Experimental study of structure formation in binary Al–Cu alloys at different cooling rates

Materials Science and Engineering A 405 (2005) 1–10

Experimental study of structure formation in binaryAl–Cu alloys at different cooling rates

D. Eskin∗, Q. Du, D. Ruvalcaba, L. KatgermanThe Netherlands Institute for Metals Research, Rotterdamseweg 137, 2628Al Delft, The Netherlands

Received in revised form 1 April 2005; accepted 1 May 2005

Abstract

A series of casting experiments was performed with binary Al–Cu alloys with varying cooling rates, cooling conditions and copperconcentration. The quantitative relationships between the cooling rate (Vc) and composition, on one hand and the dendrite arm spacing (DAS)and grain size (Dgr) on the other hand, are clarified in the form of coefficients in equation DAS (Dgr) = AV−n

c , where coefficientA is shownto strongly depend on the copper concentration. Increasing the amount of copper in the alloy causes refinement of both dendrite arm spacingand grain size. The amount of non-equilibrium eutectic depends on the cooling rate in a more complex manner with initial increase in therange of slow cooling (<1 K/s) and then gradual decrease in the range of 1–10 K/s. Some models of microsegregation are tested but fail tor coarsening,e©

K

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eproduce the experimentally observed dependences. The reasons for such a behaviour are discussed in terms of dendrite armutectic reaction undercooling, structure refinement and homogenization upon cooling in the solid state.2005 Elsevier B.V. All rights reserved.

eywords:Solidification; Cooling rate; Dendrite arm spacing; Grain size; Non-equilibrium eutectic; Microsegregation

. Introduction

All industrial casting processes operate in a certain rangef cooling rates. This range can be as low as 0.01 K/s formassive sand casting, but also can be as high as 105 K/s

pon rapid solidification of granules and flakes. Majority ofasting processes, however, operate in the range of coolingates between 0.1 and 20 K/s.

The cooling rate affects the structure of as-cast alloys in aell-established manner, i.e. the grain size, the dendrite armpacing (DAS) and the size of structure constituents (bothrimary and eutectic) decrease with increasing the coolingate.

It should be specifically noted that the cooling rate (K/s)s not a synonym of the solidification rate (m/s). The latters the magnitude of the velocity of the solidification frontin progressive solidification) or that of the tip of a dendritein consideration of a single-grain growth). Cooling rate is

∗ Corresponding author. Tel.: +31 15 2784463; fax: +31 15 2786730.E-mail address:[email protected] (D. Eskin).

a less stringent parameter and can be represented as:solidification temperature range divided by the time requfor an alloy to pass the (non-equilibrium) solidification raor (2) a slope of the cooling curve at a specific tempera(usually at the liquidus) or (3) the rate of heat extraction fthe solidifying volume. In general, the cooling rate reflethe heat transfer conditions of solidification. Althoughsolidification rate is proportional to the cooling rate, the scific relationships between the structure parameters ancooling (or solidification) rate can be different.

The most well-established relationship is that betweecooling rate and the dendrite arm spacing. This relationhas been theoretically derived for the velocity of the dentip, thermal gradient and the secondary dendrite arm spas[1]:

SDAS= A(GR)−n, (1)

where SDAS is the secondary dendrite arm spacing,G thethermal gradient at the solid–liquid interface,R the velocityof the dendrite tip,A an alloy-dependent parameter annis the parameter equal to 0.33 for aluminium alloys. T

921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2005.05.105

2 D. Eskin et al. / Materials Science and Engineering A 405 (2005) 1–10

relationship takes into account the coarsening of dendriticarms during solidification, when finer branches disappear andthicker branches survive.

