Abstract
The present paper explores the extension of a macrocrack by connecting statistically distributed microcracks. Two issues are discussed: (1) how long a semi-infinite crack can extend by connecting collinear microcracks of equal length but distributed ligament sizes; (2) how far the crack tip can shift vertically from the original crack extension line by connecting randomly positioned and oriented microcracks. Statistical analysis is employed to calculate the expected crack extension length and the vertical shift of the crack tip. The implication of the present study for the problem of a macrocrack linking to a parallel fault is addressed.
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References
Budiansky, B. and O'Connell, R.J. (1976). ELastic moduli of a crack solid. International Journal of Solids and Structures 12, 81–97.
Christensen, R.M. and Lo, K.H. (1979). Solutions for effective shear properties in three phase sphere and cylinder models. Journal of the Mechanics and Physics of Solids 27, 315–330.
Cotterell, B. and Rice, J.R. (1980). Slightly curved or kinked cracks. International Journal of Fracture 16, 155–169.
Kachanov, M. (1992). Effective elastic properties of cracked solids: Critical review of some basic concepts. Applied Mechanics Review 45, 304–335.
Kachanov, M., Montagut, E. and Laures, J.P. (1990). Mechanics of crack–microcrack interactions. Mechanics of Materials 10, 59–71.
Mori, T. and Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 21, 571–583.
Muskhelishvili, H.N. (1953). Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen.
Rubinstein, A.A. (1985). Macrocrack interaction with semi–infinite microcrack array. International Journal of Fracture 27, 113–119.
Rubinstein, A.A. (1986). Macrocrack–microdefect–interaction. Journal of Applied Mechanics 53, 505–511.
Wu, S. and Chudnovsky, A. (1990). The effective elastic properties of a linear elastic solid with microcracks. Engineering Fracture Mechanics 37, 653–659.
Zhang, S., Yang, W. and Li, T. (1998). Statistical strength of brittle materials with strongly interacted collinear microcracks. International Journal of Solids and Structures 35, 995–1008.
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Zhang, S., Yang, W. Macrocrack Extension by Connecting Statistically Distributed Microcracks. International Journal of Fracture 90, 341–353 (1998). https://doi.org/10.1023/A:1007440012284
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DOI: https://doi.org/10.1023/A:1007440012284