Evaluation of thermophysical properties of Al–Sn–Si alloys based on computational thermodynamics and validation by numerical and experimental simulation of solidification

Accepted Manuscript Evaluation of thermophysical properties of Al-Sn-Si alloys based on computational thermodynamics and validation by numerical and experimental simulation of solidification Felipe Bertelli, Noé Cheung, Ivaldo L. Ferreira, Amauri Garcia PII: DOI: Reference:

S0021-9614(16)00068-9 http://dx.doi.org/10.1016/j.jct.2016.02.018 YJCHT 4561

To appear in:

J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

16 September 2015 14 February 2016 16 February 2016

Please cite this article as: F. Bertelli, N. Cheung, I.L. Ferreira, A. Garcia, Evaluation of thermophysical properties of Al-Sn-Si alloys based on computational thermodynamics and validation by numerical and experimental simulation of solidification, J. Chem. Thermodynamics (2016), doi: http://dx.doi.org/10.1016/j.jct.2016.02.018

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Evaluation of thermophysical properties of Al-Sn-Si alloys based on computational thermodynamics and validation by numerical and experimental simulation of solidification Felipe Bertellia, Noé Cheungb*, Ivaldo L. Ferreirac, Amauri Garciab a

Department of Mechanical Engineering and Postgraduate Program of Mechanical Engineering, Santa Cecília University – UNISANTA, 11045-907,Santos, Brazil

b

Department of Manufacturing and Materials Engineering, University of Campinas – UNICAMP, 13083-860 – Campinas, SP, Brazil. c

Institute of Technology, Federal University of Pará -UFPA, Augusto Correa Avenue 1, 66075-110 - Belém, PA, Brazil.

Abstract Modelling of manufacturing processes of multicomponent Al-based alloys products, such as casting, requires thermophysical properties that are rarely found in the literature. It is extremely important to use reliable values of such properties, as they can influence critically on simulated output results. In the present study, a numerical routine is developed and connected in real runtime execution to a computational thermodynamic software with a view to permitting thermophysical properties such as: latent heats; specific heats; temperatures and heats of transformation; phase fractions and composition and density of Al-Sn-Si alloys as a function of temperature, to be determined. A numerical solidification model is used to run solidification simulations of ternary Al-based alloys using the appropriate calculated thermophysical properties. Directional solidification experiments are carried out with two Al-Sn-Si alloys compositions to provide experimental cooling rates profiles along the length of the castings, which are compared with numerical simulations in order to validate the calculated thermophysical data. For both cases a good agreement can be observed, indicating the relevance of applicability of the proposed approach.

Keywords: Thermophysical Properties; Computational Thermodynamics; Ternary Al-Si-Sn alloys; Castings

(*) Corresponding author Tel.: +55 19 3521 3448 fax: +55 19 3289 3722 E-mail address: [email protected]

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1. Introduction

The relatively low coefficient of thermal expansion, high wear resistance and fluidity that are characteristics of hypoeutectic Al-Si alloys have attracted a range of applications in the automotive industry, especially in the manufacture of structural components. On the other hand, binary Al-Sn and Al-Si alloys, typically used for tribological applications, particularly for bearings and components of internal combustion engines, will need to be replaced with new alternatives caused by the design of new engines, which will be subjected to higher loads and velocities and hence will demand better properties to support the operation at higher temperatures. The literature reports that Al-Sn-Si alloys have a good potential for tribological applications due to the strengthening of the Al-rich matrix by Si and because the Sn particles act as a solid lubricant, yielding appropriate combination of good mechanical properties and excellent friction and wear characteristics [1-3]. The addition of Si is also shown to improve the corrosion resistance as compared with a binary Al-Sn alloy [4]. The pre-programming of these characteristics demands special attention during the processing of these alloys by conventional metallurgical routes from the melt. The solidification process is a complex phenomenon and the simulation of castings is required in industry not only to control the kinetics of solidification but also the phases evolution since they play an important role in the microstructure formation and thus, in the final properties. The core of a solidification mathematical model is described by a set of partial differential energy equations, complemented by boundary conditions, composed by geometrical, physical features and initial conditions, which particularizes the subject to be modelled. The typical differential equation is the fundamental equation of heat conduction, based on the relation between quantity of heat and temperature, considering some materials properties such as specific heat, latent heat, thermal conductivity and density. Depending on the analysis to be performed, the

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aforementioned equation is not sufficient to perform realistic simulations, and it is needed to be coupled to equations dealing with heat convection in the molten metal sub-domain, and also to equations concerning local changes of chemical constitution, known as segregation. Considering the material type, its solidification varies considerably: pure metals and eutectic alloys solidifies at a fixed temperature whilst binary and ternary alloys, over a range of temperature. Unfortunately, pure metals and binary alloy systems, that have practical applications, are limited in number to attend desired physical and mechanical properties. Assuming a more complete situation, i.e., an alloy with more than two components, flow analysis of heat, fluid and species, the challenges are not restricted only to the extensive modelling process but also to finding the physical properties required by the equations as input parameters. It is extremely important to use reliable values of such properties as they can influence critically on the simulated output results. In this sense, considerable efforts have been put into the investigations of techniques that have potential to determine such properties. Some studies [5, 6] applied an experimental technique to determine the thermal conductivity at the melting point based on Neumann´s moving boundary solution of the equation of heat conduction, and measuring the electrical resistance over the sample during the displacement of the solid/liquid interface. The position of the solid/liquid interface during solidification is identified when the electrical resistance changes. The thermal conductivity of liquids at the interface (kL) can be evaluated from the velocity of the solid/liquid interface (v), temperature gradient normal to the interface (GL), the latent heat (L) and the density (ρ), according the Eq. (1). In this approach, it is crucial to keep the gradient as set and the drawbacks are the further knowledge of other thermal properties such as ρ and L.

