Analyses of the notched tension tests of carbon steel show that ductile failure is initiated when the sum of flow stress and mean stress reaches the limit for the material, regardless of stress triaxiality. Therefore, this explicit critical stress condition could be a candidate criterion for local failure. An equation expressing the relation between stress triaxiality and critical strain was derived from the critical stress condition, and it was found that the critical strain diagram obtained by the equation nearly overlapped with that obtained by the conventional empirical equation. This suggests that the critical stress condition can be approximately determined if the critical strain diagram was obtained for a particular steel. The critical stress condition was consistent with the classical void nucleation theory, and the theory was incorporated into the void nucleation term of stress control in the Gurson–Tvergaard (GT) model—a well-known damage mechanics model for ductile failure. Since only the strain-controlled term is used in the recent GT model, herein, a finite element method (FEM) code was newly developed to implement the GT model with the stress-controlled term. Notched tension tests were analyzed with the critical stress condition using the developed code, and the analyses reproduced the failure behaviors and critical strains of the tests considerably well. These results strongly support the practicality of the stress-based criterion and demonstrate that ductile failure could be appropriately predicted by combining the GT model using the void nucleation term of stress control with the critical stress condition.

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