Application of equi-potential lines method for accurate definition of the deforming zone in the upper-bound analysis of forward extrusion problems

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Prediction of the optimal pressure is one of the objectives in the die design for the extrusion process. In this study, the concept of Equi-Potential Lines (EPLs) was applied for an accurate definition of the deforming zone in the upper-bound solution of the extrusion process. To implement the concept for the extrusion process, the initial and final shapes were considered and two different potentials were assigned to these. Then, the EPLs were drawn between the two shapes while minimizing the work path from the initial billet to the desired final shape. Bilinear, cubic Bezier, and polynomial curves were used for the definition of the deforming zone. It was shown that the coefficients of cubic Bezier curve could be replaced by the values obtained from the EPLs method. Moreover, accurate 3D streamlines representing material flow path in the deforming zone were obtained from the present method. Finally, forming pressures in the extrusion process were computed using the proposed geometry. To show the effectiveness of the proposed method, the estimated values were compared with experimental results. It was shown that the proposed method had a remarkable agreement with the experimental results.