materials science & engineering...

Materials Science & Engineering A 560 (2013) 481–491

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Materials Science & Engineering A

0921-50

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The effect of main alloying elements on the physical propertiesof Al–Si foundry alloys

F. Stadler a, H. Antrekowitsch a,n, W. Fragner b, H. Kaufmann c, E.R. Pinatel d, P.J. Uggowitzer e

a Institute of Nonferrous Metallurgy, Montanuniversitaet Leoben, Franz-Josef-Straße 18, A-8700 Leoben, Austriab AMAG Casting GmbH, Postfach 32, A-5282 Ranshofen, Austriac AMAG Austria Metall AG, Postfach 32, A-5282 Ranshofen, Austriad Dipartimento di Chimica and NIS, Universit �a degli Studi di Torino, via Giuria 7/9, Torino 10125, Italye Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland

a r t i c l e i n f o

Article history:

Received 28 August 2012

Received in revised form

25 September 2012

Accepted 27 September 2012Available online 3 October 2012

Keywords:

Al–Si foundry alloy

Compositional variation

Thermal conductivity

Thermal expansion

Thermal shock resistance

93/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.msea.2012.09.093

esponding author. Tel.: þ43 3842 4025200; f

ail address: helmut.antrekowitsch@unileoben

a b s t r a c t

In this study we describe the effect of the main alloying elements Si, Cu and Ni on the thermal

properties of hypoeutectic and near-eutectic Al–Si foundry alloys. By means of systematic variations of

the chemical composition, the influence of the amount of ‘second phases’ on the thermal conductivity,

thermal expansion coefficient, and thermal shock resistance is evaluated. Thermodynamic calculations

predicting the phase formation in multi-component Al–Si cast alloys were carried out and verified

using SEM, EDX and XRD analysis. The experimentally obtained data are discussed on a systematic basis

of thermodynamic calculations and compared to theoretical models for the thermal conductivity and

thermal expansion of heterogeneous solids.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Today, power train components of modern transportationvehicles such as engine blocks or gearbox housings are frequentlyproduced from recycled Al–Si foundry alloys on high-pressure diecasting machines – a cost-efficient combination of material andprocess applicable for sustainable mass production. The acceler-ated need for weight reduction, however, leads to higher mechan-ical and thermal loading of these aluminium castings in futurevehicles, requiring improved Al–Si foundry alloys. Therefore, inthe last couple of years, several investigations were carried outwith the objective of improving the mechanical properties ofAl–Si foundry alloys at elevated temperatures [1–6].

However, it has taken a longer time to recognise the importanceof the physical properties. In addition to high temperature strength,adequate thermal conductivity (TC) as well as low thermal expan-sion are crucial physical properties for alloys used as motorcomponents. In case of pistons, e.g., the heat generated in the courseof the compression process has to be removed as quickly as possibleto avoid thermal stresses and hot spots on the surface, whereas lowthermal expansion prevents the piston from becoming tight andseizing under operation temperature. TC as well as the coefficient of

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ax: þ43 3842 4025202.

.ac.at (H. Antrekowitsch).

thermal expansion (CTE) can therefore play a major role in deter-mining the life time of certain motor components [7].

TC is a measure of the rate at which heat is transferred througha material. It is mainly governed by electric conductivity, elasticvibrations of the lattice (phonons) and thermal consumptionprocesses (specific heat). If the contribution of phonons is negli-gible (this is the case for pure metals), TC is mainly influenced bythe mobility of electrons, i.e. the electric conductivity, se.

It is well known that se and thus TC is significantly decreasedby the addition of alloying elements, whereupon elements in solidsolution result in lower values than the same amount of elementsforming intermetallic phases. The latter typically reduce thermalconductivity proportionally with increasing volume fraction [8].

The thermal expansion coefficient of alloyed metals often variesaccording to the expansion coefficients of the solute and the solventelements. By alloying elements with a low CTE, the coefficient of thealloy can be decreased. Additions of Si, Cu and Ni reduce CTE inapproximately a linear manner, whereas Mg or Zn can increase theexpansion. Generally, the effects of alloying additions on thermalexpansion are additive, following the rule of mixtures [9,10].

Since Si, Cu and Ni are the main alloying elements in Al–Si castalloys used for high-temperature applications, the understandingof their effect on TC and CTE is fundamental defining reasonableconcentrations of these elements in the respective alloys. Conse-quently, this work aims at quantifying the effect of single Si, Cuand Ni additions as well as their combined influence on TC and

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dx.doi.org/10.1016/j.msea.2012.09.093

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F. Stadler et al. / Materials Science & Engineering A 560 (2013) 481–491482

CTE of hypoeutectic and eutectic Al–Si foundry alloys and tocompare several experimentally determined values with thoseobtained by classic theoretical models, predicting the physicalproperties of heterogeneous solids. Finally, a ranking of theparticular alloys according to their resistivity to thermallyinduced strain shall be presented, facilitating the choice of alloysfor engineering applications involving thermal stresses.

2. Experimental

2.1. Sample preparation

A series of 36 hypoeutectic and eutectic alloys based on thesystems AlSi7 and AlSi12 were fabricated by the AMAG AustriaMetall AG testing laboratory. The composition of the samples isshown in Table 1. The alloys are sectioned according to their Sicontent and Cu/Ni ratio: 1–16 (AlSi7(Mg)) and 17–36 (AlSi12(Mg)).Additionally, all alloys contain Fe and Mn in an amount comparableto recycling Al–Si foundry alloys.

All materials were melted in a 100 kg induction furnace andcast into a steel mould with a wall thickness of the test section of20 mm to form tensile test bars. The mould was preheated to atemperature of 32075 1C and coated with boron nitride beforecasting, and the melt temperature was held constant at 75075 1Cduring the whole casting process. The alloys were solution-treated at 495 1C for 8 h and subsequently quenched in water atroom temperature. Afterwards, the samples were over-aged at250 1C for 100 h. This annealing procedure was performed inorder to simulate the ‘thermal load’ in service.

