An extended mesoscaled M-K model for predicting discrete ultimate strains and evaluating the effect of normal stress on forming limits

Due to the size effect, the formability of metal sheets diminishes and the ultimate strain points exhibit a more discrete distribution. This poses a huge challenge to the process design and manufacture of microparts. This paper presents a modified mesoscopic scale forming limit model based on the M-K model. The model extends the forming limit curve (FLC) into forming limit bands to predict the discrete nature of the ultimate strain. In addition, a method for applying normal stresses to increase the forming limit of thin metal sheets is proposed. The effects of normal stresses on surface roughening and flow stresses in thin metal sheets were evaluated and quantified by uniaxial tensile experiments under normal stresses. The results show that the normal stress suppresses the increase of surface roughness and improves the work hardening rate. The effect of normal stresses on forming limits was obtained using a constructed model. The results show that the predictions of the proposed model are able to include almost all the ultimate strain points. The forming limit bands are more inclusive and safer than the single forming limit curve. In addition, the forming limits of thin plates under normal stresses are significantly increased, which is attributed to the suppression of surface roughening and the increase of strain hardening index. The forming limit bands proposed in this paper provide a more reliable form of forming limit assessment for thin metal plates. The proposed method of applying normal stresses provides a robust and inexpensive process route to address the challenge of poor formability of thin metal sheets.