The previous theoretical predictions of the compaction of a copper powder medium, based on the assumption that the punch and plug were both a rigid body, did not satisfactorily agree with the experimental results obtained for short initial powder lengths and long plug lengths. This type of compaction amounts to cases when the plug length exceeds the second critical length which will be described below. Shock waves in a powder medium and elastic waves in the elastic punch and plug, schematically shown in space coordinate-time diagrams, suggest that the elastic wave in the plug is the probable cause of the inconsistency between the theoretical and experimental data of the previous investigation. In fact, the diagrams indicate that the shock wave transmitted in the medium across the medium-plug interface exerts an effect on the compaction process when the plug length does not exceed what is termed the first critical length. In cases when the effect of die wall friction is neglected, the mean green density-initial powder length relation of the copper medium is obtained from a theoretical approximation based on energy of the medium for the compaction with the sum of the initial powder length and the plug length being constant. This relation indicates that the effect of elasticity of the plug is large as the plug length becomes large. The second critical plug length at which the effect of elasticity becomes balanced with the effect of die wall friction is established by this relation and by the previously computed density-length relation with the effect of die wall friction taken into account. More specifically, these two relations provide a relation involving the first and second critical-plug lengths. The relation inferred as such agrees qualitatively with the previous experimental data in the examined region of the initial powder length. This qualitative agreement suggests that if the effects of elasticity and die wall friction are considered, a satisfactory theoretical and experimental agreement could be obtained. Therefore, the mean green density-initial powder length relation is computed taking into account both the effects. The computed relation agrees quantitatively with the previous experimental data even for short initial powder lengths and long plug lengths.
Multishock Compactions of Powder Media Influenced by Elastic Waves in Punch and Plug
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Sano, Y., Tokushima, K., and Miyagi, K. (October 1, 1991). "Multishock Compactions of Powder Media Influenced by Elastic Waves in Punch and Plug." ASME. J. Eng. Mater. Technol. October 1991; 113(4): 372–381. https://doi.org/10.1115/1.2904115
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