New Die-Compaction Equations for Powders as a Result of Known Equations Correction—Part 3: Modernization of Plasticity Equations for a Porous Body

Equations of plasticity of a porous body proposed by different authors and obtained under the condition that the yield surface of a porous body has the shape of an ellipsoid of revolution are considered in this paper. Such equations have two independent parameters which are the functions of relative density. Various theoretical dependences of these parameters on the relative density and, as a result, various equations for describing the die-compaction of powders are presented. It is shown that the correction of two density-dependent parameters, taking into account the initial density, makes it possible to significantly increase the accuracy of approximation of experimental data on the powder compaction process (PCP) of various powders. Among the considered “continuum” equations of powder die-compaction, the PCP to a density of 0.95 is the most accurately described by the equation in which the corrected Skorokhod’s theoretical density functions are used and which contains one constant as a result. Another equation which contains four constants allows one to accurately (R2 > 0.9990–0.9999) describe the PCP to a density of >0.95. This equation is obtained by replacing one of two independent parameters in the traditional continuum equation with the lateral pressure coefficient followed by substituting, instead of those parameters, their dependencies on the density in the form of power function. The adequacy of the PCP description by this equation was verified by approximating experimental data on the die-compaction of iron powders to a relative density greater than 0.95, as well as highly plastic powders with a final density of ~1.0.