#### Vol. 1, No. 8, 2006

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### Jia Li and Xiao-Bing Zhang

Vol. 1 (2006), No. 8, 1385–1404
##### Abstract

In this work, crack initiation from a notch tip in elements subjected to a mixed mode loading was studied. Two phenomenological criteria, based on a concept of Leguillon, were proposed and applied to predict crack initiation from a $V$-notch tip in a brittle or quasibrittle material. The first criterion, called in this paper the $G$-$\sigma$ criterion, makes use of the critical strain energy release rate and the ultimate tensile stress as the main parameters of fracture. It requires calculations of strain energy release rate after an infinitesimal crack kinking. By means of some numerical effort, we established the indispensable relationships between the strain energy release rate after crack kinking and the remote mixed mode loads. These relationships enabled us to apply directly the proposed criterion to mixed-mode loaded notches. We also modified the strain energy density criterion proposed by Sih on the basis of Leguillon’s concept to form a criterion capable of predicting the crack initiation from a $V$-notch tip. This criterion, which we call the $S$-$\sigma$ criterion, benefits from its simplicity in applications. Confrontation with experimental data shows that both the criteria enable reasonably accurate prediction of fracture in elements with $V$-notches subjected to mixed mode loading. Consequently, they can be effectively applied in practical engineering applications.