− kLGL = ρLv

(1)

Another approach permitting to experimentally determine the thermal conductivity of solids consists in employing an apparatus with a coaxial central hole that contains either a heater or a sink, 3

which imposes radial outward or inward heat flow to a sample with cylindrical geometry. At steady state condition, the temperature gradient in the solid (GS) is given by [7]: GS =

dT dQ = dr A.kS

(2)

where Q is the total input power from the centre of the specimen, A is the surface area of the specimen, and kS is the thermal conductivity of the solid phase. The integration of Eq. (2) results into an expression where kS is obtained by measuring the temperature difference between two fixed points for a given power level. It can be realized that this approach excludes the dependence on ρ and L, as compared with the aforementioned technique synthesized by Eq. 1 [5, 6]. Erol and collaborators [7], established a ratio (R) between kL and kS, as a function of the ratio between the cooling rates at the liquidus ( T
L ) and solidus ( T
S ) isotherms (Eq. 3) in order to determine kL. The disadvantage of the above approach is that it involves low velocities, generally restricted to Bridgman type solidification apparatus. R=

kL GS T
L = = kS GL T
S

(3)

The methods available for measuring thermophysical properties such as the latent heat of fusion, specific heat and melting point can be divided into: differential thermal analysis (DTA) and differential scanning calorimetry (DSC) methods. DSC is one of the thermo-analytical techniques that determine the differences in heat transfer rates between a reference and a sample associated with phase change material transitions as a function of temperature and time. Another technique, which is similar to the DSC, is the differential thermal analysis (DTA). In this technique, a sample and a reference are made to undergo identical thermal cycles, and their temperature differences, either exothermic or endothermic transformations, are recorded against either time or temperature. The area under the DTA curve peak is related to the enthalpy change. DSC and DTA have been used not only in the determination of the aforementioned thermophysical properties of alloys [8, 9]

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but also in the verification of phase diagrams predicted by approaches collectively termed CALPHAD (CALculation of PHase Diagram) [10-12 ] The density of alloys has been measured by a variety of techniques. Dilatometry is the most common one for the determination of density of a sample in the form of solid, powder, paste and liquid under certain controlled time and temperature conditions [13]. The Archimedean method consists in immersing a sample totally or partially in a fluid, which is lifted up by a force equivalent to the weight of the fluid that is displaced [14]. Applying this method to liquid metals, an inert sinker, generally a silica bulb weighted with mercury or a tungsten cylinder, is weighted when immersed in the liquid metal specimen [15]. Electromagnetic levitation is a containerless technique, used to measure density, in which liquid droplets are levitated and their side view shadowgraph images are taken in order to calculate the volume at different temperatures [16]. The piknometer method consists in filling a container, having an accurately known volume, with the molten metal and its mass is determined when the system is weighed [15, 17]. Besides the experimental efforts, there are also some theoretical investigations concerning the determination of thermophysical properties through simulations of computational thermodynamics, permitting density, specific heat, heats of transformation as a function of temperature and composition to be determined [18,19]. The use of theoretical methods permits to substantially reduce the extent of the experimental attempts and also allows to theoretically evaluate great number of compositions in the search for the best materials for specific end applications. Models with quantitative prediction capability are normally supported by a thermodynamic databases containing Gibbs energy of pure elements, mixtures and compounds as a function of composition, temperature and pressure. If the Gibbs energies are reliable and accurately known, all other thermophysical properties can be calculated from basic thermodynamic relations [20]. One of the most complete thermodynamic databases for this purpose is that of the Thermo-Calc software,

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which has a communication interface with a programme written in C language called TCAPI (Thermo-Calc Application Programming Interface). Modelling of industrial processes of multicomponent Al-based alloys products, such as casting, requires thermophysical data that are rarely found in the literature. The aim of the present work is to calculate thermophysical properties such as: latent heats; specific heats; temperatures and heats of transformation; phase fractions and composition and density of Al-Sn-Si alloys as a function of temperature of solid and liquid phases. In order to achieve this objective, a numerical routine is developed in C language and connected in real runtime execution to Thermo-Calc and its database TTAL7 (ThermoTech Aluminium Thermal Database). A numerical solidification model will be used to run solidification simulations of two Al-Sn-Si alloys using the appropriate calculated thermophysical properties. With a view to validating such properties, an experimental directional solidification technique will be used to provide data of solidification cooling rates, which will be compared with the numerical simulations.

2. Numerical techniques 2.1- Interrelation between computational thermodynamics software and numerical routine

The first step of the input routine is to define a multicomponent alloy system, i.e. Al-Sn-Si in the present study. The computational thermodynamics software (Thermo-Calc) is then initialized from the numerical routine by calling the TCAPI tc_init_root() function. The aluminum thermodynamics database TTAL7 (ThermoTech Aluminium Thermal Database v.7) is retrieved by calling TCAPI interface tc open_database() function. In a next step, input data 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, solidus and eutectic surfaces and partition coefficients are determined for the entire system and stored. In order to permit the density of Al-Sn-

6

Si alloys (as a function of solute concentration and temperature) to be determined, it is necessary to provide the density of the pure elements as a function of temperature to the numerical routine. This will permit the densities of the phases that constitute the multicomponent alloy and their respective volume fractions to be calculated. The compositions and mass fraction of these phases will be provided by the computational thermodynamics software from a selection of entry thermodynamic conditions, i.e. composition of alloying elements, temperature, pressure and number of moles of the solution. The numerical routine, through the TCAPI interface, retrieves the following information from the software: 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 the computational thermodynamics software a value of zero, and a last vector 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 components. The sum of all mass fractions, wi, provided for all phases present in the database, is given by: 51

∑w =1 i

(4)

i =1

Eq. 5 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 elements present in the phase for a given input temperature. In order to automate the process, the calculation steps are executed

7

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.

