A New Formulation of Generalized Velocity Field for Axisymmetric Forward Extrusion Through Arbitrarily Curved Dies

Abstract

A new analytic method is proposd for estimating the extrusion pressure, the final effective strain of the extruded billet, and the grid distortion patterns in axisymmetric forward extrusion through arbitrarily curved dies. A generalized kinematically admissible velocity field is derived to formulate an upper-bound solution. The corresponding upper-bound extrusion pressure is then obtained by optimizing the process parameters. The effects of area reduction, frictional condition, die length, and the die profile are discussed in relation to the extrusion pressure, the distorted grid pattern, and distribution of the final effective strain on the cross-section of the extruded billet. In the computation a biquadratic polynomial is chosen for the die profile. The work-hardening effect is incorporated in the formulation. Experiments are carried out for AISI 4140 steel billets at room temperature. The theoretical predictions both in the extrusion load and deformed configuration are in excellent agreement with the experimental results and the results computed by the finite element method.