Multishock Compactions of a Die-Contained Copper Powder Medium Analyzed by Improved Theory

Abstract

In the present paper, the multishock compaction process of a die-contained copper powder medium supported by an elastic plug at one end and impacted by an elastic punch at the other end, is analyzed by means of an improved theory having the effect of elasticity of the punch and plug. The compactions computed first have a constant sum of lengths of the medium and plug S0*=110, a constant ratio of punch mass to powder mass filled in the die M*=20, and an initial punch velocity ν0=50m/s. The computations of the compactions for the medium with very short lengths and the plug with long lengths confirm the existence of the medium length Scr1* corresponding to the first critical plug-length found in the previous study, and support the compaction process and the final mean density ρmean*-initial medium length S* relation of the medium shorter than the length Scr1* which were inferred in the study. Furthermore, the effect of elastic waves in the punch and plug on the process of the medium longer than Scr1* are examined. There are one common factor and one significant different factor in the processes. Explicitly, the waves in the plug exert different influence on compaction processes of the medium with different lengths, whereas the waves in the punch have similar influence on the processes. The elastic waves in the plug and die wall friction cause the medium length Scr2* corresponding to the second critical plug-length inferred in the previous study. Moreover, the waves in the plug make the form of the computed relation curve more complicated than the inferred one. The computed curve has the lengths Scr3* and Scr4* at which the density has an extreme value, respectively. Approximate similarity conditions for the compactions with various values of S0* are given by two fixed parameters M* and ν0 in region S*<Scr1*, three fixed parameters S*/S0*, M*, and ν0 in region from Scr1* to small S* where the wall friction effect can be neglected, and three fixed parameters S*, M*, and ν0 in region S*>(1/2)S0*. The computed ρmean*–S* and ρmean*–S*/S0* relations support these conditions. Furthermore, the computations of the compactions reveal that the waves in the punch, medium, and plug behave in similar manner during the processes, though they have different strengths.