Journal of Materials Processing Technology 211 (2011) 181–186
Contents lists available at ScienceDirect
Journal of Materials Processing Technology
journa l homepage: www.e lsev ier .com/ locate / jmatprotec
etermination of heat transfer coefficient and ceramic mold materialarameters for alloy IN738LC investment castings
.H. Konrad, M. Brunner, K. Kyrgyzbaev, R. Völkl, U. Glatzel ∗
etals and Alloys, University Bayreuth, Ludwig-Thoma-Str. 36b, D-95447 Bayreuth, Germany
r t i c l e i n f o
rticle history:eceived 22 April 2010eceived in revised form 27 August 2010ccepted 31 August 2010
a b s t r a c t
Investment casting molds with different numbers of shells and pre-heating temperatures were investi-gated in this study. The primary layer consists of colloidal silica bound ZrSiO4 with additions of CoAl2O4
to achieve fine grains and to reach a good surface quality, whereas the following layers consist of
eywords:nvestment castingeat transfer coefficient
N738LC
mullite bound by colloidal silica. Interface temperatures (alloy/mold) that are necessary to determineheat transfer coefficients were obtained by linear extrapolation. Heat transfer coefficients in the rangeof 300–660 W/(m2 K) were obtained. The castings were examined with regard to grain size and sec-ondary dendrite arm spacing. Physical properties of the investment casting mold were examined bydifferential scanning calorimetry (DSC) and Laserflash methods for temperatures up to 1300 ◦C. The spe-cific heat capacity was determined to 1.13 J/(g K), thermal diffusivity was found to be in the range of
ther
uperalloys (4–5) × 10−7 m2/s and the
. Introduction
Investment casting is a well established manufacturing processor blades and vanes in aircraft engines and stationary gas turbines.hese parts have to fulfill very strict quality requirements in ordero withstand high mechanical loads at temperatures up to 1050 ◦Cor several thousand hours. The alloys used for these purposes are
ainly nickel based superalloys such as the alloy Inconel 738 lowarbon (IN738LC), which serves as model alloy in this work.
Simulation of the investment casting process is expected tohorten development times in industry. However, many materialarameters of the alloy, the mold and the alloy/mold interface haveo be known accurately.
Liu et al. (1998) measured the liquidus and solidus temperatureor the alloy IN738LC and showed the interdependency of the meltemperature with grain size. Chapman et al. (2008) measured phys-cal properties of this alloy and of different ceramic mold materials.
An important parameter is the heat transfer coefficient (HTC)hich describes the temperature drop in the contact zone of
he melt and the mold during solidification. Ozisik et al. (1993)escribed an inverse method to solve the heat conduction equa-
ion in order to determine the heat transfer coefficient. O’Mahoneynd Browne (2002) recorded carefully the transient tempera-ures inside ceramic investment casting shell moulds and insideluminum melts during solidification. With this data they could
numerically solve the inverse heat conduction problem for theunknown heat transfer coefficient by finite differences. Sahaiand Overfelt (1995) too solved inverse problems for plate andaxisymmetric geometries with the commercial software ProCastfor investment casting of the nickel based alloy 718. Aweda andAdeyemi (2009) determined the heat transfer coefficient betweensteel molds and aluminum alloys during squeeze casting. Thetransient interface temperatures versus time were identified bypolynomial curves fitting. They could verify their approach withthe results from Krishnan and Sharma (1996).
In this work a method is presented to deduce the heat transfercoefficient between alloy and investment casting mould directlyfrom recorded transient temperature data.
2. Experimental
2.1. Investment casting
All experiments were carried in a proprietary vacuum invest-ment casting furnace (Fig. 1) with a minimal pressure of3 × 10−5 mbar. Two 40 kW medium frequency induction heatingsystems with separate inductor coils are installed. The upper induc-tor is used for melting the master alloy (IN738LC) in an aluminacrucible at temperatures up to 1500 ◦C. The second induction heat-
ing system preheats the ceramic shell mold through a graphitesusceptor. When the mold has reached a predefined temperatureit is lifted into the pouring position in a few seconds. The wholecasting process, i.e. the preheating of the mold, the melting of themaster alloy and the pouring can be controlled and monitored with
182 C.H. Konrad et al. / Journal of Materials Processing Technology 211 (2011) 181–186
1aimcd
2
2
agonpttbsadT
2
wItt
Table 1Mold-parameters for the heat transfer coefficient experiments.
