Abstract
In this paper, the stress intensity factors of interacting kinked cracks in an elastic solid under remote compression and the overall strains of the solid are determined numerically. The kinked cracks are in general asymmetric, unequal, and arbitrarily oriented and located. Each kinked crack consists of a closed frictional main crack, and traction free kinks modeled by continuous dislocation distributions. The original problem is decomposed into straight crack problems such that the main cracks are subjected to dislocation and shear traction loadings. The model is used to investigate the dependence of the stress intensity factors and the overall strains on the crack configuration, i.e., a single fault of cracks, parallel faults, crossed faults, periodic and random crack arrays, and on the geometrical and physical parameters such as the fault angle and the lateral confinement.
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References
Ashby, M.F. and Hallam, S.D. (1986). The failure of brittle solids containing small cracks under compressive stress states. Acta Metallurgica 34, 497-510.
Ashby, M.F. and Sammis, C.G. (1990). The damage mechanics of brittle solids in compression. Pure and Applied Geophysics 133, 489-521.
Benveniste, Y., Dvorak, G.J., Zarzour, J. and Wung, E.C.J. (1988). On interacting cracks and complex crack configurations in linear elastic media. International Journal of Solids and Structures 25, 1279-1293.
Brace, W.F. and Bombalakis, E.G. (1963). A note on brittle crack growth in compression. Journal of Geophysical Research 68, 3709-3713.
Chen, W. and Ravichandran, R. (1996). Static and dynamic compressive behavior of aluminum nitride under moderate confinement. Journal of the American Ceramic Society 79, 579-584.
Cole, D.M. (1989). Microfracture and the compressive failure of polycrystalline ice. Proceedings of the IUTAM/IAHR Symposium on Ice-Structure Interaction, 23p.
Deng, H. and Nemat-Nasser, S. (1994). Microcrack interaction and shear fault failure. International Journal of Damage Mechanics 3, 3-37.
Erdogan, F. (1962). On the stress distribution in plates with collinear straight cuts under arbitrary loads. Proceedings of the Fourth U.S. National Congress of Applied Mechanics 1, 547-554.
Fairhurst, C. and Cook, N.G.W. (1966). The phenomenon of rock splitting parallel to the direction of maximum compression in the neighborhood of a surface. Proceedings of the First Congress of the International Society of Rock Mechanics 1, 687-692.
Fanella, D.A. (1990). Fracture and failure of concrete in uniaxial and biaxial loading. Journal of Engineering Mechanics 116, 2341-2362.
Gerasoulis, A. (1982). The use of quadratic polynomials for the solution of singular integral equations of Cauchy type. Computers & Mathematics with Applications 8, 15-22.
Horii, H. and Nemat-Nasser, S. (1986). Brittle failure in compression: splitting, faulting and brittle-ductile transition. Philosophical Transactions of the Royal Society of London A319, 337-374.
Isida, M. and Nemat-Nasser, S. (1987). A unified analysis of various problems relating to circular holes with edge cracks. Engineering Fracture Mechanics 27, 571-591.
Kachanov, M.L. (1982). A microcrack model of rock inelasticity, Part II: Propagation of microcracks. Mechanics of Materials 1, 29-41.
Lehner, F. and Kachanov, M. (1996). On modeling of ‘winged’ cracks forming under compression. International Journal of Fracture 77, R69-R75.
Lo, K.K. (1978). Analysis of branched cracks. Journal of Applied Mechanics 45, 797-802.
McClintock, F.A. and Walsh, J.B. (1962). Friction on Griffith cracks in rocks under pressure. Proceedings of the Fourth U.S. National Congress of Applied Mechanics 2, 1015-1021.
Muskhelishvili, N.I. (1977). Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Leyden, 732p.
Nemat-Nasser, S. and Obata, M. (1988). A microcrack model of dilatancy in brittle materials. Journal of Applied Mechanics 55, 24-35.
Niu, J. (1997). Interactions of Morphologically Complex Cracks under Tension and Compression, Ph.D. thesis, 241p.
Niu, J. and Wu, M.S. (1997). Strong interactions of morphologically complex cracks. Engineering Fracture Mechanics 57, 665-687.
Ravichandran, G. and Subhash, G. (1995). A micromechanical model for high strain rate behavior of ceramics. International Journal of Solids and Structures 32, 2627-2646.
Schulson, E.M. (1990). The brittle compressive fracture of ice. Acta Metallurgica et Materialia 38, 1963-1976.
Steif, P.S. (1984). Crack extension under compressive loading. Engineering Fracture Mechanics 20, 463-473.
Wu, M.S. (1993). Effective moduli of finite anisotropic media with cracks. Mechanics of Materials 12, 139-158.
Wu, M.S. (1994). Material anisotropy effects on stress intensity factors and the effective elastic compliance. Engineering Fracture Mechanics 48, 177-198.
Wu, M.S. and Niu, J. (1995a). Micromechanical prediction of the compressive failure of ice: Model development. Mechanics of Materials 20, 9-32.
Wu, M.S. and Niu, J. (1995b). Micromechanical prediction of the compressive failure of ice: Numerical simulations. Mechanics of Materials 20, 33-58.
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Niu, J., Wu, M.S. Analysis of Asymmetric Kinked Cracks of Arbitrary Size, Location and Orientation – Part I. Remote Compression. International Journal of Fracture 89, 19–57 (1998). https://doi.org/10.1023/A:1007428827074
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DOI: https://doi.org/10.1023/A:1007428827074