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.

对于粉末压实，川北方程已用于估计模具内的粉末行为。由于模具壁上的摩擦，施加在粉末上的压缩压力不均匀。然而，使用川北方程估计的屈服压力和孔隙率是基于均匀空隙和压缩压力分布在整个粉末床的假设来定义的。在本研究中，通过考虑压缩压力的变化（对应于距加载冲头表面的距离），推导出扩展的 Kawakita 方程。从扩展 Kawakita 方程估计的屈服时间截面比通过经典方程估计的屈服时间截面更宽。该结果与用于推导扩展 Kawakita 方程的假设一致。此外，通过比较施加屈服压力前后的孔隙率变化表明，屈服压力的直接原因是粉末颗粒的空间限制。定义等效应力是为了阐明构成扩展 Kawakita 方程的关键因素。因此，“考虑模壁摩擦力”被认为是扩展川北方程中的关键因素。由于这些发现在理论上是由扩展的 Kawakita 方程确定的，因此导出了一个有用的模型，以便更好地理解模具中的粉末压实。