Number of layers Mold preheat temperature
900 ◦C 1000 ◦C 1100 ◦C 1235 ◦C
couples on the heat propagation as low as possible (see Fig. 2).The exact distances from the heads of the thermocouples to theinterface were measured after the mold was removed from thecasting.
Fig. 1. Schematic drawing of the vacuum investment casting furnace.
6 thermocouples simultaneously. In addition, pouring of the meltnd subsequent cooling of the mold can be monitored with annfrared-camera through a ZnSe inspection window. Typical ingot
ass is about 300 g of nickel based alloy. Cross-sections of theast ingots were examined to measure grain size and secondaryendrite arm spacing.
.2. Materials
.2.1. Shell moldThe shell mold with a feeder system was manufactured using
conventional lost-wax process (see Fig. 2). The chosen plateeometry (60 mm × 40 mm × 4 mm) allows the assumption of ane-dimensional heat transfer problem in the direction of the plateormal. Molds with 4, 6 and 8 layers and different preheat tem-eratures were tested. Due to the different numbers of layers thehickness of the molds varies from 4 to 11 mm. All layers besideshe innermost layer consist of mullite particles of different sizesound by colloidal silica. The innermost layer consists of colloidalilica bound ZrSiO4 with additions of CoAl2O4 for grain refinementnd a good surface quality. The parameters of the casting tests,enominated as T1000L4, T1000L6, T1000L8, T900L6, T1100L6 and1235L6 are given in Table 1.
.2.2. Alloy
The alloy IN738LC serves as model alloy throughout this
ork. The nominal composition of IN738LC is given in Table 2.t is an alloy frequently used for polycrystalline and direc-ionally solidified (Reed, 2006) lost wax investment casting ofurbine blades. The pouring temperature of the melt was 1500 ◦C
in all tests and was measured by an insulated thermocoupletype S.
2.2.3. Mold parametersSpecific heat capacity cp of the ceramic mold were measured
with a Linseis L81/1550 DSC (Selb, Germany) in the temperatureinterval 200–1200 ◦C. Cross-checks were performed with a Net-zsch 404 Pegasus® DSC (Selb, Germany) in the temperature interval200–1300 ◦C. Both measurement series were carried out underargon atmosphere and repeated three times with different samples.
Thermal diffusivity a of the mold material was measured with aNetzsch LFA427 laser flash. Two measurements were undertaken.A round ceramic sample (12.7 mm radius and 2.04 mm thickness)was used in the temperature interval 900–1300 ◦C and a squareceramic sample (10 mm × 10 mm and 1.97 mm thickness) was usedin between 15 and 1300 ◦C. Thermal conductivity � was derivedfrom thermal diffusivity measurements according to Eq. (1):
�(T) = a(T) � cp(T) (1)
The density � of ceramic mold was deduced by dividingthe mass by the volume at room temperature. The density was1.80(±0.3) g/cm3. Because density of the ceramic shell mold is sup-posed to change only slightly over the interesting temperatures itstemperature dependence was not accounted for.
2.3. Instrumentation
The molds were instrumented with 4 thermocouples (Fig. 2).A ceramic insulated thermocouple type S with wire diametersof 0.25 mm and sealed by sintered alumina slurry was used tomeasure the temperature of the melt after pouring. Three ther-mocouples type K with a diameter of 0.12 mm were used tomeasure the transient temperatures inside the ceramic shell mold.Two were placed in different depths of the mould. The third onewas used to measure the surface temperature of the mold. Allthermocouples were placed near the center of the mold, wherethe heat transfer is assumed to be one-dimensional, i.e. the heatis almost entirely transferred perpendicular to the mold wall.The thermocouples were fixed in drilled holes with diameters ofabout 1 mm with high temperature resistant glue (Ultra-Temp516, Kager, Germany) which consists of sodium silicate boundSiO2 and ZrO2. Weathers et al. (2006) found that the ideal wayof placing thermocouples in ceramic molds is parallel to theisotherms. Therefore the drill holes were inclined by 45◦ normalto the isotherms in order to keep the influence of the thermo-
Table 2Nominal composition of IN738LC (Reed, 2006).