Table 1Composition of the investigated alloys (in wt%).

Alloy nr. Alloy Si Fe

1 AlSi7(Mg) 6.93 0.40

2 AlSi7Ni0.5(Mg) 7.04 0.41

3 AlSi7Ni1(Mg) 7.24 0.39

4 AlSi7Ni1.5(Mg) 7.17 0.41

5 AlSi7Cu1(Mg) 7.06 0.40

6 AlSi7Cu1Ni0.5(Mg) 7.08 0.43

7 AlSi7Cu1Ni1(Mg) 7.20 0.41

8 AlSi7Cu1Ni1.5(Mg) 7.10 0.41

9 AlSi7Cu2(Mg) 7.14 0.40

10 AlSi7Cu2Ni0.5(Mg) 7.00 0.42

11 AlSi7Cu2Ni1(Mg) 7.14 0.40

12 AlSi7Cu2Ni1.5(Mg) 7.14 0.41

13 AlSi7Cu3(Mg) 6.90 0.40

14 AlSi7Cu3Ni0.5(Mg) 7.04 0.42

15 AlSi7Cu3Ni1(Mg) 7.01 0.42

16 AlSi7Cu3Ni1.5(Mg) 6.99 0.40

17 AlSi12(Mg) 12.15 0.43

18 AlSi12Ni1(Mg) 12.20 0.44

19 AlSi12Ni2(Mg) 12.33 0.44

20 AlSi12Ni3(Mg) 12.07 0.43

21 AlSi12Cu1(Mg) 12.05 0.39

22 AlSi12Cu1Ni1(Mg) 12.01 0.40

23 AlSi12Cu1Ni2(Mg) 12.04 0.40

24 AlSi12Cu1Ni3(Mg) 11.87 0.43

25 AlSi12Cu2(Mg) 12.05 0.41

26 AlSi12Cu2Ni1(Mg) 11.96 0.44

27 AlSi12Cu2Ni2(Mg) 11.94 0.44

28 AlSi12Cu2Ni3(Mg) 11.93 0.43

29 AlSi12Cu3(Mg) 12.26 0.40

30 AlSi12Cu3Ni1(Mg) 11.97 0.40

31 AlSi12Cu3Ni2(Mg) 12 0.40

32 AlSi12Cu3Ni3(Mg) 11.93 0.41

33 AlSi12Cu4(Mg) 12.02 0.43

34 AlSi12Cu4Ni1(Mg) 12.01 0.44

35 AlSi12Cu4Ni2(Mg) 12.02 0.46

36 AlSi12Cu4Ni3(Mg) 11.94 0.47

2.2. Microstructure analysis

Metallographic specimens were cut out within the gaugelength region of the cast samples to analyse the microstructureby means of light optical microscope (LOM) and scanning electronmicroscope (SEM) techniques. To identify the phase componentsoccurring in the alloy, energy dispersive X-ray (EDX) and X-raydiffraction (XRD) analysis were performed. Thermodynamic cal-culations to evaluate the alloys’ phase fractions were carried outusing the Thermo-Calc software package with the data baseTTAL5 [11].

2.3. Electric conductivity

Samples for measuring the electric and thermal conductivitywith a diameter of 5 mm and a length of 30 mm were taken fromtensile bars. The electric resistivity at room temperature wasdetermined using a four-point current technique. When a con-stant current I flows from contact A to contact B it is possible tomeasure the voltage drop V across the contacts C and D in themiddle of the sample and consequently calculate the electricconductivity se of the material with

se ¼Il

UA¼

l

RAð1Þ

where R is the resistance and A the cross-sectional area of thespecimen. All measurements were performed at a constantcurrent of 7000 mA. The voltage drop was measured with aHewlett Packard HP3456 digital voltmeter.

Cu Mn Mg Ni Others

o0.05 0.30 0.36 o0.05 o0.05

o0.05 0.34 0.38 0.51 o0.05

o0.05 0.30 0.40 1.06 o0.05

o0.05 0.31 0.37 1.55 o0.05

0.98 0.31 0.37 o0.05 o0.05

1.00 0.36 0.37 0.55 o0.05

1.00 0.31 0.37 1.06 o0.05

1.01 0.31 0.35 1.54 o0.05

2.09 0.31 0.35 o0.05 o0.05

1.99 0.37 0.33 0.54 o0.05

2.11 0.31 0.35 1.00 o0.05

2.11 0.31 0.35 1.53 o0.05

3.06 0.31 0.34 o0.05 o0.05

2.99 0.37 0.34 0.54 o0.05

3.01 0.37 0.34 1.01 o0.05

3.04 0.31 0.35 1.51 o0.05

o0.05 0.32 0.34 o0.05 o0.05

o0.05 0.32 0.35 1.05 o0.05

o0.05 0.31 0.35 2.11 o0.05

o0.05 0.29 0.34 3.15 o0.05

0.95 0.29 0.34 o0.05 o0.05

0.99 0.29 0.34 1.10 o0.05

0.99 0.29 0.35 2.05 o0.05

1.00 0.28 0.34 3.01 o0.05

1.96 0.30 0.34 o0.05 o0.05

1.97 0.3 0.34 0.99 o0.05

2.02 0.29 0.35 2.02 o0.05

2.05 0.28 0.35 3.02 o0.05

3.02 0.3 0.35 o0.05 o0.05

3.02 0.3 0.35 1.03 o0.05

3.05 0.29 0.35 2.12 o0.05

3.07 0.28 0.35 2.99 o0.05

3.79 0.30 0.32 o0.05 o0.05

3.8 0.29 0.32 1.00 o0.05

3.87 0.28 0.32 1.99 o0.05

3.91 0.27 0.33 2.93 o0.05

F. Stadler et al. / Materials Science & Engineering A 560 (2013) 481–491 483

2.4. Thermal conductivity

The measurement of TC is based on the temperature gradientalong the serial connection of a reference material and the samplewith unknown thermal conductivity. If the heat flux J is the samein both materials (losses over the sample’s surface are negligible),TC of the sample can be calculated with

lS ¼ lref

Aref

AS

rTref

rTS

DLS

DLrefC ð2Þ

where lref is the known conductivity of the reference material, Athe cross-section of both samples, QUOTE T the temperaturegradient within the reference material and the sample respec-tively, and L the distance between the thermocouples in bothmaterials. C corresponds to a correction term and has a value ofabout unity.