In industrial practice, it is difficult to distinguish betweenthe secondary, tertiary and higher-ordered branches of den-drites, let alone to measure the velocity of the dendrite tip.Therefore, the relationship has been validated with respect tothe cooling rateVc (that substitutes for (GR) in Eq. (1)) andthe average dendrite arm spacing[1,8]:

DAS = AV−nc . (2)

Relationship(2) is frequently used for the estimation of thecooling rate from the structure data. Different values for theparameters in Eq.(2) are, however, reported in literature fordifferent aluminium alloys. Some of these data are collectedin Table 1. One can see that the coefficients vary greatly,even within the same alloying system. Some studies on theinterrelation of cooling rate and structure parameters wherethe composition has been an independent variable show thatprimary and secondary dendrite arms spacings decrease withincreasing concentration of Mg[9], Mg and Si[10] and Cuand Si[11]. However, in other studies, no effect of composi-tion on the dendrite arms spacing has been found[12]. Thisbrief review of the literature shows that additional effortshave to be undertaken in order to make the calculation of thec

ndtbt ns ofb itlyd nglya ations cool-

Table 1Parameters in Eq.(2) for different aluminium alloys

Alloy composition (wt%) A n Reference

2.4Cu 1.2–5.9 0.23–0.38 [2]4.4Cu 2.6–5.0 0.23–0.37 [2]10Cu 1.1–3.2 0.25–0.39 [2]4.9Cu 46.6 0.29 [3]7.12Mg 1578 0.325 [9]11.07Mg 1313 0.325 [9]1.2Mn, 1.0Mg grain refined 39.6 0.38 [4]1.2Mn, 1.0Mg not grain refined 48.9 0.43 [4]0.33Fe, 0.11Si 22.1 0.39 [5]0.7Mg, 0.4Si (6063) 166 0.34 [6]0.8Mg, 0.7Si (6201) 22.1 0.39 [7]1.24Mg, 0.45Si 73.4 0.202 [10]1.55Mg, 0.37Si 58 0.253 [10]0.63Mg, 1.38Si 68.6 0.228 [10]1.0Mg, 4.47Si 58.2 0.194 [10]0.99Cu, 0.3Si 79.6 0.316 [11]0.9Cu, 1.4Si 68.4 0.303 [11]3.7Cu, 0.5Si 69.3 0.189 [11]3.95Cu, 0.95Si 69.7 0.202 [11]2.4Cu, 0.75Si 69.3 0.253 [11]2Cu, 4.8Si 54.7 0.253 [11]

ing rate), etc. The application of aDgr = f (Vc) dependenceis, therefore, restricted to the identical nucleation conditionsduring solidification, i.e. impurity level, addition of grainrefiners, etc. The alloying level, at least below the limit solu-bility, affects the grain size, with finer grains correspondingto higher concentration of alloying elements[13,14].

Yet another structure parameter that is quite important forcharacterization of non-equilibrium conditions of solidifica-tion and corresponding microsegregation is the fraction ofnon-equilibrium eutectics. This parameter, although provedto be rather important for hot tearing sensitivity[15], receivedmuch less attention in the literature. In addition, the pre-

TL ilibrium eutectics

A Variation in the amount ofnon-equilibrium eutectics withcooling rate

Commentsa Reference

2 Increase RT [18]1 Increase End-chill casting [19]2 Increase to 190 K/s, then decrease Directional

solidification[3]

2 Initial increase to 0.002–1 K/sfollowed by decrease

Q [25]

5 Increase Calculated [16]7 Increase RT [9]5 Decreaseb RT [20]7 Increaseb RT [21]0 Initi0 IncrA Decr

S Initialdecre

rature solidificatiostarts.

ooling rate from the dendrite arm spacing adequate.The grain size (Dgr) also depends on the cooling rate a

his dependence can be written in a form of Eq.(1) or (2)ut with the reported constantn closer to 0.5[1]. It is impor-ant to note that the grain size depends on the conditiooth nucleation and growth, only the latter being explicependent on the cooling rate, while the nucleation is stroffected by other factors, such as the amount of nucleites, undercooling (not necessarily connected to the

able 2iterature data on the effect of cooling rate on the amount of non-equ

lloy composition (wt%) Cooling rate range (K/s)

Cu; 3Cu; 4Cu; 4.8Cu 0.01; 0.8; 5; 50Cu; 3Cu; 4.5Cu 1–38.8Cu; 4.9Cu; 1Si 0.1–37000

Cu; 5Cu; 6Mg; 1.4Mn; alloy 2024 0.001–4

Cu 1; 3Mg; 11Mg 0.5–10000Mg (alloy 5182) 0.5–2.5Si–0.45Mg (alloy 356) 0.25–1.5.94Mg–4.11Cu 1.3–21.3.87Mg–5.07Cu 0.9–18.7l–Cu–Mg (alloy 2024);Al–Mn–Mg (alloy 3004)

0.05–8.5

teel (1.25C. 1.06Si, 6.6Mn, 1.06Al,etc.)

