Columnar to equiaxed transition in directional ... 2013.pdf · Columnar to equiaxed transition in directional solidification ... of alloys significantly affects the castings

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Acta Materialia 61 (2013) 1785–1797

Columnar to equiaxed transition in directional solidificationof inoculated melts

D.A. Pineda, M.A. Martorano ⇑

Department of Metallurgical and Materials Engineering, University of Sao Paulo, Avenida Prof. Mello Moraes 2463, Sao Paulo 05508-900, Brazil

Received 1 June 2012; received in revised form 30 November 2012; accepted 1 December 2012Available online 27 December 2012

Abstract

Experiments on transient directional solidification were carried out with Al–3% Si and Al–7% Si alloys to study the modification bymelt inoculation of the as-cast ingot macrostructure with columnar and equiaxed zones into a completely refined equiaxed structure.Without inoculation the macrostructure consists of typical columnar and equiaxed zones, separated by a relatively thin region of colum-nar to equiaxed transition. As the inoculant Al–3% Ti–1% B was added to the melt in a series of experiments relatively small equiaxedgrains were observed in the as-cast macrostructure. For larger inoculant additions the number of these equiaxed grains increased. Themacrostructure became completely refined and equiaxed as the Ti concentration in the melt increased in the small range0.002 < %Ti < 0.01 for Al–3% Si, and of 0.029 < %Ti < 0.075 for Al–7% Si. The larger inoculant additions for the Al–7% Si alloy areattributed to Si poisoning of the inoculant. This macrostructure modification occurred with an increasingly large fraction of fine equi-axed grains mixed with columnar grains, rather than by a significant decrease in the length of the columnar grains. Solidification pathswere calculated from the measured cooling curves and superimposed on dimensionless growth maps, enabling good qualitative predic-tions of the macrostructure, especially the existence of the mixed region. The maps, however, predict that the position where columnargrains are completely blocked is closer to the ingot base than that observed experimentally. This discrepancy might be related to therestrictive hypothesis assumed to construct the growth maps, not valid in the present experiments, of steady-state solidificationconditions.� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Dendritic solidification; Directional solidification; Grain refining; Columnar to equiaxed transition

1. Introduction

The morphology of grains in the as-cast macrostructuresof alloys significantly affects the castings properties. Severaltheoretical and experimental investigations have aimedat revealing the important variables and mechanismscontrolling the transition of grain shape from columnarto equiaxed, referred to as the columnar to equiaxedtransition (CET). Directional solidification experiments[1–4] together with deterministic [5–9], stochastic, [10,11]and phase-field mathematical models [12,13] have shown

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⇑ Corresponding author. Tel.: +55 11 3091 6032; fax: +55 11 3091 5243.E-mail address: [email protected] (M.A. Martorano).

the effects of processing variables on the CET. Althoughthe effects of melt inoculation on the as-cast grain size ofcompletely equiaxed structures have been exhaustivelyexamined [14–16], studies of its effects on the CET are lim-ited. These studies have been carried out under one of twotypes of unidirectional solidification conditions, namelysteady-state or transient. Steady-state unidirectional solid-ification is achieved in a Bridgman furnace, in which thetemperature gradient and the velocity of isotherms are con-trolled and kept approximately constant. In reality, theCET cannot be observed in these experiments, becausethe resulting ingot grain structure is usually uniform, with-out any type of CET, as a result of constant solidificationconditions. Using this technique Ledgard and McCartney[17] added the inoculant Al–6% Ti–0.02% C to an

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1786 D.A. Pineda, M.A. Martorano / Acta Materialia 61 (2013) 1785–1797

Al–1.8% Si alloy and, for certain solidification velocities,observed isolated equiaxed grains mixed with columnargrains in the final macrostructure. Vandyoussefi and Greer[18] added the same type of inoculant to an Al–4.15% Mgalloy and showed a macrostructure consisting of equiaxedgrains mixed with elongated grains. Mangelinck-Noel et al.[19] and Schenk et al. [20], using X-ray radiography,observed in situ the simultaneous growth of equiaxed andcolumnar grains in an Al–3.5% Ni alloy with addition ofthe inoculant Al–5% Ti–1% B.

To obtain transient directional solidification conditionsin a Bridgman furnace, triggering the CET in an otherwisecolumnar solidification, a few authors increased the solidi-fication velocity in jumps. Using this technique Camel andDupouy [21] and Jung et al. [22] added Al–5% Ti–1% B toan Al–3.5% Ni alloy, while Jung et al. [22] added this inoc-ulant to an Al–7% Si alloy. They observed a mixed regionwith columnar and equiaxed grains for a certain velocityjump. Nguyen-Thi et al. [23] used synchrotron X-ray radi-ography to observe the appearance of new equiaxed grainsin situ after a velocity jump during solidification of anAl–3.5% Ni alloy. They concluded that the mixed colum-nar–equiaxed region observed in the final as-cast structurecould be a result of equiaxed grains settling down into thezone of columnar grains. Instead of imposing solidificationvelocity jumps to obtain transient conditions, Sturz et al.[24] and Sturz and Zimmermann [25] changed the temper-ature gradient by decreasing the hot zone temperature of aBridgman furnace at a controlled rate. For Al–7% Si alloysthese authors [25] showed that, for a fixed amount of inoc-ulant addition, the macrostructure changed from one withcolumnar and equiaxed grains completely separated(“sharp” CET) to a mixed region (CET zone) withelongated and small equiaxed grains.

