Derivation of the Extended Kawakita Equation for Estimating the Yield State of Powder in Die

For powder compaction, the Kawakita equation has been used to estimate the powder behavior inside the die. The compression pressure exerted on powders is not homogeneous because of the friction on the die wall. However, the yield pressure and porosity estimated using the Kawakita equation are defined based on the assumption that homogeneous voids and compression pressure are distributed throughout the powder bed. In this study, an extended Kawakita equation was derived by considering the variation in the compression pressure as it corresponds to the distance from the loading punch surface. The yield time section estimated from the extended Kawakita equation was wider than that which was estimated via the classical equation. This result is consistent with the assumptions used to derive the extended Kawakita equation. Furthermore, a comparison of the porosity changes before and after the yield pressure was applied indicate that the direct cause of the yield is the spatial constraints of the powder particles. Equivalent stresses were defined to clarify the critical factor that constitutes the extended Kawakita equation. As a result, “taking into account the die wall friction” was considered to be the critical factor in the extended Kawakita equation. As these findings were theoretically determined by the extended Kawakita equation, a useful model was derived for a better understanding of powder compaction in die.