Analytical and numerical evaluation of crack-tip plasticity of an axisymmetrically loaded penny-shaped crack

Sumitra Chaiyat, Xiaoqing Jin, Leon M. Keer*, Kraiwood Kiattikomol

*Corresponding author for this work

Research output: Contribution to journalShort surveypeer-review

16 Scopus citations


Analytical and numerical approaches are used to solve an axisymmetric crack problem with a refined Barenblatt-Dugdale approach. The analytical method utilizes potential theory in classical linear elasticity, where a suitable potential is selected for the treatment of the mixed boundary problem. The closed-form solution for the problem with constant pressure applied near the tip of a penny-shaped crack is studied to illustrate the methodology of the analysis and also to provide a fundamental solution for the numerical approach. Taking advantage of the superposition principle, an exact solution is derived to predict the extent of the plastic zone where a Tresca yield condition is imposed, which also provides a useful benchmark for the numerical study presented in the second part. For an axisymmetric crack, the numerical discretization is required only in the radial direction, which renders the programming work efficient. Through an iterative scheme, the numerical method is able to determine the size of the crack tip plasticity, which is governed by the nonlinear von Mises criterion. The relationships between the applied load and the length of the plastic zone are compared for three different yielding conditions. To cite this article: S. Chaiyat et al., C. R. Mecanique 336 (2008).

Original languageEnglish (US)
Pages (from-to)54-68
Number of pages15
JournalComptes Rendus - Mecanique
Issue number1-2
StatePublished - Jan 2008
Externally publishedYes


  • Crack tip plasticity
  • Dugdale approach
  • Penny-shaped crack
  • Tresca criterion
  • Von Mises criterion

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials


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