Rigid-plastic boundaries approach to the analysis of arbitrary profile dies in axisymmetric extrusion

A new theoretical model to analyze arbitrary profiles of extrusion dies is proposed in this paper. In this model, generalized rigid-plastic boundaries with optional variables are used to minimize the power by the upper-bound method. To satisfy the velocity boundary conditions at the entrance and exit, the streamline function is designed in the normal form of r(η, z), which satisfies the flow conditions and the rigid-plastic boundaries. Four sets of profile dies (cosine, elliptic, hyperbolic, and conic) are represented with different slopes at the entrance and exit in order to illustrate this method. Experiments were conducted in order to compare the results with those of the theoretical model. It was found that the predicted load and flow patterns were in agreement with the experimental observation and the results from the literature.