Growth rate duringdirectional solidification(7–450�m/s)

a RT means that the cooling was not interrupted until the room tempeb Estimated from the fraction of solid at which the eutectic reaction

al increase followed by decrease Q [22]ease Q [22]ease Directionally

solidified ingots[23]

increase followed by slightase

Q [24]

is reached and Q means that the alloy was quenched after the end ofn.

D. Eskin et al. / Materials Science and Engineering A 405 (2005) 1–10 3

viously published data on the dependence of the eutecticfraction on the cooling rate are quite controversial as shownin Table 2. Interestingly enough, no adequate explanationhas been offered for the decrease in eutectic fraction withthe increasing cooling rate, except for the limited diffusionof the solute in the liquid phase at very high cooling rates.Available models that take into account hindered diffusionin solid, back diffusion and homogenization, e.g. Ref.[16]and those reviewed by Battle[17], show in the range of upto 100–200 K/s the initial rapid increase in the amount ofnon-equilibrium eutectic with subsequent slow approach toa limit value.

Flemings, based on his model[1], notes that the coolingrate during solidification has little effect on the degree ofmicrosegregation and the amount of non-equilibrium eutec-tics. Novikov and Zolotorevskii[25] suggested that theobserved effects of the cooling rate could be linked to thechanging ratio between the rate of the refinement of dendritearm spacing and the rate of narrowing the periphery zoneof dendrite arms that is enriched in solute. As a result, theamount of solute contained in the solid phase in the givenvolume will increase and the amount of eutectics decreases.These authors also mention the role of homogenization dur-ing cooling in the solid state.

Current work was planned with several aims in mind. Oneof the aims is to obtain reliable values for the coefficientsi ofc ostf elp-f ist arms tec-t ratei tion.S andt

2

inT from9 . Nom hem-i arks lesst ereu ated

Fig. 1. Example of an experimental cooling curve with explanationson the calculation of cooling rates: “total”Vc =Ttotal/ttotal; “linear”Vc =Tlinear/tlinear.

to 725◦C was poured in different moulds made of variousmaterials and either heated or water-cooled. In this case, thevariation in the cooling rate was due to the volume of thesample and the heat extraction capacity of the mould, thevolumes ranging from 160 to 10 cm3 on increasing the cool-ing rate. The temperature was recorded by a thin open-tipK-thermocouple with a wire diameter of 0.15 mm. The cool-ing rate was then calculated in two ways as illustrated inFig. 1. First, the total solidification temperature range wasdivided by the total solidification time. In this case, the latentheat evolution in the upper part of the solidification range wastaken into account. However, in our opinion, this cooling ratedoes not reflect the heat extraction by the mould during solid-ification, as the temperature decrease is obscured by the latentheat of solidification. In order to obtain results that will allowone to use Eq.(2) for the back calculation of the cooling ratefrom the structure data, we also calculated the cooling rateas the slope of the linear part of the cooling curve. At thelinear stage of cooling, the effect of the latent heat is muchless and thus calculated cooling rate can serve as a measureof heat extraction from the solidifying volume. In this paper,the cooling rate determined in the total solidification rangeis called “total” and the cooling rate calculated using the lin-ear part of the cooling curve is called “linear”. Alloys withdifferent copper concentrations (nos. 1–4 inTable 3) weretested in this way. All alloys had an equiaxed grain structurea

alloy( cef r

TC

A

CT 5–23L

n Eq. (2) for binary Al–Cu alloys solidified in the rangeooling rates from 0.1 to 20 K/s. These alloys are the mrequently used model alloys and these data will be very hul for both experimental and modelling work. Second aimo study effects of copper concentration on the dendritepacing and grain size. And finally, the variation of the euic fraction with the copper concentration and the coolings thoroughly examined as a measure of microsegregaome available models of microsegregation are tested

heir results are compared to the experiment.

