Abstract
An axisymmetrical fiber-matrix cylindrical model with a circumferential crack in the matrix of finite diameter is formulated within elastostatic scope. The problem is considered by means of integral transforms and a singular integral equation with a dominant generalized Cauchy kernel is obtained. Following the numerical solution technique developed by Erdogan, Gupta and Cook, the singular integral equation is reduced to a system of linear equations. By solving the linear equations, stress intensity factors associated with the crack length and the material properties are calculated and discussed. The solutions presented in this study are found to be general, including the solutions as special cases of the present formulation for a homogeneous solid cylindrical bar and a thick-walled shell with an outer circumferential crack.
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References
Atsumi, A. and Shindo, Y. (1979). Singular stresses in a transversely isotropic circular cylinder with circumferential edge crack. International Journal of Engineering Sciences 17, 1229–1236.
Beuth, Jr., J.L. (1992). Cracking of thin bonded films in residual tension. International Journal of Solids and Structures 29, 1657–1675.
Cook, T.S. and Erdogan, F. (1972). Stresses in bonded materials with a crack perpendicular to the interface. International Journal of Engineering Sciences 10, 677–697.
Dundurs, J. (1969). Edge-bonded dissimilar orthogonal elastic wedges. Journal of Applied Mechanics 36, 650–652.
Erdelyi, A. (1954). Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York.
Erdogan, F. and Gupta, G.D. (1972). On the numerical solution of singular integral equations. Quarterly of Applied Mathematics 30, 533–547.
Erdogan, F., Gupta, G.D. and Cook, T.S. (1973). Methods of Analysis and Solutions of Crack Problems. (Edited by G. Sih), Noordhoff International Publishing 368–425.
Erdol, R. and Erdogan, F. (1978). A thick-walled cylinder with an axisymmetric internal or edge crack. Journal of Applied Mechanics 45, 281–286.
Guo, S.Q., Kagawa, Y. and Honda, K. (1996). Metallurgical and Materials Transactions 27A, 2843–2851.
Himemiya, T. and Shindo, Y. (1982). Singular stresses in dissimilar materials with an annular crack. Transactions of Japan Society for Mechanical Engineers 48, 57–64.
Hutchinson, J.W. and Jensen, H.M. (1990). Models of fiber debonding and pullout in brittle composites with friction. Mechanics of Materials 9, 139–163.
Kant, R. and Bogy, D.B. (1980). The elastiostatic axisymmetric problem of a cracked sphere embedded in a dissimilar matrix. Journal of Applied Mechanics 47, 545–550.
Keer, L.M. and Watts, H.A. (1976). Mixed boundary value problems for a cylinder shell. International Journal of Solids and Structures 12, 723–729.
Keer, L.M., Luk, V.K. and Freedman, J.M. (1977). Circumferential edge crack in a cylindrical cavity. Journal of Applied Mechanics 44, 250–254.
Keer, L.M., Freedman, J.M. and Watts, H.A. (1977). Infinite tensile cylinder with circumferential edge crack. Letters in Applied and Engineering Sciences 5, 129–134.
Liu, Y.-F., Kagawa, Y. and Yuuki, R. Analysis of debonding propagation in layered materials, (to be submitted).
Love, A.E.H. (1944). A Treatise on the Mathematical Theory of Elasticity, Dover Publishing, New York.
Marshall, D.B., Shaw, M.C. and Morris, W.L. (1992). Measurement of interfacial debonding and sliding resistance in fiber reinforced intermetalics. Acta Metallurgica 40, 443–454.
Nisitani, H. and Noda, N. (1984). A cylindrical bar with infinite row of circumferential cracks under tension. Transactions of Japan Society for Mechanical Engineers 50, 847–853.
Sih, G.C. and Chen, E.P. (1973). Cracks in Composite Materials, Noordhoff International Publishing 178–255.
Sneddon, I.N. and Tait, R.J. (1963). The effect of a penny-shaped crack on the distribution of stress in a long circular cylinder. International Journal of Engineering Sciences 1, 391–409.
Sneddon, I.N. and Lowengrub, M. (1969). Crack Problems in the Classical Theory of Elasticity, John Wiley and Sons 131–159.
Stress Intensity Factors Handbook (1987). (Edited and Co-Edited by, Y. Murakami, S. Aoki, H. Hasebe, Y. Itoh, H. Miyata, N. Miyazaki, H. Terada, K. Tohgo, M. Toya and R. Yuuki), Vol. 2, Pergamon Press, 643–653.
Ceramic Source, (1989). American Ceramics Society 6, T8.
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Liu, YF., Tanaka, Y. & Masuda, C. Analysis of the fiber-matrix cylindrical model with a circumferential crack. International Journal of Fracture 88, 87–105 (1997). https://doi.org/10.1023/A:1007463422102
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DOI: https://doi.org/10.1023/A:1007463422102