ρFCC_A1 =

1 FCC_A1 Al

w

ρAl

+

FCC_A1 Si

w

ρSi

+

FCC_A1 Sn

w

ρSn

= +

23

∑

1 wFCC_A1 j

j=1

(5)

ρj

where FCC_A1 is the primary Al-rich phase. Eq. 6 permits the volume fraction of all phases present in the database to be calculated from the calculated phase densities and from the vector containing the mass fractions of all phases present in the database, so to automate the calculation process:

VFCC_A1 =

wFCC_A1 ρ FCC_A1 wFCC_A1 wLIQUID wFCC_A1 + + ρFCC_A1 ρLIQUID ρ FCC_A1

wFCC_A1 ρ = 51FCC_A1 w + ∑ k k =1 ρ k

(6)

The alloy density is reckoned by using Eq. 7 through linear combination of volume fractions calculated by Eq. 6 and densities obtained by the application of Eq. 5 for all phases:

51

ρAlloy_Equilibrium = ∑ Vk ρ k

(7)

k =1

The solution scheme of the model is shown in figure 1. Applying the Scheil-Gulliver model, the alloy density is again reckoned for solidification non-equilibrium conditions (phase mass and volume fractions will be different of those obtained by carrying out the Lever Rule, which is appropriate for global equilibrium conditions): 51

ρ Alloy_Non− Equilibrium = ∑ VkScheil ρ k

(8)

k =1

8

In practice, neither Scheil-Gulliver nor the Lever Rule approaches will occur, but something between both values, the so called, finite diffusion. A microsegregation parameter β must be set by applying Eq. 9 [21]:

(

)

β = 2α 1 − e −1 α − e−1 2α

(9)

where α is the standard Fourier diffusion number. This back diffusion approach was firstly proposed by Swaminathan and Voller [21] and is equivalent to that of Clyne and Kurz correction [22] of the Brody and Flemings [23] back diffusion model. According to Clyne and Kurz [22], the standard Fourier diffusion number is given by:

α=

DStf 4 DStf = P2 λ2

(10)

where α is a constant related to the appropriate dendrite arm spacing λ, and is taken as twice the length of the diffusion path P, tf is the local solidification time, and DS is the solute diffusion coefficient of the solid phase. Finally,

ρAlloy = ρAlloy_Eq β + ρAlloy_Non− Eq (1 − β )

(11)

where, ρAlloy_Eq and ρAlloy_Non-Eq are densities calculated under equilibrium and non-equilibrium conditions, respectively. In the present study, the diffusion coefficients, DS, are assumed as the same used for the liquid by Easton and co-workers [24] for Si: DLSi = 1.34 x 10−7 e − 30 RT

(12a)

For Sn, a non-linear regression has been applied to the data of Ejima et al. [25], according to Figure 2, yielding: DLSn = 0.9952 ⋅ 10 −7 e − 22600 RT

(12b)

where DL / (m2.s-1).

9

FIGURE 1. Numerical scheme for determination of density of a multicomponent alloy

by interconnecting a numerical routine with a computational thermodynamics software.

10

-8

1.1x10

-8

1.0x10

-8

9.0x10

-9

8.0x10

-9

7.0x10

-9

6.0x10

-9

5.0x10

-9

Experimental Scatter Non-Linear Fit

2

-1

Diffusion Coefficient / (m s )

1.2x10

.

-8

D (T ) = 9.952x10 Exp [-22605.75/(8.31*T )] 950

1000

1050

1100

1150

1200

1250

Temperature / K

FIGURE 2. Scatter data of diffusion coefficient as a function of temperature [25] and

non-linear fit curve of Arrhenius type.

2.2- Numerical simulation of solidification

Based on the continuum formulation, the continuity, momentum, energy, and species equations for a multicomponent alloy solidification of a two dimensional casting for a representative elementary volume (REV) are given as follows [26- 30]: Continuity

The general form of mass conservation equation can be obtained for certain phase k from Eq. 13a, considering φk = 1 , J k = 0 , and S k = M
k , yielding Eq. 13b) ∂ (ρ k φ k ) + ∇ ⋅ (ρ kVk φ k ) = −∇ ⋅ (g k ⋅ J k ) + g k S k ∂t ∂ (ρ k φ k ) + ∇ ⋅ (ρ kV k φ k ) = g k M
k ∂t

(13a) (13b)

where, J k is the surface flux vector, Vk is the velocity of phase k, and S k is the volumetric source
is the production of phase k, and g k is the volume fraction of phase k. term, M k

11

The continuum mass equation for mass conservation is obtained by summing the discrete phase conservation equations and assuming that the production of a phase k, M
k , must come at the expense of other mixture phases [27], i.e., ∂ (ρ ) + ∇ ⋅ (ρV ) = 0 ∂t

(14c)

For 2D solidification modelling, mass conservation equation becomes, (14d)

∂ρ ∂ ( ρ u ) ∂ ( ρ v ) + + =0 ∂t ∂x ∂y

where t is the time, x and y are the rectangular coordinates, u and v are velocity components according to x and y directions, respectively Momentum x

For most multicomponent solid-liquid solidification systems, the multiphase region is characterized by a fine permeable solid matrix generally considered as stationary in the case of static solidification or constrained to free body translation in the case of continuous casting. Phase interactions forces are proportional to the superficial liquid velocity relative to the porous solid. That is, Fx =

µL ρ K X ρL

(u L − uS )

(15)

where Kx and Ky are the anisotropic permeability components and (uL – uS) and (vL – vS) are the relative phase velocities.     ∂ (ρ u ) + u ∂(ρ u ) + v ∂ (ρ u ) = ρ g x − ∂p + ∂  µ l ρ ∂u  + ∂  µ l ρ ∂u  − µ L ρ (u − u s ) ∂t ∂x ∂y ∂x ∂x  ρ l ∂x  ∂y  ρ l ∂y  K X ρ l −

Cρ 2 ∂ ∂ ∂ ∂  ρ  ∂  ∂  ρ  u − u s (u − u s ) − ( ρ f S f lV R u R ) − (ρ f S f lV R u R ) +  µ l u    +  µ l u    ∂x ∂y ∂x  ∂x  ρ l   ∂y  ∂y  ρ l   K X0.5 ρ l

(16a)

    ∂ (ρ v ) + u ∂(ρv ) + v ∂ (ρ v ) = ρ g y − ∂p + ∂  µ l ρ ∂v  + ∂  µ l ρ ∂v  − µ L ρ (v − vs ) ∂t ∂x ∂y ∂y ∂x  ρ l ∂x  ∂y  ρ l ∂y  K Y ρ l −

Cρ 2 ∂ ∂ ∂ ∂  ρ  ∂  ∂  ρ  v − vs (v − vs ) − (ρ f S f lVR vR ) − ( ρ f S f lVR vR ) +  µ l v   +  µ l v    K Y0.5 ρ l ∂x ∂y ∂x  ∂x  ρ l  ∂y  ∂y  ρ l  

(16 b)

