3D profile modelling and accurate representation of the deforming region in the extrusion process of complex sections using equi-potential lines method

Abstract

The deforming zone in the die determined by the cross-sectional shape of the final product plays a key role in the extrusion process affecting the extrusion pressure and product quality. Therefore, prediction of the optimal profile of the deforming region is the main objective for an effective extrusion process. In this study, using the analogy between the conventional plasticity theorem and electrostatics, the notion of equi-potential lines (EPLs) was applied to accurate representation and 3D design of the deforming region in the extrusion process of a complex section. To implement the analogy in the extrusion, the initial and final shapes were considered, and two different potentials were assigned between the inlet and outlet surfaces. Then, the EPLs were drawn that show the minimum work path between the entry and exit sections. The drawn EPLs were connected to build up a 3D-profile for the deforming region in the extrusion process. In addition, the EPLs were used in accurate representation of the deforming region using high-order polynomial curves. The effectiveness of the proposed method was examined using a complex section (U-shaped) from the literature. Then, the extrusion pressure for different profiles in the deforming region was analyzed numerically and experimentally. Moreover, the obtained polynomial curves were used in the upper bound (UB) solution for prediction of the extrusion pressure. There were reasonable agreements between the analytical, numerical, and experimental results. An acceptable reduction in the extrusion pressure for 3D modelling of the deforming region with the EPLs was reported. It was shown that the EPLs could be used for accurate representation of the deforming region in the extrusion of complex sections.