Skip to main content
SpringerLink
Log in

Higher order terms of the crack tip asymptotic field for a wedge-splitting specimen

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The coefficients of the crack tip asymptotic field of a typical wedge-splitting specimen are computed using a hybrid crack element (HCE), which has the potential to directly calculate not only the stress intensity factor (SIF) but also the coefficients of the higher order terms of the crack tip asymptotic field. The approximate closed-form expression for SIF proposed by Guinea et al. (1996) is calibrated by the results of the HCE. Approximate expressions for the second and third order terms for the wedge-splitting specimen are obtained by fitting the computed data. Numerical results show that the coefficients for terms higher than three are negligibly small, thus the wedge-splitting specimen is more stable than other geometries.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Bruhwiler, E. and Wittmann, F.H. (1990). The wedge-splitting test: a method of performing stable fracture mechanics tests. Engineering Fracture Mechanics 35, 117–125.

    Google Scholar 

  • Du, Z.Z. and Hancock, J.W. (1991). The effect of non-singular stresses on crack tip constraint. Journal of the Mechanics and Physics of Solids 39, 555–567.

    Google Scholar 

  • Guinea, G.V., Elices, M. and Planas, J. (1996). Stress intensity factors for wegde-splitting geometry. International Journal of Fracture 81, 113–124.

    Google Scholar 

  • Karihaloo, B.L. (1995). Fracture Mechanics and Structural Concrete. Addison Wesley Longman, UK.

    Google Scholar 

  • Karihaloo, B.L. (1999). Size effect in shallow and deep notched quasi-brittle structures. International Journal of Fracture 95, 379–390.

    Google Scholar 

  • Karihaloo, B.L. and Xiao, Q.Z. (2001a). Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Engineering Fracture Mechanics 68, 1609-1630.

    Google Scholar 

  • Karihaloo, B.L. and Xiao, Q.Z. (2001b). Higher order terms of the crack tip asymptotic field for a notched threepoint bend beam. International Journal of Fracture (in press).

  • Karstensen, A.D., Nekkal, A. and Hancock, J.W. (1997). The constraint of elastic-plastic crack tip fields. Advances in Fracture Research, Proceeding of ICF9 (Edited by B.L. Karihaloo, Y.W. Mai, M.I. Ripley and R.O. Ritchie), Pergamon, Oxford, 2007–2014.

    Google Scholar 

  • Linsbauer, H.N. and Tschegg, E.K. (1986). Fracture energy determination of concrete with cube-shaped specimens. Zement und Beton 31, 38–40.

    Google Scholar 

  • Muskhelishvili, N.I. (1953). Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Holland (English translation).

    Google Scholar 

  • Nikishkov, G.P. (1998). A fracture concept based on the three-term elastic-plastic asymptotic expansion of the near-crack tip stress field. Fracture: A Topical Encyclopedia of Current Knowledge (Edited by G.P. Cherepanov), Malabar, Krieger Pub Co, Florida, 557–574.

    Google Scholar 

  • O'Dowd, N.P. and Shih, C.F. (1991). Family of crack-tip fields characterized by a triaxiality parameter: Part I – structure of fields. Journal of the Mechanics and Physics of Solids 39, 939–963.

    Google Scholar 

  • Owen, D.R.J. and Fawkes, A.J. (1983). Engineering Fracture Mechanics: Numerical Methods and Applications. Pineridge Press Ltd., Swansea, U.K.

    Google Scholar 

  • Pian, T.H.H. and Sumihara, K. (1984). Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering 20, 1685–1695.

    Google Scholar 

  • Pian, T.H.H. and Wu, C.C. (1988). A rational approach for choosing stress term of hybrid finite element formulations. International Journal for Numerical Methods in Engineering 26, 2331–2343.

    Google Scholar 

  • Sih, G.C. and Liebowitz, H. (1968). Mathematical theories of brittle fracture. In Fracture-An Advanced Treatise (Edited by H. Liebowitz), II, Academic Press, New York, 67–190.

    Google Scholar 

  • Tong, P., Pian, T.H.H. and Lasry, S.J. (1973). A hybrid element approach to crack problems in plane elasticity. International Journal for Numerical Methods in Engineering 7, 297–308.

    Google Scholar 

  • Tschegg, E.K. and Linsbauer, H.N. (1986). Test Method for the Determination of Fracture Mechanics Properties. Patent specification No. A-233/86 390 328, Austrian Patent Office.

  • Tschegg, E.K. (1990). Patent specification No. A-408/90, Austrian Patent Office.

  • Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24, 109–114.

    Google Scholar 

  • Xiao, Q.Z., Karihaloo, B.L. and Williams, F.W. (1999). Application of penalty-equilibrium hybrid stress element method to crack problems. Engineering Fracture Mechanics 63, 1–22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering, Cardiff University, Cardiff, CF24 3TB, UK

    B.L. Karihaloo & Q.Z. Xiao

Authors
  1. B.L. Karihaloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Q.Z. Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karihaloo, B., Xiao, Q. Higher order terms of the crack tip asymptotic field for a wedge-splitting specimen. International Journal of Fracture 112, 129–137 (2001). https://doi.org/10.1023/A:1013366025494

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013366025494

Search

Navigation