The process of extrusion through a chamber is analyzed. Kinematically admissible velocity fields are utilized to obtain a lower upper-bound solution for the extrusion stress. Assumptions are as follows: a spherical velocity field for the early stages of direct and indirect extrusion; a radial velocity field at end of stroke; and finally maximum shear stress
between billet and chamber for lower upper bound. When this maximum shear stress is then replaced by a lower friction stress, the solution obtained becomes an approximation for the actual extrusion stress. The cavity phenomena and piping effect are discussed. Conditions for inception of the cavity and development of the pipe are predicted. The inner radius of the pipe is determined. Results are given in mathematical form and plotted over a wide range of conditions. They are compared with Kudo’s  results.
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