Abstract
This paper investigates the Zener–Stroh crack with curved configuration in plane elasticity. A singular integral equation is suggested to solve the problem. Formulae for evaluating the SIFs and T-stress at the crack tip are suggested. If the curve configuration is a product of a small parameter and a quadratic function, a perturbation method based on the singular integral equation is suggested. In the method, the singular integral equation can be expanded into a series with respect to the small parameter. Therefore, many singular integral equations can be separated from the same power order for the small parameter. These singular integral equations can be solved successively. The solution of the successive singular integral equations will provide results for stress intensity factors and T-stress at the crack tip. It is found that the behaviors for the solution of SIFs and T-stress in the Zener–Stroh crack and the Griffith crack are quite different. This can be seen from the presented comparison results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Muskhelishvili N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, The Netherlands (1953)
Timoshenko S.P., Goodier J.N.: Theory of Elasticity. McGraw-Hill, New York (1970)
Love A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Oxford, London (1944)
Stroh A.N.: The formulation of cracks as a result of plastic flow. I. Proc. R. Soc. Lond. A223, 404–414 (1954)
Weertman J.: Zener–Stroh crack, Zener–Hollomon parameter, and other topics. J. Appl. Phys. 60, 1877–1937 (1966)
Hirth J.P., Lothe J.: Theory of Dislocations. Wiley, New York (1982)
Fan H.: Interfacial Zener–Stroh crack. ASME J. Appl. Mech. 61, 829–834 (1994)
Fan H., Xiao Z.M.: A Zener–Stroh crack near an interface. Int. J. Solids Struct. 34, 2829–2842 (1997)
Xiao Z.M., Chen B.J., Fan H.: A Zener–Stroh crack in a fiber-reinforced composite material. Mech. Mater. 10, 593–606 (2000)
Xiao Z.M., Chen B.J.: Stress analysis for a Zener–Stroh crack interacting with a coated inclusion. Int. J. Solids Struct. 38, 5007–5018 (2001)
Xiao Z.M., Zhao J.F., Fan H.: Zener–Stroh crack at the interface of multi-layered structures. Int. J. Fract. 133, 355–369 (2005)
Chen Y.Z.: Multiple Zener–Stroh crack problem in an infinite plate. Acta Mech. 170, 11–23 (2004)
Cotterell B., Rice J.R.: Slightly curved or kinked cracks. Int. J. Fract. 16, 155–169 (1980)
Dreilich L., Gross D.: The curved crack. Z. Angew. Math. Mech. 65, 132–134 (1985)
Martin P.A.: Perturbed cracks in two dimensions: an integral-equation approach. Int. J. Fract. 104, 317–327 (2000)
Chen Y.Z., Lin X.Y., Wang Z.X.: T-stress evaluation for slightly curved crack using perturbation method. Int. J. Solids Struct. 45, 211–224 (2008)
Savruk, M.P.: Two-Dimensional Problems of Elasticity for Body with Crack. Nauka Dumka, Kiev (1981) (in Russian)
Chen Y.Z., Lin X.Y.: Complex potentials and integral equations for curved crack and curved rigid line problems in plane elasticity. Acta Mech. 182, 211–230 (2006)
Chen Y.Z., Hasebe N., Lee K.Y.: Multiple Crack Problems in Elasticity. WIT Press, Southampton (2003)
Chen, Y.Z., Lin, X.Y.: T-stress evaluation for curved crack problems. Acta Mech. (2008, to appear)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, Y.Z., Lin, X.Y. & Wang, Z.X. Perturbation method for the solution of a Zener–Stroh crack with a slightly curved configuration. Acta Mech 203, 23–36 (2009). https://doi.org/10.1007/s00707-008-0044-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-008-0044-4