In a different class of transient unidirectional solidifica-tion experiments, more closely related to industrial pro-cesses, heat is extracted at the base of a cylindrical ingot,naturally imposing temperature gradients and isothermvelocities that change with time. For no inoculant additionthis type of experiment usually caused the formation of asharp CET, which was shown to be significantly affectedby (a) heat transfer at the metal–mold base interface[1,26,27], the alloy composition [1–3,26,28–30], and thesuperheat of the melt [1,26]. In similar experiments,however, Ares and Schvezov [2,30], working with Pb–Sn,Al–Zn, and Zn–Al alloys presented macrographs withsome relatively large equiaxed grains projecting into thecolumnar zone, resulting in a region in which columnarand equiaxed grains coexist, i.e. the CET was not sharp.

In this same type of transient solidification Ziv andWeinberg [27] studied how the CET observed in the as-castmacrostructure of an Al–3% Cu alloy changed in differentexperiments with larger additions of the commercial inocu-lant Al–5% Ti–1% B. Without inoculant a type of sharpCET was observed, but as inoculant was added the CEToccurred as a gradual transition in which columnar and rel-atively small equiaxed grains coexisted. Above a 172 ppm

concentration of TiB2 in the melt, obtained with largerinoculant additions, a completely fine equiaxed structureformed without CET. To the knowledge of the authors thiswas the only study that showed how the CET changed ongradually adding larger amounts of inoculant. In thisstudy, carried out with an Al–3% Cu alloy, there was noattempt to verify whether current mathematical modelscould predict the resulting grain structure.

The aim of the present investigation was to examine thechange in the CET in Al–Si alloys as the concentration ofinoculant, added in the form of an Al–3% Ti–1% B masteralloy, is gradually increased. Experiments were performedusing a transient unidirectional solidification system inwhich heat is extracted at the bottom of cylindrical ingots.Inoculants were carefully added to show very clearly howthe grain structure changed from a sharp CET to a com-pletely equiaxed structure consisting of very fine grains.The ability of growth maps to predict the experimentallyobserved macrostructures was also examined.

2. Solidification experiments and sample characterization

Charges of 1 kg consisting of an Al–20 mass% Si masteralloy and commercial purity Al were melted in a graphitecrucible inside a resistance furnace to give the nominalcompositions of either Al–3 mass% Si or Al–7 mass% Si.After melting hexachloroethane in powder was added todegas the melt and, 10 min later, a rod of the commercialinoculant Al–3% Ti–1% B was added. The melt was agi-tated with a graphite bar and kept in the furnace for10 min at 730 �C (Al–3% Si) or 700 �C (Al–7% Si) forhomogenization before pouring into a cylindrical mold,where it solidified.

The cylindrical mold was made of stainless steel (AISI310) and its top and lateral walls were thermally insulatedby an external thick layer (25 mm) of glass wool and by aninternal thin layer (3 mm) of aluminum silicate paper(Fig. 1). To establish transient unidirectional solidificationconditions the mold base was water cooled and the surfacein contact with the alloy was polished with a 400 grit emerypaper and painted with a water–graphite suspensionusing a spray gun. In four of the experiments six type K(Chromel–Alumel) thermocouples were inserted horizon-tally into the cylindrical mold cavity at different locationsalong its axis, separated by 20 mm gaps (Fig. 1). An extrathermocouple was inserted from the mold top to the moldbase, measuring the temperature at the metal–mold inter-face. These thermocouples, which are insulated by a com-pacted ceramic and sheathed by a stainless steel tube of1.5 mm external diameter, were connected to a data acqui-sition system, giving seven cooling curves at the axis of thecylindrical ingots at an acquisition rate of 10 Hz.

Before pouring the melt the mold was preheated in aresistance furnace, reaching an average internal tempera-ture of 730 �C. Three min after the end of pouring, whenpouring turbulence had apparently settled, the water cool-ing system of the mold base was turned on at a flow rate of

Fig. 1. Schematic view of a section of the cylindrical mold used in thedirectional solidification experiments (dimensions in mm). Six thermo-couples separated by 20 mm gaps were inserted horizontally into the moldcavity with the hot junction positioned at the ingot axis. An extrathermocouple inserted along the mold axis from the mold top to the baseprovided the temperature at the point of contact between the ingot and thewater-cooled base.

D.A. Pineda, M.A. Martorano / Acta Materialia 61 (2013) 1785–1797 1787

0.14 l s�1. Before turning on the cooling system all thermo-couples (including that in contact with the base) indicated atemperature above the liquidus of the alloy, implying thatno solid had formed. The thermocouple readings showedthat solidification started at the base shortly after water cir-culation had begun.

