Abstract
Crack problems are solved by the complex potential method, and the elastic stress singularities near a crack tip are identified by introducing the stress intensity factors as the characteristic parameters of the stress field ahead of a crack tip. The analytical structure of the stress field is examined by a method of the eigen-function expansion near a crack tip, which leads to the so-called Irwin–Williams expansion of the stress field of the two-dimensional crack. Also, the solution method of Muskhelishvili is presented, where the formulation of the singular integral equation is based on the Hilbert problem. Mathematical details of the Hilbert problem are separately explained in Appendix B.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bazant ZP, Estenssoro LF (1979) Surface singularity and crack propagation. Int J Solids Struct 15:405–426
Benthem JP (1977) State of stress at the vertex of a quarter-infinite crack in a half-space. Int J Solids Struct 13:479–492
Dundurs J, Comninou M (1979) Some consequences of the inequality conditions in contact and crack problems. J Elasticity 9:71–82
Gautesen AK, Dundurs J (1987) The interface crack in a tension field. J Appl Mech 54:93–98
Green AE, Sneddon IN (1950) The distribution of stress in the neighbourhood of a flat elliptical crack in an elastic solid. Proc Camb Phil Soc 46:159–163
Kassir MK, Sih GC (1975) Three-dimensional crack problems. Noordhoff, Leyden
Murakami Y (ed) (1987) Stress intensity factors handbook, vols 1 and 2. Pergamon Press, Oxford
Muskhelishvili NI (1953) Some basic problems of the mathematical theory of elasticity, English edition translated from the 3rd Russian edition. Noordhoff, Groningen-Holland
Muskhelishvili NI (1958) Singular integral equations, English edition translated from the Russian edition. Noordhoff, Groningen-Holland
Raju IS, Newman JC (1979) Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates. Eng Fract Mech 11:817–829
Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. J Appl Mech 32:418–423
Sih GC, Rice JR (1964) The bending of plates of dissimilar materials with cracks. J Appl Mech 31:477–482
Sih GC (ed) (1973) Methods of analysis and solutions of crack problems. Noordhoff, Leyden
Sneddon IN (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc Roy Soc A 187:229–260
Sneddon IN, Lowengrub M (1969) Crack problems in the classical theory of elasticity. Wiley, New York
Tada H, Paris PC, Irwin GR (1973) The stress analysis of cracks handbook. Del Research Corporation, Hellertown, Pennsylvania
Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:104–114
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this chapter
Cite this chapter
Sumi, Y. (2014). Analysis of Two-Dimensional Cracks. In: Mathematical and Computational Analyses of Cracking Formation. Mathematics for Industry, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54935-2_3
Download citation
DOI: https://doi.org/10.1007/978-4-431-54935-2_3
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-54934-5
Online ISBN: 978-4-431-54935-2
eBook Packages: EngineeringEngineering (R0)