Some semiempirical analytical techniques have been developed for computer-aided design of extrusion dies. However, these techniques are approximate and could be vastly improved by developing FEM-based computer programs for metal-flow simulation.
A scientific design of the extrusion process could use FEM to establish the following variables [52]:
Optimum number of shaped orifices in the die, e.g., in aluminum extrusion several sections are often extruded simultaneously
Location of the orifices relative to the billet axis for uniform flow through each orifice
Orientation of the orifices
Modification of the shape of the orifices to correct for thermal shrinkage and die deflection under load
Determination of die bearing lengths for balancing metal flow to avoid the twisting and bending of the extrusion emerging from each orifice
Determination of the extrusion load: quite difficult since the extruded sections are usually nonsymmetrical, resulting in a complex 3D metal flow in the deformation zone
A small-strain 2-D (axis-symmetric) elastic-plastic finite-element analysis was used to study this process. The material (commercially-pure aluminum) was assumed to be extruded slowly and under isothermal conditions, with the yield stress depending only upon strain.
In Fig. 1, metal flow pattern was simulated with the FEM, during which beta-stiffness friction model was used, with a value of friction factor m = 0.7 employed to correspond with unlubricated contact between the billet and the container and punch.
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