=HECK RW61

Density-Pressure Relationships in Powder Compaction R. W. Heckel A method is described whereby the relationship of both the "at-pressure" powder compact density and the "zero-pressure" compact density to the applied pressure may be obtained from continuous measurements of punch movement during a single compaction operation. The rate of density increase with applied pressure for the metal powders is found to be proportional to the volume fraction of pores for pressures exceeding a lower limit which varies from 15,000 to 30,000 psi, depending on the powder.

THE compaction of powdered materials is carried

out primarily to increase the density of the material. If the ultimate goal of the over-all process is the attainment of minimum porosity, compaction is responsible for most of the densification. For example, loose powdered metals have porosities of about 65 to 75 pct. Axial loading in a die or hydrostatic pressure may effectively reduce the porosity of most powders to 20 pct or lower with pressures of 50,000 psi and greater. The relationship between the density of a powder compact and the pressure needed to achieve that density is most commonly obtained by pressing several compacts, each at a different pressure. Measurement of the densities of the individual compacts when they are removed from the die then provides the density-pressure relationship. However, this method suffers from several disadvantages. Because a large number of compacts and pressing operations are required, it is inherently slow. Furthermore, since density measurements are made R. W. HECKEL, Junior Member AIME, Is Research Metallurgist, Engineering Reasearch laboratory, E. I. du Pont de Nemours & Co., Wilmington, Del. Manuscript submitted September 12, 1960. IMD

TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

I

after the specimens are removed from the die, data obtained refer only to pressures greater than those necessary to form a coherent compact. The third disadvantage is the inability of this method to provide information about the compact density at the applied pressure in the die. Because the determination of density-pressure relationships has been a slow, tedious process, investigators have sought to express the compaction behavior of powders by other means. The general terms "compactability" and "compressibility" have been used to rank powders qualitatively according to their compaction characteristics. To restore a quantitative nature to the subject and to prevent confusion, Schwarzkopf1 has proposed that compactibility be defined as the minimum pressure needed to produce a given green strength, while compressibility should be used to indicate the extent to which the density of a powder is increased by a given pressure. Probably the most widely used of the compaction parameters is the "compression ratio," which is generally defined as the ratio of the compact density obtained by pressing at a given pressure to the apparent density of the loose powder. 2 However, the description of the compaction behavior of a powder by these parameters provides only limited information about the process because of their applicability to just one specific condition such as a given green strength or a given pressure. The method of obtaining density-pressure relationships which will be described in the present paper was designed to eliminate the shortcomings of the previous techniques while maintaining equivalel)t accuracy and precision. EXPERIMENTAL TECHNIQUES The general principle employed makes use of the fact that the linear movement of the punch during a VOLUME 221, AUGUST 1961-671

0166

LOADING V)

CI

~

C

ct

ILl

IX ~

ILl CI

ct CI

oJ

or

C

"P Imal

-

- - - to

~- -

a

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-

,

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-

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- -

-

-

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S

--

UNLOADING

-

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I

-

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0 P

0

PRESSURE Fig . 1- Schematlc r epresentation of data curves along with pe rtinent values for calculating densities .

I

I

single die compaction may be used to calculate the change in volume of the powder as a function of pressure, if the cross-sectional area of the die is known. The density-pressure relationship over the entire range of pressures used in the compaction operation may then be calculated from a knowledge of the weight of the powder and the volume-pressure relationship. (It should be noted that the term "density" as used here refers to the average density of the compact.) Since only the change in the volume of the powder may be obtained as a function of pressure, the data must be referred to a known powder compact volume. Two volumes may be used: zero die volume, which corresponds to the readings taken when the top and bottom punches of the die are in physical contact, or the volume of the compacted specimen after completion of the compaction operation. Since the linear movement of the punches dur ing the application of pressure to the powder is the algebraic sum of the change in height of the compact and the elastic compressive strains in the punc hes, the latter changes must be measured exper ime ntally by a blank pressing operation in order to s eparate the two effects. These punch-elasticity data are used in the reduction of the linear punch- m ovement data to allow the calculation of compact de nsity at the applied pressure. This will be referred to as "at-pressure" density. The densities measured after the compacts are removed from the die will be known as "zero-pressure" densities. Thus far , consideration has been given to die compaction only. However, the method is adaptable to hydrostatic compaction by suitable measurements of volume decrease as a function of hydraulic pressure. Corrections for the compressibility of the hydraulic fluid and elastic deformation of the hydraulic cylinders would be necessary. 672-VOLUME 221,AUGUST 1961 "

