On the applicability of the P-α and P-λ models to describe the dynamic compaction response of highly heterogeneous powder mixtures

Abstract

The shock consolidation response of recently obtained data for a powder mixture of Ta + Bi2O3 with previously published results for mixtures of Ni + Al, Mo + Si, and Ti + Si are investigated within the context of the P-α and P-λ models to determine the applicability of these models to highly heterogeneous powder mixtures. The mixtures were found to vary significantly in densification path and crush strength (pressures required to reach full density), and no one model offers the best fit for all the mixtures. The static spherical P-α model, which uses mechanical properties of the solid materials to predict the compaction response for the powder mixtures, was found to provide the greatest disagreement with experimental data. By modifying the yield parameter to reflect measured yield properties from quasi-static densification tests, better agreement between the model and experimental data was obtained. For the empirical fitting models, the ability of a model to separate compaction into elastic and plastic components had minimal influence on goodness of fit. Conversely, homogeneity in deformation of the constituent particles was found to promote model agreement, specifically for the Mo + Si and Ti + Si powder mixtures where dynamically recovered microstructures were available for inspection.