Prediction of Forming Limit Diagrams in Sheet Metals Using Different Yield Criteria

Abstract

Based on the analysis proposed by Jones and Gillis (JG), forming limit diagrams (FLDs) are calculated from idealization of the sheet deformation into three stages: (I) homogenous deformation up to maximum load, (II) deformation localization under constant load, and (III) local necking with a precipitous drop in load. A constant cross-head speed is assumed in the deformation program for the first time. This means that the logarithmic strain rate varies during deformation, while in all previous works, the strain rate is assumed to be constant. In the calculation, three yield criteria including Hill’s 1948 quadratic criterion, Hill’s 1979 nonquadratic criterion, and Hosford’s 1979 criterion are used. Using these yield criteria and the JG model, the effects of material parameters such as strain hardening, strain-rate sensitivity, and plastic anisotropy on the shape and level of the forming limit curves are studied. In addition, the capability of the JG model to predict the limit strains is demonstrated through comparison of calculated results with experimental data for interstitial-free (IF) steel and aluminum alloys 2036-T4, 3003-O, 5052-O, and 8014-O. It is observed that while the model predicts the FLDs of 2036-T4 and 5052-O more closely, it overestimates the forming limit strains for IF steel, 3003-O, and 8014-O aluminum alloys. It is concluded that the accuracy of the prediction depends on the measured mechanical properties of the material, the applied yield criterion, and the method of strain measurement, which determines how the FLDs are passed through different points. For those cases in which the predicted FLD is above the experimental one, care must be taken not to use the models for industrial purposes.