The metal flow in the tube extrusion process is an important factor in order to design the process effectively and control the mechanical property of the extruded products.
It is, however, difficult to predict the metal flow in three-dimensional tube extrusion of complicated sections due to the difficulty in geometrical representation of the die surface and in formulating the coressponding velocity field.
The study is categorized into the following two parts depending on product shapes;
(1) Axisymmetric tube extrusion through arbitrarily curved dies.
(2) Three-dimensional tube extrusion of clover, trocoidal gear, ellipse sections as outer die shapes.
Kinematically admissible velocity fields for the forgoing types of tube extrusion are derived in order to give upper-bound solutions.
In the analyses the work material is assumed to be incompressible and the rigid-plastic boundaries are assumed to be flat planes perpendicular to the extrusion axis both at the entrance and exit. In the derivations, the axial velocity component on the intermediate cross-section in the plastically deforming region can be expressed as a general function of the coordinates and this allows a complete three-dimensional distortion of flow rendering more realistic flow patterns. Using the derived velocity field, the corresponding upper-bound extrusion pressure is then obtained by optimizing the pressure with respect to the given process parameters.
The flow patterns as well as the upper-bound extrusion are obtained on the basis of the derived velocity field. The effects of area reduction, product shape complexity, die length and frictional condition are discussed in relation to the extrusion pressure, the distorted grid pattern and distribution of the final effective strain on the cross-section of the extruded billet. In the computation three product shapes such as clover, ellipse and trocoidal gear are chosen for extruded sections.
Experiments are carried out for alluminum 2024 at room temperature. In order to visualize the plastic flow the grid marking technique is employed. The predictions are found to be in good agreement with the experimental observation both in extrusion pressure and flow pattern.
