Abstract
In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D inclined semi-elliptical surface crack in a semi-infinite body under tension. The stress field induced by displacement discontinuities in a semi-infinite body is used as the fundamental solution. Then, the problem is formulated as a system of integral equations with singularities of the form r −3. In the numerical calculation, the unknown body force doublets are approximated by the product of fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately for various geometrical conditions. The effects of inclination angle, elliptical shape, and Poisson's ratio are considered in the analysis. Crack mouth opening displacements are shown in figures to predict the crack depth and inclination angle. When the inclination angle is 60 degree, the mode I stress intensity factor F I has negative value in the limited region near free surface. Therefore, the actual crack surface seems to contact each other near the surface.
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References
Hadamard, J. (1923). Lectures on Caunchy's Problem in Linear Partical Differential Equations, Yale Univ. Press.
Isida, M. and Noguchi, H. (1982a). Tension and bending of a plate with a semi-elliptical surface crack. Transactions of the Japan Society of Mechanical Engineers 48A, 607-619 (in Japanese).
Isida, M. and Noguchi, H. (1982b). Analysis of three-dimensional crack problems using body force method. Transactions of the Japan Society of Mechanical Engineers 49A, 707-717 (in Japanese).
Isida, M., Tokumoto, A. and Noguchi, H. (1982). Oblique semi-elliptical surface crack in semi-infinite solid subjected to tension. Proceedings of Japan Society of Mechanical Engineers, No. 838–1, 4-6 (in Japanese).
Isida, M., Tokumoto, A. and Noguchi, H. (1990). Oblique semi-elliptical surface crack in semi-infinite solid subjected to tension. Engineering of Fracture Mechanics 36-6, 889-892.
Isida, M., Tsuru, H. and Noguchi, H. (1993a). New method of analysis of three-dimensional crack problems (1st Report, Basic theory and applications to infinite body problems). Transactions of the Japan Society of Mechanical Engineers 59A, 1270-1278 (in Japanese).
Isida, M., Tsuru, H. and Noguchi, H. (1993b). New method of analysis of three-dimensional crack problems (2nd Report, Application to semi-Infinite body problems with an arbitrary surface or internal crack under complex loading conditions). Transactions of the Japan Society of Mechanical Engineers 59A, 1279-1286 (in Japanese).
Murakami, Y. (1985). Analysis of stress intensity factors of modes I, II and III inclined surface cracks of arbitrary shape. Engineering of Fracture Mechanics 22-1, 101-114.
Murakami, Y. and Sakae, C. (1992). Analysis of stress intensity factors for a three-dimensional bent surface crack. Journal of The Society of Materials 41,No. 467, 1214-1220 (in Japanese).
Murakami, Y. and Isida, M. (1984). Analysis of mixed mode stress intensity factor K I, K II, K III of oblique arbitrary surface crack. Transactions of the Japan Society of Mechanical Engineers 50A, 1359-1366 (in Japanese).
Nisitani, H. (1967). The two-dimensional stress problem solved using an electric digital computer. Journal of Japan Society of Mechanical Engineers, 70, 627-632 (in Japanese).
Nisitani, H. (1968). Bulletin of Japan Society of Mechanical Engineers 11, 14-23.
Nisitani, H. and Murakami, Y. (1974a). Stress intensity factor of elliptical and semi-elliptical cracks in plates subjected to tension. Transactions of the Japan Society of Mechanical Engineers 40, 31-40. (in Japanese).
Nisitani, H. and Murakami, Y. (1974b). Stress intensity factor of an elliptical crack and semi-elliptical crack in plates subjected to tension. International Journal of Fracture 10, 353-368.
Noda, N.-A. and Oda, K. (1992). Numerical solution of the singular integral equations in the crack analysis using the body force method. International Journal of Fracture 58, 285-304.
Noda, N.-A. and Miyoshi, S. (1996). Variation of stress intensity factor and crack opening displacement of semielliptical surface crack. International Journal of Fracture 75, 19-48.
Takakuda, H., Koizumi, T. and Shibuya, T. (1984). On the solution of integral equations for crack problems. Transactions of the Japan Society of Mechanical Engineers 50A, 1184-1192 (in Japanese).
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Noda, NA., Kobayashi, K. & Yagishita, M. Variation of mixed modes stress intensity factors of an inclined semi-elliptical surface crack. International Journal of Fracture 100, 207–225 (1999). https://doi.org/10.1023/A:1018666110597
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DOI: https://doi.org/10.1023/A:1018666110597