Determination of pressure in the extradendritic liquid area during solidification
Journal of Thermal Analysis and Calorimetry
Determination of pressure in the extradendritic liquid area during solidification
P. Svidro´ 0 1 2 3
0 Department of Material Science and Technology, School of Industrial Engineering and Management, Royal Institute of Technology , Brinellva ̈gen 23, 100 44 Stockholm , Sweden
1 Department of Materials and Manufacturing - Foundry Technology, School of Engineering, Jo ̈nko ̈ping University , Gjuterigatan 5, 55111 Jo ̈nko ̈ping , Sweden
2 & P. Svidro ́
3 Department of Materials Sciences and Engineering, The Ohio State University , Columbus, OH , USA
Complex-shaped lamellar graphite iron castings are susceptible to casting defects related to the volume change during solidification. The formations of these recurring defects are caused by the flow of the liquid in the intradendritic area, between the austenite dendrite arms, and in the extradendritic area between the austenite grains. The conditions for the liquid flow, in turn, are determined by the solidification behavior. The present study suggests a new measurement method and a novel calculation algorithm to determine the pressure of the extradendritic liquid during solidification. The method involves a spherical sample suspended in a measurement device, where the temperature and the volume changes are measured during solidification. The calculation algorithm is based on the numerical interpretation of the ClausiusClapeyron equation where the temperature variation, the volume change and the released latent heat are processed to determine the local pressure of the extradendritic liquid area during solidification.
Volume change measurement; Fourier thermal analysis; Clausius-Clapeyron equation; Extradendritic liquid pressure; Lamellar graphite iron
• A. Dio´ szegi1
• P. G. J o¨nsson2
The solidification of a hypoeutectic lamellar graphite iron
under industrial conditions starts with the formation of
columnar grains nucleated on the wall of the mold. These
grains interact with the mold wall to create a zone, which
represents a container-like macro-volume of the casting.
Inside this container equiaxed grains are formed, based on
heterogeneous nucleation. The grain growth continues until
the columnar and equiaxed grains collide and form a
coherent skeleton of a metallic matrix [
]. Depending on
the dendrite morphology at the collision, a significant
fraction of liquid phase still exists between the dendrite
arms (intradendritic liquid) and in between the austenite
grains (extradendritic liquid). Thereafter, the solidification
continues with a dynamic coarsening process involving a
combination of the coarsening and an increase in the solid
fraction of austenite [
]. The decreasing fraction of liquid
which is enriched by the segregated carbon forms a
graphite austenite eutectic in the intradendritic space. Finally,
the extradendritic phase solidifies to complete the liquid–
solid transformation process.
Recent studies on lamellar graphite iron
complexshaped parts were performed to study the kinetic of the
casting defect formations. Two frequently occurring
defects were studied, namely the shrinkage porosity (SP)
and the metal expansion penetration (MEP) [
Fig. 1). In the case of an SP formation, the gaseous external
environment is pushed into the extradendritic space over
compact shape casting
continuous columnar zone
the metal–mold surface where the columnar zone has not
been formed. MEP defects form as the extradendritic liquid
is squeezed over the metal–mold interface, either by
deforming the mold surface or by penetrating between the
sand grains. Upon the solidification of compact geometries,
where the columnar zone was coherent, neither SP or MEP
defects were observed [
An important piece of information to understand the
formation of SP and MEP defects is the conditions when
the formation is driven by the mass transport over the
casting surface in different directions. In the case of an SP
defect formation, a pressure reduction that can be
expressed as an expansion pressure on the extradendritic liquid is
believed to be necessary to promote a gas intrusion.
However, in the case of a MEP defect, the formation of a
pressure increment that can be expressed as a compressive
pressure on the extradendritic liquid is believed to be the
driving force for the metal extrusion. It should be stressed
that no methods for direct measurements of the expansion
and compressive pressures of liquid metals have been
reported in the open literature, according to the authors’
knowledge. However, analytical equations to determine
these properties are available [
The scope of the present paper is to present a novel
measurement and calculation method to predict the
pressure of the liquid phase during solidification of lamellar
Volume change measurement during the solidification of
cast alloys is reported by only a few authors [
of the authors of the present paper have published a review
on the problems of volume change measurement [
Based on that study, an idea for a new experimental
arrangement was developed. This arrangement included a
spherical sample, which was designed for the experimental
purposes. The components of the sampler are presented in
1. Spherical metal mold made of steel with a wall
thickness of 0.5 mm. The diameter of the top opening
is 12 mm
2. Lid made of the same material and the same wall
thickness as the spherical metal mold. The diameter of
the lid is 18 mm, and it is welded to a steel tube.