After complete solidification and cooling to room tem-perature the cylindrical ingots were removed from the moldand cut into two by sectioning along their longitudinal axis(parallel to the heat flow). One longitudinal section wasground and polished by traditional metallographic tech-niques and finally etched for 15 s in a chemical reagent(66 ml of HNO3, 33 ml of HCl, and 1 ml of HF) to revealthe grain macrostructure. From the other half of the ingota slice was cut 0.12 m from the ingot base to observe themicrostructure of a transverse section (perpendicular tothe heat flow). This slice was ground, polished, and etchedwith a chemical reagent (10 g of NaOH, 5 g of K4Fe(CN)6,and 100 ml of distilled water) to reveal the microstructure.The micrograph of these ingot top slices always showed anequiaxed grain structure for all ingots. The average grainsize was measured by the circular line intercept methodaccording to ASTM standard E112-96 [31]. Another slicewas cut 0.05 m from the base of all ingots and chemicallyanalyzed by inductively coupled plasma atomic emissionspectroscopy (ICP AES) to give the chemical composition,i.e. the concentrations of Si, Ti, and B. In two experimentsthe chemical composition of an extra slice cut 0.10 m fromthe ingot base was measured and compared with the com-position of the first slice, showing no significant macroseg-regation of elements.

3. Effects of inoculation on the grain macrostructure

The sequence of macrographs in Figs. 2a–e and 3a–e dis-plays, for Al–3% Si and Al–7% Si, respectively, how thegrain structure changes as a result of gradually increasingthe amount of added inoculant and the corresponding con-centrations of Ti and B. The compositions and the amountsof inoculant added to each ingot are given in Table 1,which shows variations relative to the nominal Si concen-tration (3% and 7% Si), probably as a result of Si and Aloxidation during melt preparation. Two dotted horizontalwhite lines are superimposed on the macrographs to indi-cate the CET region. The upper line has only equiaxedgrains above its, whereas the lower line has only columnargrains below it.

Without inoculant addition the macrostructures of theAl–3% Si and Al–7% Si ingots (Figs. 2a and 3a, respectively)consist of a relatively large columnar zone of about 0.107 mlength for the Al–3% Si alloy and 0.097 m length for the Al–7% Si alloy. Thus it decreased by 0.01 m with an increase insolute concentration from 3% to 7% Si. Although thecolumnar zone length has also been shown to decrease withincreasing solute concentrations in Sn–Pb alloys [26,28],Gandin [3] and Peres et al. [29] did not observe any signifi-cant change for Al–Si alloys. In Figs. 2a and 3a the CET wasnot sharp, occurring in a relatively small region withinwhich both columnar and relatively large equiaxed grainscoexisted, as also observed by Ares and Schvezov [2,30] inPb–Sn, Al–Zn, and Zn–Al alloys.

When inoculant was added to the Al–3% Si alloy, result-ing in 0.002%Ti, very small equiaxed grains appearedwithin the columnar zone (Fig. 2b), giving rise to a mixedcolumnar–equiaxed grain region and enlarging the CETregion, indicated by a downward shift of the lower dottedline to the ingot bottom. The decrease in the length ofcolumnar grains (upper dotted line) from 0.127 to0.101 m, however, is relatively small. A further increasein the inoculant addition to 0.006% Ti (Fig. 2c) or0.008% Ti (Fig. 2d) increased the number of small equiaxedgrains mixed with the columnar grains, but the length ofthese columnar grains was almost unchanged, as illustratedin Fig. 4. Despite the nearly unaltered length of columnargrains with an increase in %Ti from 0.001 to 0.008, a signif-icant decrease in the average equiaxed grain size from 3.1to 1.1 mm (Table 1) occurred, implying that inoculationin fact occurred. For a further increase in %Ti to 0.01 agrain structure consisting completely of very fine equiaxedgrains was observed (Fig. 2e), becoming even more refined(0.2 mm) for 0.1% Ti (Fig. 2f). To summarize, completemacrostructural transformation of the Al–3% Si ingotsfrom almost completely columnar to completely equiaxedoccurs with a variation in %Ti in the relatively narrowrange 0.002–0.010.

A similar behavior to that for the Al–3% Si ingots wasobserved for the Al–7% Si ingots as the amount of inocu-lant was gradually increased (Fig. 3). Nevertheless, moreinoculant had to be added to the Al–7% Si melts to obtain

Fig. 2. As-cast grain macrostructures of the Al–3% Si ingots with different amounts of inoculant additions, corresponding to the following mass% Ti: (a)0.001% (0.107 m < CET < 0.127 m); (b) 0.002% (0 < CET < 0.101 m); (c) 0.006% (0 < CET < 0.102 m); (d) 0.008% (0 < CET < 0.092 m); (e) 0.01%; (f)0.10%. The CET zone, when present, is indicated by the horizontal dotted white lines.


similar grain macrostructures, as can be seen in Fig. 4. Asan example, to completely eliminate the columnar grains inthe Al–7% Si ingots and obtain a completely equiaxedstructure 0.075% Ti had to be added, while in the Al–3%Si ingots 0.01% Ti was sufficient. Furthermore, small equi-axed grains begin to appear in the columnar zone of the

Al–7% Si ingots only for 0.012 < %Ti < 0.029, whereas inthe Al–3% Si ingots some equiaxed grains are observedfor a %Ti as low as 0.002. Actually, in the Al–7% Si ingots,inoculant addition was not very effective for %Ti up to0.012, because the average grain size was unchanged(Table 1). In all, the macrostructure of the Al–7% Si ingots

Fig. 3. As-cast grain macrostructures of the Al–7% Si ingots with different amount of inoculant additions, corresponding to the following mass% Ti: (a)0.002% (0.097 m < CET < 0.118 m); (b) 0.012% (0.096 m < CET < 0.115 m); (c) 0.029% (0 < CET < 0.102 m); (d) 0.05% (0 < CET < 0.086 m); (e) 0.075%;(f) 0.12%. The CET zone, when present, is indicated by the horizontal dotted white lines.


completely changed to a fine equiaxed structure for a %Tiin the range 0.029–0.075.