The third term on the right hand side of Eq.16a represents inertial forces established as a consequence of variations in relative phase velocities. This inertial contribution appears only in the 12

multiphase region, for the case of extremely small permeability and its influence is negligible as compared with Darcy’s dumping forces. Darcy´s flow is used to describe the liquid flow in the mushy zone. Then the final continuum equation for momentum conservation can be expressed as, ∂ (ρ u ) ∂( ρ u ) ∂ (ρ u ) ∂p ∂  ρ ∂u  µ L ρ ρ ∂u  ∂   +  µL − +u +v = ρ g X − +  µ L (u − uS ) ∂t ∂x ∂y ∂x ∂x  ρ L ∂x  ∂y  ρ L ∂y  K X ρ L

(16c)

Momentum y

In the case of y momentum, the last term on the right-hand side of Eq.17 is caused by natural convection using the Boussinesq approximation. ∂ (ρ v ) ∂ (ρ v ) ∂(ρ v) ∂p ∂  ρ ∂v  µ L v ρ ∂v  ∂   +  µL − +u +v = ρ g Y − +  µ L (u − us ) ∂t ∂x ∂y ∂y ∂x  ρ L ∂x  ∂y  ρ L ∂y  K Y

(17)

where, p is the pressure, µ is the viscosity and K is the permeability. Depending on the number of species, can be written as:   i g X, Y = g 0 β T (T − T0 ) + ∑ β Si Cli − C l,0  Sn, Si  

[ (

)]

(18)

C is the inertial coefficient, βT is the thermal expansion coefficient, βSi is the solutal expansion coefficient, g is the gravitational acceleration, the subscripts S and L refer to the solid and liquid phases, T is temperature and CSi is the mass fraction gX and gY, and, in our current set up, gX = 0. Energy     ∂ (ρH ) + ∇(ρVH ) = ∇ k ∇H  + ∇ k ∇(H S − H ) − ∇(ρ (V − VS )(H L − H )) ∂t c c  S   S 

(19)

where H is the enthalpy, k is the thermal conductivity, and c is the specific heat. The first two terms on the right-hand side of Eq.19 represent the net Fourier diffusion flux. The last term represents the energy flux associated with the relative phase motion. The in the following energy equation, Eq. 20, a simplification is assumed by neglecting the energy flux associated with relative phase motion and write a translation transport, i.e., advective terms on the left-side and diffusion terms on the right-

13

side as a function of temperature instead of enthalpy. In Eq.20 the third term on the right-side encompasses the latent heat released as solidification proceeds. (20)

∂ (ρ c P T ) + ∂ (ρ c P u T ) + ∂ (ρ c P v T ) = ∂  k ∂T  + ∂  k ∂T  − ∂ (∆H f ρ S g S ) ∂t ∂x ∂y ∂x  ∂x  ∂y  ∂y  ∂t

Species

The continuum species conservation equation is obtained by summing the conservation equations for each phase and recognizing that the production of species α in phase k must be accompanied by a destruction of species α in other phases, i.e., the variation of solute in the liquid phase in a given volume element should be equal to the net loss or gain of solute due to convection, diffusion, interfacial reaction and solidification contraction [26, 27]. Then, the obtained expression is the following: ∂ ρ C α + ∇ ρ VC α = ∇ ρ D ∇C α + ∇ ρ D∇ C Lα − C α − ∇ ρ (V − VS ) C Lα − C α ∂t

(

)

(

) (

)

(

(

))

(

(

))

(21)

The two terms on the left-side of Eq. 19 are relative to the translation of species α by advective transport. The first two terms on the right-hand side of Eq. 22 represent the net Fourier diffusion flux and the last term represents the species flux associated with the relative phase motion. In the simplified form of Eq. 22 only the net Fourier diffusion flux term is presented. ∂ ∂ ∂ ∂  ∂C Sn  ∂  Sn ∂C Sn   + D  ρ C Sn + u ρ C Sn + v ρ C Sn =  D Sn ∂t ∂x ∂y ∂x  ∂x  ∂y  ∂y 

(22a)

∂ ∂ ∂ ∂  ∂C Si  ∂  Si ∂C Si   + D  ρ C Si + u ρ C Si + v ρ C Si =  D Si ∂t ∂x ∂y ∂x  ∂x  ∂y  ∂y 

(22b)

(

(

)

)

(

(

)

)

(

(

)

)

A micro-scale model is invoked to extract nodal values of liquid concentration CL from each solute density field (ρC ) , where ζ = Sn, Si . The key variable in this calculation is the nodal liquid ζ

fraction calculated in the previous step. A detailed discussion was previously presented by Voller [31], in which the application of the back diffusion model proposed by Wang and Beckermann [32] is suggested.

14

The local liquid concentration of each species is given by:

[C ]

=

[C ]

=

Sn L P

Si L P

old old [ρC ]SnP − [ρC]Sn, + [ρ L g Pold + β Sn ρ S (1 − g Pold )k 0Sn ][C LSn ]P P

(23a)

[ρC ]SiP − [ρC ]Si,Pold + [ρ L g Pold + β Si ρ S (1 − g Pold )k 0Si ][CLSi ]old P

(23b)

ρ L g Pn +1 + β Sn ρ S (1 − g Pn+1 ) k 0Sn + (1 − β Sn )ρ S k 0Sn ( g Pold − g Pn +1 )

ρ L g Pn +1 + β Si ρS (1 − g Pn +1 )k 0Si + (1 − β j )ρ S k 0Si ( g Pold − g Pn +1 )

3. Experimental procedure

In order to permit a wide range of solidification cooling rates in a single casting experiment to be obtained, solidification experiments in a water-cooled apparatus (Figure 3), which promotes transient directional solidification, were carried out with ternary Al-based alloys having the following nominal compositions: Al - 15 wt%Sn -5 wt%Si and Al – 25 wt%Sn – 5 wt%Si. The reasons for choosing these alloys have been based on previous studies on similar Sn and Si content in Al-Si and Al-Sn alloys concerning their mechanical and wear resistances [33], and based on hardness analyses performed on ternary Al-Sn-Si alloys [34]. The chemical compositions of metals that were used to prepare these alloys are presented in table 1. The chemical compositions were furnished by the supplier, which was certified by a specialized laboratory of chemical analysis (Centro de Qualidade Analítica). The technique used was the flame atomic-absorption spectrometry, one of the most precise chemical composition analysis technique, with relative standard deviation of 0.1 %. The directional solidification technique is a versatile experimental procedure permitting appropriate correlations between microstructure features of a multicomponent alloy and the corresponding solidification thermal parameters such as the growth rate and cooling rate to be established [35].

