- Email: [email protected]
Application of computational thermodynamics to the determination of thermophysical properties as a function of temperature for multicomponent Al-based alloys
Accepted Manuscript Title: Application of computational thermodynamics to the determination of thermophysical properties as a function of temperature for multicomponent Al-based alloys Author: Fabiana C. Nascimento Mara C.C. Paresque Jos´e A. de Castro Paulo A.D. J´acome Amauri Garcia Ivaldo L. Ferreira PII: DOI: Reference:
S0040-6031(15)00369-X http://dx.doi.org/doi:10.1016/j.tca.2015.09.013 TCA 77348
To appear in:
Thermochimica Acta
Received date: Revised date: Accepted date:
18-2-2015 17-7-2015 14-9-2015
Please cite this article as: F.C. Nascimento, M.C.C. Paresque, J.A. Castro, P.A.D. J´acome, A. Garcia, I.L. Ferreira, Application of computational thermodynamics to the determination of thermophysical properties as a function of temperature for multicomponent Al-based alloys, Thermochimica Acta (2015), http://dx.doi.org/10.1016/j.tca.2015.09.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Application of computational thermodynamics to the determination of thermophysical properties as a function of temperature for multicomponent Al-based alloys
Fluminense Federal University, Graduate Program in Metallurgical Engineering, Av. dos Trabalhadores, 420-27255-125 – Volta Redonda, RJ, Brazil 2
Fluminense Federal University, Graduate Program in Mechanical Engineering, Av. dos Trabalhadores,
us
420-27255-125 – Volta Redonda, RJ, Brazil 3
cr
1
ip t
Fabiana C. Nascimento1, Mara C. C. Paresque2, José A. de Castro1, Paulo A. D. Jácome2, Amauri Garcia3*, Ivaldo L. Ferreira2
University of Campinas -UNICAMP, Department of Manufacturing and Materials Engineering, 13083 –
an
860 Campinas, SP, Brazil
Abstract
M
Despite the technological importance of Al-Si-Cu alloys in manufacturing processes involving heat transfer, such as welding, casting and heat treatment, thermophysical properties of this system of alloys
d
are very scarce in the literature. In this paper, a model connected to a computational thermodynamics
Ac ce pt e
software is proposed permitting density and specific heats as a function of temperature and enthalpy of transformations to be numerically determined. The model is pre-validated against experimental density as a function of temperature for liquid and solid phases of A319 and 7075 alloys found in the literature and validated against experimental density values for the solid phase of an Al-6wt%Cu-1wt%Si alloy determined in the present study. In both cases the numerical predictions are in good agreement with the experimental results. Specific heat and temperatures and heats of transformation are also numerically determined for this ternary Al-based alloy.
Keywords: Numerical Simulation; Thermophysical Properties; Computational Thermodynamics; Dilatometry; Ternary Al-Cu-Si alloys.
(*) Corresponding author Tel.: +55 19 35213320; Fax: +55 19 32893722 E-mail address: [email protected]
1 Page 1 of 27
1. Introduction
Al-based alloys castings have played an important role in the growth of the aluminum industry. Aluminum alloys are used in the aerospace industry since the late
ip t
1930s, with a large substitution of steel parts by aluminum equivalent parts, because of
cr
their peculiar properties such as high mechanical strength, corrosion resistance and recyclability among other physicochemical properties [1, 2]. The resultant properties are
us
generally determined by alloy composition, crystalline arrangement, size and arrangement of the phases forming the microstructure and additional thermal and
an
mechanical treatments. In this way, the experimental determination of thermophysical
M
properties should consider a large amount of combinations of alloying elements, which in practice becomes unviable by the high cost of equipment and consumables [3]. For
d
experimental determination of density of a sample in the form of solid, powder, paste
Ac ce pt e
and liquid under certain controlled time and temperature conditions, the most common used technique is dilatometry [4]. Brooks et al. [5] first applied an electromagnetic levitation method typically used for measuring thermophysical properties at elevated temperatures, for measuring the density of liquids. In this method, a levitated drop of a known metal mass is heated and then optical images of this drop are taken in three orthogonal directions to be used to determine its volume. Recent advances of this technique are associated with the rapid development of CCD cameras and computational methods used to analyze the geometry of the drop [6]. Narender et al. [7] determined the temperature dependence of density, thermal expansion and coefficient of linear attenuation of wrought Al-Cu alloys in a range from 298 to 773 K, by a gamma ray attenuation technique. Tribula et al. determined the partial Gibbs energy of Li in Al2 Page 2 of 27
Li-Zn alloys by using electromotive force measurements [8]. Despite the potential of applications of these alloys in the aerospace industry, data on their thermodynamic properties are scarce in the literature. Schumacher et al. [9] have used a differential scanning calorimetry technique in the investigation of inter-relations of microstructure,
ip t
solute content and quenched-induced precipitates during cooling of solution annealing
cr
of Al-Si alloys.
The directional solidification technique is a versatile experimental procedure
us
permitting appropriate correlations between microstructure features of a given alloy and the corresponding solidification thermal parameters such as the growth rate and cooling
an
rate to be established [10]. The effect of microstructural features such as the
M
morphology, distribution and length scale of the phases forming the alloys microstructure, porosity, etc, can be associated with local alloy composition and cooling
d
rate along the length of directionally solidified (DS) castings [11]. This permits growth
Ac ce pt e
laws and experimental correlations with final application properties to be derived, which can be used in the tailoring of the microstructure with a view to specific applications [12]. Ferreira et al. [13] used a DS Al-6wt%Cu-1wt%Si casting to investigate the evolution of macrosegregation and porosity along the length of the casting. It was shown that Si alloying increases significantly the volumetric fraction of pores, which increases with the position (P) from the cooled surface to the top of the casting. In contrast the density was shown to be inversely proportional to the local porosity, decreasing with P. On the other hand, the simulation of thermophysical properties by using computational thermodynamics allows the determination of density, specific heat, heats of transformation as a function of temperature, pressure and composition. Furthermore, 3 Page 3 of 27
various types of stable phase diagrams and meta-stable properties and diagrams of complex multicomponent systems, Scheil-Gulliver simulation of solidification, liquidus surfaces, Pourbaix diagrams, Ellingham diagrams, partition coefficients, etc, can also be determined from a combination of experimental results of thermodynamics properties
ip t
such as the Gibbs free energy of phases associated with certain alloying elements [14].
cr
Utilizing the method of minimizing the free energy of phases, allows the mathematical
extrapolation of properties of complex multicomponent alloys to be determined with
us
great accuracy. One of the most used programs for this purpose is the Thermo-Calc, its databases and the communication interface between a program written in C language
an
and the Thermo-Calc called TCAPI (Thermo-Calc Application Programming Interface).
M
In the present study a numerical model developed in C language is proposed, which connects in real runtime execution to Thermo-Calc and its database TTAL7
d
(ThermoTech Aluminum Thermal Database) for determination of thermophysical properties
Ac ce pt e
such as: enthalpy; internal energy; Gibbs free energy; specific heats; heats of reaction; phase fractions and composition, necessary to calculate the density of multicomponent alloys as a function of temperature of solid and liquid phases. A dilatometer will be used to measure the density of solid samples of an Al-Cu-Si alloy as a function of temperature with a view to validating the numerical model. Specific heat as a function of temperature, and heats of transformation will also be determined.
