A new formulation of the modified maximum force criterion (MMFC)

In the paper the authors propose an improved version of the Modified Maximum Force Criterion (MMFC) initially developed by Hora and his co-workers. The most appealing characteristic of this model is the fact that no assumptions related to the existence of voids or other defects are needed. The MMFC model is based on the hypothesis that a plane-strain state develops during the localized necking. Due to the related stress change, there is an additional hardening effect, which ‘hesitates’ out the localized necking. The improvement proposed in the frame of this paper consists in adding two material constants to the MMFC model. Their values are determined by enforcing a couple of experimental constraints on the model. In this way, the quality of the theoretical predictions can be improved. As proven by the numerical tests, the most appropriate constraints are related to the necking occurrence in plane strain and biaxial tension, respectively. By controlling these points of the FLD, the discrepancies between Hora’s model and experiments can be minimised. If no experimental data is available, the constraints could be generated by using some other model for the FLD determination (e.g., empirical formulas or the model developed by Marciniak and Kuczynski). The performances of the new model are evaluated by comparing its predictions with Hora’s necking criterion and experimental FLD’s corresponding to different sorts of sheet metals.