The temperature gradient in both the sample and the referencematerial (in our case Al99.99) was measured over a well-defineddistance of 2570.01 mm with two thermocouples each. Allmeasurements were carried out at a temperature between 20 1Cand 60 1C and the temperature gradient from the top plate to thebottom plate was constant at 40 1C. All measurements wereperformed at a vacuum of 10�5 mbar in order to minimiseconvection effects.

2.5. Thermal expansion

A Netzsch DIL 805 A/D high-resolution differential dilatometerwas used to record the length change of cylindrical specimens of

Table 2Volume fractions of the different phases at 250 1C (predicted by simulation) as well as

Alloy Si Mg2Si Al15(Fe,Mn)3Si2 Al2Cu Al9FeNi Al3Ni Al3Niall at 250 1C

1 7.75 0.79 1.90 – – – –

2 7.90 0.80 1.63 – 1.60 – –

3 8.04 0.82 1.52 – 2.90 – –

4 8.14 0.83 1.54 – 2.94 1.03 –

5 7.75 – 1.97 0.71 – – –

6 7.84 – 1.90 – 0.31 – 1.09

7 7.98 – 1.68 – 1.72 – 1.20

8 8.13 – 1.58 – 2.97 0.09 1.28

9 7.90 – 2.01 2.01 – – –

10 7.94 – 2.01 – – – 0.57

11 8.02 – 2.03 – – – 2.72

12 8.18 – 1.82 – 1.16 – 3.03

13 8.08 – 2.05 3.34 – – –

14 8.08 – 2.06 0.52 – – –

15 8.16 – 2.07 – – – 1.77

16 8.24 – 2.09 – – – 3.94

17 13.70 0.82 2.16 – – – –

18 14.27 0.87 1.74 – 3.43 – –

19 14.82 0.90 1.73 – 3.80 1.97 –

20 14.91 0.91 1.66 – 4.01 4.01 –

21 13.68 – 2.02 0.70 – – –

22 14.07 – 1.71 – 2.13 1.29

23 14.47 – 1.65 – 3.36 1.11 1.39

24 14.71 – 1.64 – 4.19 2.63 1.46

25 13.95 – 2.16 2.11 – – –

26 14.16 – 2.18 – – – 2.85

27 14.53 – 1.80 – 2.80 – 3.41

28 14.97 – 1.67 – 4.26 1.01 3.69

29 14.47 – 2.18 3.60 – – –

30 14.31 – 2.20 – – – 1.98

31 14.75 – 2.00 – 1.01 – 5.29

32 15.10 – 1.73 – 3.30 – 5.76

33 14.44 – 2.31 4.72 – – –

34 14.60 – 2.25 – 0.33 – 0.61

35 14.96 – 2.22 – 0.75 – 4.78

36 15.25 – 2.00 – 2.08 – 7.12

10 mm in length and 5 mm in diameter, taken from tensile bars.With this instrument, the difference between the sample and aninert reference sample was measured, resulting in a resolution ofabout 70.05 mm. The dilatometric measurements were per-formed under flowing high purity argon to protect the specimensfrom oxidation.

3. Results

3.1. Thermodynamic calculations

Table 2 shows the volume fractions of the intermetallic phases inthe respective alloys for the equilibrium condition at 250 1C.Obviously, nine different phases, including Si, Mg2Si, Al15(Fe.Mn)3Si2,Al2Cu, Al9FeNi, Al3Ni, Al3Ni2, Al7Cu4Ni and Al5Cu2Mg8Si6, werepredicted.

3.2. Microstructure analysis

3.2.1. LOM and SEM analysis

Fig. 1 shows the microstructure of the investigated materialusing the example of alloys 2, 10 and 14. Each LOM-picture isopposed to the respective SEM-micrograph and the chemicalcomposition of the individual phases is shown in Table 3.

The primary phases in the Cu-free alloy two were analysed tobe the Fe-containing blocky type of Al15(Fe,Mn)3Si2 (a-phase),which appears grey in the LOM-micrograph and the stripe-like

TC and CTE of the investigated alloys.

2 (Al3CuNi) Al7Cu4Ni Al5Cu2Mg8Si6 TC [W/mK] CTE [�10�6 K�1]20–60 1C 250 1C

– – 187.0 22.89

– – 184.1 23.25

– – 179.1 22.67

– – 174.6 22.78

– 1.18 183.4 23.23

– 1.19 175.8 23.27

– 1.21 175.4 23.01

– 1.24 171.5 22.80

– 1.21 181.8 23.30

1.42 1.21 177.1 23.19

0.06 1.23 174.1 23.25

– 1.25 167.8 22.86

– 1.23 178.8 23.38

2.41 1.24 177.3 23.34

1.84 1.25 171.1 23.23

0.45 1.26 163.9 22.94

– – 175.0 21.98

– – 157.5 21.74

– – 158.1 21.47

– – 141.2 21.56

– 1.22 175.0 21.99

– 1.26 164.6 21.92

– 1.30 157.3 21.74

– 1.34 150.8 21.32

– 1.24 172.1 21.78

0.06 1.27 160.9 21.71

– 1.35 152.0 21.28

– 1.40 150.4 21.28

– 1.21 169.1 21.67

1.92 1.33 159.9 21.65

– 1.37 148.6 21.49

– 1.41 148.4 21.22

– 1.23 162.4 21.75

3.77 1.23 159.2 21.49

1.32 1.26 148.1 21.08

– 1.35 142.7 20.52


reddish Ni-containing phases Al3Ni and Al9FeNi, respectively,where some parts of Si and Mn can be incorporated.