4 Page 4 of 27
2. Numerical Model
Since one system of multicomponent alloys is defined, i.e. Al-Cu-Si in the present study, the Thermo-Calc is initialized from the numerical model by calling
ip t
TCAPI tc_init_root() function. The aluminum thermodynamics database TTAL7
cr
(ThermoTech Aluminum Thermal Database v.7) or any other database is retrieved by calling TCAPI interface tc_open_database() function. After initialization procedures, input data
us
such as the alloy composition and reference state is necessary for initial equilibrium calculation. If the equilibrium calculation is succeed, specific heat, latent heat, liquidus,
an
solidus and eutectic surfaces and partition coefficients are determined for the entire
M
system and stored. To calculate the density of Al-Cu-Si alloys as a function of composition and temperature one should initially provide to the numerical model the
d
density of the pure elements as a function of temperature, with a view to permitting the
Ac ce pt e
densities of the phases present in the alloy and their respective volume fractions to be calculated. The Thermo-Calc, from a selection of entry thermodynamic conditions, such as bulk composition of alloying elements, absolute temperature, pressure and number of moles of the solution then provides the phases present, the composition of these phases and their mass fractions for the given input conditions. The numerical model through the TCAPI interface retrieves the following information from the Thermo-Calc calculation: character vector containing the names of all phases present in the database, a vector containing only the phases present in the calculation of equilibrium for the given conditions, a vector for each phase containing their composition and mass fraction. Finally, phases that are present in the database, but not present for the equilibrium conditions receive from Thermo-Calc a value of zero, and a last vector 5 Page 5 of 27
containing the mass fractions of all the phases present in the database, in the same order vector of characters with the names of the phases for the equilibrium conditions of entry. Vectors of characters containing phase names and composition variables cited here make very easy the generalization procedures for alloys of any number of
ip t
components.
cr
Eq. 1 presents the sum of all mass fractions, wi, provided for all phases present
51
∑w
i
=1
(1)
an
i =1
us
in the database,
M
Eq. 2 calculates the density (ρ) of each phase, from data obtained from the vector that contains mass composition of alloy constituents of each phase and the density of the
d
elements present in the phase for a given input temperature. In order to automate the
Ac ce pt e
process, the calculation steps are executed for the 51 phases and 23 elements present in the database, with the null values of mass fraction indicating an element that is not present in a certain equilibrium phase at a given temperature.
ρ FCC _ A1 =
1
w
FCC _ A1 Al
ρ Al
+
FCC _ A1 Cu
w
ρ Cu
+
FCC _ A1 Si
w
ρ Si
= +"
1 23
∑ j =1
_ A1 w FCC j
(2)
ρj
where FCC_A1 is the primary Al-rich phase. Eq. 3 provides a mean to calculate the volume fraction of all phases present in the database, from the calculated phase densities and from the vector containing the mass
6 Page 6 of 27
fractions of all phases present in the database so to automate the calculation process. Thus,
VFCC _ A1 =
wFCC _ A1
ρ FCC _ A1 wFCC _ A1
+
ρ LIQUID
+
wFCC _ A1
ρ FCC _ A1
+"
ρ FCC _ A1 51
wk
k =1
k
∑ρ
(3)
cr
ρ FCC _ A1
wLIQUID
=
ip t
wFCC _ A1
us
The alloy density is reckoned by using Eq. 4 through linear combination of volume fractions calculated by Eq. 3 and densities obtained by the application of Eq. 2 for all
51
ρ Alloy _ Equilibrium = ∑ Vk ρ k
(4)
d
k =1
M
an
phases. Then,
Ac ce pt e
The solution scheme of the model is shown in Fig. 1. Now, applying the Scheil-Gulliver model, the alloy density is again reckoned for nonequilibrium conditions, once phase mass and volume fractions will be different from those obtained by carrying out the Lever Rule for global equilibrium conditions. 51
ρ Alloy _ Non − Equilibrium = ∑ VkScheil ρ k
(5)
k =1
In practice, neither Scheil-Gulliver nor the Lever Rule will occur, but something between both values, the so called, finite diffusion. A microsegregation parameter β must be set by applying the following equation [15]:
β = 2α (1 − e −1 α ) − e −1 2α
(6)
where α is the standard Fourier diffusion number. This back diffusion approach was firstly proposed by Swaminathan and Voller [15] and is equivalent to that of Clyne and 7 Page 7 of 27
Kurz correction [16] of the Brody and Flemings [17] back diffusion model. According to Clyne and Kurz, the Standard Fourier diffusion number is given by:
α=
DS t f 2
L
=
4 DS t f
(7)
λ2
ip t
where α is a constant related to the appropriate dendrite arm spacing λ, and is taken as twice the length of the diffusion path L, tf is the local solidification time, and DS is the
cr
solute diffusion coefficient of the solid phase.
us
Finally,
ρ Alloy = ρ Alloy _ Eq β + ρ Alloy _ Non − Eq (1 − β )
(8)
an
Where, ρAlloy_Eq and ρAlloy_Non-Eq are density calculated under equilibrium and non-
M
equilibrium conditions, respectively.
In the present study, the diffusion coefficients, DS, are assumed as the same used for the
Ac ce pt e
DSSi = 1,34 x 10 −7 e −30 RT
d
liquid by Easton and co-workers [18], for Cu and Si.
DSCu = 1,06 x 10 −7 e −24 RT
(8a) (8b)
where DS [m2/s].
8 Page 8 of 27
Data Entry: Alloy composition and reference state, Database TTAL7
ip t
Thermo-Calc and database TTAL7 initialization
cr
Temperature Ti
us
TC-API direct access to Thermo-Calc and TTAL7 to yield phases composition, phases mass fraction
an
Calculation of phases density, phases volume fraction and alloy density at temperature Ti
Yes
M
One more
No
Ac ce pt e
d
Program terminates
Fig. 1 - Solution scheme for determination of density of a multicomponent alloy by calling Thermo-Calc and TTAl7 through a C language program.
3. Experimental procedure
The directional solidification (DS) casting assembly used to experimentally
obtain the alloy samples has been detailed in previous articles [19-21]. The experimental setup consists of a water-cooled mold with heat being extracted from the bottom, promoting a vertical upward directional solidification (Fig. 2a). The stainless steel mold had an internal diameter of 50 mm, a height of 110mm and a wall thickness 9 Page 9 of 27
of 3mm (Fig. 2b). Experiments were performed with an Al–6 wt%Cu–1 wt%Si alloy (ASTM 319.2), under thermally and solutally stable solidification conditions. During directional solidification of metallic alloys the thermal profile is expected to cause stability against convection only in the upward vertical solidification (melt on top and
ip t
solid below). However, the solute profile inside the mushy zone and in the overlying
cr
melt immediately ahead of dendrite tips would be stable only if solute enrichment
increases the melt density for vertical upward solidification [22, 23], which is the case
us
of Si and Cu in the Al-Cu-Si alloy examined. Continuous temperature measurements in the casting were monitored during solidification via the output of a bank of fine type K
an
thermocouples sheathed in 1.6mm OD stainless steel tubes, and positioned at 5, 10, 15,
M
30, 50 and 70 mm from the heat-extracting surface at the bottom of the crucible. All thermocouples were connected by coaxial cables to a data logger interfaced with a
d
computer and the temperature data were acquired automatically.
Ac ce pt e
The casting was sectioned in the longitudinal direction and the macrostructure was examined (Fig. 2c – left side). Next, the sample pieces were sectioned into transverse slices (Fig. 2c – right side)and a square central part was cut by the use of a precision saw (Buehler Isomet 4000 with a 0.3mmthick diamond disk) into pieces of approximately 1.0mm. Subsequently, the samples were investigated by a Rigaku Rix 3100 X-ray fluorescence spectrometer to estimate its average concentration through an area of 100 mm2 probe (probe effective area or the so-called “mask radiated area”). The same sample is rearranged in the mask in order to permit a total of 10 readings of composition at different positions in the DS casting to be obtained. Four samples were extracted from the DS casting at 20 mm from the cooled surface having a composition closest to that of the nominal composition of the alloy. Cylinders of 5.08 mm hight and 10 Page 10 of 27
6.6 mm OD were carefully machined from these samples to fit into the NETZSCH 402 C dilatometer sample holder. The dilatometer was calibrated with an alumina standard sample considering a steady Ar gas flowing at a constant rate. The temperature was increased at a rate of 10oC/min from 25oC until 1700 oC. The calibration was repeat
ip t
once more. After calibration, an Al-6wt%Cu-1wt%Si sample was heated at 10oC/min
cr
from 25oC to 500 oC, i.e. before the ternary eutectic temperature was reached. Dilatation
data were recorded and afterwards used to calculate the volume variation as a function
us
of temperature [24].
Ac ce pt e
d
M
an
11 Page 11 of 27
cr
ip t
100 mm
us
(c)
an
Fig. 2. (a) Schematic representation of the experimental setup: 1) rotameter; 2) heatextracting bottom; 3) thermocouples; 4) computer and data acquisition software; 5) data logger; 6) casting; 7) mold; 8) temperature controller; 9) electric heaters; 10) insulating
M
ceramic shielding; (b) Split mold and water-cooled bottom; (c) Columnar
Ac ce pt e
4. Results and discussion
d
macrostructure of the DS casting (left) and central samples extracted for XRF analyses.