C.H. Konrad et al. / Journal of Materials Processing Technology 211 (2011) 181–186 183
d inst
3
dt
h
Tmcc
q
Ti
q )
wpaasc
TM
the solidification interval. The heat transfer coefficient too can thenbe calculated directly through Eqs. ((2)–(4)) for every time step.
All assumptions that have been made for the identification ofthe heat transfer coefficient are summarized below:
Fig. 2. a) Wax model; b) mol
. Theory
The heat transfer coefficient h of the alloy/mold interfaceepends on the total heat flux q̇ through the interface and theemperature drop �T at the interface:
= q̇
�T= q̇c + q̇s
�T(2)
he total heat flux consists of the flux q̇c the melt looses to theold and the flux q̇s due to the exothermic nature of the solidifi-
ation. The flux q̇c is calculated by the temperature decrease in theonsidered volume:
˙ c = �s x cp(T(t) − T(t + �t))�t
(3)
he flux q̇s is assumed to decrease linearly in the solidificationnterval:
˙ s = 2(1 − ((t − tliquid)/(tsolid − tliquid)))�s x Es
�t(tliquid ≤ t ≤ tsolid)(4
here �s is the density of the melt, x is half the thickness of the
late, cp is the heat capacity of the melt, T(t) is the temperaturet the time t, �t is the time increment, Es is the latent heat of thelloy, tliquid is the beginning of solidification and tsolid is the end ofolidification. The material parameters for IN738LC entered in thealculations are given in Table 3.
able 3aterial parameters for IN738LC taken from literature (Chapman et al., 2008).
�s 7400 kg/m3
cp 800 J/(kg K)Es 256 kJ/kg�t 0.5 s
rumentation (cross-section).
For the calculation, several simplifications have been made. Theheat transfer in the alloy is much faster than in the mold, hencethe alloy is assumed to have everywhere the temperature mea-sured by the thermocouple in the center of the casting at position−1 mm in Fig. 3. The temperature at the mold side of the interfaceis estimated by linear extrapolation of the temperatures measuredby the thermocouples in the mould. The difference between thesetwo temperatures at the interface is the temperature drop �T. �Tis determined by the extrapolation procedure for every time step in
Fig. 3. Determination of the temperature drop �T at the interface alloy/mold. Exam-ple for time step t = 20 s.
184 C.H. Konrad et al. / Journal of Materials Processing Technology 211 (2011) 181–186
•••
•
4
4
1ohccst
4
pet(
4
asf
Fig. 4. Specific heat capacity of the ceramic mold.
Heat is only transported perpendicular to the mold surface.The heat transfer in the melt is infinitely high.The temperature propagation in the mold is linear because of con-stant heat conductivity in the mold. Therefore the temperatureof the mold at the interface can be extrapolated.The solidification energy decreases linearly during freezing.
. Results
.1. Specific heat capacity
With the Linseis L81/1550 DSC a mean heat capacity of.15 J/(g K) between 200 and 1200 ◦C was measured for the ceramicf the mold. With the Netzsch 404 Pegasus® DSC a slightly lowereat capacity of 1.12 J/(g K) was measured. Both measurementsoincide well with values presented by Chapman et al. (2008) foreramic molds with similar composition (ZrO2–Al2O3–SiO2). Fig. 4hows the specific heat capacity of ceramic mold versus tempera-ure.
.2. Thermal diffusivity
Fig. 5 plots the thermal diffusivity over temperature in com-arison with literature data. An estimated error bar is shownxemplarily for a measurement at 600 ◦C. The thermal diffusivi-ies are in very good agreement with the results of Chapman et al.2008) for a similar ceramic mold material.
.3. Thermal conductivity
Thermal conductivity � values calculated according to Eq. (1)re presented in Fig. 6. Errors in thermal conductivity, density andpecific heat multiply. The resulting total error is again indicatedor the value at 600 ◦C.
Fig. 5. Thermal diffusivity of ceramic mold in comparison with literature.
Fig. 6. Thermal conductivity of ceramic mold.