. Experimental

Binary Al–Cu alloys with the compositions givenable 3were prepared in an electrical resistance furnace9.9% pure aluminium and an Al–48% Cu master alloyelt treatment or grain refinement was performed. The c

cal composition of the alloys was determined by a sppectrum analysis. The total amount of impurities washan 0.1%. Three different techniques of solidification wsed. In the first series of experiments, the melt overhe

able 3hemical composition and cooling rate ranges of tested Al–Cu alloys

lloy 1 2

u (wt%) 0.98 2.12otal cooling rate (K/s) 0.3–13.5 0.2–10inear cooling rate (K/s) 0.4–12 0.3–10.5

s shown inFig. 2.In the second series of experiments, an Al–1.83% Cu

no. 5 inTable 3) was melted inside a cylindrical resistanurnace in alumina crucibles of about 4 cm3 in volume. Prio

3 4 5 6

3.24 4.3 1.83 1.860.2–12.5 0.2–9 0.15–16 0.10.3–13 0.3–12 – –


Fig. 2. Grain structure of tested alloys: (a) Al–0.98% Cu, 0.3 K/s; (b) Al–0.98% Cu, 13.6 K/s; (c) Al–4.3% Cu, 0.2 K/s; (d) Al–4.3% Cu, 9.1 K/s. Dendrite armspacing and grain size slightly refine with increasing copper concentration (compare a and c) and strongly refine with increasing cooling rate (a,b andc,d).

to melting, aK-thermocouple was embedded in the solidsample in a specially drilled hole. In order to assure thegood contact between the thermocouple and the melt, a steel-sheathed thermocouple assembly with an external diameterof 1 mm was used. Liquid samples were overheated to 710◦Cand then cooled inside or outside the furnace to the room tem-perature, with still or forced air, oil or water as cooling media.The “total” cooling rate was then calculated from the coolingcurve.

In the third series of experiments, an Al–1.86% Cu alloy(no. 6 in Table 3) was processed as in the second series,however, the samples were quenched in water as soon asthey were fully solid.1

Samples were cut in the horizontal plane as close as pos-sible to the position of the thermocouple tip. These sampleswere then ground, polished and examined in an optical micro-scope. Samples for calculation of the grain size were addi-

1 Quenching was performed at 544◦C for a cooling rate of 0.15 K/s; at541◦C for 0.35 K/s and at 536◦C for 0.8 K/s; no additional quenching wasperformed for higher cooling rates as the corresponding samples were water-quenched during solidification.

tionally oxidized in a 5% water solution of fluoroboric acid.The dendrite arm spacing, the volume fraction of the eutecticphase and the grain size were calculated using standardlinear intercept method, both manually and using an image-analysis software. Statistical analysis of the results wasperformed.

3. Results and discussion

3.1. Dendrite arm spacing

The measurements of the average dendrite arm spacingshow the refinement of dendritic constitution with increasingboth the cooling rate and the copper concentration (see alsostructures inFig. 2). Fig. 3a demonstrates the plots of DASversus the “total” cooling rate. The technique of calculat-ing the cooling rate does not qualitatively change the results.However, there are some differences in the coefficients inEq. (2) as demonstrated inTable 4. The coefficients calcu-lated using the “linear” cooling rate are somewhat higher.


Fig. 3. (a) Effect of “total” cooling rate and copper concentration on the average dendrite arm spacing and (b) effect of copper concentration on coefficientsA(Y-axis) andn (numbers on the plot) in Eq.(2).

Table 4Coefficients in Eq.(2) calculated using experimental data on the average dendrite arm spacing for binary Al–Cu alloys

Cu (%) A n R2 A Fixedn R2

Coefficients in Eq.(2) with “total” cooling rate (DAS in�m)0.98 134.8± 4.4 0.40± 0.01 0.985 137.8± 7.3 0.33 0.962.12 101.4± 2.8 0.40± 0.01 0.996 107.6± 5.6 0.33 0.973.24 83.6± 0.01 0.37± 0.02 0.988 87.8± 3.1 0.33 0.984.3 76.1± 0.01 0.40± 0.02 0.990 79.9± 3.9 0.33 0.97