For a pre-validation of the thermodynamic model proposed with a view to
determining the density of multicomponent alloys as a function of temperature, a theoretical-experimental confront was carried out with experimental density results from two Al-based alloys available in the literature [25], whose compositions are shown in Table 1. Figs. 3 and 4 show good agreement between the numerical predictions and the experimental results for all given temperatures in the solid and in the liquid phases.
12 Page 12 of 27
Table 1 – Alloys Chemical Composition [wt%]. Al
Cu
Mg
Mn
Ni
Si
Zn
Other
A319
89.4
3.0
0.1
0.4
0.4
5.0
1.0
0.7
Alloy
Al
Cr
Cu
Fe
Mg
Mn
Si
Ti
Zn
7075
88.7
0.2
1.6
0.5
2.5
0.4
0.4
0.2
5.5
Alloy A1-LM4 (A319)
2760
M
2720 2680 2640
d
2600
Numerical, Solid Experimental, Solid [25] Numerical, Liquid Experimental, Liquid [25]
2560
Ac ce pt e
-3
cr
us an
2800
Density [kg.m ]
ip t
Alloy
2520 2480 2440 2400
0
100
200
300
400
500
600
700
800
900
o
Temperature [ C]
Fig. 3 –Comparison between numerical predictions and experimental density results of solid and liquid phases as a function of temperature for an A319 alloy.
13 Page 13 of 27
2840
Alloy A1-7075-T6
2800 2760
2680 2640
Num erical, Solid Experim ental Solid [25] Num erical, Liquid Experim ental, Liquid [25]
2600 2560
ip t
-3
Density [kg.m ]
2720
2520
cr
2480 2440
0
100
200
300
400
500
600 o
700
800
900
M
an
Tem perature [ C]
us
2400
Fig. 4 –Comparison between numerical predictions and experimental density results of solid and
Ac ce pt e
d
liquid phases as a function of temperature for a 7075 alloy.
The composition of Cu and Si along the length of the directionally solidified Al-
6wt%Cu-1wt%Si casting was determined by R-ray fluorescence and is shown in Fig. 5a. The casting region close to the cooled surface was subjected to a more detailed analysis with a view to determining more accurately the Cu inverse segregation profile, as depicted in Fig. 5b.
14 Page 14 of 27
8
Experimental - Cu Experimental - Si
6
cr
ip t
5
us
1,0
0,5
an
Composition [wt% Cu, Si,]
7
0,0 0
20
40
60
80
100
Position [mm]
M
d
(a)
7,50 7,25
Ac ce pt e
Al-6wt%Cu-1wt%Si
7,00
Composition [wt% Cu, Si]
6,75 6,50 6,25 6,00
Cu Si
5,75
1,2
0,9
0,6
0
2
4
6
8
10
Position [mm]
12
14
16
18
Fig. 5. (a) XRF results of Cu and Si profiles along the length of the DS casting; (b) Detailed results corresponding to positions close to the casting surface highlighting the Cu inverse segregation 15 Page 15 of 27
Al-alloys castings are subjected to porosity formation when the casting operation is not carried out under a controlled inert atmosphere. The local solute composition as well as the local volume fraction are known to affect the local density [13]. With a view to permitting the effects of Si alloying in the fraction of pores to be analyzed some
ip t
experimental results of evolution of porosity in Al-Cu and Al-Cu-Si alloys DS castings,
cr
from previous studies from some of the present authors[13,19], have been synthesized in Fig. 6. It can be seen that Si alloying affects significantly the pores fraction, and that
us
the evolution of pores tend to increase from the cooled bottom to the top of the DS
an
casting.
M
10
d
6
Experimental Al-6.2 wt% Cu Experimental Al-6.0 wt% Cu-1.0 wt% Si Experimental Al-6.0 wt% Cu-4.0 wt% Si Numerical
Ac ce pt e
Pores [ % ]
8
4
2
0
0
20
40
60
80
Position from the casting cooled surface [ mm ]
100
Fig. 6 – Effect of Si alloying on the volumetric fraction of pores along the length of DS castings [13, 19]
16 Page 16 of 27
Fig. 7 shows the numerical predictions furnished by the model compared with the experimental density of the solid phase as a function of temperature, determined in the present study for the Al-6wt%Cu-1wt%Si alloy. As reported in the Experimental section, the samples experimentally examined were extracted at 40mm from the casting
ip t
cooled surface, i.e. having a solute concentration close to the nominal composition of
2840
Al-6wt%Cu-1wt%Si
2800
an
2760 2720
M
2680 2640 2600
d
2560 ) k r o W t n e s e r P ( d i l d o i d u i l q o i
2520
Numerical, S Numerical, L Experimental, S
Ac ce pt e
-3
Density [kg.m ]
us
cr
the alloy (Fig. 5a) and a mean value of pores fraction of about 2% (Fig. 6).
2480 2440 2400
0
100
200
300
400
500
600
700
800
900
o
Temperature [ C]
Fig. 7 – Comparison between numerical predictions and experimental density results of solid phase as function of temperature for the Al-6wt%Cu-1wt%Si alloy. Density of the liquid phase was numerically calculated.
Fig. 8 shows the model predictions of specific heat as a function of temperature for the Al-6wt%Cu-1wt%Si alloy. 17 Page 17 of 27
cr
ip t
.
1200
Al-6wt%Cu-1wt%Si
us
1100
an
1050
M
1000 950
Numerical Simulation
900
d
-1
-1
Specific heat [J.kg .K ]
1150
Ac ce pt e
850 800
0
100
200
300
400
500
600
700
800
900
o
Temperature [ C]
Fig. 8 – Numerical calculation of specific heat as function of temperature for the solid and liquid phases for the Al-6wt%Cu-1wt%Si alloy.
With a view to permitting comparisons with results of constant density and specific heat of the solid, adopted in a previous study from the literature for simulations of thermal parameters of a directionally solidified Al-6wt%Cu-1wt%Si alloy casting, the numerical values of Figs 7 and 8 are also shown in Table 2. It can be seen that the 18 Page 18 of 27
use of the present range of values in such simulation, instead of the constant value used in the previous study, would permit a more appropriate evolution of solidification thermal parameters with temperature to be determined.
Temperature
Units
an
100 Density
200
kg/m³
Ac ce pt e
100 Specific Heat
200
J/kg.K
Present Work
2797.8 2774.4 2751.1 2727.7 2650.3
d
500
2713.4
M
300 400
[16,17]
us
(°C)
cr
values from the literature [26, 27] Properties
with
ip t
Table 2 -Density and specific heat of the Al-6wt%Cu-1wt%Si alloy compared
910 1063
964.4
300
1041
400
1168
500
1407
Fig. 9 shows two calculated pseudo-binary phase diagrams for Al-Cu-Si system
of alloys, i.e., Al-Xwt%Cu-1wt%Si and Al-6wt%Cu-Ywt%Si, respectively. As can be easily noticed this system encompasses the following phases: Liquid, α-phase FCC_A1, eutectic phase Al2Cu and Silicon. The transformation temperatures and heats are given in Table 3. Scheil-Gulliver simulations obtained the transformation heats provided in Table 3. 19 Page 19 of 27
Ac ce pt e
d
M
(a)
an
us
cr
ip t
(b) Fig. 9 – Calculated pseudo-binary phase diagrams: (a) Al-Xwt%Cu1wt%Si and (b) AlYwt%Si6wt%Cu alloys. 20 Page 20 of 27
Fig. 10 shows the Scheil-Gulliver simulation of temperature as a function of mass fraction of all solid phases for the Al-6wt%Cu-1wt%Si alloy, with a view to evaluating the volume fraction of phases for non-equilibrium condition so to reckon the non-
Ac ce pt e
d
M
an
us
cr
ip t
equilibrium alloy density, according to Eq. (5).
Fig. 10 – Scheil-Gulliver simulation of mass fraction of all solid phases for the Al6wt%Cu-1wt%Si alloy.
21 Page 21 of 27
Table 3 - Temperatures and heats of transformation for the Al-6wt%Cu-1wt%Si alloy.
