Abstract
The configuration of a Z-shaped crack is defined by a web length, two flange lengths, and two flange-web angles. A Z-shaped crack is said to be slender if the flange-web ratios are small. These ratios may then be characterized by a slenderness parameter ε. The associated elasticity problems are solved asymptotically in terms of this small parameter. Formal asymptotic expansions are developed, and explicit procedures are given for obtaining a solution accurate to the order of ε. This solution is fundamental to the determination of the maximum energy-release rate in linear clastic fracture mechanics. Using the maximum-energy-release-rate criterion, a tension-compression specimen with a crack is studied in the accompanying paper.
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References
Erdogan, G. and Sih, G. C., “On the Crack Extension in Plates under Plane Loading and Transverse Shear”, J. Basic Engrg., Trans. ASME, (1963) 519–527.
Sih, G. C., “Introductory Chapter: A Special Theory of Crack Propagation”, Mechanics of Fracture 1, Noordhoff (1972).
Griffith, A. A., “The Phenomena of Rupture and Flow in Solids”, Phil. Trans. R. Soc. A 221 (1921) 163–198.
Griffith, A. A., “The Theory of Rupture”, Proc. 1st Int. Congr. Appl. Mech., Delft, (1924) 55–63.
Hussain, M. A., Pu, S. L., and Underwood, J., “Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II”, ASTM-STP-560, (1974) 2–28.
Palaniswamy, K. and Knauss, W. G., “On the Problem of Crack Extension in Brittle Solids under General Loading” Calif. Inst. Tech. Report SM (1974) 74–8.
Chatteriee, S. N., “The Stress Field in the Neighborhood of a Branched Crack in an Infinite Elastic Sheet”, Int. J. Solids Struct. 11 (1975) 521–538.
Wu, C. H., “Maximum-Energy-Release-Rate Criterion Applied to a Tension-Compression Specimen with Crack”, Journal of Elasticity 8 (1978) number 3.
Sih, G. C. and Liebowitz, H., “On the Griffith Energy Criterion for Brittle Fracture”, Int. J. Solids Struct. 3 (1967) 1–22.
Sih, G. C. and Liebowitz, H., “Mathematical Theories of Brittle Fracture”, Chapter 2 of Fracture edited by Liebowitz, H., Academic Press, (1968) 67–190.
England, A. H., Complex Variable Methods in Elasticity, Wiley-Interscience (1971).
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Supported by U.S. Army Research Office-Durham under Grant DAAG-20-76-G-0272.
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Wu, C.H. Elasticity problems of a slender Z-crack. J Elasticity 8, 183–205 (1978). https://doi.org/10.1007/BF00052482
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DOI: https://doi.org/10.1007/BF00052482