Refined Dugdale plastic zones of an external circular crack

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The refined Dugdale-type plastic zones ahead of an external circular crack, subjected to a uniform displacement at infinity, are evaluated both analytically and numerically. The analytical method utilizes potential theory in classical linear elasticity with emphasis on the contrast from the internal crack problem. A closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition. The analytical solution is also used to benchmark the results obtained from the numerical method, which show good agreement. Through an iterative scheme, the numerical technique is able to estimate the size of crack tip plasticity zone, which is governed by the non-linear von Mises criterion. The relationships between the applied displacement and the length of the plastic zone are compared for the different yielding conditions. Computational modeling has demonstrated that the plastic constraint effect based on the true yield condition can significantly influence the load-bearing capacity. It is also discovered from the comparative study that the stress components predicted by the three different yield conditions may differ notably; however, the stress triaxiality in the ligament region has only small deviations. The proposed study may find applications in predicting the plastic flow in a circumferentially notched round bars under tension.

Original languageEnglish (US)
Pages (from-to)1127-1146
Number of pages20
JournalJournal of the Mechanics and Physics of Solids
Issue number4
StatePublished - Apr 2008


  • Crack tip plasticity
  • Deeply notched bar
  • Dugdale approach
  • Plastic constraint factor
  • Stress triaxiality

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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