Different authors have observed that the average equi-axed grain size in a completely equiaxed structure is largerin Al–7% Si than in Al–3% Si alloys for the same amount

of added inoculant [15,32]. This effect has been referredto as “poisoning” by Si of the TiB2 inoculant particlesintroduced into the melt by addition of a Al–Ti–B masteralloy for grain refining. This poisoning effect adverselyaffects the ability of TiB2 particles to act as a substrate

Fig. 4. The vertical bars indicate the regions of the columnar to equiaxedtransition (CET) in each of the Al–3% Si and Al–7% Si ingots as afunction of their corresponding measured Ti concentrations.

Table 1The parameters concentration (mass%) of Si, Ti, and B obtained by chemical analysis of an ingot slice, amount (mass%) of inoculant Al–3% Ti–1% Badded to the melt (Inoc), mean linear intercept (L) and standard deviation obtained in the average grain size measurements, number of measurement fields(N), and the number density of grains (n) calculated from L for each ingot (the macrostructure is given in the indicated figure).

Ingot Macrostructure %Si %Ti %B %Inoc L (mm) n (m�3) N

1a Fig. 2a 2.3 0.001b 0.0002b 0 3.1 ± 0.3 1.7 � 107 82 Fig. 2b 2.5 0.002 0.0003 0.0203 Fig. 2c 2.3 0.006 0.001 0.13 1.6 ± 0.1 1.2 � 108 84 Fig. 2d 2.3 0.008 0.002 0.23 1.1 ± 0.1 3.8 � 108 75a Fig. 2e 2.4 0.010 0.002 0.34 0.3 ± 0.1 1.8 1010 106 Fig. 2f 2.4 0.10 0.023 2.96 0.2 ± 0.1 6.2 � 1010 157a Fig. 3a 7.6 0.002b 0.0002b 0 3.5 ± 0.4 1.2 � 107 98 Fig. 3b 7.1 0.012 0.002 0.31 3.6 ± 0.4 1.1 � 107 89 Fig. 3c 7.3 0.029 0.006 0.79 1.9 ± 0.2 7.3 � 107 810 Fig. 3d 7.6 0.050 0.010 1.67 1.8 ± 0.2 8.6 � 107 811 Fig. 3e 7.2 0.075 0.009 3.17 1.3 ± 0.1 2.3 � 108 1412a Fig. 3f 6.5 0.12 0.005 8.5 0.9 ± 0.1 6.8 � 108 18

a Thermocouples were placed within the mold cavity for these experiments, allowing acquisition of cooling curves.b These elements come from impurities in the commercial purity Al and Al–20%Si master alloy.


for heterogeneous nucleation [16]. In the present work theSi poisoning effect on the CET is shown for the first time.

The macrostructural transformation from columnar to acompletely equiaxed structure as inoculant is graduallyadded does not occur, as might be expected, by a gradualdecrease in the length of the columnar grains until they dis-appear. Instead, an increasingly large number of smallequiaxed grains appear mixed with nearly constant lengthcolumnar grains, which eventually disappear. This typeof mixed columnar–equiaxed CET region was alsoobserved by other authors when inoculants were added[18,21,22,25], but complete macrostructural transformationwas not shown. Ziv and Weinberg [27], however, showedthis transformation in an Al–3% Cu alloy on addition ofthe inoculant Al–5% Ti–1% B. In this study a completelyequiaxed structure was obtained for 0.015 < %Ti < 0.017,

which is of the same order of magnitude as that observedin the present work (0.01% Ti) for the Al–3% Si ingots.

4. Cooling curves and thermal parameters

The cooling curves measured by the thermocouplesplaced along the longitudinal axis of four of the Al–3%Si and Al–7% Si ingots with and without inoculant addi-tion are given in Fig. 5. One of the thermocouples was incontact with the mold base (0 mm) and the others wereplaced at approximately 20 mm from each other. Thesecooling curves are very similar to those presented byGandin [3] and Peres et al. [29], showing small plateauxat the liquidus and eutectic temperatures. For the samenominal Si concentration the cooling curves in the experi-ments with and without inoculant were very similar, reflect-ing the effort to maintain the same thermal conditions in allexperiments.

Several thermal parameters were calculated from themeasured cooling curves. The average cooling rate at eachthermocouple position was calculated as R = (TL � TE)/tf,as suggested in the literature [33,34], where TL and TE arethe liquidus and eutectic temperatures, respectively, and tf

is the local solidification time, i.e. the time for the temper-ature to decrease from TL to TE (577 �C). Note that TL andTE are the temperatures at which solidification begins andends, respectively, and the difference between these temper-atures is the solidification temperature range. The values ofTL for the measured compositions (Table 1) were calcu-lated from local linear approximations to the liquidus lineof the binary Al–Si phase diagram around the liquidustemperatures of the nominal compositions Al–3% Si andAl–7% Si. These linear approximations are TL (�C) =640 � 6(%Si � 3) for the Al–3% Si ingots and TL

(�C) = 618 � 6.5(%Si � 7) for the Al–7% Si ingots [3],where %Si is the measured composition. The time ti whenthe liquidus or eutectic isotherms were at the position ofthermocouple i, defined as xi (measured from the ingot