Coefficients in Eq.(2) with “linear” cooling rate (DAS in�m)0.98 144.7± 0.01 0.44± 0.03 0.99 145.3± 10.2 0.33 0.932.12 110.2± 2.9 0.47± 0.02 0.99 116.6± 9.2 0.33 0.933.24 94.4± 1.8 0.40± 0.02 0.99 96.8± 3.9 0.33 0.984.3 85.6± 3.8 0.41± 0.01 0.97 88.4± 5.8 0.33 0.94

This table also shows the difference in coefficients calcu-lated using the best fit technique for two cases: (1) with theassumption ofn= 0.33 and (2) with the adjustment of bothAandn coefficients in Eq.(2). In the latter case, better correla-tion is found as can be seen from regression coefficientsR2.The effect of the copper concentration on the coefficients isclearly demonstrated inFig. 3b. The “composition-sensitive”coefficientAdecreases with increasing copper concentrationin the alloy, while coefficientn is much less sensitive to thealloy composition.

The refinement of dendrite arm spacing with the increasingconcentration of solute in the alloy (Cu in (Al) in our case)is a known phenomenon ascribed to slower coarsening ofdendritic branches, lower dendrite tip velocity and smallerdendrite tip diameter in alloys containing more solute[2,26].

The variation of the dendrite arm spacing with both thecooling rate and the composition should be taken into accountwhen using the experimentally measured DAS for the calcu-lation of the cooling rate in large ingots and billets that may

have considerable macrosegregation of main alloying com-ponents.

3.2. Grain size

The grain structure becomes finer with increased coolingrate. The increased concentration of copper also has a refiningeffect, especially, in the range of slow cooling.Fig. 4showsthe variation of the grain size with the alloy composition andthe “total” cooling rate andTable 5gives the coefficients in

Table 5Coefficients in equationDgr [mm] = AV−n

c for different Al–Cu alloys

Cu (wt%) A n R2

0.98 2.62 0.33 0.972.12 2.18 0.29 0.893.24 1.94 0.26 0.854.3 1.47 0.27 0.90


Fig. 4. Dependence of the grain size on the alloys composition and coolingrate.

Eq.(2) with the grain size substituting for DAS. One can seethat the “composition-sensitive” coefficientAdecreases withthe increase in copper concentration. Coefficientn remainsfairly close to 0.3. Note that these quantitative relationshipscannot be directly used for calculation of the cooling rate fromthe structure as the grain size depends on more factors thanjust cooling conditions, the most important of these factorsbeing the conditions of grain nucleation.

Some grain refinement with increasing solute concen-tration is caused by the hindered grain growth due to thesolute pile-up at the solid–liquid interface, enhanced grainnucleation due to the constitutional undercooling and gen-eral narrowing of the non-equilibrium solidification rangewith increased copper concentration. Similar dependence ofthe grain structure on the alloy composition was observedduring direct-chill casting[15].

3.3. Non-equilibrium eutectics

The examined alloys solidified under equilibrium condi-tions would be single-phased. However, due to the microseg-regation during solidification caused by incomplete diffusionprocesses and therefore incomplete mixing and redistribu-tion of alloying components in solid and liquid phases, theliquid phase is enriched in the solute while the solid phaser equi-l hes e ofm ctict Thisp rateso

Fig. 5. Effect of cooling rate and copper concentration on the amount ofnon-equilibrium eutectics in binary Al–Cu alloys.

Table 2gives some flavour of the controversy that exists inthe literature regarding the effects of the cooling rate on theamount of non-equilibrium eutectics. The most adopted opin-ion is that the amount of non-equilibrium eutectics increaseswith the increasing cooling rate (limited diffusion in thesolid), reaches saturation close to the value predicted by theScheil approximation of non-equilibrium solidification (nodiffusion in the solid) and may then again decrease at veryhigh cooling rates (>102 to 103 K/s) due to the hindered diffu-sion in the liquid phase and the corresponding solute trappingin the liquid.

Our first series of experiments (performed at differentcooling rates obtained by different moulds) yields the resultsshown inFig. 5. One can see that increasing the amount ofcopper increases the amount of non-equilibrium eutectics inthe range of very slow cooling, though the maximum valueremains almost two times below that predicted by the Scheilapproximation. In the range from 1–2 to 10 K/s, however, theeutectic fraction decreases that is not in line with most exper-imental results reported before and with most of modellingapproaches existing to date, though similar dependences havebeen previously observed by some other researchers (seeTable 2).

