(77e) Nonlinear Radial Stress Response during Uniaxial Die Decompression

Bullard, J. W., Vertex Pharmaceuticals
A nonlinear curve is generally observed at a plot of the radial stress versus axial stress during the entire loading/unloading procedure of a uniaxial die compression. At initial stages of unloading, the relationship is generally accepted to be linear. This observation serves as the basis of the argument that the compact exhibits linear elastic behavior during this period, and elastic constants such as Young’s modulus and Poisson’s ratio can be easily calculated. As such, the calculated elastic constants are further assumed to stand for the overall elastic constants of the powder compact. Here we propose, however, that the presumed linear relationship during the initial unloading is instead a transitional moment during which the die wall friction force changes direction. This is observed through analysis of compression in which axial force transmission and the coefficient of friction (CoF) are evaluated continuously during both the loading and unloading phases of compaction. Additionally, the effect of compact thickness on these parameters is studied, and observed to have a significant effect on force transmission but no impact on CoF values. This result supports the assertion that friction forces change direction when the compression cycle transitions from loading to unloading, which provides an alternative framework in which to understand the apparent profile linearity. The phenomenon is observed in materials exhibiting a broad array of mechanical properties. Using this analysis, we propose an alternative approach to determining fundamental elastic constants, in which an assumption of linear elastic strain was made to the overall (instead of a small portion) elastic recovery of a compact during unloading. With this new approach the elastic constants such as Young’s modulus and Poisson’s ratio can be calculated which is different from published data.