4.4. Temperature propagation
Fig. 7 shows a temperature profile with the extrapolated val-ues at the alloy/mold interface. At time t = 0 the alloy is pouredinto the mold. Negative times are plotted to show the cooling ofthe mold while it is lifted from the heating to the pouring posi-tion. In these 4 s the mold cools down from 1000 to about 900 ◦C atthe outside, but remains at 1000 ◦C at the inner surface. When themold is completely filled the central thermocouple at −1 mm givesa temperature of the still liquid alloy of 1410 ◦C. The temperaturein the mold-wall increases rapidly within the first seconds, due tothe heat transfer from the melt. The maximum temperature at themold/alloy interface of 1247 ◦C is reached after 26 s. Thereafter thetemperature of the mold decreases steadily.
Solidification is apparently completed after about t = 60 s whenthe cooling curves of the alloy kinks downward (see Fig. 7). Theremaining temperature drop at the interface between alloy andmold is most probably due to a microscopic gap between moldand solidified surface. The extrapolated temperature drop remainsconstant until a macroscopic gap opens between alloy and moldcaused by different thermal expansions.
4.5. Liquidus and solidus temperature
Liquidus temperatures were identified at the intersection pointsof two tangents to the concave kinks of the cooling curves (seeFig. 7). Solidus temperatures were identified at the intersectionpoints of two tangents to the first convex kinks of the coolingcurves. The average liquidus and solidus temperature from theexperiments are given in Table 4.
4.6. Grain size and secondary dendrite arm spacing
Figs. 8 and 9 show the expected behavior that grain size andsecondary dendrite arm spacing increase with mold pre-heatingtemperature and mold thickness due to slower cooling rates.
4.7. Heat transfer coefficient
The temperature dependent heat transfer coefficient is shownin Fig. 10 for the test T1000L6. For all experiments the heat transfercoefficient is higher at the upper end of the solidification intervalwhen the alloy is mostly liquid and becomes lower approaching theend of solidification. The mean heat transfer coefficient in the solid-
Table 4Liquidus and solidus temperatures of IN738LC.
Experiment Liu et al. (1998) Chapman (2004)
Tliq in ◦C 1329 ± 4 1330 1317Tsol in ◦C 1278 ± 9 1282 1233
C.H. Konrad et al. / Journal of Materials Processing Technology 211 (2011) 181–186 185
Fig. 7. Temperature profile du
Fig. 8. Grain size and secondary dendrite arm spacing as functions of the moldpre-heating temperature.
Table 5Heat transfer coefficients (outlier in italics).
show the expected behavior. Higher mold temperatures and thickermolds result in retarded solidification and thus in larger grains andlarger secondary dendrite arm spacing. The absolute values for thegrain sizes are generally four times lower than expected from the
Fig. 9. Grain size and secondary dendrite arm spacing as functions of the moldthickness.
fication interval as well as the values at the beginning and the endf the solidification interval are listed in Table 5 for all experiments.he low heat transfer coefficient for T900L6 of 250 W/(m2 K) is con-idered as an outlier, even though no experimental error could be
dentified.
ring casting (T1000L4).
5. Discussion
The specific heat capacity and the thermal diffusivity of theceramic shell mold system measured in this study were 1.1 J/(g K)and 4.6 × 10−7 m2/s, respectively. These values are in the samerange as the results given by Chapman et al. (2008) for similar shellmold systems.
Liquidus and solidus temperature are in very good agreementwith DTA measurements from Liu et al. (1998) (see Table 4). On theother hand Chapman (2004) published 12 and 45 ◦C lower liquidusand solidus temperatures, respectively. However, Liu et al. (1998)pointed out that variations of the boron content typically encoun-tered in commercial grade alloys may have a great influence on theliquidus and solidus temperature.
The measured grain sizes and secondary dendrite arm spacings
186 C.H. Konrad et al. / Journal of Materials Proce
F(
rocc
wsSct
ahB(
bsatp
FiT
ig. 10. Heat transfer coefficient for 1000 ◦C preheating temperature and 6 layersT1000L6).
esults of Liu et al. (1998) for a melt temperature of 1500 ◦C with-ut homogenization. Hence the grain sizes observed in this studylearly reflect the grain refining capability of the primary mold layerontaining CoAl2O4.