It is obvious that such results cannot be explained justby limited diffusion in the solid. Other phenomena must beinvolved. The fact that we used larger sample volumes fors mightrs romg creaseo

emains diluted. As a result, when the alloy reaches itsibrium solidus during solidification, some liquid rich in tolute remains in the system. Giving a sufficient degreicrosegregation, the last liquid will solidify at the eute

emperature thus producing non-equilibrium eutectics.henomenon can be observed even at very slow coolingf less than 0.1 K/s[1,25].

lower cooling rates suggested that the observed effectsesult from more active thermosolutal convection[27] andhrinkage-driven flow in the larger volumes and thus freater macrosegregation and a corresponding local def the amount of eutectics.


Fig. 6. Effect of cooling rate and the cooling regime on amount of non-equilibrium eutectics in Al–1.8% Cu alloys.

In order to exclude this factor, we repeated the experimentswith an Al–1.83% Cu alloy using identical sample volumes(the second series of experiments). The results are given inFig. 6 and the trend of decreasing the volume fraction ofnon-equilibrium eutectics becomes even more pronounced.Therefore, the influence of the different volumes and cor-responding thermosolutal convection and shrinkage-drivenflow cannot be the cause of the observed decrease. Othereffects are known to influence the degree of microsegrega-tion and the amount of non-equilibrium eutectics, i.e. backdiffusion of solute in the solid during solidification and thehomogenization of the solid phase during cooling of thealloy below the solidus. Both processes involve solid-statediffusion and obviously, should be more efficient when thestructure is finer, which can be a result of higher coolingrates. At the same time, higher cooling rates allow less timefor diffusion, which may result in less back diffusion and lesshomogenization in the solid state. Therefore, the effect of thecooling rate and corresponding structure refinement on thedegree of microsegregation may be different, depending onthe ratio between the structure refinement and the degree ofdiffusion-driven equilibration of the system. Back diffusionalways acts to some extent during solidification, effectivelydecreasing the amount of non-equilibrium eutectics as com-pared to the Scheil approximation[17]. Homogenization inthe solid state can be prevented if the alloy is quenchedi eend 6%C et cticsw ncedi thatt ing

Fig. 7. Results of modelling using different models.

dissolution of non-equilibrium eutectics is to a great extentresponsible for the observed dependence. At the same time,the amount of non-equilibrium eutectics still has a tendencyto decrease with the increasing cooling rate. And that callsfor some further explanations.

Though the original scope of this work did not includecomputer simulations, some main models of microsegrega-tion available from the literature were tested in an attempt toreproduce, at least qualitatively, the experimental results.

According to the literature, most of the models adequatelypredict the increase of the amount of non-equilibrium eutec-tics at low cooling rate and then show the plateau[17,28–32].Some models, as described in e.g.[3,28], are able to repro-duce the decrease in the amount of eutectics, but only atcooling rates 1–2 orders of magnitude higher than those usedin the present work. In this case, the hindered diffusion inthe liquid is responsible for this effect. The decrease in theamount of non-equilibrium eutectics with grain refinement ata cooling rate of 1 K/s is reported in Ref.[16].

Fig. 7 shows some of our modelling results with theBrody–Flemings[17], Alstruc[33] and pseudo front tracking(PFT)[30] models.

With the Brody–Flemings model, it is assumed that duringsolidification as soon as liquid concentration is equal to theeutectic composition, the eutectic reaction is invoked imply-ing no eutectic undercooling is required for this reaction. Fort them lcu-ld sur-p thet

ndh rma-t as acm rvedt

mmediately after the end of solidification. That has bone in the third series of experiments with an Al–1.8u alloy. The results are shown also inFig. 6. One can se

hat the decrease of the amount of non-equilibrium euteith increasing cooling rate becomes much less pronou

n the quenched samples. Therefore, we may concludehe homogenization of the solid solution with correspond

he cooling rates ranging from 0.1 to 10 K/s, with half ofeasured SDAS as solidification domain length, the ca

ated solid-state Fourier numbers are at the order of 10−2 andecrease very slowly as cooling rate increase. It is notrising that the Brody–Flemings model cannot produce

rend observed experimentally in this work.The Alstruc model is a 1D model of solidification a

omogenization that takes into account phase transfoions during solidification and considers the structureylindrical dendrite arm, as described elsewhere[34]. Thisodel also cannot reproduce the experimentally obse

rend.


