An Analysis Method for the Dynamic Compaction Processes of Powder Media Within a Die

Abstract

A method of analysis for the multishock compaction process of die-contained powder media with a plug at one end and an impacting punch at the other end is presented. In the method assumptions are made that the media are of a simple rigid-plastic type, and compressed only at the fronts of the shock waves passing through, and furthermore the punch and plug are rigid bodies. Based on the assumptions, particle velocities of elements between the punch surface and a shock wave front are the same and equal to the punch velocity, while velocities of elements between the front and the plug surface are equal to a velocity of the plug surface, i.e., zero. Therefore, it is possible to use jump conditions at the front and equations of motion for the punch and medium moving with the same velocity as it, instead of partial differential equations, i.e., conservation equations which were used in other methods. The equations of motion, together with the jump conditions and rigid-plastic constitutive relation equations provide two sets of equations governing the process. It is shown that there exist unique solutions of the equations of motion, and the equations are analyzed for a copper powder medium. Exact solutions obtained are compared with approximate solutions analyzed previously by the von Neumann and Richtmyer method. A fairly good agreement of the solutions by both the methods indicates that the approximate solutions are effective.