High Temperatures ^ High Pressures, 2000, volume 32, pages 109 ^ 113
14 ECTP Proceedings pages 137 ^ 141
DOI:10.1068/htwu520
Measurement of the volumetric expansion and bulk
density of metals in the solid and molten regions
Ju«rgen Blumm, Jack B Henderson
NETZSCH-Gera«tebau GmbH, Wittelsbacherstrasse 42, D-95100, Selb/Bavaria, Germany;
fax: +49 9287 881 44; email: [email protected]
Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany,
5 ^ 9 September 1999
Abstract. Over the past few decades, the metals industry has increased its efforts to raise product
quality and improve production processes. In particular, the casting process and mould design
have been continuously improved. High-speed computers and finite-element casting simulations
are widely used to improve control and understanding of the solidification process of metals.
The quality of the numerical simulations is strongly dependent on the accurate knowledge of the
thermophysical properties of the metals. Thermophysical properties, such as thermal conductivity,
thermal diffusivity, specific heat or density change in the solid, liquid, or mushy zones, being
critical parameters for the accurate simulation of such casting processes, must be known. The
topic of this work is to introduce a new method for measurement of the volumetric expansion
and density change in the solid, liquid, and mushy regions by the use of a standard pushrod
dilatometer. The new method was tested on copper and iron. Additionally, measurements were
carried out on an aluminium alloy, LM-25, and a nickel-based superalloy, Inconel 718.
1 Introduction
The thermophysical properties of metals are of paramount importance for the accuracy
of casting simulations. These properties are well known for many pure metals, but not for
the innumerable number of different alloys. For most of the alloys, the thermophysical
properties cannot be found in literature. Therefore, measurements have to be carried out
in order to achieve the highest possible accuracy of numerical simulations. The thermal
diffusivity can be measured by the laser-flash method (Parker et al 1961). This method
can be applied to liquid metals by the use of special liquid metal sample holders (Taylor
et al 1993; Henderson 1994). The specific heat can be determined by high-temperature
differential scanning calorimetry (Henderson et al 1988). By the use of platinum crucibles
with alumina liners, this method allows measurements on liquid metals. However, to the
authors' knowledge very little reliable data exist for the density change of metals during
melting and in the liquid regions.
2 Experimental
Pushrod dilatometers are widely used to measure the linear thermal expansion and
shrinkage of bulk materials. Such instruments allow measurements of coefficients of
thermal expansion, phase transitions, and density changes of solids. The pushrod
dilatometers usually allow measurement in one dimension. The capabilities of a standard
pushrod dilatometer were extended to carry out measurements of metals in the liquid
regions as well as during melting.
The measurements were carried out with a NETZSCH model 402 C pushrod
dilatometer capable of operation between 25 and 2000 8C. The system is vacuum-tight by
design. Therefore, measurements can be carried out under vacuum or in pure inert or
oxidising atmospheres. Depending on the temperature range of interest, the system was
equipped with fused silica or alumina sample holders. For measurement of volumetric
expansion and density change during melting and in the liquid phase, novel liquid metal
sample holders were designed. To carry out tests on liquid metals in a pushrod dilatometer
110
J Blumm, J B Henderson
15 ECTP Proceedings page 138
tube
piston
piston
Figure 1. Design of the liquid-metal sample holders.
these containers must fulfill several requirements: first of all, the containers must
be tight against a liquid metal. No, or only negligible, reaction should occur between
the sample and the container material. The liquid-metal sample holder should be
adaptable to the standard sample holder system of a dilatometer. The container should
have well-defined dimensions with known thermal expansion. Therefore, the influence on
the experimental data should be correctable. The design of the liquid-metal sample
holder is presented in figure 1. It consists of a tube with two pistons on each side.
Extreme care was taken with the dimensions of the system, eg on the outer diameter of the
pistons and the inner diameter of the tube. The difference was less than 10 mm. The close
tolerance yields the tightness of the container on molten metals. Depending on the
material tested, sample holders of graphite, sapphire, or polycrystalline alumina were
employed. Graphite containers were used for the aluminium alloy and copper, while
sapphire and polycrystalline alumina containers were employed for Inconel 718 and iron,
respectively. The samples were cut to lengths of approximately 12 mm. They were
prepared such that their diameter and the inner tube diameter were the same at the
melting point. The container was therefore completely filled with a solid body near the
solid/liquid transition. To correct system influences like the expansion of the sample
holder, the dilatometer was calibrated with a sapphire standard prior to all
measurements. The calibration runs were carried out in the liquid-metal sample holders
under the same conditions used for the samples. All tests were carried out in a dynamic
helium atmosphere.
Analysis of the experimental data in the solid and molten regions needs special
requirements. The dilatometer yields experimental data which represent the linear thermal
expansion in the solid region. For isotropic materials, such as those examined in this
work, the volumetric expansion can be calculated by equation (1):
2 3
DV
DL
DL
DL
ˆ3
‡
.
(1)
‡3
V0
L0
L0
L0
DV=V0 is the volumetric expansion and DL=L0 is the measured linear thermal
expansion. In the liquid region the experimental data yield the volumetric expansion of
the sample overlaid by the radial expansion of the container. Therefore, the measurement
results need to be corrected for the influence of the container. To overcome these
problems a special software package was developed for consideration of the radial
expansion of the container and the combination of linear and volumetric expansion
(in the solid and liquid regions, respectively).
3 Results and discussion
Depicted in figure 2 are the volumetric expansion and the density of the copper sample.
The measurements were carried out between room temperature and 1175 8C. The
heating rate was 3 K minÿ1. As can be seen, the volumetric expansion increases with
increasing temperature. The melting temperature was detected at 1088 8C. The deviation
between measurement and literature value for copper, 1084.6 8C (Lide 1995), is
approximately 3 K. At the melting point, a volume increase of 5.3% was measured.
