accuracy improvement of upper bound analysis of bimetallic rods extrusion using a new velocity field

in this paper, the direct extrusion process of bimetallic rods in conical dies is analyzed by an improved upper bound method. the deformation zone is subdivided into six smaller zones and by considering a non-spherical entrance boundary to the deformation zone, a velocity field is presented which is different from velocity fields employed in previous studies. the total power consumption of the process including internal, shear and frictional powers is obtained using this velocity field, and then the forming force is calculated by employing the upper bound theory. the superior accuracy of the proposed analysis is demonstrated by comparing the computed force with available experimental data and results of an upper bound analysis in the literature. finally, the developed model is employed to study the effect of some process parameters on the forming load. i t is observed that there is an optimal die angle that minimizes the extrusion force. the value of this optimum angle increases with friction coefficient.