3. Steel tube made of the same material as the spherical
metal mold, which is closed at one end.
The arrangement of the measuring units is presented in
1. Push rod made of engineering grade full-fired 99.8%
polycrystalline alumina. The three push rods transfer
the displacement of the surface to the linear variable
differential transformer (LVDT). The LVDT has a
measuring range of ± 3 mm, a sensitivity of
85.20 mV/V mm, and a linearity of ± 0.05% for a
2. Representation of the field-of-view of the infrared (IR)
thermometer. The IR unit is equipped with a two-color
spectral sensor and has a measuring range of
The spherical metal mold is filled up through the
circular opening when the sample collector is immersed in the
liquid metal. The spherical shell moves independently from
the adherent lid. The filled sample is then lifted to the
measuring position while hanging on the lid. The sensitive
end of the thermocouple is situated in the geometric center
of the sphere T1. The thermocouple is N type as described
in the ASTM E608/E608M standard. The LVDT and the IR
sensors are distributed equally around the sample on a
plane that crosses the geometrical center of the sphere.
Moreover, each sensor is oriented perpendicularly to the
surface of the sphere. The T2A, T2B and T2C represent the
spots for the temperature measurements. The sA, sB and sC
represent the spots for the displacement measurements on
the surface of the sample. The use of a steel tube allows for
the reuse of the thermocouple, due to the protection from
erosion from the melt. The selection of alumina rods serves
as to protect the LVDTs. The accuracy of the displacement
measurement is maintained as the linear thermal expansion
coefficient of the alumina is 6.3 [10-6 gr C-1].
The investigated alloy was taken from a 4-ton induction
furnace by using a hand-held ceramic fiber cup, at a melt
temperature of 1450 C. The chemical composition of the
alloy was determined by using an optical emission
spectrometer, and the result is shown in Table 1.
During an experiment, the spherical sample was
submerged into the cup holding the melt for 2.5 s. The
measurement started as the measurement device touched
the surface of the spherical sample with the push rods.
The temperature values from the thermocouple, the IR
values, and the displacement values from the LVDTs
were registered with a sampling frequency of ten samples
Solidification is usually described as a phase
transformation under the assumption that the solid/liquid interface is
under local thermodynamic equilibrium. The driving force
of the solidification is the change of the free energy, which
is driven by the temperature undercooling below the
equilibrium temperature. The solid/liquid curvature, the
temperature, the chemical composition and the pressure
variation are considered as influencing parameters on the
]. The change in free energy of the liquid
and solid with small changes in temperature DTp can be
expressed using Eq. (1), which is the Clausius–Clapeyron
where DP is the pressure variation, Dv is the specific
volume change, and Ds is the specific entropy change of the
solidification. The entropy change as it was defined by
Clausius can be expressed as a function of the heat release
at solidification L and the absolute temperature of the
By including Eq. (2) into (1) and by considering
differential notation for the pressure and temperature term, the
following relationship can be obtained:
Equation (3) equates the slope of the tangent to the
coexistence curve (between two phases), ddPT at any given
point on the curve, to the function TLDv. As such, it is valid
for condensed phases, and consequently for the liquid/solid
Since Eq. (3) was derived by assuming a constant
pressure and temperature, it is possible to transform the
partial derivatives into total derivatives.
Considering the solidification interval of the metallic
alloy (e.g., hypoeutectic cast iron), the solidification
interval can be divided in solidification increments
delimited by time intervals. Consequently, the pressure change
for a small solidification increment can be calculated, by
considering the release of latent heat and the specific
volume change strictly related to the considered solidification
increment. For this scope, the latent heat of solidification L
(J kg-1), which represents the released latent heat within
the whole solidification interval is replaced with the heat
quantity Qs (J kg-1), which represents the released latent
heat only during the considered solidification increment.