Fig. 5. Cooling curves measured at the indicated distances from the ingotbase by thermocouples placed along the ingot vertical axis for experimentswith and without inoculant additions: (a) Al–3% Si; (b) Al–7% Si. Theliquidus (TL) and eutectic (TE) temperatures for each alloy are also shown.


base along its axis), was easily obtained from the coolingcurve of the corresponding thermocouple. The liquidusand eutectic isotherm velocities, VL and VE, respectively,at a distance (xi+1 + xi)/2 from the ingot base were calcu-lated from V = (xi+1 � xi)/(ti+1 � ti). Note that xi+1 andxi represent the positions of two adjacent thermocouplesalong the ingot longitudinal axis, xi+1 being located abovexi. When the liquidus isotherm was at xi, i.e. at the positionof thermocouple i, upward and downward temperaturegradients at this isotherm were calculated fromGU = (Ti+1 � TL)/(xi+1 � xi) and GD = (TL � Ti�1)/(xi � xi�1), respectively, as suggested by Gandin [3].

The addition of inoculant did not significantly changethe evolution with time of the position of the liquidus

and eutectic isotherms, as can be seen in Fig. 6a and b.In the four experiments the mushy zone length (the hori-zontal distance between TE and TL) increased with time,which is consistent with the observed decrease in magni-tude of the temperature gradients GU and GD (Fig. 6eand f), as reported by several authors in different alloysand under different thermal conditions [1,3,28]. The veloc-ity of the liquidus isotherm (VL) in Fig. 6c and d for Al–3%Si and Al–7% Si, respectively, decreases from the beginningof solidification, reaches a minimum, and increases, per-haps as a result of heat losses at the ingot top. A similarbehavior was reported by Siqueira et al. [1,28], but Pereset al. [29] showed no minimum, i.e. VL always decreased,whereas Gandin [3] observed an increase in VL up to amaximum value. These differences are probably related todifferent heat transfer conditions. The average cooling rate(R) at the positions of the liquidus isotherm (Fig. 7)decreased along the ingot for all experiments, as reportedby different authors [1,28,29].

The growth front of columnar grains usually movesclose to the liquidus isotherm (constrained growth)[3,35,36]. Therefore, the position, velocity, temperaturegradient, and cooling rate at the liquidus isotherm (Figs. 6and 7) are approximately those at the columnar front.Observations of these thermal parameters at the positionof the CET have indicated that the CET occurs as thethermal gradients and cooling rates decrease and as the liq-uidus isotherm velocity increases. Based on these observa-tions, critical values of temperature gradient GC [26,27] andcooling rate RC [1,28] below which the CET occurs wereproposed. Later, a critical liquidus isotherm velocity VC

[24,37] was also defined. In the present experiments thethermal parameters GU, R, and VL were obtained at theposition of the upper dotted line defining the CET regionin Figs. 2 and 3, i.e. at the position where columnar grainswere completely blocked. These parameters were estimatedby interpolation from the curves in Figs. 6 and 7 at theCET position. These curves are available for only two ofthe experiments with inoculant addition, one for Al–3%Si (0.01% Ti) and the other for Al–7% Si (0.12% Ti). Sincethe curves for different experiments were very similar theywere used to obtain the thermal parameters in all the otherexperiments with inoculant. In Table 2 the estimated ther-mal parameters are compared with critical values proposedby several authors for Al–Si alloys. Except for those givenby Ares et al. [37], the values of VC reported by differentauthors changed within one order of magnitude, namelyfrom O(10�4) to O(10�5) m s�1, whereas the cooling ratesvaried within the relatively narrow range between 0.16and 0.42 K s�1. The critical temperature gradient GC, how-ever, shows a relatively large variation.

One important practical motivation to define and deter-mine these critical values is to enable prediction of theCET. The concept of a critical value is only useful if it isunchanged by the solidification conditions and alloy com-position. The existence of a universal critical value, how-ever, is not supported by the model of Hunt [8] used to

Fig. 6. Thermal parameters as a function of the distance from the ingot base. (a, b) Time when the liquidus and eutectic isotherms were at the distancefrom the ingot base given on the abscissa for (a) Al–3% Si and (b) Al–7% Si. (c, d) Velocities of the liquidus (VL) and eutectic (VE) isotherms for (c) Al–3%Si and (d) Al–7% Si. (e, f) Upward (GU) and downward (GD) temperature gradients at the liquidus isotherm for (e) Al–3% Si and (f) Al–7% Si.

Fig. 7. Cooling rate at the position of the liquidus isotherm as a functionof the distance from the ingot base for the Al–3% Si and Al–7% Si ingotswith and without inoculant additions.


predict the CET. This model shows that if the growthvelocity of the columnar front changes for the same alloycomposition, a different temperature gradient is requiredto block this front and cause the CET, preventing the def-inition of a universal critical temperature gradient. Alterna-tively, if the temperature gradient changes, the velocity atwhich the CET occurs also changes.

5. Predicting the columnar to equiaxed transition using

growth maps

The thermal parameters in Fig. 6 were used to constructsolidification paths consisting of the curve of the liquidusisotherm velocity (VL) as a function of the upward temper-ature gradient at the isotherm (GU), both at the same posi-tion, during solidification. Since VL is calculated only atlocations in between two thermocouples, the values ofGU, calculated at the thermocouple positions, were interpo-lated to those locations. These paths yield a useful analysisof the CET when combined with the steady-state growthmaps, originally proposed by Hunt [8].