In alloy 10, Cu and Ni form the Al3Ni2 phase, where more orless Cu can replace Ni forming the ternary phase Al3CuNi. Thelatter often has a more or less ring-like shape [12]. Additionally, inalloy 14 a second high Cu-containing phase of type Al7Cu4Nioccurs. Mg and parts of Cu are bonded in the quaternaryAl5Cu2Mg8Si7 phase.

Fig. 1. LOM and SEM micrographs of alloys 2 (a), 10 (b) and 14 (c) in over-aged condi

Table 3Composition of intermetallic phases in alloys 2, 10 and 14 (in wt%).

Spectrum Al Si Fe

Alloy 21 60.02 9.56 16.33

2 63.26 4.39 4.51

3 66.61 3.52 4.18

Alloy 101 50.52 4.07 6.17

2 55.43 9.17 13.17

Alloy 141 46.52 3.93 6.08

2 28.68 – –

3 22.21 27.71 –

3.2.2. Phase identification by XRD

Using the example of alloys 2 and 14, XRD-measurementswere carried out to physically verify the phases predicted byThermo-Calc.

Fig. 2 shows the respective XRD-profiles, whereby the differentphases were indexed using the ICDD database [13]. Obviously, thephase identification by XRD is in good agreement with SEMobservation and predictions from the thermodynamic modelling.

tion (250 1C/100 h); the composition of the respective phases is shown in Table 3.

Cu Mn Mg Ni Phase

– 10.70 – 3.39 Al15(Fe,Mn)3Si2

– 1.01 – 24.64 Al9FeNi (Al3Ni)

– 1.52 – 20.18 Al9FeNi (Al3Ni)

14.55 2.16 – 20.39 Al3Ni2 (Al3CuNi)

7.45 10.57 – 2.58 Al15(Fe,Mn)3Si2

20.75 1.70 – 19.29 Al3Ni2 (Al3CuNi)

56.41 – – 14.91 Al7Cu4Ni

21.75 – 26.72 – Al4Cu2Mg8Si7

Fig. 2. XRD profiles of (a) alloy 2 and (b) alloy 14.

Fig. 3. Measured and calculated values of thermal conductivity by using the Wiedemann-Franz law; (a) System AlSi7(Mg) and (b) System AlSi12(Mg).

Fig. 4. Effect of Si on the thermal conductivity and comparison with literature

values [14].



The measured TC data of the various alloys are summarised inTable 2. The values range from 141 to 187 [W/mK] indicating asignificant influence of the main alloying elements.

As already mentioned in the introduction, the thermal con-ductivity can be estimated by the electric conductivity, by simplyusing the Wiedemann–Franz law, which can be expressed math-ematically as [8]

le ¼ LseTþC ð3Þ

where le and se are the thermal and electric conductivity,L the Lorenz constant, T the temperature and C a constant.The theoretical value for the Lorenz constant is L¼

2.45�10�8 WO K�2 [8], whereby in literature the experimen-tally determined constants in Eq. (3) can vary. For aluminiumalloys Hatch [9] relates L to the Si content withL¼2.1�10�8

þ0.021�10�8� (wt% Si) and proposes a value of

12.6 W/mK for C.Fig. 3 shows a comparison of the measured values of thermal

conductivity of the alloys in Table 1 and those obtained by electricconductivity transformed by the Wiedemann–Franz law [8].

A quite acceptable correlation can be achieved for both thehypoeutectic and the eutectic alloys by using the Lorenz constantproposed by Hatch [9]. Thereby it can be concluded that in theinvestigated alloys heat transport is mainly achieved by electronsand much less by phonons.

In the following section, the influence of the main alloyingelements on the thermal conductivity is explained from a phe-nomenological viewpoint. All measurements were carried out inthe temperature range between 20 1C and 60 1C. Please note, thatall statements are only valid regarding the present heat treatmentconditions.

The effect of Si on TC is illustrated in Fig. 4. For this purpose, a‘matrix’ alloy AlSi1Mg0.35Fe0.4Mn0.3 was produced to measure itsTC. This ‘matrix’ basically does not contain any eutectic Si.However, 1% Si had to be added to enable the formation ofAl15(Fe,Mn)3Si2. TC of this alloy was determined to be 201 W/mK

Fig. 5. Effect of (a) Cu and (b) Ni on the TC of AlSi7(Mg) and AlSi12(Mg).

Fig. 6. Effect of Ni on the TC of the Cu-containing alloys; (a) hypoeutectic alloys and (b) eutectic alloys.

Fig. 7. Effect of Si on the CTE at 250 1C. (For interpretation of the references to

color in this figure, the reader is referred to the web version of this article.


at 40 1C. With increasing Si content an almost linear decrease ofTC to 175 W/mK at 12% Si can be observed.

Furthermore, Fig. 4 shows the influence of Si on the thermalconductivity as proposed by Zhang et al. [14], though in their casethe matrix is of Al99.99. Note, that the decrease of TC shows ahyperbolic trend.

Fig. 5a shows the thermal conductivity as a function of the Cucontent. TC decreases almost linearly with increasing Cu-concentration from 187 W/mK to 179 W/mK in case of thehypoeutectic alloys and from 175 to 162 W/mK in case of theeutectic variants, respectively.

The effect of Ni on the thermal conductivity is illustrated inFig. 5b. The decrease of TC with increasing Ni content is much moredistinctive compared to Cu, from 187 to 175 W/mK in the case ofAlSi7(Mg) and from 175 to 141 W/mK in case of AlSi12(Mg).