15

FIGURE 3. Schematic vertical upward directional solidification casting assembly and mould

details The casting assembly and mould details used in the directional solidification experiments, shown in figure 3, have been detailed in previous study [36]. The apparatus consists of a watercooled mould with heat being extracted only from the bottom. A stainless steel mould was used, having an internal diameter of 50 mm, a height of 110 mm and a wall thickness of 3 mm. The inner vertical surface was covered with a layer of insulating alumina to minimize radial heat losses, thus permitting unidirectional heat flow to be attained. The bottom part of the mould was closed with a 3 mm thick carbon steel sheet. Fine K-type thermocouples, were inserted at different positions along the centre of the cylindrical mould cavity (figure 3 – right side). All the thermocouples were connected by coaxial cables to a data logger interfaced with a computer, capable of automatically record temperature data. An etching solution (4 % hydrofluoric acid (HF) and 2 % hydrochloric acid (HCl) in distilled

16

water) applied during 10 seconds was used to reveal the microstructures. The optical microscopy was performed using an Olympus Inverted Metallurgical Microscope (model 41GX). Experimental investigations were carried out using the Differential Scanning Calorimetry (DSC, Netzch 200F3) at a cooling rate of 10 ºC.s-1. For these DSC experiments, approximately 16 mg of each sample were used in an alumina crucible. The data output from each experiment includes heat flow and temperature. These data were then analysed to identify the values of transition temperatures obtained from the cooling spectrum. The samples used for segregation analysis were extracted from different positions along the length of the DS casting. Such analyses were performed in a fluorescence spectrometer (FRX), model Shimadzu EDX-720 in order to estimate local average solute concentrations through an area of 100 mm2 probe. Some samples were selected and subjected to X-ray diffraction (XRD) analyses with a view to determining the microstructure phases. XRD patterns were obtained by a Panalytical X'pert PRO diffractometer in the 2θ range from 5 ° to 90 ° using Cu Kα radiation with a wavelength of 0.15406 nm. TABLE 1 Chemical composition as mass per cent of metals used to prepare the alloys Element

Al

Sn

Si

Cu

Fe

Zn

Ni

Pb

Ca

Al

balance

0.005

0.055

0.010

0.073

0.05

0.006

0.006

-

Sn

0.005

balance

-

0.004

0.008

-

0.0001

0.047

-

Si

0.110

-

balance

-

0.320

-

0.010

-

-

4. Results and discussion

Figure 4 shows the calculated pseudo-binary phase diagram, where the silicon composition was set to 5 wt% and tin content was varied. The dashed arrows indicate the alloys evaluated in this study. It can be realized that this system encompasses the following phases: liquid (L´and L”), Si,

17

Sn and α-Al. The thermophysical properties of each alloy determined by the proposed approach are given in tables 2 and 3. Figures 5 (a) and (b) shows the calculated solidification paths (Scheil-Gulliver simulations) for the two alloys analysed, provided by the computational thermodynamics software, where mass fraction of the solid phases are indicated as a function of temperature. It may be noted that the increase in the Sn content of the alloy changes the interval size in which the phases are formed, as well as the amount of mass fraction.

FIGURE 4. Pseudo-binary phase diagrams of Al – Sn – 5 wt%Si alloys with indications of the

alloys compositions examined in the present study [Thermo-Calc database].

18

(a)

(b) FIGURE 5. Scheil-Gulliver simulations of mass fraction of all solid phases for:

(a) Al – 15 wt%Sn – 5 wt%Si and (b) Al – 25 wt%Sn – 5 wt%Si alloys

Figures (6a) and (6b) show respectively, for the Al – 15 wt%Sn – 5 wt%Si and Al - 25 wt%Sn – 5 wt%Si alloys, three peaks both during cooling and heating along DSC analysis. The first cooling peak (Peak A) represents the formation of the primary α-(Al) phase, the second peak (Peak B) stands for the formation of Si particles, and finally the third peak (Peak C), is associated with the Sn phase. Analysing the DSC spectrum, for the Al – 15 wt%Sn – 5 wt%Si and Al – 25

19

wt%Sn - 5 wt%Si alloys, it can be seen that the Liquidus Temperature (tL), Si phase formation temperature (tSi) and Sn phase formation temperature (tSn) are given by: 607 oC, 562 oC, 233 oC; and 592 oC, 560 oC and 233 oC, respectively. The aforementioned transformation temperatures are in conformity with those theoretically determined by the Thermo-Calc® thermodynamics software.

(a)

(b)

FIGURE 6. DSC spectra at 10 ºC . min-1 rate a) Al – 25 wt%Sn – 5 wt%Si;

b) Al – 15 wt%Sn – 5 wt%Si

The alloys compositions along the length of the castings were determined by X-ray fluorescence and are shown in Figure 7. It can be realized an inverse Sn segregation profile only for the Al – 25 wt%Sn – 5 wt%Si alloy while Si remained mostly constant along the casting length (Figures 7a and 7b). Since the DS castings were solidified vertically upwards, it seems that, during solidification the higher density Sn-rich liquid L” tends to flow downwards through the interdendritic channels (gravity-driven interdendritic flow) accumulating at the bottom of the casting, thus causing the inverse Sn segregation profiles. It can be seen in Figures 4 and 5 that L” is present along a wide range of temperatures until the final formation of the solid Sn phase.