It is possible to replace L with Qs in Eq. (3) and to carry
out an integration. The left-hand side term is integrated
from P1 to P2, which are the pressure in the beginning and
at the end of the solidification increment. Furthermore, the
right-hand side term is integrated from T1,start to T1,end,
which are the central temperature of the sample in the
beginning and at the end of the solidification increment:
Qs ln T1;end
DP ¼ Dv T1;start
We obtain an expression for the pressure variation for
the considered solidification increment
The left-hand side of Eq. (5) expressed as DP ¼ P2
P1 is the unknown pressure variation (Pa), while the terms
on the right-hand side of the Eq. (5) can be calculated
based on temperature and volume change measurements.
The released latent heat Qs within a delimited
solidification increment is calculated from the following equation:
where qs (W m-3) is the volumetric heat release within the
solidification increment, which is calculated using a
Fourier thermal analysis (FTA). The parameter M (kg) is
the measured mass of the sample, V (m3) is the current
sample volume calculated from the dilatation
measurement, and Dt (s) is the duration time of the studied
FTA is an iteration algorithm based on a numerical
interpretation of the Fourier heat conduction equation with
the scope to interpret the registered temperature differences
within the phase transformation of a sample domain (e.g.,
solidification of cast iron in a spherical sample).
Furthermore, it is possible to determine the released latent heat
during the phase transformation. Beside the registered
cooling rates, the following tabulated data were used as
input for the FTA calculation: Heat capacity of liquid iron,
cliq = 740 J kg-1 K-1; Density of the liquid iron, qliq =
7100 kg m-3; Heat capacity of austenite, cgPr =
1950 J kg-1 K-1; Density of austenite, qaus = 7400
kg m-3; Heat capacity of graphite, cgPr = 1950
J kg-1 K-1; Density of graphite, qgr = 2200 kg m-3. The
heat capacity values were calculated by using ThermoCalc
]. Density values were used from the literature.
The FTA algorithm was developed in the department of
Material and Manufacturing, J o¨nko¨ ping University, and
has previously been published in the present journal
]. The specific volume change Dv (m3 kg-1) within
a delimited solidification increment is calculated by using
the following equation:
Dv ¼ M
where DV (m3) is the volume change of the sample within
a solidification increment calculated from the measured
sample volume change and the measured sample mass
M. The temperature terms T1,start and T1,end in Eq. (5) are
given in Kelvin units.
Results and Discussions
The cooling curves collected during the solidification
experiment are presented as a function of the fraction of
solidified material calculated by the FTA algorithm in
T1 is the cooling curve registered from the geometrical
center of the spherical sample, and T2 is the average of the
temperatures measured at three different positions on the
surface of the sample. Figure 4 includes also the calculated
volume change, based on the measured surface
displacement. The sample volume decreases from the start of the
solidification until the total fraction of solid fs reaches a
value of 0.32. In terms of solidification morphology, the
columnar zone (casting skin) forms on the internal surface
of the casting sample, when the solidification starts.
Thereafter, it continues to grow and coarsen until the
graphite precipitation starts in the columnar zone. The start
of the graphite precipitation is also confirmed by a
temperature minimum at fs = 0.32 at the surface temperature
T2. The consequent volume increase continues until the
internal domain (the equiaxed zone) reaches a temperature
minimum on the central cooling curve T1 at fs = 0.52. The
volume starts to increase when the graphite formation
starts, which is confirmed by the peak of the eutectic
reaction on the T2 curve. The minimum value on the T1
curve corresponds to the beginning of recalescence, which
is the beginning of a massive solidification with a
significant release of latent heat. The decrease in volume is
related to an insufficient graphite formation to compensate
for the austenite shrinkage due to the temperature decrease.
From this moment, the total volume of the sample will
decrease toward the end of the solidification.
Heat transport from the spherical sample to the
surrounding is equally distributed over the sample shell.
Consequently, the columnar zone precipitation will create a
container-like domain, which hinders a direct contact
between the outer atmosphere and the bulk liquid. The
equiaxed austenite grains precipitating inside the container
consist of a mixture of a dendrite network and an
intradendritic liquid, which transforms into a solid granular
unit when the intradendritic liquid transforms to graphite
and eutectic austenite. The extradendritic area will be the
last solidifying area. The interaction between the
intradendritic and extradendritic liquid during solidification
cannot be interpreted from this measurement. For the sake
of simplicity, the calculated pressure change based on
Eq. 5. will be interpreted as the pressure change of the
liquid phase in the extradendritic zone.
