Determination of Geometrical Parameters of the Dead Metal Zone and Exit Curvature Profile in the Extrusion Process of Non-Symmetrical Flat Dies

To determine the curvature of the exit profile in the extrusion process of non-symmetrical flat dies, the dead metal zone profile was predicted using the energy minimization method. The dead zone is a natural non-linear die for the process and it is pragmatic to use this non-linear die to estimate the value of the exit profile curvature and the required bearing length for reducing this deviation. The velocity field is calculated based on Hermite cubic spline and some additional assumptions. In non-symmetrical dies the entrance section of the deformation region is not flat. Considering this fact, axial velocity decreases with increasing the distance to die center line which is in agreement with experiment. After determination of the velocity field, the strain rates in different directions are calculated. Subsequently, the required power for the process is estimated using the upper bound method. Since the material tends to consume less energy, to determine the profile of the dead zone, the coefficients of the curve are set so as to minimize the consumed power. Finally, using this curve, the value of the exit profile curvature is estimated. Dead metal zone for different angles of the deformation region at entry and different friction constant coefficients was determined and compared with the results of simulations of the finite element software (ABAQUS v6.9). Additionally, the deviation calculated from theoretical method was verified with the results of the commercially available bulk forming simulation software (Deform-3D v5). This method does not depend on the exit section and is applicable to non-symmetrical dies as well. The analytical results for non-symmetrical T-die are in good agreement with results of the finite element simulations.