Analysis of the bending effects and the biaxial pre-straining in sheet metal stretch forming processes for the determination of the forming limits

Abstract

The most common failure criterion in sheet metal forming operations is the forming limit diagram (FLD). Typically, the FLD is evaluated with the Nakajima test, which is a stretch forming-based test that allows the analysis of stretching under different stress conditions. The results of the Nakajima tests are considered ideally achieved under linear strain path deformation. However, due to the hemispherical form of the punch, the induced strain path starts in biaxial condition and switches to a linear path after the first contact between punch and specimen. In addition, the strain distribution is evaluated on the outer surface of the specimen. Consequently, the results are affected by a non-linear strain path and a bending component due to the sheet thickness and punch diameter. These effects have a consequence on the FLD, and thus it is not directly comparable with the ideal FLD that is analytically evaluated since the analytical models in the literature do not consider the process effects like bending and the biaxial pre-straining. In this paper, a study of biaxial pre-straining and bending effects is observed for different stress conditions and materials. The investigation of the bending will be considered under the experimental and numerical aspect. Nakajima tests are conducted with different punch diameters to discover the effects of different material thickness to punch radius ratios. The results are also compared with the outcomes of a numerical model, used for the analysis of the strains on the outer, middle and inner layers. The biaxial pre-stretching is analysed by comparing the outcomes of the FLD achieved by the Nakajima punch with the results of the Marciniak test. In this paper, an efficient method based on the correlation coefficient for the evaluation of pre-straining is presented. The biaxial pre-stretching will be compared to the strain paths and the tendencies will be analyzed. Finally, considerations about the phenomenology of the effects in dependency of the material classes are given.