A constitutive model for compaction of granular media, with account for deformation induced anisotropy

A constitutive model is proposed for the cold compaction of metal powders. It relies on classical concepts for elasto-plastic materials. For cemented carbides, which is the current application of the model, it is shown by experimental data that there develops significant anisotropy during a non-isostatic compaction. The model encompasses anisotropy through a kinematic hardening mechanism. For a certain state of hardening the back stress magnitude depends on the mean stress, such that there is a rotation (around the origin) of the yield surface. The need for a two-dimensional hardening parameter set, the relative density and a measure of the intensity of the anisotropy, is demonstrated. A compactness tensor P that holds the current relative density as det(P) and the directionality of the compaction history is conceived. The flow direction is derivable from a non-associated flow potential, but is more easily represented as the ratio of magnitude of deviatoric plastic increment to magnitude of volumetric plastic increment. The basic assumption of a flow potential is needed only to establish the form of the deviatoric flow component. Various functions of the model are mapped by series expansions from irregularly spaced experimental data in the sense of least-square fits. Copyright © 1999 John Wiley & Sons, Ltd.