Volumetric expansion and bulk density of metals
111
15 ECTP Proceedings page 139
9.0
1096 8C
volumetric expansion
density
8.8
12
5.3%
10
8.6
1088 8C
8
6
8.4
8.2
4
Density=g cmÿ3
Volumetric expansion=%
14
8.0
2
7.8
0
0
200
400
600
800
1000
1200
Temperature=8C
Figure 2. Volumetric expansion and density change of copper between room temperature and
1175 8C.
1540 8C
12
3.46%
10
7.8
7.7
7.6
1520 8C 7.5
8
volumetric expansion
density
7.9
7.4
6
7.3
7.2
4
Density=g cmÿ3
Volumetric expansion=%
8.0
14
7.1
2
7.0
6.9
0
0
200
400
600
800
1000
1200
1400
1600
6.8
Temperature=8C
Figure 3. Volumetric expansion and density change of 99.9% pure iron between room temperature
and 1650 8C.
The literature value for the volume change at the solid ^ liquid transition is 5.1%
(Askeland 1996). The sample melts over a temperature range of 8 K. The melting range
as well as the deviation from the literature values for the melting point are due to the
temperature gradient in the container walls and dynamic heating, respectively. The
density was calculated with a room-temperature bulk density of 8.91 g cmÿ3 and the
volumetric expansion of the sample. It can be seen that the density decreases from 8:27
to 7:88 g cmÿ3 on melting. In the liquid region a nearly linear volumetric expansion
was observed.
The volumetric expansion and the density change of 99.9% pure iron between room
temperature and 1650 8C are shown in figure 3. The measurement was carried out at a
heating rate of 5 K minÿ1. At approximately 910 8C, a decrease in the sample volume
was detected. This is due to a phase transition in the material. The body-centred crystal
structure changes to a face-centred structure. The literature value for this phase
transition is 910 8C (Touloukian and Buyco 1970). The shrinkage is due to the higher
packing of the face-centred structure. At approximately 1400 8C, a further step is visible
in the volumetric expansion and the density. Again, this effect is due to a phase
transition (face-centred to body-centred structure). The literature value for the transition
temperature is 1400 8C (Touloukian and Buyco 1970). Melting of the sample was
112
J Blumm, J B Henderson
15 ECTP Proceedings page 140
detected at 1520 8C. This temperature is 18 K lower than the literature value for iron
(Lide 1995). It must be pointed out, however, that the melting temperature for iron is
strongly influenced by impurities which usually lower the melting temperature. The
impurity content of the sample examined was 0:1%. This could explain the lower
melting temperature. The melting range was between 1520 and 1540 8C. The volume
change was 3.46%. This value is in good agreement with the literature value, 3.4%
(Askeland 1996), for iron. For calculation of the density change, the room-temperature
bulk density of the sample (7.86 g cmÿ3 ) and the volumetric expansion were used. Here,
the density decreases to 6:87 g cmÿ3 at 1625 8C.
The volumetric expansion and density change of the nickel-based superalloy
(Inconel 718) are presented in figure 4. The heating rate was 5 K minÿ1. The measurement
was carried out between room temperature and 1450 8C. As can be seen, the volumetric
expansion increases almost linearly up to 775 8C. At 775 8C, a change in the rate
of expansion was measured. This effect is probably due to a phase transition in the alloy.
Melting of the sample started at 1292 8C. Here, the melting occurs over a much broader
temperature range (54 K) compared to the copper sample. This effect can be explained
by the dynamic heating and the wide melting range of Inconel 718. The volume change
8.2
1346 8C
10
8.0
3.1%
7.9
8
1292 8C 7.8
6
volumetric expansion
density
8.1
7.7
4
7.6
2
7.5
Density=g cmÿ3
Volumetric expansion=%
12
7.4
0
0
200
400
600
800
1000
Temperature=8C
1200
7.3
1400
Figure 4. Volumetric expansion and density change of Inconel 718 between room temperature and
1450 8C.
2.60
620 8C
2.55
8
5.1%
6
580 8C
4
2.50
2.45
2
2.40
0
2.35
200
400
600
Density=g cmÿ3
Volumetric expansion=%
10
0
volumetric expansion
density
2.65
12
800
Temperature=8C
Figure 5. Volumetric expansion and density change of the aluminium alloy LM-25 between room
temperature and 800 8C.
Volumetric expansion and bulk density of metals
113
15 ECTP Proceedings page 141
during melting was 3:1%. The density change was calculated using the roomtemperature bulk density of 8.18 g cmÿ3. The bulk density decreases to 7:33 g cmÿ3 at
the end temperature.
The volumetric expansion and density change for the aluminium alloy are shown in
figure 5. The heating rate was 3 K minÿ1. The test was carried out between room
temperature and 800 8C. A nearly linear volumetric expansion was detected up to 575 8C.
Melting of the sample was measured between 580 and 620 8C. In the mushy zone, two
melting steps with slightly different rates of expansion were detected. The temperature
range for melting as well as the two-step character of the melting process are in good
agreement with the differential scanning calorimetry results published elsewhere (Blumm
et al 1998). The volume change measured during melting was 5.1%. This is lower than
the literature value for the volume increase of pure aluminium, 7% (Askeland 1996),
at the melting point.
4 Conclusions
A new method for extending a standard pushrod dilatometer to measurements on liquid
metals was developed. By the use of special liquid-metal sample holders and newly
developed software, the volumetric expansion and density change can be measured in the
solid and molten regions of metals. The new method was employed for tests on copper,
iron, an aluminium alloy, and a nickel-based superalloy. The difference of the measured
volume change at the melting point and literature values for copper and iron was less
than 5%.
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ß 2000 a Pion publication printed in Great Britain