Influence of the die arc on formability in cylindrical cup-drawing

The incremental updated Lagrangian elasto-plastic finite-element method was applied in this study towards analyzing cylindrical cup-drawing under axisymmetric conditions. The extended r-minimum technique was employed such that each incremental step size is determined by not only the yielding of an element gaussian point but also by the change of the boundary conditions along the tool-metal interface. The Coulomb friction law was also adopted in calculating the influence of friction coefficients on the drawing process. A low-carbon steel (BA-CQ 2) was used as the test material in the experiments. Also, five various die-arc radii were designed, of value four-times to twelve-times the blank thickness, each die being used to draw the blank in the experiments. Results obtained for the punch-load in drawing, the material thickness variation after drawing and the limit drawing ratio (LDR) were compared both with the results of experiment and with the results of FEM analysis: the experimental and FEM results both confirmed that a greater LDR and a generally greater thickness would be obtained as a larger die-arc radius is used in the die-arc portion. These results have not only verified the reliability and accuracy of the computer simulation, but also could be used as references in the designing and manufacturing of dies for industrial applications.