Symbol
Value/Unit
DTA-DSC
TL
638°C
638.5
Initial Al2Cu Transformation Temperature
TIE
530.2°C
527.1 oC
Final Al2Cu Transformation Temperature
TFE
527.6°C
524.6oC
Silicon Precipitation Temperature
TPSi
513.2°C
512.2 oC
ΔH 1
289,600 J.kg-1
280700 J.kg-1
ΔH 2
15,800 J.kg-1
14400 J.kg-1
ΔH 3
57,200 J.kg-1
68400 J.kg-1
M
an
liquidus temperature
us
cr
Simulation
Value/Units
ip t
Properties
Latent Heat of Fusion - 638 to 530.2 °C
Ac ce pt e
d
Latent Heat of Fusion - 530.2 to 527.60 °C Latent Heat of Fusion - up to 513.20 °C
5. Conclusions
A numerical model, based on the the coupling of the computational
thermodynamics software Thermo-Calc and the database TTAL7 with a C language numerical code that accesses and controls the Thermo-Calc by employing TCAPI interface, with a view to numerically determining thermophysical properties of multicomponent alloys, was proposed. The numerical and experimental results confronted for density as a function of temperature for aluminum alloys A356 and 7075 22 Page 22 of 27
and solid Al-6wt%Cu-1wt%Si alloy, allow us to state that the proposed model furnishes quite accurate predictions. Although simple equations have been used to calculate the density and the volume fraction of the phases, the bulk phases present, their mass fractions and phase compositions were calculated using Thermo-Calc considering the
ip t
excess terms, so that errors from volumetric data calculated by the numerical model are
cr
minimized. It was also shown that the model permits the determination of specific and
transformation heats, allowing the access to important information on Al-based
an
us
multicomponent alloys that are very scarce in the literature.
M
Acknowledgements
The authors acknowledge the financial support provided by FAPERJ (The Scientific
d
Research Foundation of the State of Rio de Janeiro, Brazil), FAPESP- São Paulo
Ac ce pt e
Research Foundation, Brazil (grant 2013/23396-7), CAPES and CNPq (The Brazilian Research Council).
References
[1] A. Kelkar, R. Roth, J. Clark. JOM 53 (2001) 28-32. [2] E. L. Rooy: in Metals Handbook, vol. 15, ASM International, Materials Park, Ohio, 1988, pp.743-770 [3] J.A.J. Robinson, R.F. Brooks, P.N. Quested. High. Temp. Mater. Proc. 31 (2012) 237-242. [4] J. Blumm, J. Henderson. High Temp. – High Press. 32 (2000) 109-113. 23 Page 23 of 27
[5] R.F. Brooks, A.P. Day, K.C. Mills, P.N. Quested. Int. J. Thermophys. 18 (1997) 471480. [6] P.N. Quested, R.F. Brooks, ASM Handbook, v. 22B, Metals Process Simulation, 2010,
ip t
pp.33-40. [7] K. Narender, A.S. Madhusudhan Rao, K. Gopal Kishan Rao, N. Gopi Krishna.
cr
Thermochim. Acta 569 (2013) 90-96.
us
[8] M. Trybula. P. Fima, W. Gasior. Thermochim. Acta 588 (2014) 16-21.
an
[9] P. Schumacher, S. Pogatscher, M.J. Starink, C. Schick, V. Mohles, B. Milkereit.
M
Thermochim. Acta 602 (2015) 63-73.
[10] C. Brito, T.A. Costa, T.A. Vida, F. Bertelli, N. Cheung, J.E. Spinelli, A. Garcia. Metall.
d
Mater. Trans. 46A (2015) 3342-3355.
Ac ce pt e
[11] F. Bertelli, C. Brito, I.L. Ferreira, G. Reinhart, H. Nguyen-Thi, N. Mangelinck-Noel, A. Garcia. Mater. Des. 72 (2015) 31-42.
[12] M. Dias, T. Costa, O. Rocha, J.E. Spinelli, N. Cheung, A. Garcia. Mater. Character. 106 (2015) 52-61.
[13] I.L. Ferreira, J.F.C. Lins, D.J. Moutinho, L.G. Gomes, A. Garcia. J Alloys Comp 503 (2010) 31-39.
[14] U.R. Kattner, JOM, 49 (1997)14-19. [15] C. R. Swaminathan, V. R. Voller. Int. J. Heat Mass Transfer, 40 (1997), 28592868. [16] T. W. Clyne, W. Kurz. Metall. Trans. 12A (1981), 965- 971. 24 Page 24 of 27
[17] H. B. Brody, M. C. Flemings. Transactions AIME, 236 (1996), 615- 624. [18] Mark Easton, Cameron Davidson, David St John. Metall. Mater. Trans. 41A (2010), 1528-1538 [19] D.J. Moutinho, L.G. Gomes, O.L. Rocha, I.L. Ferreira, A. Garcia. Mater. Sci.
ip t
Forum, 730-732 (2013)883-888.
cr
[20] I.L. Ferreira, V.R. Voller, B. Nestler, A. Garcia. Comp. Mater. Sci. 46 (2009)358366.
us
[21] I.L. Ferreira, C.A. Santos, V.R. Voller, A. Garcia. Metall. Mater. Trans. B 35 (2004) 285-297.
an
[22] J.E. Spinelli, M.D. Peres, A. Garcia. J Alloys Comp. 403 (2005) 228-238
271-282
M
[23] J.E. Spinelli, D.M. Rosa,, I.L. Ferreira, A. Garcia. Mater. Sci. Eng. A 383 (2004)
Ac ce pt e
Mater. 403 (2010) 160-166.
d
[24] D.E. Burkes, C.A.. Papesch, A.P. Maddison, T. Hartmann, F.J. Rice. J. Nuclear
[25] K.C. Mills: Recommended Values of Thermophysical Properties for Selected Commercial Alloys. Cambridge. Woodhead Publishing Ltd. 2002. [26] P.A.D. Jácome, M.C. Landim, A. Garcia, A.F. Furtado, I.L. Ferreira. Thermochim. Acta, 523 (2011) 142-149.
[27] I.L. Ferreira, D.J. Moutinho, L.G. Gomes, O.L. Rocha, P. R. Goulart, A. Garcia. Mater. Sci. Forum 636-637 (2010) 643-650.
25 Page 25 of 27
Figure Captions
Fig. 1 - Solution scheme for determination of density of a multicomponent alloy by calling Thermo-Calc and TTAl7 through a C language program.
ip t
Fig. 2. (a) Schematic representation of the experimental setup: 1) rotameter; 2) heat-
cr
extracting bottom; 3) thermocouples; 4) computer and data acquisition software; 5) data
logger; 6) casting; 7) mold; 8) temperature controller; 9) electric heaters; 10) insulating
us
ceramic shielding; (b) Split mold and water-cooled bottom; (c) Columnar macrostructure of the DS casting (left) and central samples extracted for XRF analyses.
an
Fig. 3 –Comparison between numerical predictions and experimental density results of
M
solid and liquid phases as a function of temperature for an A319 alloy. Fig. 4 –Comparison between numerical predictions and experimental density results of
d
solid and liquid phases as a function of temperature for a 7075 alloy.
Ac ce pt e
Fig. 5. (a) XRF results of Cu and Si profiles along the length of the DS casting; (b) Detailed results corresponding to positions close to the casting surface highlighting the Cu inverse segregation
Fig. 6 – Effect of Si alloying on the volumetric fraction of pores along the length of DS castings [13, 19]
Fig. 7 – Comparison between numerical predictions and experimental density results of solid phase as function of temperature for the Al-6wt%Cu-1wt%Si alloy. Density of the liquid phase was numerically calculated. Fig. 8 – Numerical calculation of specific heat as function of temperature for the solid and liquid phases for the Al-6wt%Cu-1wt%Si alloy.
26 Page 26 of 27
Fig. 9 – Calculated pseudo-binary phase diagrams: (a) Al-Xwt%Cu1wt%Si and (b) AlYwt%Si6wt%Cu alloys. Fig. 10 – Scheil-Gulliver simulation of mass fraction of all solid phases for the Al-
ip t
6wt%Cu-1wt%Si alloy.
us
Table 1 – Alloys Chemical Composition [wt%].
cr
Table Captions
Table 2 -Density and specific heat of the Al-6wt%Cu-1wt%Si alloy compared
an
values from the literature [26, 27]
with
A model coupled to a computational thermodynamics software is proposed to
Ac ce pt e
•
d
Research Highlights
M
Table 3 - Temperatures and heats of transformation for the Al-6wt%Cu-1wt%Si alloy.
compute thermophysical properties.
