Abstract
In this paper, an upper bound approach is used to analyze the process of backward tube extrusion through arbitrarily curved punches. Based on the assumptions of proportional angles and proportional distances from the mandrel surface in the deformation zone, two kinematically admissible velocity fields are proposed and those are used in upper bound solution. By using the developed upper bound solution, optimum punch lengths which minimize the extrusion forces are determined for a streamlined punch shape and also for a conical punch. The corresponding results are also determined by using a finite element code, ABAQUS, and by doing some experiments and compared with the analytical results. This comparisons show a good agreement.
Highlights
In backward extrusion, there is no relative movement between the initial billet and the container and it is characterized by the absence of friction between the initial billet surface and the container
Among various analytical and numerical approximate methods of solution, the upper bound technique and the finite element method have been widely used for the analysis of the extrusion process
2.1 Velocity field in the deformation zone Two assumptions that were used by Gordon et al [18] for forward rod extrusion are used here for backward tube extrusion process
Summary
There is no relative movement between the initial billet and the container and it is characterized by the absence of friction between the initial billet surface and the container. Avitzur [1,2,3] developed models for forward rod extrusion through conical dies using the upper bound approach. Yang et al [9] as well as Yang and Han [10] developed upper bound models for forward rod extrusion with streamlined dies. An upper bound solution for strain hardening materials has been developed by Yang et al for tube extrusion through streamlined dies [11]. They extended the same analysis for three-dimensional forward extrusion of arbitrarily shaped tubes [12]. Ebrahimi et al [17] proposed a kinematically admissible velocity field for forward tube extrusion through conical dies. The investigation is performed using the finite element code, ABAQUS and by doing some experiments
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