Application of the Equi-Potential Lines Method in Upper Bound Estimation of the Extrusion Pressure

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Forming pressure plays a key role in extrusion processand widely affects product quality. Therefore, prediction of the optimal pressure is the main objective for effective extrusion process. In this study, the notion of Equi-Potential Lines (EPLs) was applied to pressure estimation in extrusion process for the first time. To implement analogy in the extrusion, the initial billet and square die were considered and two different potentials were assigned to them, and then EPLs were drawn between two shapes that show the minimum work path between the entry and exit cross sections. The drawn EPLs were connected to each other to buildup a 3D-die. In the following, cubic polynomial curve was fitted between the initial and final shapes in the designed die. The constructed curve was the accurate assumption for deformation zone in the extrusion that was later used in a written code and upper bound formulation for pressure estimation. Effectiveness of the proposed method was examined via theory and experiment. From the results, there was noticeable agreement between the theory and experiment. As a result, application of the EPLs methodin upper bound formulation can lead to accurate results from theory.