New Die-Compaction Equations for Powders as a Result of Known Equations Correction: Part 1–Review and Analysis of Various Die-Compaction Equations

Abstract

The well-known equations for the powder compaction process (PCP) in a rigid die published from the beginning of the last century until today were considered in this review. Most of the considered equations are converted into the dependences of densification pressure on the powder’s relative density. The equations were analyzed and their ability to describe PCP was assessed by defining the coefficient of determination when approximating experimental data on the compaction of various powders. It was shown that most of the equations contain two constants the values of which are determined by fitting the mathematical dependence to the experimental curve. Such equations are able to describe PCP with high accuracy for the compaction of powders up to a relative density of 0.9–0.95. It was also shown that different equations can describe PCP in the density range from the initial density to 0.9 with the same high accuracy, but when the process of compaction is extrapolated to higher values of density, the curves diverge. This indicates the importance of equations that can unambiguously describe PCP to a relative density equal to or close to 1.0. For an adequate description of PCP for relative density greater than 0.95, equations containing three or four constants have proven useful.

New Die-Compaction Equations for Powders as a Result of Known Equations Correction: Part 2—Modernization of M Yu Balshin’s Equations

“…Therefore, the contact pressure p k increases during compaction. To take into account the strengthening of particles during PCP, M. Balshin refined Equation (1) and wrote it as:…”

“…Let us show this with examples of approximation with Equation ( 9) of the experimental data on the compaction of various powders. To begin, of interest is the ability of Equation ( 9) to describe the compaction process of iron, copper, and nickel powders from [5][6][7], respectively, which we used in article [1], as well as nickel powder, an equivolume mixture of nickel powder with oxide aluminum, and powder of Al 6 and 7), and they are shown in Table 1. The approximation results of the compaction process of these powders are shown in Figure 2, and the values of constant parameters and coefficient R 2 are listed in Table 2.…”

“…(a) (b) Therefore, Figure 6 and expression (17) indicate that the strengthening coefficient, according to Equation ( 16), is able to describe a wide variety of PCP in a rigid die. In this regard, we will perform an approximation by Equation ( 15) of the unique experimental data on the densification of iron powders presented in Table 4 and in Table 5 of Part 1 [1]. The results of the performed approximation are presented in Figure 7, and the values of the constant parameters are listed in Table 6.…”

“…Hence, it is appropriate to recall the J. Secondi equation, which was considered in Part 1 [1] and describes cases of PCP in a rigid die when it is impossible to achieve the density of a compact material. In Part 1 [1], an approximation by the Secondi Equation ( 18) was performed for three powders from [12] (FeKH3, FeKH6, and FeKH9), and a high approximation accuracy for the experimental PCP was shown as well (see Table 6 in [1]).…”

“…In Part 1 of this article [1], the frequently used equations for describing PCP in a rigid die are considered, analyzed, and, in some cases, refined. They were proposed mainly in the form of mathematical functions for an adequate description of PCP as well as in the form of semi-empirical equations.…”