The effect of Ni on the thermal conductivity of the Cu-containing alloys is demonstrated in Fig. 6a (hypoeutectic alloys)and Fig. 6b (eutectic alloys). Generally, TC decreases with increas-ing Ni content, whereas this trend is more distinctive in theeutectic alloys, when up to 3% Ni is added.

3.4. Thermal expansion

The following section illustrates the results of the thermalexpansion measurements at 250 1C. All measured data are sum-marised in Table 2.


Fig. 7 shows the CTE of AlSi7(Mg) and AlSi12(Mg), marked bythe red circles. Increasing the Si content from 7 to 12% results in adecrease of CTE from 22.89 to 21.98 [�10�6 K�1]. The additionaldata points in Fig. 7 will be explained in further detail in thediscussion section.

Fig. 8a shows the influence of Cu on CTE of AlSi7(Mg) andAlSi12(Mg) at a temperature of 250 1C. The effect of the additionof up to 4% Cu is obviously very low. The same is observed for Ni,whose negative effect on the CTE is not very distinctive, as shownin Fig. 8b.

The effect of Ni on the thermal expansion of the Cu-containingalloys can be seen in Fig. 9. Generally, CTE decreases withincreasing Ni content, whereas this trend is more distinctive incase of the eutectic alloys, when up to 3% Ni is added.

4. Discussion


4.1.1. Effect of Si

The TC of single-phase materials is understood quite well, butmost industrially used alloys are heterogeneous. In simplifiedterms, we consider Al–Si alloys as a two-phase system, consistingof the matrix and eutectic Si.

As it is frequently desirable to estimate the physical properties ofa two or more phase material from knowledge of the properties ofthe respective components, a model has to be chosen, representing

Fig. 8. Effect of (a) Cu and (b)

Fig. 9. Effect of Ni on the CTE of the Cu-containing allo

the distribution of the single components within the mixture, whichin the present case could be simplified to be spherical particlesincorporated in a macroscopically isotropic matrix [15].

One of the earliest models solving the problem for randomly-sized spherical particles distributed in another medium is that ofMaxwell [16]. The thermal conductivity is thereby given by

lmix

l1¼

1þ2w�2V w�1� �

1þ2wþV w�1� � ð4Þ

where w is the ratio of the conductivities of the continuous anddispersed phases l1/l2 and V is the volume fraction of thedispersed phase. Hashin–Shtrikman (HS) bounds [17] are anotherpossibility to establish upper (HSup) and lower (HSlo) bounds onthe effective thermal conductivity of macroscopically isotropiccomposites with an arbitrary microstructure

lloþV

1=lh�lloþ1�V=3llo¼ llower r lef f rlupper

¼ lhþ1�V

1=llo�lhþV=3lhð5Þ

lh and V are the thermal conductivity and volume fraction of thehigh-conductive phase and llo is the thermal conductivity ofthe low-conductive phase. The upper bound usually accountsfor the case where the less-conductive phase is embedded in thebetter conducting matrix, as is the case with our composite, andequates the Maxwell model, the lower bound, on the other hand,generally corresponds to the case where the better conductingphase is embedded in a matrix of less-conducting phase.

Ni on the CTE at 250 1C.

ys; (a) hypoeutectic alloys and (b) eutectic alloys.


The thermal conductivity of bulk single-crystalline Si atambient temperature is reported to be 145 W/mK [18]. However,with this value the application of the above-mentioned modelsdoes not result in a satisfying estimation, neither for the dataobtained by Zhang et al. [14] nor for the values determined in ourwork (see Fig. 10; note, that for both cases a concentration of 1% Siwas chosen as a starting point for the application of the twomodels, considering the substantial solubility of Si in Al atsolutionizing temperature). TC of eutectic Si is therefore supposedto deviate significantly from TC of single-crystalline Si, as it isreported in literature. Wei et al. [19] and Uma et al. [20]determined a value of 15–25 W/mK for un-doped thin poly-crystalline Si-layers, which is almost an order of magnitude lessthan that of single-crystal silicon. Applying lSi¼25 W/mK to themodels of Maxwell and Hashin–Shtrikman results in a muchbetter representation of the actually measured values of this workas well as—with less accordance—for the data determined byZhang et al. [14] (see Fig. 10).

4.1.2. Effect of Cu

With the addition of Cu, an increasing volume fraction ofsecondary precipitates like y-Al2Cu and Q-Al5Cu2Mg8Si7 (seeTable 2) is formed in the course of over-aging at 250 1C, decreas-ing the thermal conductivity of the material. With regard to thehypoeutectic alloys, the whole contingent of Cu and Mg isdissolved in the a-solid solution, when the alloys are heat treatedat 495 1C for 8 h. In the case of AlSi12Cu4(Mg) however, part ofthe Cu cannot be dissolved and persists in the form of primaryintermetallic phases. This can be assumed to cause the moresignificant drop in thermal conductivity between 3 and 4% withthe eutectic alloys.

4.1.3. Effect of Ni

Since Fe and Ni have a negligible solubility in the a-Al solidsolution, the formation of Fe- and Ni-rich intermetallic com-pounds is inevitable even at low concentration of the respectiveelements [8]. Obviously, in equilibrium the formation of Al9FeNiis dominant in alloys with low Ni contents, while with increasingNi concentration Al3Ni forms at the expense of Al9FeNi (seeTable 2). However, with the formation of primary Ni-containingphases, the characteristic of the material is assumed to change toa more complex composite [21].

