Slab Method of Analysis for Three Dimensional Forward Extrusion of Squared End Section

Slab method of analysis has been used for solving metal forming problems for a long time. However it has been restricted to plane strain and axisymmetric problems due to limitations in its formulations. In this paper a new formulation has been proposed so that it could be applied to three dimensional problems in metal forming. A parametric slab has been considered in this analysis and the force balance on the slab was carried out to obtain equilibrium equations in terms of these parameters. The parameters in fact are related to the geometry of the final extruded shape, the die and the material flow regime assumed in the formulation. In this way most of the limitations encountered in previous formulations were surpassed. In fact the parametric slab considered in this formulation is a very general element that could be adjusted to any changes made in the process. As an example the forward extrusion of a square cross section was analyzed using the new formulation. The effect of reduction of area, frictional conditions and other process parameters on the extrusion pressure was investigated. The theoretical results obtained in this paper were compared with similar results of previous work from other methods and good agreement was observed. Dies were designed and manufactured based on this analysis for several reductions of area. Tests were done using above dies and the experimental data were found to verify the theoretical results. It was concluded that the new slab method of analysis gave reasonable results for the problem analyzed and that it could be applied to other bulk metal forming processes such as rolling, wire drawing and forging.