Sheet metal forming process is widely used in industries due to its various advantages. With the increasing need from industries, there have been remarkable advances in the sheet metal forming analysis by the finite element method. In order to save the time and the effort in the product and process design, the finite element approach is indispensable for accurate sheet metal forming analysis. The computational efficiency becomes the important issue when the lead time should be reduced by making the discrepancy between the analysis and the reality as slight as possible. Finite element analysis of the sheet metal forming problem usually adopts one of three analysis methods based on the membrane, shell and continuum element. The membrane element has been widely used in finite element analysis because of its computational efficiency and better convergence than the shell or continuum element. The membrane element, however, does not consider the bending effect inherently and has to tolerate inaccuracy in the bending dominant problem. To overcome the inaccuracy, a modified membrane element was proposed, which was fortified with the advantage of the shell element by considering the bending effect. The plastic dissipation term was decomposed into the two terms: the term due to the mean stretching throughout the thickness; and the term due to the bending deformation over the thickness. In this paper, by this idea a modified membrane finite element formulation considering bending effect is derived for sheet metal forming analysis of the rigid plastic materials with planar anisotropy obeying Hill's quadratic yield criterion in evaluating the membrane and bending energy term.
In order to successfully simulate sheet metal forming of planar anisotropic materials, there needs a technique to deal with the blank holding force since the thickness distribution becomes more irregular in the flange region than that for isotropic or normal anisotropic materials. The blank holding force is a very important process variable to have an effect on the deformed shape of a product by controlling the material inflow. In real sheet metal forming, the blank holding force does not act on the whole region of the flange, but on the part where the contact occurs between the sheet metal and the die. Since it depends on the thickness of the sheet metal in the flange region, the blank holding force should be correctly calculated from the thickness variation. This paper proposes a new scheme to effectively apply the blank holding force to the proper flange region in order to predict more accurate deformed shapes in deep drawing processes of sheet metal.
Cylindrical cup, square cup and rectangular cup drawing processes are simulated by the implemented code for demonstration its validity. In the simulation of cylindrical cup drawing process, the earing phenomenon is exaggerated due to the unrealistic distribution of the blank holding force. This exaggerated simulation of the earing phenomenon can be controlled reasonably by the new scheme proposed where the blank holding force varies with the thickness change. The thickness distribution , the punch load and the flange shape contour are compared with the experimental results. The results from the analysis proposed in this paper are in better agreement with the experimental results than the results from the analysis of normal anisotropic material. In the simulation of square cup and rectangular cup drawing processes, the punch load obtained from the analysis is in good agreement with the experimental result. And to investigate the effect of the rolling direction in the initial blank, the simulations of the rectangular cup drawing are carried out varying the rolling direction in the initial blank. Finally, the effect of the coefficients introduced in the evaluation of the compressive stress due to the blank holding force is investigated. The proper values for the coefficients in rectangular cup drawing process are suggested. Consequently, it is proved that the developed algorithm can predict accurate punch load and deformed shape in deep drawing processes.
