An advanced model of designing controlled strain rate dies for axisymmetric extrusion

This paper presents an advanced model for the design of stream-lined axisymmetric extrusion dies based on a prescribed strain rate variation. This is vital to the preparation of the workpieces with mechanical properties that are very sensitive to the strain rate distribution during a manufacturing process. The proposed model, which incorporates Tresca’s yield criterion and velocity field with the die angularity, can give an accurate prediction of the die shape. Influences of the interfacial friction and the ram velocity on the die geometry are also studied. As a verification of the proposed model, an updated Lagrangian formulated, elasto-plastic finite element program was developed to analyze the axisymmetric extrusion process. A clear derivation of the load-correction matrix, which is in dispensable for the surface traction rate equilibrium in the updated Lagrangian formulation, is described for the application of the finite element simulation. A friction-correction matrix based on a constant shear law is used to solve the interfacial friction. From the comparison of the resultant strain rate distribution, it verifies that the advanced model can determine the surface angularity and friction force in the extrusion process.