Generally, the thermal behaviour of such heterogeneousmaterials lies between that of its components and mainlydepends on the volume fractions of the respective phases. In thefollowing section, a comparison of the experimentally determined

Fig. 10. Literature values [14] and measured values of TC as a fun

values with those obtained by the above-mentioned classictheoretical models, predicting the thermal conductivity of hetero-geneous solids, will be presented using the example of Ni. To simplifythe subsequent considerations, the amounts of Al12(Fe,Mn)3Si2 andMg2Si in the respective alloys are considered to be constant andindependent of the Ni content (see Table 2). Again a ‘matrix’ can bespecified for AlSi7(Mg) and AlSi12(Mg), now composed of a-solidsolution, eutectic Si, primary Al12(Fe,Mn)3Si2 phases and secondaryMg2Si precipitates (b), for which the particular thermal conductivityis set to be 187 W/mK and 175 W/mK, respectively (see Fig. 5b). TheNi-containing intermetallic phases are assigned as ‘second phase’.

Very little work has been reported on the physical properties ofNi-containing IMPs. Egry et al. [22] proposed an average value forthe electric conductivity of Al3Ni in the high-temperature range(1400–1650 K) of se(T)¼10165þ0.59(T�T1) [S/m] (T1¼1400 K),which leads to an estimated value of the respective thermal con-ductivity of 19.32–19.36 W/mK (calculated by use of Wiedemann–Franz law [9]). Terada et al. [23,24] determined a value of 35 W/mKfor Al3Ni at 300 K and investigated the effect of ternary elements witha sufficient solubility into NiAl on the thermal conductivity. It turnedout that ternary element additions generally degrade the thermalconductivity of NiAl-based intermetallics.

As the aforementioned models are applicable for just two-phasecomposites, the Ni-containing phases in Table 2 were summed up toa total value of second phases, which was used in the subsequentsection to check the applicability of the individual models. Thethermal conductivity of Al3Ni mentioned in literature reaches avalue of approximately 20–35 W/mK. As Al9FeNi makes a highercontribution to the total amount of Ni-containing phases, meaningTC could be even lower than 20 W/mK, three different values of lIMP

from 15 to 35 W/mK were defined to validate the models in a nextstep. Fig. 11 shows a comparison of the measured values of thermalconductivity and the values obtained by the models of Maxwell andHashin–Shtrikman.

Obviously, altering the value of TC for the Ni-containingphases strongly affects the lower bound of Hashin–Shtrikman,whereas for Maxwell the effect of altering lIMP is negligible. In theinstance of AlSi7(Mg) the Maxwell model (equating the upperbound of the Hashin–Shtrikman model HSup) correlates well tothe measured values, whereas HSlo is not likely to be applicable inthe present case. However, for the eutectic alloys the Maxwellmodel overestimates the actual measured values by far, especiallyin case of AlSi12Ni3(Mg).

This can partly be explained by the fact that by increasing thevolume fraction of intermetallic phases, the composition of theabove-defined ‘matrix’ is altered as well (the volume fraction of Siincreases from 13.7% for alloy 17 to 14.9% for alloy 20), resulting in a

ction of the Si content and comparison with models [16,17].

Table 4Effect of alloying elements on the thermal expansion of aluminium [9].

ElementChange in alloy constant (weighting factor)per wt% addition (annealed temper)a

Cu –0.0033

Fe –0.0125

Mg þ0.0055

Mn –0.010b

Ni –0.0150

Si –0.0107

Zn þ0.0032

a Constant is 1.0000 for high-purity aluminium.b Estimated.

Fig. 11. Comparison of the measured values of thermal conductivity with the values obtained by the models of Maxwell and Hashin–Shtrikman; (a) AlSi7(Mg)

and (b) AlSi12(Mg).


decrease of the initial TC value of the matrix. Furthermore, it has beenreported that the Maxwell model agrees with experimental measure-ments for dispersed particles of a good conductor in a poorlyconducting material better than for dispersions of a poor conductorin a good conductor; in the latter case, the dispersed phase tends tohave a greater effect than the theory predicts [15].

4.1.4. Combined effect of Cu and Ni

Cu in combination with Ni forms a number of Cu–Ni alumi-nides like Al3CuNi, Al7Cu4Ni, which are thermally stable andcannot be dissolved in the course of a solution treatment [3].Thermal conductivity is therefore decreased with increasingvolume fraction of poor conducting primary intermetallic phases.

4.2. Thermal expansion measurements

4.2.1. Effect of Si

The change in alloy constant for different alloy additions toaluminium per weight percent of addition is shown in Table 4. Theeffects of alloying additions are additive in most cases, following therule of mixtures. However, elements which were in solid solutionafter a solution treatment may combine to form phases, e.g. Mg2Si,resulting in thermal expansions different from those expected froma calculation based on the individual metal additions [9].

Hatch [9] proposes a value of 27 [10�6 K�1] for the CTE of pureAl99.99 at a temperature of 250 1C. To investigate the effect of Siand compare the above-mentioned value to AlSi7(Mg) andAlSi12(Mg) it has to be considered that the latter contain Fe, Mnand Mg which altogether will reduce the CTE appreciably. Forthe following considerations we therefore assume the CTE of Al

containing 0.4% Fe, 0.3% Mn and 0.35% Mg according to Table 4 [9]to be 26 [10�6 K�1] at 250 1C. This value and the measured CTEdata of AlSi7(Mg) and AlSi12(Mg) are shown in Fig. 7.

Using the data in Table 4, additions of 7 and 12% Si result in adecrease in CTE of about 7.5 and 12.8% or in absolute values to24.05 and 22.67 [10�6 K�1] for AlSi7(Mg) and AlSi12(Mg), respec-tively. This data deviates substantially from the measured values(AlSi7(Mg): 22.89 [10�6 K�1], AlSi12(Mg): 21.98 [10�6 K�1]).