Die compaction of powdered materials may be carried out under one of many possible experimental conditions . In particular, a tensile bar die of 1.00:. sq in. cross-sectional area with cavity dimensions specified by the Metal Powder Association 3 and having the die body supported by springs so that the die behaved in a double-action manner was used in the present investigation. The chOice of die was arbitrary ; any die of interest could have been used. Die lubrication was carried out by painting the body and punches with a 3 pct solution of stearic acid in carbon tetrachloride. The die was cleaned after each compaction operation. One-half cubic inch (0.50 in. depth) apparent volume 2 of powder was used for the compacts, which averaged about 0.20 cu in. in volume after pressing to 100,000 psi. The loading was accomplished on a 120,000-lb capacity Baldwin tension-test machine. A loading rate of 6000 psi per min was used throughout. The measurement of the 'amount of punch movement in the die was carried out with the dial gage and lever assembly hav- , ing a precision of 0.0001 in. The base of the assembly was fixed to the table of the testing machine and the lever contacted the crosshead. As the table moved upward, preSSing the punches of the die into the die body, the relative movement of the crosshead and table, identically equal to the amount of punch movement, was indicated on the dial gage. ANALYSIS OF THE EXPERIMENTAL DATA If the scale on the dial gage is chosen so that the dial-gage readings decrease as the load is applied to the die, the experimental data, when plotted, take the form shown schematically in Fig. 1 by the curves RS and ST. These curves represent the data taken on the application and removal of the pressure during the pressing operation, respectively. The mathematical reduction of the experimental data into curves relating the average denSity of the powder compact and the applied pressure requires the following information: a) The weight of the powder in the die, b) the cross-sectional area of the die cavity, c) the elastic changes which take place in the die itself as a function of the applied pressure (if the at-pressure densities are to be calculated), and d) either the dial-gage reading at zero die volume without an applied pressure or the thickness of the powder compact when removed from the die. The weight of the powder and the dimensions of the die cavity may be measured directly, the die elasticity may be measured by a blank run (without powder), the zero-volume gage reading may be taken before placing the powder in the die, and the compact thickness may be measured after the preSSing operation when it is removed from the die. Because of the extremely small difference in cross -sectional area between the die cavity and the compact when it is removed fron the cavity, the areas of the two may be assumed to be equal without affecting the accuracy of the analysis. TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

The r eduction of the dial-gage readings vs a pplied-pressure data to give average compact d 'nsity at ze?'o p?'e sslwe vs pressure may be obtai neo through the use of Fig. 1. The relationship betw('cn zero-pressure density and the applied pressure indicates the compact density, measured after removal from the die, which may be obtained by pressing at the given pressure. In terms of Fig. 1, by loading the die to the point S, a density characteristic of the point T is obtained. Thus, we may consider the curve S T to be a curve of constant zeropressure density. The zero-pressure density of the compact may be calculated for any pressure P up to P max ' assuming that, if we would have unloaded the die after having reached, for instance, point M (pressure P), we would have proceeded along curve MN, such that x -Uo

= lp -up

[1]

and, by vertical displacement, curves MN and OT can be brought into coincidence. The average zeropressure compact density, PR " may be calculated o from the general expression Pp

o

= WI Vp 0

[2]

where W is the weight of the powder in the compact and VPo is the calculated compact volume which would be measured experimentally if the pressure were dropped from the value P to zero; i.e., the volume of the compact at point N. Actually, the volume of the compact at point N may be express,ed as VPo =

ex -uo + to)·A

Substituting from Eq. [1], VPo = (lp -up + to)·A

Thus, from Eq. [2], W

If a calculation based on a zero-volume reading, a, is desired, the substitution

to

= Uo -

a

[4]

may be made in Eq. [3]. In general, experimental data and calculations based on to will be made more easily and will have greater inherent accuracy, especially in the more important high-pressure range, since actual measurement of the compact establishes the denSity value at P max' However, for materials whose compacting characteristics are desired, but whose poor interparticle coheSion, even at the maximum pressure, does not permit their removal from the die intact, the density calculations must necessarily be based on a zero-volume measurement. At-pressure densities may be obtained from punchmovement data as a function of the applied pressure by modifying Eq. [3] to take into account the axial elastic compressive strains in the punches. In terms of the notation used previously, the at-presTRANSACTIONS OF THE METAllURGICAL SOCIETY OF AIME

10r--------------------------c~~-r~~

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P Reduced Pressure. -3 (To Fig. 1-Normalized density-pressure curve. R. W. HECKEL, Junior Member AIME, is Research Metallurgist, E.!. du Pont de Nemours & Co., Inc., Experimental Station, Engineering Research laboratory, Wilmington, Del. Mdnuscript submitted February 21, 1962. IMD

vOLUME 224, OCTOBER 1962-1073

0173

Table I. Description of the various powders whose density-pressure curves are normalized In Fig. 1. Compaction Parameters Powder

Partlc Ie Size

Iron" Iron· Iron· Iron" Iron" Iron b SAE 4630 Steel Spherical Nickel Spherical Nickel Annealed Nickel Spherical Copper Spherical Copper Tungsten

. 80 Mesh +140 Mesh +200 Mesh +250 Mesh -250 Mesh -140 +200 Mesh -80 Mesh -140 +200 Mesh -250 Mesh -250 Mesh -140 +200 Mesh -250 Mesh - 151' -40 -80 -140 -200

Source Charies Hardy Co. Charles Hardy Co. Charles Hardy Co. Charles Hardy Co. Ch aries Hardy Co. George Cohen Co. Vanadium Alloy Steel Co. Linde Co. Linde Co. Charles Hardy Co. Linde Co. Linde Co. Charles Hardy Co.

A 0.67 0.73 0.68 0.73 0.77 0.70 0.68 0.92 0.98 0.87 0.72 0.90 0.62

1.86 1. 91 1.99 1. 91 1.81 1.90 1.08 1.38 1.56 1.48 3.81 3.00 0.76

x 10-' x 10-' x 10-' x 10-' x 10-' X 10-' x 10-' x 10-' x 10-' x 10-' x 10-' x 10-' x 10-'

·Star Grade (Electrolytic) bSlntrex (E lectrolytic)

where: D is the relative density. of the compact

1-

+Relative density Is defined as the ratio of the density of the compact to that of the metal without porosity.

Do is the relative apparent density of the powder P is the applied pressure, and K and B are constants Eq. [1] is valid above the pressure necessary to achieve interparticle bonding, which takes place within the range from 5000 to 25,000 psi depending on the powder. Experimental observationsl! have shown K to be related to the nominal yield strength of the powdered metal by the following equation: K = 2.08 x 10-e + 0.320

,

.

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