Finite Element Modelling of Materials under an Axisymmetric Forward Bar Extrusion; Part I: Flow Formulation

Abstract

The current research paper, dealing with the application of finite element (FE) technique to simulationof bulk forming processes, consists of a series of two parts. An Eulerian finite element flow formulation byassuming that materials under deformation behave identically to a viscous incompressible, macroscopicallyhomogeneous and isotropic non-Newtonian fluid has been adopted and presented in the first part of paper. Tomodel the viscoplastic behavior of a material under extrusion process with isothermal condition, the Binghamûsmodel has been chosen to describe the constitutive relation of the material. In the present work, only anaxisymmetric case is considered and 2-D solid finite elements are employed to simulate a forward bar extrusion.The boundary friction between the workpiece and tooling parts; i.e., punch, container and die does not take intoconsideration in the current formulation. In a complete forward bar extrusion process, quality products areusually produced in a fairly steady state as the material flows through the die. To take advantage of investigatingthe steady state forming part, an Eulerian description has to be employed which sets the coordinate axes fixedin space as a material particle passes through. With this manner, it can also help to reduce the demand of greatlynumerical simulation; e.g. re-meshing throughout the process would be inevitable.