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 for predicting the one-dimensional compaction process of a powder medium caused by punch impact are first derived. The medium is assumed to be discontinuously compressed only at a shock wave front both when the front propagates toward an assumed rigid plug and when it propagates back to an assumed rigid punch. The equations suggest that the effect of the friction force on the process becomes large as the front propagates toward the plug. This friction effect suggests that a continuous compression will occur in the medium between the impacted surface and the front if the effect is large. Next, the general-form solution of the shock fitting equations is obtained. This solution is compared with the solution by the pseudo-viscosity method without using the assumption that the medium is compressed only at the front. Both the solutions agree well for the compaction with a short initial medium length where 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 stage. Explicitly, the former predicts the discontinuous compression only at the front, as is clear from the assumption made, while the latter predicts not only the discontinuous compaction at the front but also the continuous compression between the impacted surface and the front due 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 results in errors in the earlier stage for long initial medium lengths.