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Introduction
The forming of a sintered component begins with the densification of the metal powder
in a rigid die having a cavity of more or less complicated contour. In this operation, high
pressures (usually 650 N/mm2
) are exerted upon the powder in the die cavity,
simultaneously from top and bottom, via two or more vertically moving compacting
punches.
Under the influence of such high compacting pressures, the powder particles are
being squeezed together so closely that their surface irregularities interlock and a certain
amount of cold welding takes place between their surfaces.
After ejection from the die, if the compacting operation was successful, the compact
owns sufficient strength (so-called green-strength) to withstand further handling without
damage. In order to facilitate the compacting operation and reduce tool-wear to a
minimum, a lubricant is admixed to the powder before compacting.
In order to fully comprehend the possibilities and limitations of powder compacting, it is
required not only to study the empirical phenomena of this process, but also to reveal the
basic mechanisms behind them.
4.1 Density - Porosity - Compacting Pressure
At first, some definitions are required:
• Specific Weight: ρ = m/Vt
(measured in g/cm3); m = mass of the material; Vt
= true
volume of the material.
• Density: δ = m/Vb (measured in g/cm3
); m = mass of the powder resp. compact;
Vb = bulk volume (enveloping volume).
• Theoretical Density: δth = density of a (practically not attainable) pore-free powder
compact (measured in g/cm3
).
• Porosity: φ = 1 - δ/δth ( number without dimension).
• Compacting Pressure (die compacting): P = compacting force/face area of compact
(measured in N/mm2 or MN/m2).
• Compacting Pressure (isostatic compacting): P = pressure of the hydraulic medium
(measured in MPa or MN/m2
).
Empirical Density-Pressure Curves
Powder Compacting in a Cylindrical Die.
The strength properties of sintered components increase with increasing density but
their economy drops with increasing energy input and increasing load on the
compacting tool. Thus, it is most desirable, for both economic and technical reasons, to
achieve the highest possible compact density at the lowest possible pressure.
Density-pressure curves give information about the frame within which a suitable
compromise may be found. These curves are generally obtained from standard
laboratory tests where a number of compacts are made at different pressures in a carbide
die having a cylindrical bore of 25 mm diameter. The densities of the compacts are
plotted against compacting pressures. The diagram at Fig. 4.1 shows density-pressure
curves for two commercial iron powders (NC100.24 and ASC100.29).
A striking feature of these curves is the fact that their slope decreases considerably with
increasing compacting pressures, and that the density of massive pure iron (7.86 g/cm3)
obviously cannot be reached at feasible pressures. We notice, further, that the two iron
powders despite their chemical identity yield different density-pressure curves. This
different compacting behavior arises from differences of their particle structure.
See Chapter 3.
Isostatic Powder Compacting.
A powder under isostatic pressure shows a similar densification behavior as in diecompacting.
This is illustrated by the following example: Samples of electrolytic iron
powder, hermetically enclosed in thin rubber jackets and embedded in a hydraulic
medium, were subjected to varying isostatic pressures.
Principle Limits to Densification
Since early in the 1930’s, powder metallurgists have endeavored to find a suitable
mathematical description of the process of powder densification. The number of
formulae which to this effect have been suggested over the last three decades is legion.
However, non of these formulae, most of them extracted from simple curve-fitting
exercises, has proven to be sufficiently universal and substantiated by general physical
principles to be acceptable as sound theory of powder densification.
In work shop practice, such formulae are dispensable because it is far more reliable
and hardly more tedious to establish relevant densification curves experimentally than to
calculate them from complicated and questionable formulae.
On the other hand, it is quite useful to understand, in principle at least, in which
way the process of powder densification is influenced and limited by general laws of
physics and mechanics.
Deformation Strengthening of Powder Particles.
Disregarding, for the moment, the problem of wall friction in die-compacting and
considering isostatic compacting of powder only, we recognize that the problem of
powder densification arises from an underlying physical problem which can be defined as
follows:
• With increasing densification, the powder particles are plastically deformed and
increasingly deformation strengthened, i.e. their yield point is steadily being raised.
• Simultaneously, the contact areas between particles are increasing and, consequently,
the effective shearing-stresses inside the particles are decreasing. Thus, at constant
external pressure, decreasing shearing-stresses meet a rising yield point, and all
further particle deformation ceases, i.e. the densification process stops.
The deformation strengthening of the powder particles can be made evident by means of
X-ray structural analysis. At Fig. 4.5, three photo-records of X-ray back-reflections are
shown, obtained (A) from a commercial sponge-iron powder, (B) from a compact of this
powder pressed at 290 N/mm2
, and © from the same compact after soft-annealing for
2 minutes at 930°C.
