Analytical modeling of the extrusion process using the electrostatics concept

• Analogy between the metal forming process and electrostatics is investigated.
• Extrusion process is modeled based on the electrostatic field.
• Electrostatic method accurately predicts the material flow in the deforming region.
• There is no mesh deformation in the electrostatic modeling of extrusion process.
• Electrostatic modeling of the extrusion process is fast and accurate.

Analytical and numerical modeling of metal forming processes has been studied by many researchers during the past decades. So far, several methods have been introduced to model material behavior during forming processes. In this research, the analogy between the classical plasticity theorem and electrostatic field line formation has been investigated for the first time. It is shown that the velocity potential function of movement in the plasticity and the charge-free electrostatic field are both in the form of Laplace’s relation. The aim of the current research is to model the metal forming processes using the equations governing the electrostatic fields. To demonstrate the effectiveness of the proposed method, the extrusion process is used as the benchmark. A three-dimensional CAD model of the deformation region is constructed and two different voltages are applied to the entry and exit sections based on the geometrical and extrusion parameters. Then, the Laplace’s relation is solved numerically and the relative extrusion pressure, particle flow path in the deforming region, and maximum plastic strain are calculated.To verify the proposed method, different sections are modeled and the results are compared with those in the literature. Finally, some experimental tests are conducted for the extrusion process of the round billets to complex sections. Significant agreement has been observed between the experimental results and the analytical ones. It is shown that the extrusion process could be modeled easily and accurately using the mathematical formalism of the electrostatics.