Another possibility estimating the CTE of Si-containing alloysis the appliance of theoretical models predicting the thermalexpansion coefficient of a two-phase composite, consisting of anAl matrix and eutectic Si, embedded therein. Predicting the CTE ofsuch a material is somehow difficult, because its thermal beha-viour is influenced by various parameters such as the matrix yieldstrength, creep resistance, internal stress distribution and loadtransfer and the architecture of the composite (e.g. particle sizeand shape). Nevertheless, several theoretical models have beenreported in literature for its prediction. A brief discussion of themost commonly used models follows.

4.2.2. The rule of mixtures (ROM)

The ROM model simply relates the CTE of metal matrixcomposites (MMCs) to the CTEs and volume fractions of thereinforcement(s) and the matrix and does not consider suchfactors as the morphology and distribution of the reinforcement.This model is expressed analytically as [25]

amix ¼ a1V1þa2V2 ð6Þ

where a is the CTE, V the volume fraction and the subscripts mix,and 1 and 2 refer to the composite , the matrix and reinforcement,respectively. amix is thus the arithmetic mean of the CTE of eachphase, weighted by the volume fractions.

4.2.3. Turner’s model

Turner [26] derived the CTE of composites by making thefollowing assumptions: (i) homogeneous distribution of reinfor-cement material, (ii) homogeneous strain throughout the composite,(iii) each constituent of the composite changes dimensions withtemperature at the same rate as the composite, and (iv) sheardeformation is negligible. The model is expressed mathematicallyas [26]

amix ¼a1V1K1þa2V2K2

V1K1þV2K2ð7Þ


where K, V, and a are bulk modulus, volume fraction and CTE, andthe subscripts mix, and 1 and 2 refer to the composite, metal matrixand reinforcement, respectively. Especially, composites with three-dimensional continuous reinforcements and matrix phases can bewell described by the Turner model, because it is expected that theyapproach the assumption of the same dimension change in theaverage (expansion and shrinkage, respectively) of each componentof the composite in comparison with the composite itself [27].

4.2.4. Kerner’s model

The Kerner model [28] assumes that (i) the composite is madeup of spherically shaped reinforcements, (ii) the reinforcementsare wetted by a uniform layer of matrix, and (iii) there is perfectmechanical bonding between the matrix and the particle. It isexpressed mathematically as [28]

amix ¼ aþV2n 1�V2ð Þn a2�a1ð ÞnK2�K1

1�V2ð ÞK1þV2K2þ 3K2K1=4G1

� �" #

ð8Þ

where a is the CTE calculated using the ROM model, K is the bulkmodulus, G is the shear modulus, V is the volume fraction, a is theCTE, and the subscripts mix, 1 and 2 refer to the composite, metalmatrix and reinforcement, respectively. The bulk, Young’s (E) andshear moduli are interrelated as shown below [28]

K ¼E

3 3�E=G� � ¼ E

3 1�2nð Þð9Þ

where n is Poisson’s ratio.The results obtained by the application of the above-mentioned

models are demonstrated in Fig. 7.It turns out that the ROM model basically corresponds to the

data in Table 4, which is in accordance with Hatch [9].The Turner model correlates quite well with the measured

values, whereas the Kerner model is obviously less applicable inthe present case. The measured CTE value of AlSi7(Mg) seemscomparatively low, which is also noticeable when the effects ofCu and Ni are analysed (see below). The value predicted by Turnerwould fit much better.

4.2.5. Effect of Cu

A continuous decrease of the CTE would be expected withincreasing Cu content. However, in the hypoeutectic alloys, aslight increase of CTE has been observed. This can only be relatedto measurement errors and the small deviation of CTE of theparticular alloys. According to the data in Table 4, additions of3 and 4% Cu result in a decrease in CTE of about 0.9 and 1.2% and0.21 and 0.26 [10�6 K�1] in absolute values for AlSi7(Mg) andAlSi12(Mg), respectively, which is in the range of the measure-ment error and cannot be determined exactly.

4.2.6. Effect of Ni

Using the data in Table 4, the addition of 1.5% Ni results in adecrease of CTE of 2.25% (0.52 [10�6 K�1]) in the hypoeutecticalloys. In the eutectic variants, the trend is easier to identify. Theaddition of 3% Ni decreases CTE by about 4.5% (0.99 [10�6 K�1]).

4.2.7. Combination Cu–Ni

Cu in combination with Ni forms a number of Cu–Ni alumi-nides like Al3CuNi, Al7Cu4Ni (see Table 2). The CTE of IMPs in Alpiston alloys was studied intensively by Chen et al. [29]. Depend-ing on the crystal structure of the particular phase, thermalexpansion anisotropy can occur. However, in summary CTE ofNi-containing IMPs is in the range of 10–20 [10�6 K�1], whichis significantly lower than that of pure Al. Therefore, CTE isdecreased with increasing volume fraction of primary intermetallic

phases with a lower expansion coefficient, whereas this effect ismore distinctive the eutectic alloys, when up to 3% Ni is added andthe volume fraction of IMPs reaches higher values.

4.3. Thermal shock resistance

Despite the fact that no measurements concerning thermalshock resistance were actually carried out, a ranking of theparticular alloys according to their resistivity to thermallyinduced strain will be presented subsequently. In choosingbetween materials for a particular engineering application invol-ving thermal stresses, thermal shock parameters can be applied tocompare the competing alloys concerning their fracture-initiationresistance. A higher value of thermal shock parameter thereforemeans a better resistance to thermal shock, which is alwaysassociated with high values of strength and thermal conductivityand low values of Young’s modulus and CTE, respectively [30,31].

There are three thermal shock parameters, which can beexpressed mathematically as

RS ¼ scrit1�nEa K½ � ð10Þ

RS0 ¼ lscrit

1�nEa

W

m

� �ð11Þ

RS00 ¼ lscrit

1�nEarcp

m2K

s

� �ð12Þ

where scrit is the critical strength, l the thermal conductivity, rthe density, n Poisson’s ratio, E Young’s modulus, a the CTE and cp

the heat capacity of the respective material. RS is usedin situations where the heat transfer rate is essentially infinite,like quenching a hot part in cold water. In cases of constant heattransfer, RS is expanded to RS

0 by using the factor l. The furtherexpanded form RS* is used in situations, where there is a constantrate of heating or cooling on the surface of the material [30,31].

