Calculation of forming limit diagrams using Hill's 1993 yield criterion

Based on the analysis proposed by Jones and Gillis (JG), forming limit diagrams (FLDs) are calculated from idealization of sheet deformation into three stages: (I) homogeneous deformation up to maximum load, (II) deformation localization under constant load, and (III) local necking with precipitous drop in load. In the calculation, Hill's 1993 yield criterion is used. Using this yield criterion and the JG model, effects of materials parameters such as ratio of uniaxial to equi-biaxial yield stress, strain hardening, strain rate sensitivity and plastic anisotropy on the shape and level of forming limit curves are studied. In addition, the capability of the JG model to predict limit strains is demonstrated through comparison of calculated results with experimental data for the interstitial free (IF) steel and aluminum alloys 3003-O and 8014-O. It is concluded that although the model predicts the effect of material parameters reasonably well, the calculated limit strains are higher than the experimental FLDs. The observed discrepancy may be attributed to the assumption of planar isotropy, cavitation and the nature of texture present in the sheets. Due to the overestimation of the predictions, care must be taken when using this approach for industrial purposes.