Abstract
The shape of a tapered crack is more alike cracks in brittle materials than an elliptical crack. The deformation and stress fields for a tapered crack are therefore estimated for hydrostatic pressure and tensional stress by applying the method of complex potentials. The stress fields for the tapered and elliptical cracks are quite similar, which suggests that the elliptical crack can be used as a model for the stress fields for cracks in general. However, the tapered crack has a larger tensional stress at the crack tip, which show that fracture propagation occur at lower applied stresses than for the elliptical crack. A tapered shape of fluid filled fractures can account for their discontinuous propagation. The discontinuous fracture propagation is observed in a large scale by volcanic eruptions where the fracture propagation generates seismic activity.
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References
Aki, K., Fehler, M. and Shamita, D. (1977). Journal of Volcanology and Geothermal Research 2, 259–287.
Batchelor, G.K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, 615 pp.
Barenblatt, G.I. (1962). Advances of Applied Mechanics 7, 55–129.
Eaton, J.P. and Murata, K.J. (1960). Science 132, 925–938.
Griffith, A.A. (1921). Proceedings First International Congress of Applied Mechanics, 55–63.
Jaeger, J.C. and Cook, N.G.W. (1969). Fundamentals of Rock Mechanics. Methuen & Co., London, 513 pp.
Murrell, S.A.F. (1964). British Journal of Applied Physics, 1211–1223.
Muskhelishvili, N.I. (1963). Some Basic Problems of the Mathematical Theory of Elasticity. P. Noordhoff, Groningen, 704 pp.
Olesiak, Z. and Wnuk, M. (1968). Journal of Fracture Mechanics 4, 383–396.
Rummel, F. (1987). Fracture Mechanics of Rocks. Academic Press, London, 217–239.
Spence, D.A. and Turcotte, D.L. (1985). Journal of Geophysical Research 90, 575–580.
Timoshenko, S.P. and Goodier, J.N. (1970). Theory of Elasticity. McGraw-Hill, New York, 567 pp.
Zobak, M.D. and Harjes, H.-P. (1997). Journal of Geophysical Research 102, 18,477–18,491.
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Maaløe, S. The elastic stress fields of elliptic and tapered cracks with predefined shapes. International Journal of Fracture 110, 155–173 (2001). https://doi.org/10.1023/A:1010853620142
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DOI: https://doi.org/10.1023/A:1010853620142