An analytical model for predicting the extrusion force for the torsion extrusion process of metals

Torsion extrusion (TE) method as a severe plastic deformation (SPD) process can effectively refine the microstructures and improve the mechanical properties of materials. Accurate and rapid prediction of the extrusion force in the process of TE is an important problem in industry. This paper proposed an analytical model using upper bound method (UBM) for predicting the extrusion force in the TE process. The kinematically admissible velocity field is established based on a continuous spherical extrusion velocity field coupled with a torsional velocity field constrained in a conical die. The torsional angular velocities along the radial and axial directions are assumed with quadratic and cubic function, respectively, due to the radial and axial nonlinearity of torsional velocity in the deformation zone. In addition, considering its complexity, the shape of the deformation zone is mapped to a rectangular zone. By establishing the torsional velocity field in the mapped zone, the torsional velocity field of the deformation zone is obtained according to the mapping relation. The UBM model is validated by comparing the predicted extrusion force with the simulation results obtained from the finite-element method (FEM). Moreover, the influences of the friction factor, reduction ratio and die angle on the extrusion force were investigated as well.