Vector j-integral analysis of crack interaction with pre-existing singularities

Lifeng Ma, Tian Jian Lu, Alexander M. Korsunsky

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In this paper, the mechanics of a semi-infinite crack interacting with near crack-tip singularities (e.g., dislocations) in two-dimensional solids is investigated using the concept of potential energy release rate. The spontaneous relationship between the crack potential energy release rate and the well-known vector conservative integral Ji (i = 1, 2) is derived. It is demonstrated that J1 and J2 integrals are equally important in solving crack problems. This allows a more rational criterion to be proposed, based on the criterion of maximum energy release rate, to assess the so-called shielding/ amplification effect on the crack tip due to the presence of the singularities. It is shown that the new criterion can not only assess the shielding/amplification effect under pure mode I or mode II remote loading, but also efficiently assess crack-singularity interaction under mixed mode remote loading. Simultaneously, it is found by re-examining the Ji integrals that there exists a simple but universal relation among the three values of the vector Ji integral corresponding separately to the contributions induced from the semiinfinite crack tip, the singularity, and the remote loading. Next, a multi-singularity-crack interaction model is addressed, and the closed-form solution is obtained. Finally, as an example, the problem of a single dislocation interacting with a main crack is solved to demonstrate the validity of the proposed model and the new criterion.

Original languageEnglish
Pages (from-to)876-883
Number of pages8
JournalJournal of Applied Mechanics, Transactions ASME
Issue number5
Publication statusPublished - Sep 2006
Externally publishedYes


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