Skip to main content
SpringerLink
Log in

Frobenius’ method for curved cracks

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

Abstract

The distribution of stresses produced by an undulated crack in a plane elastic solid, and in particular, at its tips where stresses approach infinity, requires the solution of two coupled singular integral equations. Except for simple crack geometries such as rectilinear and circular arcs in infinite plates, for which explicit analytic solutions have been obtained, the integral equations require numerical solutions. We propose a treatment of the integral equations by Frobenius’ method, which is particularly suitable for evaluating the stress intensity factors of slightly curved cracks.

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

  • Brandinelli, L. (1997). Characterization of planar curvilinear cracks and development of a probabilistic crack propagation model for brittle materials. M.S. Thesis, Case Western Reserve University, OH.

  • Y.Z. Chen D. Gross Y.J. Huang (1991) ArticleTitleNumerical solution of the curved crack problem by means of polynomial approximation of the disclocation distribution Engineering Fracture Mechanics 39 IssueID5 791–797 Occurrence Handle10.1016/0013-7944(91)90184-3

    Article  Google Scholar 

  • B. Cotterell J.R. Rice (1980) ArticleTitleSlightly curved or kinked cracks International Journal of Fracture 16 IssueID2 155–169 Occurrence Handle10.1007/BF00012619

    Article  Google Scholar 

  • L. Dreilich D. Gross (1985) ArticleTitleDer gekrümmte Riss Zeitschrift Fur Angewandte Mathematik und Mechanik 65 132–134

    Google Scholar 

  • J. Dundurs G.P. Sendeckyj (1965) ArticleTitleBehavior of an edge dislocation near a bimaterial interface Journal of Applied Physics 36 IssueID10 3353–3354 Occurrence Handle10.1063/1.1702981

    Article  Google Scholar 

  • Grigolyuk, E. and Tolkachev, V. (1987). Contact Problems in the Theory of Plates and Shells. Mir, Moscow.

  • Muskhelishvili, N.I. (1953). Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen.

  • L.R.F. Rose (1987) ArticleTitleCrack reinforcement by distributed springs Journal of the Mechanics and Physics of Solids 35 IssueID4 383–405 Occurrence Handle0612.73105 Occurrence Handle900774 Occurrence Handle10.1016/0022-5096(87)90044-5

    Article  MATH  MathSciNet  Google Scholar 

  • Savruk, M.P. (1981). Two-Dimensional Problems of Elasticity for Body with Crack. The University Press, Kiev (in Russian).

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Case Western Reserve University, Cleveland, OH, 44106-7201, USA

    Roberto Ballarini

  2. Dipartimento di Ingegneria Strutturale, Universitá di Pisa, Pisa, Italy

    Piero Villaggio

Authors
  1. Roberto Ballarini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Piero Villaggio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roberto Ballarini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ballarini, R., Villaggio, P. Frobenius’ method for curved cracks. Int J Fract 139, 59–69 (2006). https://doi.org/10.1007/s10704-006-6730-0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-006-6730-0

Keywords

Search

Navigation