On the formability of sheet metals: Part A: Prediction of forming limits based on Hill's 1993 yield criterion. Part B: Effect of drawbeads on sheet formability

The first part of this dissertation investigates the application of this yield criterion in the forming limit prediction. The analysis is based on the M-K approach in conjunction with Hill's 1993 yield criterion. Since the effective strain is not derivable due to the non-homogeneous form of the yield function, it is calculated numerically based on the flow theory of plasticity, where a perturbation procedure is proposed to determine the stress and strain ratios. The analysis shows that the forming limit prediction agrees well with experimental data for both steel and aluminum due to the flexibility of the yield criterion. To further investigate the applicability of this yield criterion, the bifurcation analysis is pursued based on the deformation theory of plasticity. A general form for the instantaneous moduli of the rate form of the constitutive equation is derived and strain rate sensitivity is introduced in the analysis. It is found that the bifurcation analysis predicts forming limits lower than those of the M-K analysis, which makes the bifurcation analysis basically applicable for aluminum.; Real time control of the drawbead restraining force by active drawbeads can compensate the external disturbances to the forming process and enhance the formability of panels. However, industrial application of the active drawbead requires a thorough understanding of the effect of drawbeads on deformation characteristics of sheet metals. The finite element method is, therefore, used to simulate the deformation pattern near the drawbead end. Simulation based on a single drawbead model shows that a large drawbead end radius improves the deformation severity near the drawbead end.; To investigate the effect of different drawbead penetration trajectories on sheet formability, a finite element model of full panel forming is created using LS-Ingrid. The simulation based on LS-Dyna3d finite element package illustrates that a trajectory with early penetration and early retraction of drawbeads increases sheet formability. However, the strain path is hardly affected by the drawbead trajectory. These observations by FEA are verified by tests conducted by drawing full panels with an experimental die. Comparison of predicted with experimental data shows that predicted strains in the part are lower than measured strains in the critical zone which is prone to necking. This suggests that FEA results should be compared with the lowest forming limit curve since one shell element in the sheet thickness direction cannot simulate localized necking. (Abstract shortened by UMI.)...