•
The model applies to multicomponent alloys and has been validated against experimental results
•
Density and specific heat as a function of temperature are computed for Al-SiCu alloys
27 Page 27 of 27
S0040-6031(15)00369-X http://dx.doi.org/doi:10.1016/j.tca.2015.09.013 TCA 77348
To appear in:
Thermochimica Acta
Received date: Revised date: Accepted date:
18-2-2015 17-7-2015 14-9-2015
Please cite this article as: F.C. Nascimento, M.C.C. Paresque, J.A. Castro, P.A.D. J´acome, A. Garcia, I.L. Ferreira, Application of computational thermodynamics to the determination of thermophysical properties as a function of temperature for multicomponent Al-based alloys, Thermochimica Acta (2015), http://dx.doi.org/10.1016/j.tca.2015.09.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Application of computational thermodynamics to the determination of thermophysical properties as a function of temperature for multicomponent Al-based alloys
Fluminense Federal University, Graduate Program in Metallurgical Engineering, Av. dos Trabalhadores, 420-27255-125 – Volta Redonda, RJ, Brazil 2
Fluminense Federal University, Graduate Program in Mechanical Engineering, Av. dos Trabalhadores,
us
420-27255-125 – Volta Redonda, RJ, Brazil 3
cr
1
ip t
Fabiana C. Nascimento1, Mara C. C. Paresque2, José A. de Castro1, Paulo A. D. Jácome2, Amauri Garcia3*, Ivaldo L. Ferreira2
University of Campinas -UNICAMP, Department of Manufacturing and Materials Engineering, 13083 –
an
860 Campinas, SP, Brazil
Abstract
M
Despite the technological importance of Al-Si-Cu alloys in manufacturing processes involving heat transfer, such as welding, casting and heat treatment, thermophysical properties of this system of alloys
d
are very scarce in the literature. In this paper, a model connected to a computational thermodynamics
Ac ce pt e
software is proposed permitting density and specific heats as a function of temperature and enthalpy of transformations to be numerically determined. The model is pre-validated against experimental density as a function of temperature for liquid and solid phases of A319 and 7075 alloys found in the literature and validated against experimental density values for the solid phase of an Al-6wt%Cu-1wt%Si alloy determined in the present study. In both cases the numerical predictions are in good agreement with the experimental results. Specific heat and temperatures and heats of transformation are also numerically determined for this ternary Al-based alloy.
Keywords: Numerical Simulation; Thermophysical Properties; Computational Thermodynamics; Dilatometry; Ternary Al-Cu-Si alloys.
(*) Corresponding author Tel.: +55 19 35213320; Fax: +55 19 32893722 E-mail address: [email protected]
1 Page 1 of 27
1. Introduction
Al-based alloys castings have played an important role in the growth of the aluminum industry. Aluminum alloys are used in the aerospace industry since the late
ip t
1930s, with a large substitution of steel parts by aluminum equivalent parts, because of
cr
their peculiar properties such as high mechanical strength, corrosion resistance and recyclability among other physicochemical properties [1, 2]. The resultant properties are
us
generally determined by alloy composition, crystalline arrangement, size and arrangement of the phases forming the microstructure and additional thermal and
an
mechanical treatments. In this way, the experimental determination of thermophysical
M
properties should consider a large amount of combinations of alloying elements, which in practice becomes unviable by the high cost of equipment and consumables [3]. For
d
experimental determination of density of a sample in the form of solid, powder, paste
Ac ce pt e
and liquid under certain controlled time and temperature conditions, the most common used technique is dilatometry [4]. Brooks et al. [5] first applied an electromagnetic levitation method typically used for measuring thermophysical properties at elevated temperatures, for measuring the density of liquids. In this method, a levitated drop of a known metal mass is heated and then optical images of this drop are taken in three orthogonal directions to be used to determine its volume. Recent advances of this technique are associated with the rapid development of CCD cameras and computational methods used to analyze the geometry of the drop [6]. Narender et al. [7] determined the temperature dependence of density, thermal expansion and coefficient of linear attenuation of wrought Al-Cu alloys in a range from 298 to 773 K, by a gamma ray attenuation technique. Tribula et al. determined the partial Gibbs energy of Li in Al2 Page 2 of 27
Li-Zn alloys by using electromotive force measurements [8]. Despite the potential of applications of these alloys in the aerospace industry, data on their thermodynamic properties are scarce in the literature. Schumacher et al. [9] have used a differential scanning calorimetry technique in the investigation of inter-relations of microstructure,
ip t
solute content and quenched-induced precipitates during cooling of solution annealing
cr
of Al-Si alloys.
The directional solidification technique is a versatile experimental procedure
us
permitting appropriate correlations between microstructure features of a given alloy and the corresponding solidification thermal parameters such as the growth rate and cooling
an
rate to be established [10]. The effect of microstructural features such as the
M
morphology, distribution and length scale of the phases forming the alloys microstructure, porosity, etc, can be associated with local alloy composition and cooling
d
rate along the length of directionally solidified (DS) castings [11]. This permits growth
Ac ce pt e
laws and experimental correlations with final application properties to be derived, which can be used in the tailoring of the microstructure with a view to specific applications [12]. Ferreira et al. [13] used a DS Al-6wt%Cu-1wt%Si casting to investigate the evolution of macrosegregation and porosity along the length of the casting. It was shown that Si alloying increases significantly the volumetric fraction of pores, which increases with the position (P) from the cooled surface to the top of the casting. In contrast the density was shown to be inversely proportional to the local porosity, decreasing with P. On the other hand, the simulation of thermophysical properties by using computational thermodynamics allows the determination of density, specific heat, heats of transformation as a function of temperature, pressure and composition. Furthermore, 3 Page 3 of 27
various types of stable phase diagrams and meta-stable properties and diagrams of complex multicomponent systems, Scheil-Gulliver simulation of solidification, liquidus surfaces, Pourbaix diagrams, Ellingham diagrams, partition coefficients, etc, can also be determined from a combination of experimental results of thermodynamics properties
ip t
such as the Gibbs free energy of phases associated with certain alloying elements [14].
cr
Utilizing the method of minimizing the free energy of phases, allows the mathematical
extrapolation of properties of complex multicomponent alloys to be determined with
us
great accuracy. One of the most used programs for this purpose is the Thermo-Calc, its databases and the communication interface between a program written in C language
an
and the Thermo-Calc called TCAPI (Thermo-Calc Application Programming Interface).
M
In the present study a numerical model developed in C language is proposed, which connects in real runtime execution to Thermo-Calc and its database TTAL7
d
(ThermoTech Aluminum Thermal Database) for determination of thermophysical properties
Ac ce pt e
such as: enthalpy; internal energy; Gibbs free energy; specific heats; heats of reaction; phase fractions and composition, necessary to calculate the density of multicomponent alloys as a function of temperature of solid and liquid phases. A dilatometer will be used to measure the density of solid samples of an Al-Cu-Si alloy as a function of temperature with a view to validating the numerical model. Specific heat as a function of temperature, and heats of transformation will also be determined.
4 Page 4 of 27
2. Numerical Model
Since one system of multicomponent alloys is defined, i.e. Al-Cu-Si in the present study, the Thermo-Calc is initialized from the numerical model by calling
ip t
TCAPI tc_init_root() function. The aluminum thermodynamics database TTAL7
cr
(ThermoTech Aluminum Thermal Database v.7) or any other database is retrieved by calling TCAPI interface tc_open_database() function. After initialization procedures, input data
us
such as the alloy composition and reference state is necessary for initial equilibrium calculation. If the equilibrium calculation is succeed, specific heat, latent heat, liquidus,
an
solidus and eutectic surfaces and partition coefficients are determined for the entire
M
system and stored. To calculate the density of Al-Cu-Si alloys as a function of composition and temperature one should initially provide to the numerical model the
d
density of the pure elements as a function of temperature, with a view to permitting the
Ac ce pt e
densities of the phases present in the alloy and their respective volume fractions to be calculated. The Thermo-Calc, from a selection of entry thermodynamic conditions, such as bulk composition of alloying elements, absolute temperature, pressure and number of moles of the solution then provides the phases present, the composition of these phases and their mass fractions for the given input conditions. The numerical model through the TCAPI interface retrieves the following information from the Thermo-Calc calculation: character vector containing the names of all phases present in the database, a vector containing only the phases present in the calculation of equilibrium for the given conditions, a vector for each phase containing their composition and mass fraction. Finally, phases that are present in the database, but not present for the equilibrium conditions receive from Thermo-Calc a value of zero, and a last vector 5 Page 5 of 27
containing the mass fractions of all the phases present in the database, in the same order vector of characters with the names of the phases for the equilibrium conditions of entry. Vectors of characters containing phase names and composition variables cited here make very easy the generalization procedures for alloys of any number of
ip t
components.
cr
Eq. 1 presents the sum of all mass fractions, wi, provided for all phases present
51
∑w
i
=1
(1)
an
i =1
us
in the database,
M
Eq. 2 calculates the density (ρ) of each phase, from data obtained from the vector that contains mass composition of alloy constituents of each phase and the density of the
d
elements present in the phase for a given input temperature. In order to automate the
Ac ce pt e
process, the calculation steps are executed for the 51 phases and 23 elements present in the database, with the null values of mass fraction indicating an element that is not present in a certain equilibrium phase at a given temperature.
