Modelling dynamic and irreversible powder compaction
Résumé
A multiphase hyperbolic model for dynamic and irreversible powder compaction
is built. Four important points have to be addressed in this case. The first one is
related to the irreversible character of powder compaction. When a granular media is
subjected to a loading–unloading cycle, the final volume is lower than the initial one.
To deal with this hysteresis phenomenon, a multiphase model with relaxation is built.
During loading, mechanical equilibrium is assumed corresponding to stiff mechanical
relaxation, while during unloading non-equilibrium mechanical transformation is
assumed. Consequently, the sound speed of the limit models are very different during
loading and unloading. These differences in acoustic properties are responsible for
irreversibility in the compaction process. The second point is related to dynamic
effects, where pressure and shock waves play an important role. Wave dynamics is
guaranteed by the hyperbolic character of the equations. Phase compressibility as
well as configuration energy are taken into account. The third point is related to
multi-dimensional situations that involve material interfaces. Indeed, most processes
with powder compaction entail
free surfaces.
Consequently, the model should be able
to solve interfaces separating pure fluids and granular mixtures. Finally, the fourth
point is related to gas permeation that may play an important role in some specific
powder compaction situations. This poses the difficult question of multiple-velocity
description. These four points are considered in a unique model fitting the frame
of multiphase theory of diffuse interfaces . The ability of the model to deal with these
various effects is validated on basic situations, where each phenomenon is considered
separately. Except for the material EOS (hydrodynamic and granular pressures and
energies), which are determined on the basis of separate experiments found in the
literature, the model is free of adjustable parameter.