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Peridynamics is a recent nonlocal theory of continuum mechanics that is suitable to describe fracture problems in solid mechanics. In this paper, a new failure criterion based on the stress field is developed by adopting the damage correspondence model in the ordinary state-based peridynamic theory. The proposed stress tensor-based failure criterion is capable of predicting more accurately crack propagation in the mixed mode I-II fracture problems different from other failure criteria in peridynamics. The effectiveness of the proposed model is demonstrated by performing several examples of mixed-mode dynamic fracture in brittle materials.