ρ FCC _ A1 =
1
w
FCC _ A1 Al
ρ Al
+
FCC _ A1 Cu
w
ρ Cu
+
FCC _ A1 Si
w
ρ Si
= +"
1 23
∑ j =1
_ A1 w FCC j
(2)
ρj
where FCC_A1 is the primary Al-rich phase. Eq. 3 provides a mean to calculate the volume fraction of all phases present in the database, from the calculated phase densities and from the vector containing the mass
6 Page 6 of 27
fractions of all phases present in the database so to automate the calculation process. Thus,
VFCC _ A1 =
wFCC _ A1
ρ FCC _ A1 wFCC _ A1
+
ρ LIQUID
+
wFCC _ A1
ρ FCC _ A1
+"
ρ FCC _ A1 51
wk
k =1
k
∑ρ
(3)
cr
ρ FCC _ A1
wLIQUID
=
ip t
wFCC _ A1
us
The alloy density is reckoned by using Eq. 4 through linear combination of volume fractions calculated by Eq. 3 and densities obtained by the application of Eq. 2 for all
51
ρ Alloy _ Equilibrium = ∑ Vk ρ k
(4)
d
k =1
M
an
phases. Then,
Ac ce pt e
The solution scheme of the model is shown in Fig. 1. Now, applying the Scheil-Gulliver model, the alloy density is again reckoned for nonequilibrium conditions, once phase mass and volume fractions will be different from those obtained by carrying out the Lever Rule for global equilibrium conditions. 51
ρ Alloy _ Non − Equilibrium = ∑ VkScheil ρ k
(5)
k =1
In practice, neither Scheil-Gulliver nor the Lever Rule will occur, but something between both values, the so called, finite diffusion. A microsegregation parameter β must be set by applying the following equation [15]:
β = 2α (1 − e −1 α ) − e −1 2α
(6)
where α is the standard Fourier diffusion number. This back diffusion approach was firstly proposed by Swaminathan and Voller [15] and is equivalent to that of Clyne and 7 Page 7 of 27
Kurz correction [16] of the Brody and Flemings [17] back diffusion model. According to Clyne and Kurz, the Standard Fourier diffusion number is given by:
α=
DS t f 2
L
=
4 DS t f
(7)
λ2
ip t
where α is a constant related to the appropriate dendrite arm spacing λ, and is taken as twice the length of the diffusion path L, tf is the local solidification time, and DS is the
cr
solute diffusion coefficient of the solid phase.
us
Finally,
ρ Alloy = ρ Alloy _ Eq β + ρ Alloy _ Non − Eq (1 − β )
(8)
an
Where, ρAlloy_Eq and ρAlloy_Non-Eq are density calculated under equilibrium and non-
M
equilibrium conditions, respectively.
In the present study, the diffusion coefficients, DS, are assumed as the same used for the
Ac ce pt e
DSSi = 1,34 x 10 −7 e −30 RT
d
liquid by Easton and co-workers [18], for Cu and Si.
DSCu = 1,06 x 10 −7 e −24 RT
(8a) (8b)
where DS [m2/s].
8 Page 8 of 27
Data Entry: Alloy composition and reference state, Database TTAL7
ip t
Thermo-Calc and database TTAL7 initialization
cr
Temperature Ti
us
TC-API direct access to Thermo-Calc and TTAL7 to yield phases composition, phases mass fraction
an
Calculation of phases density, phases volume fraction and alloy density at temperature Ti
Yes
M
One more
No
Ac ce pt e
d
Program terminates
Fig. 1 - Solution scheme for determination of density of a multicomponent alloy by calling Thermo-Calc and TTAl7 through a C language program.
3. Experimental procedure
The directional solidification (DS) casting assembly used to experimentally
obtain the alloy samples has been detailed in previous articles [19-21]. The experimental setup consists of a water-cooled mold with heat being extracted from the bottom, promoting a vertical upward directional solidification (Fig. 2a). The stainless steel mold had an internal diameter of 50 mm, a height of 110mm and a wall thickness 9 Page 9 of 27
of 3mm (Fig. 2b). Experiments were performed with an Al–6 wt%Cu–1 wt%Si alloy (ASTM 319.2), under thermally and solutally stable solidification conditions. During directional solidification of metallic alloys the thermal profile is expected to cause stability against convection only in the upward vertical solidification (melt on top and
ip t
solid below). However, the solute profile inside the mushy zone and in the overlying
cr
melt immediately ahead of dendrite tips would be stable only if solute enrichment
increases the melt density for vertical upward solidification [22, 23], which is the case
us
of Si and Cu in the Al-Cu-Si alloy examined. Continuous temperature measurements in the casting were monitored during solidification via the output of a bank of fine type K
an
thermocouples sheathed in 1.6mm OD stainless steel tubes, and positioned at 5, 10, 15,
M
30, 50 and 70 mm from the heat-extracting surface at the bottom of the crucible. All thermocouples were connected by coaxial cables to a data logger interfaced with a
d
computer and the temperature data were acquired automatically.
Ac ce pt e
The casting was sectioned in the longitudinal direction and the macrostructure was examined (Fig. 2c – left side). Next, the sample pieces were sectioned into transverse slices (Fig. 2c – right side)and a square central part was cut by the use of a precision saw (Buehler Isomet 4000 with a 0.3mmthick diamond disk) into pieces of approximately 1.0mm. Subsequently, the samples were investigated by a Rigaku Rix 3100 X-ray fluorescence spectrometer to estimate its average concentration through an area of 100 mm2 probe (probe effective area or the so-called “mask radiated area”). The same sample is rearranged in the mask in order to permit a total of 10 readings of composition at different positions in the DS casting to be obtained. Four samples were extracted from the DS casting at 20 mm from the cooled surface having a composition closest to that of the nominal composition of the alloy. Cylinders of 5.08 mm hight and 10 Page 10 of 27
6.6 mm OD were carefully machined from these samples to fit into the NETZSCH 402 C dilatometer sample holder. The dilatometer was calibrated with an alumina standard sample considering a steady Ar gas flowing at a constant rate. The temperature was increased at a rate of 10oC/min from 25oC until 1700 oC. The calibration was repeat
ip t
once more. After calibration, an Al-6wt%Cu-1wt%Si sample was heated at 10oC/min
cr
from 25oC to 500 oC, i.e. before the ternary eutectic temperature was reached. Dilatation
data were recorded and afterwards used to calculate the volume variation as a function
us
of temperature [24].
Ac ce pt e
d
M
an
11 Page 11 of 27
cr
ip t
100 mm
us
(c)
an
Fig. 2. (a) Schematic representation of the experimental setup: 1) rotameter; 2) heatextracting bottom; 3) thermocouples; 4) computer and data acquisition software; 5) data logger; 6) casting; 7) mold; 8) temperature controller; 9) electric heaters; 10) insulating
M
ceramic shielding; (b) Split mold and water-cooled bottom; (c) Columnar
Ac ce pt e
4. Results and discussion
d
macrostructure of the DS casting (left) and central samples extracted for XRF analyses.
For a pre-validation of the thermodynamic model proposed with a view to
determining the density of multicomponent alloys as a function of temperature, a theoretical-experimental confront was carried out with experimental density results from two Al-based alloys available in the literature [25], whose compositions are shown in Table 1. Figs. 3 and 4 show good agreement between the numerical predictions and the experimental results for all given temperatures in the solid and in the liquid phases.