Fig. 8. Solidification paths showing the evolution of the liquidus isothermvelocity and temperature gradient at the liquidus in the experiments inwhich the cooling curves were measured. Also included are the pathsobtained from the cooling curves presented by Martorano et al. [6] andGandin [3].

Table 2Critical thermal parameters obtained by different authors for the columnar to equiaxed transition in Al–Si alloys, velocity of liquidus temperature isotherm(VC), temperature gradient at the liquidus isotherm (GC) and cooling rate (RC).

Authors Alloy VC (m s�1) GC (K m�1) RC (K s�1)

Sturz et al. [17] Al–7% Si 2.2 � 10�4 450Al–7% Si (+ inoculant) 1.7 � 10�4 1150

Ares et al. [29] Al–5% Si, Al–7% Si 1.1 � 10�2 to 1.9 � 10�2 –420 to 67Peres et al. [25] Al–3% Si, Al–5% Si, Al–7% Si �4.7 10�4 �325 �0.16Gandin [24] Al–7% Si 2 � 10�4 a 140Present work Al–3% Si 0.001% Ti b 12.4 � 10�4 �213 0.42

0.002% Ti 8.4 � 10�4 117 0.420.006% Ti 8.8 � 10�4 94 0.420.008% Ti 5.6 � 10�4 281 0.42

Al–7%Si 0.002% Ti b 10.6 � 10�4 94 0.180.012% Ti 10.2 � 10�4 108 0.180.029% Ti 8.7 � 10�4 195 0.200.050%Ti 6.0 � 10�4 304 0.25

a This critical velocity was obtained from the calculated dendrite tip velocity and not from the liquidus isotherm velocity.b This Ti content was a result of impurities in the melting charge, since no inoculant was added.


The solidification paths in the four experiments forwhich cooling curves were measured are shown in Fig. 8,together with the paths calculated from the cooling curvespresented by Martorano et al. [6] and Gandin [3] for direc-tionally solidified Al–3% Si and Al–7% Si alloys withoutinoculant addition. Each symbol in these curves corre-sponds to the following distances from the ingot base (posi-tions in between two adjacent thermocouples): 0.012 (firstsymbol on the right), 0.03, 0.05, 0.07, 0.09, and 0.115 m(first symbol on the left). If the path is followed from rightto left the ingot is traversed from bottom to top. As can beverified, all paths in the present experiments are very simi-lar as a result of similar thermal conditions imposed duringsolidification. The paths obtained from Gandin’s experi-ments [3] always have lower isotherm velocities, probablydue to lower heat extraction rates.

Although the solidification paths in the presentexperiments without inoculant and those from Gandin’sexperiments [3] are different, the CET occurred at approx-imately the same position in the two cases. On the otherhand, for the present experiments with and without inocu-lant the CET differed significantly, despite the similarity inthe paths. To understand and predict this behavior thesolidification paths were superimposed on growth mapsin Fig. 9. These maps, which were first proposed by Hunt[8] for steady-state solidification and instantaneousnucleation, were extended by Martorano and Biscuola[38] to the case of nucleation within a temperature interval(i.e. not instantaneous). The maps display three regionsof different growth morphologies: columnar, equiaxed,and mixed columnar–equiaxed. The following equationdescribes the boundary curves separating these regions [38]:

G� ¼ 0:617u�V �1=m ð1Þwhere G� ¼ G=ðn1=3

T DT NÞ and V � ¼ V =ðADT NmÞ are the

dimensionless temperature gradient and isotherm velocity,respectively, in which G is the temperature gradient at theliquidus isotherm, nT is the number density of all substrateparticles for heterogeneous nucleation in the melt, DT N isthe average of a given distribution of nucleation undercoo-lings, V is the velocity of the isotherms, which equals thecolumnar front velocity when columnar growth prevails,and A and m are constants of the model to calculate thedendrite tip velocity, expressed as V = ADTm, where DT

is the dendrite tip undercooling relative to the liquidustemperature of the alloy.When a log-normal distributionof nucleation undercoolings is assumed the functionu� ¼ u�ðV �;m; ru; eblock

g Þ in Eq. (1) is given by [38]:

u� ¼ 3

ðmþ 1Þ0:66

ln 1� eblockg

� ��1

1

ru

ffiffiffiffiffiffi2pp

8><>:

�Z V�1=m

0

1� DT �NV �

1=m

� �mþ1" #3

1

DT �Nexp � 1

2

lnðDT �NÞru

� �2" #

dDT �N

9=;

1=3

ð2Þ

Fig. 9. Growth maps for (a) Al–3% Si (m = 3) and (b) Al–7% Si (m = 2.7)displaying a pair of curves for different values of the shape parameter (ru)of the log-normal nucleation undercooling distribution. Each pair ofcurves establishes the predominance of equiaxed growth on the left,columnar growth on the right and mixed columnar–equiaxed in betweenthe curves. The dimensionless solidification paths for the experimentswithout and with inoculant additions (%Ti is indicated) are given alongwith the paths for Gandin’s [3] experiments (without inoculant addition).The distances indicated in (a) for each point are the positions of theliquidus isotherm at which the isotherm velocity and temperature gradientwere calculated.