4.2 Radial Pressure - Axial Pressure
When the piston of a hydraulic cylinder exerts pressure upon the liquid inside the
cylinder, the pressure applied in axial direction is transformed 1:1 to radial pressure upon
the cylinder wall. When a powder is being compacted in a rigid cylindrical die, the axial
pressure, exerted upon the powder by the compacting punch, is only partly transformed
to radial pressure upon the die wall.
This radial pressure can be quite substantial, but it cannot reach the level of the axial
pressure because a powder is no liquid and has no hydraulic properties.
4.2.1 Hysteresis of the Radial Pressure
The way in which the empirical relationship between radial and axial pressure is
governed by general laws of physics and mechanics can be understood, in principle at
least, from a simple model, suggested in 1960 by W.M. Long1
, and presented in detail
below. First, we consider a free-standing cylindrical plug of metal having a modulus of
elasticity E and a Poisson factor ν. A compressive axial stress σa, applied to the end-faces
of the plug, provokes, by laws of elasticity, a radial stress σr , and the radius of the plug is
expanded by the factor
εr = (σr - νσr - νσa)/E (4.7)
We now imagine the same plug being put into a tightly fitting cylindrical die. The die is
assumed to have a modulus of elasticity much larger than that of the metal plug. Further,
it is assumed that the die is extremely well lubricated, such that any friction between the
plug and the die-wall is negligible. Exerting, via two counteracting punches, axial
pressure upon the plug, its radial expansion εr is negligibly small because the die expands
extremely little due to its large modulus of elasticity. Thus, εr = 0 is a sufficiently close
approximation of reality, and from (4.7), it follows:
σr - νσr - νσa = 0 (4.8)
Hence, the relationship between radial and axial stress in the plug is:
σr = σaν/(1 - ν), elastic loading
4.2.2 Influence of the Yield Point.
From Long’s model, it is evident that the radial pressure, which a metal plug or a mass of
metal powder under axial pressure exerts upon the wall of a compacting die, is the
smaller the higher the yield point of the metal is. Vice versa, from the same model, it can
be concluded that a metal powder with extremely low yield point and negligible
tendency to deformation strengthening, like lead powder for instance, should exhibit a
nearly hydraulic behavior when compacted in a rigid die.
Experimental proof is in the diagram shown at Fig. 4.10. The entire loading-releasing
cycle for lead powder does not show any hysteresis, and its very slight deviation from the
ideal hydraulic straight line is due to frictional forces at the die wall.
These findings suggest that higher and more homogeneous densities in metal powder
compacts could be achieved, if the compacting procedure would be executed at elevated
temperatures where the yield point of the metal is lower than at R.T.
Experiments with various iron powder mixes, carried out at the Höganäs laboratory,
and pilot production runs, initiated by Höganäs, have proven that already an increase of
the powder temperature to 150 - 200°C is sufficient to achieve substantially higher
densities and improved properties3 4.
The principle influence of a temperature depended yield point on the relationship
between axial and radial pressure emerges from the theoretical hysteresis curves shown at
Fig. 4.11. From these curves, it can be seen that the maximum radial pressure increases
but the residual radial pressure, after complete release of the axial pressure, decreases
when the yield point is lowered at elevated temperatures.
4.3 Axial Density Distribution
Frictional forces at the wall of the compacting die restrain the densification of the
powder because they act against the external pressure P exerted by the compacting
punch. With increasing distance from the face of the compacting punch, the axial stress
σa, available for the local densification of the powder, decreases. This becomes especially
adversely apparent in the manufacturing of long thin-walled bushings which at their
waist line show substantially lower densities than at their two ends. In order to find an
explanation to this phenomenon, we take a closer look at the balance of forces in the
powder mass during densification.
We consider densification of powder in a deep cylindrical compacting die with inner
diameter 2r. The upper punch is assumed to have entered the die and already compacted
the powder to a certain degree so that the axial stress in the powder directly underneath
the punch face is σa(0). The variable vertical distance from the punch face be x. We
imagine the powder column in the die as being composed of thin discs stacked upon one
another like coins. We select one disc at distance x from the punch face. Its height be dx,
its cross-sectional area is F = πr
2
, and its small lateral area is f = 2rπ dx.
See sketch at Fig. 4.12.
The axial stress, acting upon the top face of this disc, is σa(x). Due to friction between
the lateral face of the disc and the die wall, the axial stress σa(x+dx), acting upon the
bottom face of the disc, is somewhat smaller than σa(x). We assume that the frictional
force is approximately proportional to the axial stress σa(x) and to the lateral face f of the
disc. After these preliminaries, we calculate the equilibrium between all forces acting
upon the selected disc.