12 Page 12 of 27
Table 1 – Alloys Chemical Composition [wt%]. Al
Cu
Mg
Mn
Ni
Si
Zn
Other
A319
89.4
3.0
0.1
0.4
0.4
5.0
1.0
0.7
Alloy
Al
Cr
Cu
Fe
Mg
Mn
Si
Ti
Zn
7075
88.7
0.2
1.6
0.5
2.5
0.4
0.4
0.2
5.5
Alloy A1-LM4 (A319)
2760
M
2720 2680 2640
d
2600
Numerical, Solid Experimental, Solid [25] Numerical, Liquid Experimental, Liquid [25]
2560
Ac ce pt e
-3
cr
us an
2800
Density [kg.m ]
ip t
Alloy
2520 2480 2440 2400
0
100
200
300
400
500
600
700
800
900
o
Temperature [ C]
Fig. 3 –Comparison between numerical predictions and experimental density results of solid and liquid phases as a function of temperature for an A319 alloy.
13 Page 13 of 27
2840
Alloy A1-7075-T6
2800 2760
2680 2640
Num erical, Solid Experim ental Solid [25] Num erical, Liquid Experim ental, Liquid [25]
2600 2560
ip t
-3
Density [kg.m ]
2720
2520
cr
2480 2440
0
100
200
300
400
500
600 o
700
800
900
M
an
Tem perature [ C]
us
2400
Fig. 4 –Comparison between numerical predictions and experimental density results of solid and
Ac ce pt e
d
liquid phases as a function of temperature for a 7075 alloy.
The composition of Cu and Si along the length of the directionally solidified Al-
6wt%Cu-1wt%Si casting was determined by R-ray fluorescence and is shown in Fig. 5a. The casting region close to the cooled surface was subjected to a more detailed analysis with a view to determining more accurately the Cu inverse segregation profile, as depicted in Fig. 5b.
14 Page 14 of 27
8
Experimental - Cu Experimental - Si
6
cr
ip t
5
us
1,0
0,5
an
Composition [wt% Cu, Si,]
7
0,0 0
20
40
60
80
100
Position [mm]
M
d
(a)
7,50 7,25
Ac ce pt e
Al-6wt%Cu-1wt%Si
7,00
Composition [wt% Cu, Si]
6,75 6,50 6,25 6,00
Cu Si
5,75
1,2
0,9
0,6
0
2
4
6
8
10
Position [mm]
12
14
16
18
Fig. 5. (a) XRF results of Cu and Si profiles along the length of the DS casting; (b) Detailed results corresponding to positions close to the casting surface highlighting the Cu inverse segregation 15 Page 15 of 27
Al-alloys castings are subjected to porosity formation when the casting operation is not carried out under a controlled inert atmosphere. The local solute composition as well as the local volume fraction are known to affect the local density [13]. With a view to permitting the effects of Si alloying in the fraction of pores to be analyzed some
ip t
experimental results of evolution of porosity in Al-Cu and Al-Cu-Si alloys DS castings,
cr
from previous studies from some of the present authors[13,19], have been synthesized in Fig. 6. It can be seen that Si alloying affects significantly the pores fraction, and that
us
the evolution of pores tend to increase from the cooled bottom to the top of the DS
an
casting.
M
10
d
6
Experimental Al-6.2 wt% Cu Experimental Al-6.0 wt% Cu-1.0 wt% Si Experimental Al-6.0 wt% Cu-4.0 wt% Si Numerical
Ac ce pt e
Pores [ % ]
8
4
2
0
0
20
40
60
80
Position from the casting cooled surface [ mm ]
100
Fig. 6 – Effect of Si alloying on the volumetric fraction of pores along the length of DS castings [13, 19]
16 Page 16 of 27
Fig. 7 shows the numerical predictions furnished by the model compared with the experimental density of the solid phase as a function of temperature, determined in the present study for the Al-6wt%Cu-1wt%Si alloy. As reported in the Experimental section, the samples experimentally examined were extracted at 40mm from the casting
ip t
cooled surface, i.e. having a solute concentration close to the nominal composition of
2840
Al-6wt%Cu-1wt%Si
2800
an
2760 2720
M
2680 2640 2600
d
2560 ) k r o W t n e s e r P ( d i l d o i d u i l q o i
2520
Numerical, S Numerical, L Experimental, S
Ac ce pt e
-3
Density [kg.m ]
us
cr
the alloy (Fig. 5a) and a mean value of pores fraction of about 2% (Fig. 6).
2480 2440 2400
0
100
200
300
400
500
600
700
800
900
o
Temperature [ C]
Fig. 7 – Comparison between numerical predictions and experimental density results of solid phase as function of temperature for the Al-6wt%Cu-1wt%Si alloy. Density of the liquid phase was numerically calculated.
Fig. 8 shows the model predictions of specific heat as a function of temperature for the Al-6wt%Cu-1wt%Si alloy. 17 Page 17 of 27
cr
ip t
.
1200
Al-6wt%Cu-1wt%Si
us
1100
an
1050
M
1000 950
Numerical Simulation
900
d
-1
-1
Specific heat [J.kg .K ]
1150
Ac ce pt e
850 800
0
100
200
300
400
500
600
700
800
900
o
Temperature [ C]
Fig. 8 – Numerical calculation of specific heat as function of temperature for the solid and liquid phases for the Al-6wt%Cu-1wt%Si alloy.
With a view to permitting comparisons with results of constant density and specific heat of the solid, adopted in a previous study from the literature for simulations of thermal parameters of a directionally solidified Al-6wt%Cu-1wt%Si alloy casting, the numerical values of Figs 7 and 8 are also shown in Table 2. It can be seen that the 18 Page 18 of 27
use of the present range of values in such simulation, instead of the constant value used in the previous study, would permit a more appropriate evolution of solidification thermal parameters with temperature to be determined.
Temperature
Units
an
100 Density
200
kg/m³
Ac ce pt e
100 Specific Heat
200
J/kg.K
Present Work
2797.8 2774.4 2751.1 2727.7 2650.3
d
500
2713.4
M
300 400
[16,17]
us
(°C)
cr
values from the literature [26, 27] Properties
with
ip t
Table 2 -Density and specific heat of the Al-6wt%Cu-1wt%Si alloy compared
910 1063
964.4
300
1041
400
1168
500
1407
Fig. 9 shows two calculated pseudo-binary phase diagrams for Al-Cu-Si system
of alloys, i.e., Al-Xwt%Cu-1wt%Si and Al-6wt%Cu-Ywt%Si, respectively. As can be easily noticed this system encompasses the following phases: Liquid, α-phase FCC_A1, eutectic phase Al2Cu and Silicon. The transformation temperatures and heats are given in Table 3. Scheil-Gulliver simulations obtained the transformation heats provided in Table 3. 19 Page 19 of 27
Ac ce pt e
d
M
(a)
an
us
cr
ip t
(b) Fig. 9 – Calculated pseudo-binary phase diagrams: (a) Al-Xwt%Cu1wt%Si and (b) AlYwt%Si6wt%Cu alloys. 20 Page 20 of 27
Fig. 10 shows the Scheil-Gulliver simulation of temperature as a function of mass fraction of all solid phases for the Al-6wt%Cu-1wt%Si alloy, with a view to evaluating the volume fraction of phases for non-equilibrium condition so to reckon the non-
Ac ce pt e
d
M
an
us
cr
ip t
equilibrium alloy density, according to Eq. (5).
Fig. 10 – Scheil-Gulliver simulation of mass fraction of all solid phases for the Al6wt%Cu-1wt%Si alloy.
21 Page 21 of 27
Table 3 - Temperatures and heats of transformation for the Al-6wt%Cu-1wt%Si alloy.