Table 6Parameters in 1D PFT model

Parameter Calculation

S1 F1 A1

Alloy Al–1.8 wt% Cu (Al–0.767 at.% Cu)Phase diagram Linear binary phase diagramNominal composition X(Cu) = 0.00767

Thermal condition/cooling rate 0.4 K/s 13 K/s 13 K/sDiffusion Dα

Cu = 0.65× 10−4e−136000/RT

DlCu = 3 × 10−9

Solid seedNumber 1 1 1Size [�m] 0.5 0.75 0.75Position Left border Left border Left borderλ 0 0 0

Space and timeDomain size [�m2] 73× 1 20× 1 13× 1DAS [�m] 146 40 26Number of cells 100× 1 40× 1 20× 1Solidification time [s] 268 8.2 8.2Solidification finish temperature [◦C] 547 547 547Solid phase fraction [wt%] Simulation Simulation SimulationAl2Cu fraction [at.%] 0.887039 1.05153 0.873608Eutectic fraction [wt%] 2.72 3.22 2.68

The pseudo front tracking model solves the diffusion equa-tions both in the solid and the liquid numerically and allowsone to use a temperature-dependent diffusion coefficient anda non-linear phase diagram as the input parameters. In a 1Dmode of the PFT model calculations with half-DAS as thecalculation domain size, for cooling rates of 0.4 K/s (S1 inTable 6) and 13 K/s (F1 inTable 6), the calculated eutecticfraction still increases with the cooling rate. The parame-ters of the model as well as the results are given inTable 6.However, for a cooling rate of 13 K/s, in an artificial 1DPFT calculation with a finer DAS as the calculation domainsize (26�m instead of experimentally measured 40�m, A1in Table 6), the calculated eutectic fraction (2.68 wt%) wasindeed less than the calculated result for cooling rate of0.4 K/s (S1 inTable 6). This artificial calculation supports theexplanation of Novikov and Zolotorevskii[25] as shown inFig. 8; more solute remained in the primary phase at a highercooling rate as a result of efficient diffusion in the solid con-tributed by a higher solid concentration gradient. That meansthat if microstructure is fine enough and the correspondingsolute gradients are high, the solid-state (back) diffusion isso efficient that it decreases the degree of microsegregation.Upon slow cooling, the degree of microsegregation is also lowbecause of a longer solidification time and correspondinglylonger time available for diffusion. In both cases, the frac-tion of non-equilibrium eutectics can be lower than at somei la-t tureo fort atelyd

Yet another indication of the role of dendrite finenesson the degree of microsegregation is a simple exercise innormalizing the experimentally measured fraction of non-equilibrium eutectic on the experimentally determined den-drite arm spacing. The obtained values (DAS fromFig. 3,non-equilibrium eutectic fraction fromFig. 5) are plotted inFig. 9 against the cooling rate. The dependences appear tobe linear and the normalized value of the eutectic fractionincreases with the increasing cooling rate.

These results show that the tested models cannot ade-quately reproduce experimentally observed dependence. It

F ased

ntermediate cooling rates. Although this artificial calcuion reveals the important effect of the finer microstrucn the final eutectic fraction, it cannot be directly used

he explanation of the observed trend due to the deliberecreased calculation domain size.

ig. 8. Accumulation of copper concentration in the primary (Al) phuring solidification of an Al–1.8% Cu alloy at two cooling rates.


