Stress gradient within powder en masse during hydrostatic compression

Non-homogeneous density of compressed powder has been known and documented. This phenomenon suggests that the stress inside a powder en masse is not homogeneous during the compaction process. This hypothesized stress distribution inside powder bulk suggests a relationship between the dimension of powder bulk under compaction and the level of internal stress. To elucidate this relationship, stress changes inside a powder bulk during hydrostatic compression were measured using a fundamental mechanical tester, namely, a cubical triaxial tester. We found that the internal stress decreased when the distance from the load-acting surface became larger. For example, along the central line of the sample with 100. kPa of hydrostatic stress, the internal stress decreased 32.2% from 94.7. kPa to 64.2. kPa and down to 55.1. kPa (41.9% decrease), when the distance from the surface increased from the pressured surface to 1.52. cm and to 3.04. cm. To quantify the contribution of distance from the load-acting surface to the decreasing stress, a linear relationship and an exponentially decaying function were tested. It was shown that the exponentially decaying function explains the decreasing stress well. The rationale of the exponential decaying function was discussed with respect to the classical elasticity formulation.