The integration of through-thickness normal stress and friction stress in the M-K model to improve the accuracy of predicted FLCs

Abstract The through-thickness normal stress and the friction stress in the forming process have significant impact on the forming limit curves (FLCs) of sheet metal. In this work, the through-thickness normal stress expression is first established based on the analysis of the stress state and the stress gradient of specimens in the Nakazima test and then introduced into the original M-K (Marciniak-Kuczynski) model. By analyzing the friction condition on the contact surface of the specimen and the punch, the friction stress expression is then set up and considered in the M-K model. On this basis, the original M-K model is modified, and a comparison of the forming limits is performed among our modified M-K model, other M-K models and the experiment results. The conclusion can be drawn from the comparison that the prediction accuracy of the FLCs is significantly improved by our modified M-K model. Moreover, the influence of the material parameters and the model parameters on the FLCs are further investigated.