20

20

36

Al - 15 wt%Sn - 5 wt%Si

Al - 25 wt%Sn - 5 wt%Si

18

32 28

14

Composition / (wt %)

Composition / (wt %)

16

12

6 4

Sn Si Average composition

2

10

20

30

40

50

60

70

Position from metal/mold surface / mm

(a)

80

20

6 4

Sn Si Average composition

2

0 0

24

90

0 0

10

20

30

40

50

60

70

80

90

Position from metal/mold surface / mm

(b)

FIGURE 7. Experimental solute distribution along the DS castings length:

a) Al – 15 wt%Sn – 5 wt%Si b) Al – 25 wt%Sn – 5 wt%Si alloys

Microstructures characterized by a fully Al-rich dendritic matrix can also be observed for the ternary Al-Sn-Si alloys (Figure 8). The secondary phases within the interdendritic regions, identified by both the optical image of Figure 8 and XRD analysis in figure 9, include the following phases: α-Al, Si particles and Sn pockets, as a result of monotectic, binary eutectic and ternary eutectic reactions that occur during cooling [34]. Very similar 2θ peaks associated with these phases can be seen for both alloys examined in Figure 9. It can be realized that the diffracted peak concerning Sn (2θ= 30.7 º) is stronger in the Al - 25wt%Sn – 5 wt%Si alloy sample due to the higher content of Sn as compared with that of the Al – 15wt%Sn – 5 wt%Si alloy sample.

21

FIGURE 8. Typical microstruture of the Al-Sn-Si alloy (Optical Image) 3000

Al - 15 wt%Sn - 5 wt%Si 2500 α− Al(65.12)

Intensity

2000

1500

1000 Sn(32) Sn(38.5)

500

Sn(30.7)

Sn(44.9) Sn(78.3)

Si(47.3)

Si(28.5)

0 0

10

20

30

40

50

60

70

80

90

2θ

(a)

22

3000

Al - 25 wt%Sn - 5 wt%Si 2500

Sn(30.7)

Intensity

2000

1500

1000

α− Al(65.12)

Sn(32)

Sn(55.4)

Sn(38.5)

500

Sn(44.9)

Si(28.5)

Sn

Si(47.3)

0 0

10

20

30

40

50

60

70

80

90

2θ

(b) FIGURE 9. Typical X-ray diffraction (XRD) patterns: (a) Al - 15 wt%Sn –5 wt%Si and

(b) Al - 25 wt%Sn - 5 wt%Si alloys samples. The angular positions (2θ) of the diffracted peaks of radiation are in parenthesis Figure 10 shows the numerical predictions of density for a wide range of temperatures (0900ºC), furnished by the numerical routine proposed in the present study, for the Al – 15 wt%Sn 5 wt%Si and Al – 25 wt%Sn – 5 wt%Si alloys.

3200

3000

Al - 15 wt%Sn - 5 wt%Si

2900

3100

2850

3050 -3

Density / (kg m )

.

Al - 25 wt%Sn - 5 wt%Si

3150

-3

Density / (kg m )

2950

2800

.

Numerical, Solid Numerical, Liquid#2 Numerical, Liquid

2750 2700 2650

3000 2950 2900 2850

2600

2800

2550

2750

Numerical, Solid Numerical, Liquid#2 Numerical, Liquid

2700

2500 0

100

200

300

400

500 o

t/ C

600

700

800

900

0

100

200

300

400

500

600

700

800

900

o

t/ C

FIGURE 10. Numerical predictions of density of solid and liquid phases as a function of

temperature for Al – 15 wt%Sn – 5 wt%Si and Al – 25 wt%Sn – 5 wt%Si alloys.

23

TABLE 2 Thermophysical data for the Al – 15 wt%Sn – 5 wt%Si alloy. Properties Liquidus temperature - tL FCC_A1 final temperature Eutectic Temperature tE FCC_A1 final concentration Eutectic Concentration CE Silicon Transformation Temperature – tSi Tin Transformation Temperature – tSn Aluminium fusion temperature - tF Thermal conductivity (solid) - kS Thermal conductivity (liquid) - kL Density (solid) - ρS Density (liquid) - ρL Specific heat (solid) - cS Specific heat (Liquid) - cL Latent heat of fusion – L1 from (604.75 to 561.56) °C Latent heat of fusion – L2 from (561.56 to 550.83) °C Latent heat of fusion – L3 at 550.83°C Latent heat of fusion – L4 at (550 to 227) °C Latent heat of fusion – L5 at 227 °C Liquidus slope - m LSn from (638.1 to 561.56) °C Sn Liquid#1 slope - mLiquid#1 from (561.56 to 550.83) °C

Units / °C / °C / °C / (wt %) / (wt %) / °C / °C / °C

Al – 15 wt%Sn -5wt%Si 604.75 561.56 550.83 40.0 23.3 554.13 227.00 660 -1 -1 165 / (W.m .K ) 80 / (W.m-1.K-1 ) -3 2921.7 / (kg.m ) 2653.6 / (kg.m-3) -1 -1 861.8 / (J.K .kg ) -1. -1 1008.0 . / (J K kg ) 212300 / (J.kg-1) -1 108800 / (J.kg ) 85000 / (J.kg-1) -1 12000 / (J.kg ) -1 9500 . / (J kg ) -1.756 / (°C.wt %-1) 0.659 / (°C.wt %-1) / (°C.wt %-1)

-1.123

Liquidus slope - mLSi from (639.2 to 562.9) °C

/ (°C.wt %-1)

-7.157

Si Silicon slope - mSilicon from (562.9 to 550.8) °C

/ (°C.wt %-1)

1.955

Si Liquid#1 slope - mLiquid#1 from (578 to 550.8) °C

/ (°C.wt %-1) -

-10.074

-

0.14193

Liquid#1 slope -

Sn mLiquid#1

from (577.0 to 550.83) °C

Tin partition coefficient - k0Sn Silicon partition coefficient -

k0Si

0.02

TABLE 3 Thermophysical data for the Al – 25 wt%Sn – 5 wt%Si alloy. Properties Liquidus temperature - tL Eutectic Temperature tE Tin melt Temperature tSn FCC_A1 phase final Sn concentration Eutectic Sn Concentration CE FCC_A1 phase final Si concentration Eutectic Si concentration CE Aluminium fusion temperature - tF

Units / °C / °C / °C / (wt %) / (wt %) / (wt %) / (wt %) / °C

Al-25wt%Sn-5wt%Si 584.85 561.56 227.0 39.0 25.3 8.0 5.0 660

24

Thermal conductivity (solid) - kS Thermal conductivity (liquid) - kL Density (solid) - ρS Density (liquid) - ρL Specific heat (solid) - cS Specific heat (Liquid) - cL Latent heat– L1 from (584.85 to 550.83) °C Latent heat – L2 at 550.83 Eutectic Latent heat – LE at 550.83 to 227) °C Latent heat – L3 at 227 °C Liquidus slope - m LSn from (584.85 to 559.7) °C