Fig. 9. Dependence of the fraction of non-equilibrium eutectic (NeqE)normalized to the dendrite arm spacing (d) on the cooling rate during solid-ification.

should be noted that none of the existing models of microseg-regation includes all the known effects that may occur duringsolidification, namely limited diffusion in the solid phase,back diffusion in the solid during solidification, tempera-ture dependences of diffusion coefficients in the solid andliquid, structure refinement with increasing cooling rate, den-drite coarsening with dissolution of finer branches, under-cooling of the eutectic reaction with the shift of the eutec-tic point, thermodynamics of alloy solidification and soluteaccumulation in the liquid with mixing dependent on thediffusion rate. In addition, most of these models are one-dimensional and do not include the geometry of the den-dritic structure. The scale of the structure is usually takeninto account as the secondary arm spacing or the grainsize.

In our opinion, three factors are quite important in theunderstanding of the experimentally observed phenomenon.Firstly, the coarsening of the dendritic arms, which means thatfine branches formed at higher temperatures and containingless solute dissolve and coarser branches thicken by “attach-ing” the solid phase containing more solute. As a result, thesurrounding liquid is diluted of the solute and the amountof non-equilibrium eutectic eventually decreases. This pro-cess should be active in the medium range of cooling rates(at very low cooling rates the branches are too thick to bedissolved) and the effect has to increase with the increasingc cticr lutec olutei ndi-t thedt ion in

our experimental cooling curves decreases considerably withthe increasing cooling rate as shown below.

Cooling rate (K/s) 0.16 0.4 0.9 1.4Temperature of the eutectic reaction 545 543.5 539 528

And thirdly, structure refinement with increasing coolingrate may result in more active back diffusion with the corre-sponding decrease in the amount of non-equilibrium eutecticsas has been shown by modelling[16] and the 1D PFT calcu-lations in this work.

A recently developed 2D PFT microsegregation modelcan predict the grain morphology of the primary phase andits effect on secondary phase formation[30]. Rather complexand time-consuming 2D PFT calculations that use the mea-sured grain sizes as input parameters of calculation domainsize to reproduce the dendrite arm spacing observed in themeasurements are, in our opinion, required for taking intoaccount the effect of grain morphology on the formation ofeutectic fraction.

4. Conclusions

(1) Quantitative relationships between the average dendritearm spacing, grain size and the cooling rate are found

%reasetion.theoef-

( on-cop-n theticsand

( ge ofd by

( frac-cang ofeac-re.

iumcon-tics.

A

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ooling rate[35]. Secondly, the undercooling of the euteeaction with the shift of the eutectic point to a higher sooncentration and the increased concentration of the sn the solid phase at the solid–liquid interface under coions of the hindered diffusion in the solid should result inecreased amount of non-equilibrium eutectics[28,29]. The

emperature that can be assigned to the eutectic react

experimentally for Al–Cu alloys containing from 1 to 4Cu. The dendrite arms spacing and grain size decwith increasing cooling rate and copper concentraThe latter factor is reflected in the decrease withcooper concentration of the composition-sensitive cficientA.

2) The experimentally determined amount of nequilibrium eutectics increases with the increasingper concentration and depends in a complex way ocooling rate. The amount of non-equilibrium eutecincreases with the cooling rate in the range 0–1 K/sthen decreases in the range 1–10 K/s.

3) The decrease in the amount of eutectics in the ranmoderate cooling rates cannot be presently predicteavailable 1D models.

4) The experimentally observed dependence of thetion of non-equilibrium eutectics on the cooling ratebe qualitatively explained in terms of the coarseninthe dendrite arms, the undercooling of the eutectic rtion and more active back diffusion in a finer structuThe homogenization and dissolution of non-equilibreutectics upon cooling in the solid state can furthertribute to the observed decreasing amount of eutec

cknowledgements

This work is performed within a framework of the sntific research program of Netherlands Institute for Meesearch (Project 4.02134) (www.nimr.nl). Authors would

http://www.nimr.nl/


like to thank Mr. F. Bodea whose measurements gave thebackground for this research and M.Sc. V.I. Savran for help-ing in image analysis of structures. Fruitful discussions of theresults with Prof. V.S. Zolotorevskii and Dr. A.L. Dons aregratefully acknowledged. We are also thankful to A.L. Donsof SINTEF for providing us with some calculation resultsfrom Alstruc model and to Erik-Paul van Klaveren of CORUSfor helping us with calculations using a PTF model imple-mented in a CalcoSoft code.

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Documents

Experimental study of structure formation in binary Al–Cu alloys at different cooling rates