Compaction equations: a comparison of the Heckel and Kawakita equations

The background and theoretical and experimental requirements of powder compaction equations have been briefly reviewed. There have been many equations proposed. However, the equations most commonly used today are the Heckel and Kawakita ones, because they alone have claimed to be able to relate to the physical properties of the materials being compacted. There has been much discussion about their relative merits, and in their form, they appear very different. The two equations are discussed in detail and examples are given, and their relative merits are discussed. However, it is first shown for applied pressures, which are low compared to the yield strength of the particles, that they are identical in form. It is then shown mathematically that if a pressure dependent term is used in the Heckel equation then the resulting modified equation is very similar to the Kawakita one and, in fact, becomes identical in form for a particular, likely value of the pressure dependency term. It is concluded that the Kawakita equation is a special case of the more general, modified Heckel equation. It is further concluded that compaction equations need further development to take into account the anisotropy in compacts made by uniaxial compaction. It is shown that the Poisson's ratio of compacts will also increase with applied pressure, and this must be considered.