Finite element analysis of steady-state three-dimensional extrusion of sections through curved dies

Abstract

A finite element analysis is made for steady-state three-dimensional extrusion of non-circular sections such as elliptic and clover-leaf sections through curved dies. In treating the incompressibility, the penalty constraint method, based on the rigid-plastic material model, is used. The initial guess for the initial velocity field is based on that of general upper-bound solutions for extrusion of arbitrarily shaped sections from round billets. Finite element computations are carried out for extrusion of elliptic and clover-leaf sections, but the present analysis can be further applied to general non-circular sections. The work-hardening effect is considered by integrating the effective strain rate along each stream line through interpolation by the least squares method. Experiments are carried out at room temperature and the experimental results are compared with numerical results in flow pattern and strain distribution. It is thus shown that the proposed numerical method is effective for detailed and reliable analysis of steady-state three-dimensional extrusion. © 1989.