GENERAL-FORM SOLUTION OF SHOCK FITTING EQUATION INCLUDING DIE WALL FRICTION FOR THE MULTISHOCK POWDER COMPACTION

In this paper, shock fitting equations including wall friction force f or predicting the one-dimensional compaction process of a powder mediu m caused by punch impact are first derived. The medium is assumed to b e discontinuously compressed only at a shock wave front both when the front propagates toward an assumed rigid plug and when it propagates b ack to an assumed rigid punch. The equations suggest that the effect o f the friction force on the process becomes large as the front propaga tes toward the plug. This friction effect suggests that a continuous c ompression will occur in the medium between the impacted surface and t he front if the effect is large. Next, the general-form solution of th e shock fitting equations is obtained. This solution is compared with the solution by the pseudo-viscosity method without using the assumpti on that the medium is compressed only at the front. Both the solutions agree well for the compaction with a short initial medium length wher e the effect is not remarkable. For the compaction with a long initial medium length where the effect is remarkable, however, the solutions predict different types of the process, especially in its earlier stag e. Explicitly, the former predicts the discontinuous compression only at the front, as is clear from the assumption made, while the latter p redicts not only the discontinuous compaction at the front but also th e continuous compression between the impacted surface and the front du e to the remarkable friction effect. In its later stage, they predict the compression only at the front. Thus, the general-form solution is valid for the compaction with short initial medium lengths, but result s in errors in the earlier stage for long initial medium lengths.