Analysis of extrusion of generalized sections considering three-dimensional plastic deformation

Abstract

The metal flow in the extrusion process is an important factor in order to design the process effectively and control the mechanical property of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of complicated sections due to the difficulty in geometrical representation of the die surface and in formulating the corresponding velocity field. Despite of increasing demand and application of three-dimensional extrusion of various sections through continuous dies, so far there has been no systematic and general analysis to predict the plastic flow properly. For effective die design, an efficient design method and the related method of theoretical analysis are required for the extrusion of complicated sections. The study is categorized into the following three parts depending on product shapes; (1) Axisymmetric extrusion through arbitrarily curved dies (2) Three-dimensional extrusion of clover sections from round billets (3) Three-dimensional extrusion of arbitrarily-shaped sections from arbitrarily shaped billets Kinematically admissible velocity fields for the foregoing types of extrusion are derived in order to give upper-bound solutions. In the analyses the work material is assumed to be incompressible and the rigid-plastic boundaries are assumed to be flat planes perpendicular to the extrusion axis both at the entrance and exit. In the derivations, the axial velocity component on the intermediate section in the plastically deforming region can be expressed as a general function of the coordinates and this allows a complete three-dimensional distortion or flow rendering more realistic flow patterns. Using the derived velocity field, the corresponding upper-bound extrusion pressure is then obtained by optimizing the pressure with respect to the process parameters. In generalized three-dimesional extrusion of sections through continuous dies, a new method of die surface representation using a blending function...