A simple path-independent integral for calculating mixed-mode stress intensity factors

Zhiliang Zhang, Timo Mikkola

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


A path‐independent integral is introduced for calculating stress intensity factors. The derivation of the integral is based on the application of the known Bueckner's fundamental field solution for a crack in an infinite body and on the reciprocal theorem. The method was applied to two‐dimensional linear elastic mixed‐mode crack problems. The key advantage of the present path‐independent integral is that the stress intensity factor components for any irregular cracked geometry under any kind of loading can be easily obtained by a contour integral around the crack tip. The method is simple to implement and only the far field displacements and tractions along the contour must be known. The required stress analysis can be made by using any analytical or numerical method, e.g. the finite element method, without special consideration of the modelling of crack tip singularity. The application of this integral is also independent of the crack type, that is, there is no difference between an edge crack and an embedded crack, provided that the crack tip asymptotic behaviour exists.
Original languageEnglish
Pages (from-to)1041-1049
JournalFatigue & Fracture of Engineering Materials & Structures
Issue number10
Publication statusPublished - 1992
MoE publication typeA1 Journal article-refereed


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