A Theory on the Mechanics of Axisymmetric Extrusion through Conical Dies

Abstract

For axisymmetric extrusion through conical dies, an admissible velocity field without discontinuities was obtained by superposition of basic flow patterns. Based on this velocity field, the upper bound to the average forming pressure and the detailed mechanics were calculated for the extrusion of a rod with a semi-cone angle of 45° and a reduction of 75 per cent in area. Three different friction conditions along the die were considered and their influence on the deformation characteristics was discussed. Flow lines, velocity components, grid distortion, strain-rate components, effective strain rate, effective strain, and stress components were plotted. A comparison of the present results with those obtained experimentally (visioplasticity) shows good agreement.

Discussion: “Analysis of Tube Extrusion” (Mehta, H. S., Shabaik, A. H., and Kobayashi, Shiro, 1970, ASME J. Eng. Ind., 92, pp. 403–410)

“…Thus comparisons were made not only for the velocity components but also for grid-distortion, strain, strain-rate, and stresses. The reason that the theoretical grid-distortions were compared with the observed grid-distortions is to avoid possible errors involved in the 2 College of Engineering, University of Kentucky, Lexington, Ky.…”

Determining the Drawing Force in a Wire Drawing Process Considering an Arbitrary Hardening Law

“…The first solution of this class has been presented in [16]. Other solutions have been derived in [17][18][19]. A distinguishing feature of the solution [17] is that the kinematically admissible velocity field is continuous.…”

“…Other solutions have been derived in [17][18][19]. A distinguishing feature of the solution [17] is that the kinematically admissible velocity field is continuous. Paper [18] has focused on the formation of a rigid region near the friction surface.…”