/ (W.m-1 .K-1) / (W.m-1 .K-1) / (kg.m-3) / (kg.m-3) / (J.K-1.kg-1) / (J.K-1.kg-1) / (J.kg-1) / (J.kg-1) / (J.kg-1) / (J.kg-1) / (°C.wt %-1)

145 65 3099.82 2870.84 859.0 902.6 139200 213200 20000 15900 -1.795

Sn Liquid#1 slope - mLiquid#1 from (559.7 to 550.83) °C

/ (°C.wt %-1)

0.659

Sn Liquid#1 slope - mLiquid#1 from (550.0 to 227.0) °C

/ (°C.wt %-1)

-1.123

Liquidus slope - m LSi from (639.2 to 555.85) °C

/ (°C.wt %-1)

-9.000

Si Silicon slope - m Silicon from (555.85 to 550.8) °C

/ (°C.wt %-1)

1.955

Si Liquid#1 slope - mLiquid#1 from (578 to 550.8) °C

/ (°C.wt %-1) -

-10.074 0.01578

-

0.1840

Tin partition coefficient - k 0Sn Silicon partition coefficient -

k 0Si

The analysis of heat transfer that occurs at the casting/mould interface is a fundamental task for simulation of unsteady solidification in permanent mould casting processes. In the present study, an inverse heat conduction problem (IHCP) technique is used for estimating the boundary heat transfer coefficient at the metal/ mould interface from experimental temperatures in the casting. The metal/mould thermal resistance varies with time, and is incorporated in a global heat transfer coefficient defined as hg. In water- cooled moulds, to take into account the simultaneous effects of thermal resistances due to air gap, cooling fluid and thickness of the mould wall, an overall heat transfer coefficient, hg is defined:

1 1 e 1 = + + hg hi k M hW

(24)

where hg is the global heat transfer coefficient between the casting surface and the cooling fluid (W.m-2 .K-1), e is the thickness of the mould which separates the metal from the cooling fluid 25

(m), kM is the mould thermal conductivity (W.m-1 .K-1 ), and finally, hW is the mould/cooling fluid heat transfer coefficient (W.m-2.K-1). It has been proved that hi is described by a power law relating hi with time (hi=a.t-m), where “a” and “m” are constants, and m < 0.5 [37]. Some studies stated that such multiplier “a” is mainly linked to the wettability of the liquid layer in contact with the mould inner surface i.e., related to the variation of fluidity of the molten alloy as a function of the alloy solute content considering a certain metallic system [38,39]. It can be considered that hg follows the hi power law behaviour because the thermal resistance associated with the air gap is much larger than the other two components of Eq. (24) [40]. At time t < 0 , the alloy is in the molten state at the nominal alloy concentration and with an initial temperature distribution as a function of distance in the casting from the metal/mould interface (z), T0 ( z) = −a ⋅ z 2 + b ⋅ z + c , which is based on experimental thermal readings [37,41]. Figure 11 shows the experimental cooling curves during solidification compared with the predictions provided by the numerical solidification model described in section 2.2, and the best theoretical-experimental fit has generated the appropriate transient hg profile for each alloy casting (Figure 12). A three-dimensional phase diagram has been calculated prior to simulations by a TCAPI (Thermo-Calc API Interface) interface, which couples the proposed numerical routine and the Thermo-Calc TCMP2 Thermal Aluminium Database in order to avoid unnecessary simplifications in the phase diagram. Figure 12 compares the time dependence of hg as a function of time of both ternary alloys experimentally examined. It can be seen that the increase in the alloy Sn content promotes a significant increase in the hg profile, which includes the wettability of the mould by the molten alloy, characterized by the initial values of hg. It is important to state that a realistic hg profile is directly dependent on reliable thermal properties of the alloys, otherwise meaningless hg will be determined via IHCP, because hg centralizes into itself all imprecise thermal properties input. In this sense, an accurate application of thermodynamics analysis is able to assure an effective solidification simulation of aluminium-base multicomponent alloys. 26

FIGURE 11. Experimental thermal responses compared with numerical simulations to determine

hg. The variable z refers to the position from the cooled surface of the castings

FIGURE 12. Evolution of metal/mould heat transfer coefficient, hg, of Al – 5 wt%Si - 15 wt%Sn

and Al – 5 wt%Si – 25 wt%Sn alloys as function of time.

27

The thermal data around the liquidus temperature, provided by the cooling curves recorded by each thermocouple positioned along the length of the casting, were used to determine the coefficients of a 5th-order polynomial via the least square method in order to generate T=f(t) •

functions. The derivative of these functions with respect to time yielded cooling rate functions T

=f(t). The experimental time corresponding to the liquidus front passing by each thermocouple is •

then inserted into the T =f(t) function permitting the experimental cooling rate to be determined. •

As reported in the literature, the cooling rate ( T ) is the main thermal parameter controlling the evolution of solidification during transient heat flow conditions, which encompasses the majority of industrial castings processes [42]. It synthesizes the thermal gradient (G) and the solidification rate •

(V), i.e. T = GV . The only analytical solidification heat transfer model for binary alloys available in the literature [43,44], derived an expression relating the cooling rate to the main thermophysical properties, in which it can be seen that

•

T

is affected not only by the main thermophysical values of

tables 2 and 3, but also by the transient overall heat transfer coefficient, hg. This expression is given by [44]:

 T
=   π .α SL

  ´   2  m (Tp − TL ) 2α SL φ 2    2 kSφ 2 (TE − T0 )  φ 2 [1 − erf ( m´ φ 2 )] exp( m´ φ 2 ) 2    n π (T − T ) exp( φ 2 )[ M + erf (φ )]h + S L  L 0 1 1 g  

2

(25)

where: m´ is the square root of the ratio of thermal diffusivities of mushy zone and liquid, (αSL /αL)1/2; αL is the liquid thermal diffusivity (kL/cLρL); T0 is the environment temperature; Tp is the initial melt temperature; n is the square root of the ratio of thermal diffusivities of solid and mushy zone; M is the ratio of heat diffusivities (kcρ)1/2 of solid and mould material and SL is the position of liquidus isotherm from metal/mould interface. Solidification constants φ1 and φ2 are associated with the displacement of solidus and liquidus isotherms, and depend on the alloy latent heat.