where eblockg is the minimum volume fraction of equiaxed

grains suggested by Hunt [8] as a requirement to mechani-cally block the growth of columnar grains either com-pletely (eblock

g ¼ 0:49), resulting in only equiaxed grains, orpartially (eblock

g ¼ 0:0066), giving rise to a mixture of colum-nar and equiaxed grains. In Eq. (2) DT �N ¼ DT N=DT N is the

dimensionless nucleation undercooling in which DT N isthe nucleation undercooling calculated in relation to theliquidus temperature, and DT N and ru are the geometricalaverage and the shape parameter, respectively, of the log-normal distribution of nucleation undercooling given by:

dnd DT Nð Þ ¼

nT

ruDT N

ffiffiffiffiffiffi2pp exp � 1

2

ln DT N=DT N

� �ru

!224

35 ð3Þ

where n is the number density of substrate particles thathave been activated for nucleation, which equals the num-ber density of grains if a particle is assumed to cause theheterogeneous nucleation of at most one grain. Wheninstantaneous nucleation is assumed ru ! 0, and Eq. (2)reduces to:

u� ¼ 3

ðmþ 1Þ0:66

ln 1� eblockg

� ��1

264

375

1=3

½1� V ��ð1þ1=mÞ � ð4Þ

Using Eq. (1) in combination with either Eq. (2) for ru > 0or Eq. (4) for ru ¼ 0 the dimensionless boundary curves ofthe growth maps were calculated for the Al–3% Si andAl–7% Si alloys considering different shape parametersru. The calculations of u� from Eq. (2) were carried outby numerical integration with Simpson’s rule dividing theintegration domain into 1000 intervals with the help ofan electronic spreadsheet. The final maps are given inFig. 9, showing pairs of curves for each ru value, whereru ¼ 0 represents the instantaneous nucleation case. Theupper curve of the pair is for eblock

g ¼ 0:49 and the lowercurve is for eblock

g ¼ 0:0066. According to Hunt [8] each pairof curves indicates the predominance of equiaxed growthon the left, columnar growth on the right, and mixedgrowth (columnar–equiaxed) in between the curves. To cal-culate these curves the exponent of the dendrite growthmodel m was determined for the two alloys by curve fittingto the dendrite growth model proposed by Lipton et al.[39]. In this model the following properties were adopted:the diffusion coefficient of Si in the liquid (7 � 10�9 m2

s�1); the Gibbs–Thompson coefficient (1.96 � 10�7 m K);the liquidus temperature (644 �C for Al–3% Si or 614 �Cfor Al–7% Si); the slope of the liquidus line of the phasediagram (�600 K%Si�1 for Al–3% Si or �650 K%Si�1

for Al–7% Si); the solute partition coefficient (0.12 forAl–3% Si or 0.13 for Al–7% Si). The curve fitting gavem = 3.0 (Al–3% Si) and m = 2.7 (Al–7% Si). Sinceu� ¼ u�ðV �;m; ru; eblock

g Þ, the exponent m is the onlyparameter that differs for the two Si concentrations. Conse-quently, the curves for the same ru value in Fig. 9a and bare very similar.

The dimensionless solidification paths of the presentexperiments, given in Fig. 9, were calculated from the val-ues of GU and VL shown in Fig. 8, using the definitions ofthe dimensionless parameters, namely G� ¼ GU=ðn1=3

T DT NÞand V � ¼ V L=ðADT N

mÞ, presented earlier. As explained inSection 4, owing to the very similar heat transfer behavior


in all experiments the same GU and VL curves used for oneexperiment with inoculant addition were also used to calcu-late the path for all other experiments with different inocu-lant contents but the same nominal %Si. The same curvefitting to obtain m in the model V ¼ ADT m was used todetermine A = 1.45 � 10�5 m s�1 K�3 for Al–3% Si, and3.29 � 10�6 m s�1 K�2.7 for Al–7% Si. The number densityof substrate particles for heterogeneous nucleation nT wasassumed equal to the number density of grains given inTable 1 and calculated from n = 0.5/L3 [14], where L isthe measured average size of equiaxed grains. The assump-tion nT ¼ n implies instantaneous nucleation, for which apredefined nucleation undercooling DT N should also bedefined. In the experiments with inoculant additionDT N ¼ 0:5 K was adopted, because possible lower valuesdid not change any conclusions, as explained later. Forthe present experiments without inoculant DT N ¼ 4:3 K(Al–3% Si) and 8 K (Al–7% Si), while for Gandin’s exper-iments [3] the values were DT N ¼ 3 K (Al–3% Si) and 6 K(Al–7% Si). These values (experiments without inoculant)were selected so that the CET, which occurs at the positionassociated with the first symbol on the left end of the path,coincided with the boundary curve dividing the columnarand equiaxed growth regions. These adopted nucleationundercoolings for no inoculant addition give nucleationtemperatures slightly above the relatively long plateauxof primary solidification observed in the cooling curves atthe ingot top (140 mm from the base), given in Fig. 5.Therefore, the assumed nucleation undercoolings are phys-ically possible, which is an indication of the consistency ofthe map predictions.