Symbol
Value/Unit
DTA-DSC
TL
638°C
638.5
Initial Al2Cu Transformation Temperature
TIE
530.2°C
527.1 oC
Final Al2Cu Transformation Temperature
TFE
527.6°C
524.6oC
Silicon Precipitation Temperature
TPSi
513.2°C
512.2 oC
ΔH 1
289,600 J.kg-1
280700 J.kg-1
ΔH 2
15,800 J.kg-1
14400 J.kg-1
ΔH 3
57,200 J.kg-1
68400 J.kg-1
M
an
liquidus temperature
us
cr
Simulation
Value/Units
ip t
Properties
Latent Heat of Fusion - 638 to 530.2 °C
Ac ce pt e
d
Latent Heat of Fusion - 530.2 to 527.60 °C Latent Heat of Fusion - up to 513.20 °C
5. Conclusions
A numerical model, based on the the coupling of the computational
thermodynamics software Thermo-Calc and the database TTAL7 with a C language numerical code that accesses and controls the Thermo-Calc by employing TCAPI interface, with a view to numerically determining thermophysical properties of multicomponent alloys, was proposed. The numerical and experimental results confronted for density as a function of temperature for aluminum alloys A356 and 7075 22 Page 22 of 27
and solid Al-6wt%Cu-1wt%Si alloy, allow us to state that the proposed model furnishes quite accurate predictions. Although simple equations have been used to calculate the density and the volume fraction of the phases, the bulk phases present, their mass fractions and phase compositions were calculated using Thermo-Calc considering the
ip t
excess terms, so that errors from volumetric data calculated by the numerical model are
cr
minimized. It was also shown that the model permits the determination of specific and
transformation heats, allowing the access to important information on Al-based
an
us
multicomponent alloys that are very scarce in the literature.
M
Acknowledgements
The authors acknowledge the financial support provided by FAPERJ (The Scientific
d
Research Foundation of the State of Rio de Janeiro, Brazil), FAPESP- São Paulo
Ac ce pt e
Research Foundation, Brazil (grant 2013/23396-7), CAPES and CNPq (The Brazilian Research Council).
References
[1] A. Kelkar, R. Roth, J. Clark. JOM 53 (2001) 28-32. [2] E. L. Rooy: in Metals Handbook, vol. 15, ASM International, Materials Park, Ohio, 1988, pp.743-770 [3] J.A.J. Robinson, R.F. Brooks, P.N. Quested. High. Temp. Mater. Proc. 31 (2012) 237-242. [4] J. Blumm, J. Henderson. High Temp. – High Press. 32 (2000) 109-113. 23 Page 23 of 27
[5] R.F. Brooks, A.P. Day, K.C. Mills, P.N. Quested. Int. J. Thermophys. 18 (1997) 471480. [6] P.N. Quested, R.F. Brooks, ASM Handbook, v. 22B, Metals Process Simulation, 2010,
ip t
pp.33-40. [7] K. Narender, A.S. Madhusudhan Rao, K. Gopal Kishan Rao, N. Gopi Krishna.
cr
Thermochim. Acta 569 (2013) 90-96.
us
[8] M. Trybula. P. Fima, W. Gasior. Thermochim. Acta 588 (2014) 16-21.
an
[9] P. Schumacher, S. Pogatscher, M.J. Starink, C. Schick, V. Mohles, B. Milkereit.
M
Thermochim. Acta 602 (2015) 63-73.
[10] C. Brito, T.A. Costa, T.A. Vida, F. Bertelli, N. Cheung, J.E. Spinelli, A. Garcia. Metall.
d
Mater. Trans. 46A (2015) 3342-3355.
Ac ce pt e
[11] F. Bertelli, C. Brito, I.L. Ferreira, G. Reinhart, H. Nguyen-Thi, N. Mangelinck-Noel, A. Garcia. Mater. Des. 72 (2015) 31-42.
[12] M. Dias, T. Costa, O. Rocha, J.E. Spinelli, N. Cheung, A. Garcia. Mater. Character. 106 (2015) 52-61.
[13] I.L. Ferreira, J.F.C. Lins, D.J. Moutinho, L.G. Gomes, A. Garcia. J Alloys Comp 503 (2010) 31-39.
[14] U.R. Kattner, JOM, 49 (1997)14-19. [15] C. R. Swaminathan, V. R. Voller. Int. J. Heat Mass Transfer, 40 (1997), 28592868. [16] T. W. Clyne, W. Kurz. Metall. Trans. 12A (1981), 965- 971. 24 Page 24 of 27
[17] H. B. Brody, M. C. Flemings. Transactions AIME, 236 (1996), 615- 624. [18] Mark Easton, Cameron Davidson, David St John. Metall. Mater. Trans. 41A (2010), 1528-1538 [19] D.J. Moutinho, L.G. Gomes, O.L. Rocha, I.L. Ferreira, A. Garcia. Mater. Sci.
ip t
Forum, 730-732 (2013)883-888.
cr
[20] I.L. Ferreira, V.R. Voller, B. Nestler, A. Garcia. Comp. Mater. Sci. 46 (2009)358366.
us
[21] I.L. Ferreira, C.A. Santos, V.R. Voller, A. Garcia. Metall. Mater. Trans. B 35 (2004) 285-297.
an
[22] J.E. Spinelli, M.D. Peres, A. Garcia. J Alloys Comp. 403 (2005) 228-238
271-282
M
[23] J.E. Spinelli, D.M. Rosa,, I.L. Ferreira, A. Garcia. Mater. Sci. Eng. A 383 (2004)
Ac ce pt e
Mater. 403 (2010) 160-166.
d
[24] D.E. Burkes, C.A.. Papesch, A.P. Maddison, T. Hartmann, F.J. Rice. J. Nuclear
[25] K.C. Mills: Recommended Values of Thermophysical Properties for Selected Commercial Alloys. Cambridge. Woodhead Publishing Ltd. 2002. [26] P.A.D. Jácome, M.C. Landim, A. Garcia, A.F. Furtado, I.L. Ferreira. Thermochim. Acta, 523 (2011) 142-149.
[27] I.L. Ferreira, D.J. Moutinho, L.G. Gomes, O.L. Rocha, P. R. Goulart, A. Garcia. Mater. Sci. Forum 636-637 (2010) 643-650.
25 Page 25 of 27
Figure Captions
Fig. 1 - Solution scheme for determination of density of a multicomponent alloy by calling Thermo-Calc and TTAl7 through a C language program.
ip t
Fig. 2. (a) Schematic representation of the experimental setup: 1) rotameter; 2) heat-
cr
extracting bottom; 3) thermocouples; 4) computer and data acquisition software; 5) data
logger; 6) casting; 7) mold; 8) temperature controller; 9) electric heaters; 10) insulating
us
ceramic shielding; (b) Split mold and water-cooled bottom; (c) Columnar macrostructure of the DS casting (left) and central samples extracted for XRF analyses.
an
Fig. 3 –Comparison between numerical predictions and experimental density results of
M
solid and liquid phases as a function of temperature for an A319 alloy. Fig. 4 –Comparison between numerical predictions and experimental density results of
d
solid and liquid phases as a function of temperature for a 7075 alloy.
Ac ce pt e
Fig. 5. (a) XRF results of Cu and Si profiles along the length of the DS casting; (b) Detailed results corresponding to positions close to the casting surface highlighting the Cu inverse segregation
Fig. 6 – Effect of Si alloying on the volumetric fraction of pores along the length of DS castings [13, 19]
Fig. 7 – Comparison between numerical predictions and experimental density results of solid phase as function of temperature for the Al-6wt%Cu-1wt%Si alloy. Density of the liquid phase was numerically calculated. Fig. 8 – Numerical calculation of specific heat as function of temperature for the solid and liquid phases for the Al-6wt%Cu-1wt%Si alloy.
26 Page 26 of 27
Fig. 9 – Calculated pseudo-binary phase diagrams: (a) Al-Xwt%Cu1wt%Si and (b) AlYwt%Si6wt%Cu alloys. Fig. 10 – Scheil-Gulliver simulation of mass fraction of all solid phases for the Al-
ip t
6wt%Cu-1wt%Si alloy.
us
Table 1 – Alloys Chemical Composition [wt%].
cr
Table Captions
Table 2 -Density and specific heat of the Al-6wt%Cu-1wt%Si alloy compared
an
values from the literature [26, 27]
with
A model coupled to a computational thermodynamics software is proposed to
Ac ce pt e
•
d
Research Highlights
M
Table 3 - Temperatures and heats of transformation for the Al-6wt%Cu-1wt%Si alloy.
compute thermophysical properties.
•
The model applies to multicomponent alloys and has been validated against experimental results
•
Density and specific heat as a function of temperature are computed for Al-SiCu alloys
27 Page 27 of 27