28

The approach used in the present study intends to combine the use of a computational thermodynamics model, which substantially reduces the extent of experimental attempts in determining specific thermophysical properties, and an experimental validation based on this particular thermal parameter, i.e.

•

T

, which has, as aforementioned, a particular characteristic of

synthesizing most of the main thermophysical properties. The simulated

•

T

was numerically determined by the solidification model, using the

thermophysical values synthesized in tables 2 and 3 and the hg=f(t) profiles as boundary conditions, and then compared with the

•

T

experimental profiles. The comparison can be observed in Figure 13,

where for both cases the good agreement observed indicates the relevance of applicability of the proposed approach for the appropriate determination of thermophysical properties. The cooling rate is a fundamental thermal parameter for casting processing, since it determines the length scale of the primary phase forming the alloys microstructure, as well as the size and distribution of second phases [45]. Moreover, the microstructural length scale has been shown to affect the tensile properties of a number of alloys [46, 47]. The aforementioned correlations emphasize the importance the thermophysical properties of multicomponent alloys may have, since they can be used in the planning of casting operations via the pre-programming of cooling rates with a view to attaining optimized microstructures and desired final mechanical properties.

29

•

FIGURE 13. Comparison between numerical and experimental cooling rate ( T ) of Al – 15 wt%Sn

– 5 wt%Si and Al – 25 wt%Sn – 5 wt%Si alloys, as function of position.

5. Conclusions

In this paper, a numerical routine was developed and connected in real runtime execution to a computational thermodynamic software, which permitted important thermophysical properties of Al-Sn-Si alloys to be determined, i.e. latent heats; specific heats; temperatures and heats of transformation; phase fractions and composition and density as a function of temperature. These properties were used to run numerical simulations of cooling rate during solidification of two AlSn-Si alloys compositions, using a solidification heat transfer model for multicomponent alloys. An inverse heat conduction approach was used to provide the necessary boundary condition at the metal/mould interface characterized by a transient heat transfer coefficient, hg, which plays a key role in the effective design of castings. Realistic hg values can only be determined from reliable thermal properties of the alloys that were effectively obtained by the proposed numerical routine coupled to the Thermo-Calc software. The approach used in the present study combined the use of a computational thermodynamics model, which substantially reduces the extent of experimental attempts to determine specific thermophysical properties, and an experimental validation based on a particular thermal parameter, i.e. the cooling rate, which has a particular characteristic of 30

synthesizing most of the main thermophysical properties. A directional solidification technique was used to experimentally determine the cooling rates profiles along the two Al-Sn-Si alloys castings. These experimental profiles were compared with those numerically simulated and a good agreement was observed for both alloys castings, indicating the applicability of the proposed approach in the determination of thermophysical properties of multicomponent alloys. These properties can be used in the pre-programming of cooling rates with a view to attaining optimized as-cast microstructures and desired final mechanical properties.

Acknowledgements

The authors acknowledge the financial support provided by FAPESP - São Paulo Research Foundation, Brazil (grants 2012/16328-2, 2013/23396-7 and 2014/21893-6) and CNPq - The Brazilian Research Council (grants 471581/2012-7, 475480/2012-0). The authors would like to thank the Brazilian Nanotechnology National Laboratory — LNNano for the use of X-ray diffractometer.

References

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List of Figure Captions

FIGURE 1. Numerical scheme for determination of density of a multicomponent alloy by

interconnecting a numerical routine with a computational thermodynamic software. FIGURE 2. Scatter data of diffusion coefficient as a function of temperature [25] and non-linear fit

curve of Arrhenius type. FIGURE 3. Details of the schematic vertical upward directional solidification casting assembly and

the mould. FIGURE 4. Pseudo-binary phase diagrams of Al – Sn – 5 wt%Si alloys with indications of the

alloys compositions examined in the present study [Thermo-Calc database]. FIGURE 5. Scheil-Gulliver simulations of mass fraction of all solid phases for: (a) Al – 15 wt%Sn

– 5 wt%Si and (b) Al – 25 wt%Sn – 5 wt%Si alloys. FIGURE 6. DSC spectra at 10 ºC.min-1 rate a) Al – 25 wt%Sn – 5 wt%Si; b) Al – 15 wt%Sn – 5

wt%Si FIGURE 7. Experimental solute distribution along the DS castings length:

a) Al – 15 wt%Sn – 5 wt%Si b) Al – 25 wt%Sn – 5 wt%Si alloys FIGURE 8. Typical microstruture of the Al-Sn-Si alloy (Optical Image) FIGURE 9. Typical X-ray diffraction (XRD) patterns: (a) Al - 15 wt%Sn – 5 wt%Si and

(b) Al - 25 wt%S –5 wt%Si alloys samples FIGURE 10. Numerical predictions of density of solid and liquid phases as a function of

temperature for Al – 15 wt%Sn – 5 wt%Si and Al – 25 wt%Sn – 5 wt%Si alloys. 34

FIGURE 11. Experimental thermal responses compared with numerical simulations to determine

hg. The variable z refers to the position from the cooled surface of the castings FIGURE 12. Evolution of metal/mould heat transfer coefficient, hg, of Al-5wt%Si-15wt%Sn and

Al – 5 wt%Si – 25 wt%Sn alloys as function of time. •

FIGURE 13. Comparison between numerical and experimental cooling rate ( T ) of Al – 15 wt%Sn

– 5 wt%Si and Al – 25 wt%Sn – 5 wt%Si alloys, as function of position.

Table Captions

Table 1 – Chemical composition as mass per cent of metals used to prepare the alloys. Table 2 – Thermophysical data for the Al - 15 wt%Sn – 5 wt%Si alloy. Table 3 - Thermophysical data for the Al – 25 wt%Sn – 5 wt%Si alloy.

35

Research Highlights

•

A numerical routine coupled to a computational thermodynamics software is proposed to calculate thermophysical properties

•

The approach encompasses numerical and experimental simulation of solidification

•

Al-Sn-Si alloys thermophysical properties are validated by experimental/numerical cooling rate results

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