Analysis of plate drawing processes by the upper bound method using theoretical work-hardening materials

The present paper analyses the plate drawing processes carried out in converging dies using theoretical work-hardening materials. The analysis has been carried out by the upper bound method (UBM), modelling the plastic deformation zone by triangular rigid zones (TRZ) and considering that the processes occur under plane strain and partial friction conditions. Explicit expressions for the calculation of the necessary power and the non-dimensional total energy to carry out the process using theoretical work-hardening materials have been established. The results have been compared with those obtained using rigid-perfectly plastic materials. In spite of the fact that the energy involved in the process using a work-hardening material is higher than when a rigid-perfectly plastic material is used, the number of possible sets of variables (die geometries, cross-sectional area reductions and partial friction coefficients) increases, since the stability limit of the process increases as well.