A novel three-dimensional M-K model by integrating GTN model for accurately identifying limit strains of sheet metal

Abstract

To accurately identify the limit strains and improve the prediction accuracy of forming limits for sheet metal, a novel three-dimensional M-K model by integrating GTN model is developed and named 3D M-K-GTN model. By introducing the through-thickness normal stress and friction stress, the original M-K model is extended for adapting to the three-dimensional stress state. Furthermore, the empirical failure criterion is replaced by integrating the GTN model, and thus the limit strain is identified when the void volume fraction within the groove accumulates to a critical value. Besides, the voids nucleation and growth expressions are also re-derived and modified by embedding the friction stress and normal stress. Finally, the comparison between predicted forming limit curves and experimental limit strains of AA6016-T4 sheet indicates that the 3D M-K-GTN model solves the significant overestimation of prediction results under large strain paths, and always provides a high prediction accuracy for each strain path given.