The heat transfer coefficients between 430 and 560 W/(m2 K) areithin the range of values published in literature for nickel based
uperalloy melts in contact to ceramic shell molds. For exampleahai and Overfelt (1995) give values of around 300 W/(m2 K) forylindrical geometries and of 50–5000 W/(m2 K) for plate geome-ries of the nickel based superalloy IN718.
All experiments show higher heat transfer coefficient valuest the beginning of solidification than at the end. A decliningeat transfer coefficient during solidification was also observed byrowne and O’Mahoney (2001) as well as by Sahai and Overfelt1995).
Improvements of the presented direct method can be expectedy placing the thermocouples directly between the individualhells of the mold during the manufacturing process. This wouldllow placing the thermocouples closer to the interface and aligninghem more parallel to the isotherms in the mold. Also the error-
rone drilling of the mold could be avoided.
The material parameters determined in this work are used byranke et al. (submitted for publication) for case studies of thenvestment casting process with the commercial software ProCast.here the correlation of solidification conditions with secondary
ssing Technology 211 (2011) 181–186
dendrite arm spacing is simulated. Their results, which are in goodagreement with the experimental observations, are submitted forpublication in Metallurgical and Materials Transactions A.
6. Summary
The presented fairly simple direct method allows determiningthe heat transfer coefficient in investment castings with high pre-cision. The large scatter of mold material properties of investmentcasting molds do not affect the result of the heat transfer coefficientobtained by this method, because these properties do not enter thecalculations. Additionally, the experimental setup gives access toall kind of temperatures that occur in the melt and mold and henceallow a very good control of the casting process.
References
Aweda, J.O., Adeyemi, M.B., 2009. Experimental determination of heat transfer coef-ficients during squeeze casting of aluminum. Journal of Materials ProcessingTechnology 209, 1477–1483.
Browne, D.J., O’Mahoney, D., 2001. Interface heat transfer in investment casting ofaluminum alloys. Metallurgical and Materials Transactions A 32A, 3055–3062.
Chapman, L.A., 2004. Application of high temperature DSC technique to nickel basedsuperalloys. Journal of Materials Science 39, 7229–7236.
Chapman, L.A., Morrell, R., Quested, P.N., Brooks, R.F., Chen, L.-H., Ford, D., 2008.PAMRIC: Properties of Alloys and Molds Relevant to Investment Casting, NPLReport MAT 9. National Physics Laboratory, UK.
Franke, M.M., Hilbinger, R.M., Konrad, C.H., Glatzel, U., Singer, R., submitted for publi-cation. Numerical determination of secondary dendrite arm spacing for IN738LCinvestment castings. Metallurgical and Materials Transactions A 02.07.2010.
Krishnan, M., Sharma, D.G.R., 1996. Determination of the interfacial heat transfercoefficient h in unidirectional heat flow by Beck’s nonlinear estimation proce-dure. International Communications in Heat and Mass Transfer 2, 203–214.
Liu, L., Zhang, R., Wang, L., Pang, S., Zhen, B., 1998. A new method of fine grainedcasting for nickel-base superalloys. Journal of Materials Processing Technology77, 300–304.
O’Mahoney, D., Browne, D.J., 2002. Use of experiment and an inverse method to studyinterface heat transfer during solidification in the investment casting process.Experimental Thermal and Fluid Science 22, 111–122.
Ozisik, M.N., Orlande, H., Hector Jr., L.G., Anyalebechi, P.N., 1993. Inverse problemof estimating interface conductance during solidification via conjugate gradi-ent method. In: Güceri, S. (Ed.), First International Conference on TransportPhenomena In Processing. Technomic Publishing Company, Inc, pp. 250–265.
Reed, R.C., 2006. Superalloys. Cambridge University Press.Sahai, V., Overfelt, R.A., 1995. Contact conductance simulation for alloy 718 invest-
ment castings of various geometries. Transaction of the American Foundrymen’sSociety 103, 627–632.
Weathers, J., Johnson, A., Luck, R., Walters, K., Berry, J.T., 2006. Transiente Temper-aturmessung. Giesserei-Praxis 10.
