fracture Mechanics 4, 257-265.
Weertman, J. (1996). Dislocation Based Fracture Mechanics. World Scientific, Singapore.
Xiao, Z.M. and Chen, B.J. (2000). An edge dislocation interacting with a coated fiber. International Journal of Solids and Structures (submitted).
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Xiao, Z., Chen, B. Stress intensity factor for a Griffith crack interacting with a coated inclusion. International Journal of Fracture 108, 193–205 (2001). https://doi.org/10.1023/A:1011066521439
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DOI: https://doi.org/10.1023/A:1011066521439