In the present case RS0 is used to rank the investigated alloys

according to their thermo shock resistance. Young’s modulus as wellas Poisson’s ratio are quite insensitive to small additions of alloyingelements, which is why these values are set to be E¼70 GPa undn¼0.34. However, there are three factors remaining, determiningthe aforementioned parameter: (i) the critical strength at 250 1C, (ii)the thermal conductivity and (iii) the CTE at 250 1C.

As a matter of fact, thermal conductivity was measured at40 1C, though it is assumed that the difference between theparticular alloys will remain constant up to a temperature of250 1C, while the absolute values will increase. For the criticalstrength, i.e. the maximal tension the material can resist, wechose the yield strength at 250 1C [3]. Table 5 shows the rankingof thermal shock resistance according to RS

0 for the investigatedalloys. As expected, the eutectic alloys are located in the upperrange of the ranking, except for the Cu-free alloys AlSi12(Mg),AlSi12Ni1(Mg), AlSi12Ni2(Mg) and AlSi12Ni3(Mg), which exhibitcomparatively low RS

0 values. Conversely, the highest value isachieved by AlSi12Cu3(Mg), combining good mechanical proper-ties as well as a high thermal conductivity, whereas AlSi7(Mg) isbottom of the table, showing a thermal shock resistance, which isalmost 40% lower than in case of alloy 13.

5. Conclusions

As the physical properties play a major role in determining thelife time of certain motor components, this work aims to quantifythe effect of Si, Cu and Ni on both the thermal conductivity and thethermal expansion coefficient of Al–Si cast alloys. The characteristicof the investigated alloys was assumed to resemble complex poly-

Table 5Ranking of thermal shock resistance according to RS

0 .

Rank Alloy RS0 [W/m] RS

0/RS0max Rank Alloy RS

0 [W/m] RS0/RS

0max

1 AlSi12Cu3(Mg) 7801 1.000 19 AlSi7Cu3Ni0.5(Mg) 6224 0.798

2 AlSi12Cu4Ni2(Mg) 7765 0.995 20 AlSi12Ni2(Mg) 6143 0.787

3 AlSi12Cu1Ni3(Mg) 7737 0.992 21 AlSi7Cu1(Mg) 5977 0.766

4 AlSi12Cu1Ni1(Mg) 7689 0.986 22 AlSi7Cu1Ni1(Mg) 5965 0.765

5 AlSi12Cu1Ni2(Mg) 7606 0.975 23 AlSi7Cu3Ni1.5(Mg) 5875 0.753

6 AlSi12Cu4(Mg) 7540 0.966 24 AlSi7Cu3Ni1(Mg) 5853 0.750

7 AlSi12Cu4Ni3(Mg) 7510 0.963 25 AlSi7Cu2(Mg) 5788 0.742


9 AlSi12Cu3Ni3(Mg) 7438 0.953 27 AlSi7Cu2Ni1(Mg) 5742 0.736


11 AlSi12Cu1(Mg) 7383 0.946 29 AlSi7Cu2Ni1.5(Mg) 5669 0.727




15 AlSi12Cu2(Mg) 7046 0.903 33 AlSi7Ni1.5(Mg) 5242 0.672

16 AlSi12Cu2Ni2(Mg) 6981 0.895 34 AlSi12(Mg) 5023 0.644

17 AlSi7Cu3(Mg) 6455 0.827 35 AlSi7Ni0.5(Mg) 4217 0.541

18 AlSi7Cu1Ni1.5(Mg) 6283 0.805 36 AlSi7(Mg) 3389 0.434


phase composites. Analysing the experimentally obtained datarevealed a significant influence of the main alloying elements onthe thermal conductivity and the thermal expansion coefficient. Theresults were selectively discussed on a systematic basis of thermo-dynamic calculations and compared to theoretical models for thethermal conductivity and thermal expansion of heterogeneoussolids. The following conclusions were drawn:

�
Analysing the TC data of the various alloys revealed a valuerange from 141 to 187 [W/mK]. Al–Si alloys were consideredas a two-phase system, consisting of the matrix and eutectic Si.Applying lSi¼25 W/mK to the models of Maxwell and Hashin–Shtrikman resulted in an acceptable representation of theactually measured values of this work. � With the addition of Cu, secondary precipitates like y-Al2Cu
and Q-Al5Cu2Mg8Si7 are formed in the course of over-aging at250 1C, decreasing the thermal conductivity of the material.
� When Ni is added, the formation of Fe- and Ni-rich intermetallic
compounds is inevitable even at low concentration of the respec-tive elements. The IMPs were assigned as ‘second phase’ to checkthe applicability of the models of Maxwell and Hashin–Shtrikman.
� Generally, CTE decreases with increasing content of alloying
elements, whereas this trend is more distinctive in case of highvolume fractions of primary IMPs embedded in the Al matrix.
� The influence of Si on the CTE was estimated by applying the linear
rule of mixture and the models of Turner and Kerner, predictingthe thermal expansion coefficient of a two-phase composite,consisting of an Al matrix and eutectic Si, embedded therein.
� The single effect of Cu and Ni on the CTE was difficult to
determine due to the small deviation of CTE of the particularalloys and the range of the measurement error.
� By applying the second thermal shock parameter RS
0, anintuitively understandable factor, which is mainly affected bythe mechanical and physical properties evaluated in our work,it is possible to compare the competing alloys concerning theirfracture-initiation resistance.

Acknowledgements

The authors would like to thank AMAG Austria Metall AG andthe Austrian Research Promotion Agency for the financial support ofthis research project and for the permission to publish the results.

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