A new three-dimensional solution for the extrusions of sections with larger dimensions than the initial billet

A new analysis for the three-dimensional solution for the extrusion of sections with larger dimensions than the initial billet or container is presented in this paper. A generalized kinematically admissible velocity field was formulated using the upper bound theorem. The problem tackled in this paper is a practical one encountered in the extrusion industry where for the production of sections whose dimensions are larger than the container or billet diameter there exist some difficulties and sometime it is impossible to produce such products. The solution to this problem was suggested in a new design for the extrusion die which was done using the upper bound analysis. In this design unlike flat-faced dies the material has to flow over two kinds of surfaces namely converging and diverging surfaces, the combination of which causes the material flow in a smooth manner and with the correct speed so that the required final shape would be achieved. For such geometries kinematically admissible velocity fields were obtained. Using this new formulation, extrusion of shapes such as square and rectangle were analyzed. Influence of the process parameters such as friction, extrusion ratio and aspect ratio on the extrusion load was investigated and the optimum die length was obtained. Finite element analysis for the same problem was also carried out and the comparison of the results showed good agreement. The finite element simulation was especially used to assist the theoretical analysis with regards to the material flow and filling of the die cavity. Based on the analytical results, extrusion dies for the rectangular sections were designed and manufactured and experiments were carried out. The results of the tests showed that the dies performed very well and complete filling of the die cavity and a successful extruded profile was observed.