The calculated pressure variation is presented together
with the measured temperature in the geometrical center in
Fig. 5, with the calculated volume change in Fig. 6, and
with the calculated released latent heat in Fig. 7. In all
cases as a function of fraction solidified material.
The deviation from the atmospheric pressure DP ¼ 0
starts as soon as the solidification starts and continues until
the end of solidification. A continuous deviation is
observed based on the performed calculations. Positive
values on the y-axis are interpreted as a compressive
pressure, while negative values are considered to be an
expansion pressure. The alteration between the
compressive and expansion pressures is strictly related to the
measured temperature (Fig. 5), the calculated volume
change (Fig. 6) and released latent heat (Fig. 7) variation.
The investigated hypoeutectic cast iron in the present paper
seems to develop expansion pressures in two distinct
intervals of the solidification. The first interval developing
expansion pressure (indicated as II.) can be connected to
the expansion of the columnar zone (casting shell), which
causes a volume expansion lasting to the start of the
eutectic reaction in the equiaxed zone. The second interval
where an expansion pressure is developed (indicated as
IV.) starts behind the eutectic minimum temperature of the
equiaxed zone. Thereafter, it lasts until the maximum
recalescence of the equiaxed zone is reached. The
remaining intervals are characterized to have a
compressive pressure (indicated as I, III and V).
The maximum expansion pressure in both intervals is
– 1.5 9 107 Pa. One of the few existing literature data by
Campbell discusses an analytical model and calculates the
hydrostatic tension of the solidifying liquid in different
pure alloys [
]. Furthermore, it presents information related
to a planar solidification front and different deformation
characteristics of the solidifying crust. Campbell reports a
dimension-dependent hydrostatic tension. For small
calculation domains of trapped liquids (10-6 m), the reported
hydraulic tension data were in the range of - 109 to
-1010 Pa. The discrepancies between the present and
literature data may be due to the differences of the alloy, the
differences between the deformation characteristic of the
solidifying crust and the used input data.
Several measurements of alloys with similar chemical
compositions as the present investigated alloy were
performed. Since the reproducibility of the instrument was not the
scope of the present paper, the reproducibility will be reported
in a future work. The accuracy of the implemented sensors in
the measurements is described in the experimental chapter.
Integration of the heat release in the whole solidification
interval within the FTA calculation gives the sum of the latent
heat of solidification L = 254 J kg-1. It is worth to note that
the calculated latent heat in the present work corresponds well
to the calculated latent heat when using the ThermoCalc [
software for the composition indicated in Table 1.
The present investigation confirms the various pressure
states, tensile and compressive loads of the solidifying
liquid in the extradendritic area at solidification of lamellar
graphite iron. Consequently, the driving forces for the
formation of SP and MEP defects are demonstrated to exist
within the same solidification process. Further utilization of
the present method is aimed to investigate the extremely
sensitive solidification process of cast iron alloys with
respect to parameters such as the composition, morphology
and refining treatments.
The focus was the determination of the pressure in the
extradendritic liquid area during solidification of lamellar
graphite iron. A new method based on the interpretation of
the Clausius–Clapeyron equation was introduced. The
pressure variation of the liquid iron in the extradendritic
area was determined with help of a novel experimental
setup, where the temperature variation and the surface
displacement are measured during solidification. A
continuous deviation from the atmospheric pressure alternating
between a compressive pressure and an expansion pressure
was calculated. The alteration points between the positive
and negative pressures can be connected to metallurgical
key events that take place during solidification. A
pre-eutectic expansion pressure is caused by an expansion of the
casting skin. In total, three compressive and two expansion
pressure intervals were identified for the investigated
hypoeutectic alloy. The presence of expansion and
compressive pressures in the extradendritic liquid indicates the
existing driving forces at the SP and MEP defect
formations during solidification of lamellar graphite iron. When
comparing the predicted data to the existing literature data,
the calculated pressure deviation is lower than the values
based on analytical calculations.
Acknowledgements The present work was performed within the
Casting Innovation Centre and financed by the Swedish Knowledge
Foundation. Cooperating parties in the project are Jo¨nko¨ping
University, Scania CV AB and Volvo Group Trucks Operations. The
participating persons from these institutions/companies are
acknowledged for their support throughout this study.
Open Access This article is distributed under the terms of the
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