Non - steady state upper - bound analsiys of non - axisymmetic backward extrusion

Abstract

The prediction of metal flow and final-stage extrusion load in the backward extrusion processes is very important. It provides necessary information and guide lines for the effective design of extrusion dies. It is desirable to develop a method of analysis in order to predict such information more realistically. The present study is concerned with the final stage in backward extrusion of arbitrarily-Shaped tubes in the cross-section. During backward extrusion of artrarily-shaped tubes, the metal flow developed is nonuniform in the cross-section of the billet and in the longitudinal direction. That is, backward extrusion of arbitrarily-shaped tubes is characterized by three-dimensional deformation. For the analysis of backward extrusion of arbitrarily-shaped tubes a kinematically admissible velocity field to incorporate the three-dimensional deformation is proposed. From the proposed velocity field the upper-bound load and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. In computation the deforming region is divided into two elements and the workhardening effect is considered for the total deformation region. The analysis is categorized into the following three parts according to the sectional shape: i) analysis of backward extrusion of internally elliptic-shaped tubes from round billets ii) analysis of backward extrusion of internally arbitrarily-shaped tubes from round billets; for examples, internally trochoidal gear-shaped tubes, involute gear-shaped tubes and rounded rectangular-shaped tubes iii) analysis of backward extrusion of internally circular-shaped tubes from arbitrarily-shaped billets; for examples, regular polygonal-shaped billets and rounded rectangular-shaped billets In order to confirm the validity of the proposed velocity field, experiments have been carried out with annealed AISI-2024 aluminum billets at room temperature for the different geometrical shape...