Although the solidification paths given in Fig. 8 werevery similar in all the experiments, they clearly differ inthe dimensionless form of Fig. 9, because they actually rep-resent different growth conditions. For Al–3% Si and Al–7% Si without inoculant addition the paths are located inthe lower part of the maps owing to the relatively largenucleation undercooling (DT N ¼ 4:3K for Al–3% Si and8 K for Al–7% Si). As DT N decreases to 0.5 K in the exper-iments with inoculant the paths are shifted upwards andparallel to the upper inclined part of the boundary curvesof the maps. A change in DT N to any value ~62 K doesnot modify the horizontal position of the paths relativeto the boundary curves, nor change the growth region inwhich they are located. The mixed growth region widensin the upper part of the boundary curves, increasing thepossibility that a solidification path could cut through thismixed region, resulting in a mixture of columnar and equi-axed grains. This tendency is observed in the grain macro-structures of the present experiments for both Al–3% Si(Fig. 2) and Al–7% Si (Fig. 3): an increase in inoculantaddition caused the formation of many equiaxed grainswithin an otherwise completely columnar region, givingrise to a mixed region. Without inoculant addition DT N

is relatively large and the path traverses a region of themap in which the mixed region is very thin or nonexistentif instantaneous nucleation is assumed (ru ¼ 0Þ, implying

that the CET region is much thinner, as observed inFigs. 2a and 3a.

The path for Al–3% Si with 0.01% Ti (Fig. 9a) and forAl–7% Si with 0.12% Ti (Fig. 9b) are completely locatedwithin the equiaxed region, explaining the completely equi-axed grain macrostructure of the ingots (Figs. 2e and 3f).When the amount of inoculant is reduced (lower nT) thepaths shift to the right and, in some cases, enter the mixedgrowth region. This behavior can be observed in the mac-rostructures of Al–3% Si when the inoculant content corre-sponding to 0.01% Ti (Fig. 2e) is first decreased to 0.008%Ti (Fig. 2d) and then to 0.006% Ti (Fig. 2c), increasing thenumber of columnar grains mixed with equiaxed grains.An analogous behavior exists for Al–7% Si when the inoc-ulant addition of 0.12% Ti (Fig. 3f) was decreased first to0.05% Ti (Fig. 3d) and then to 0.029% Ti (Fig. 3c).

Although the growth map predictions for the effects ofinoculant addition are in qualitative agreement with thepresent experiments, a quantitative comparison revealssome discrepancies. All solidification paths presented inFig. 9b for the inoculated Al–7% Si alloy are almost com-pletely within the equiaxed growth region regardless of theru value, i.e. whether instantaneous nucleation is assumedor not. However, for 0.029% Ti the upper boundary of theCET region shown in Fig. 3c is at 0.102 m, which is a loca-tion corresponding approximately to the first symbol onthe left of the solidification path (0.115 m). Therefore, themap indicates that blocking of the columnar grainsoccurred earlier, i.e. closer to the ingot bottom, thanobserved. The same type of discrepancy is observed forthe path for 0.05% Ti. In the case of Al–3% Si (Fig. 9a)the upper boundaries of the CET for 0.006% Ti (Fig. 2c)and 0.008% Ti (Fig. 2d) are 0.102 and 0.092 m, respec-tively. In the map in Fig. 9a the corresponding solidifica-tion paths cross the boundary into the completelyequiaxed region for a position equal to or above the loca-tion of the fourth point from right to left, corresponding toa distance from the ingot base equal to or greater than0.07 m, which is lower than the observed positions of theCET upper boundaries. Again, the maps predict completeblocking of columnar grains at a lesser distance from theingot base than that observed. Note that this comparisonis almost unchanged whether instantaneous nucleationðru ¼ 0Þ or nucleation within a temperature interval(0 < ru 6 10) is assumed, because the curves in the upperpart of the map are almost coincident.

The discrepancies between the growth map predictionsand the measured upper boundary positions of CETregions can be attributed to the steady-state conditionsassumed to construct the maps, because the experimentswere carried out under transient conditions. Another rea-son for the discrepancy might be related to the definitionof the equiaxed grain fraction necessary to completelyblock the columnar grains, proposed by Hunt [8] aseblock

g ¼ 0:49. If a larger fraction were used in the modelthe boundary curves separating the mixed and equiaxedregions of the map would be shifted to the left, improving


prediction of the CET position. Some tests showed that ifeblock

g ¼ 0:99 this discrepancy would be eliminated for Al–3% Si with 0.006% or 0.008% Ti, but would still remainfor Al–7% Si with 0.029% or 0.05% Ti. Such a large block-ing fraction, however, seems unlikely, as shown by Biscu-ola and Martorano [40].

6. Summary and conclusions

The effects of gradually increasing the amount of inocu-lant added (in the form of Al–3% Ti–1% B) on the grainmacrostructure, especially the CET of directionally solidi-fied cylindrical ingots of Al–3% Si and Al–7% Si alloyswere investigated. Without inoculant addition the ingotmacrostructures consisted of a columnar zone, a thin(�0.02 m) CET region, and an equiaxed zone at the top.As inoculant is gradually added, increasing the Ti contentfrom 0.002% to 0.01% in the Al–3% Si alloy and from0.029% to 0.075% in the Al–7% Si alloy, the macrostruc-tures transform into completely equiaxed by a gradualincrease in the number of very small equiaxed grains mixedwith columnar grains (CET region) within the originalcolumnar zone extending from the ingot bottom. As thenumber of equiaxed grains increases the columnar grainseventually disappear, forming a completely equiaxed struc-ture. During this transformation extension of the columnargrains up to the top of the CET region is relatively small,contrary to expectations. Although the types of grain mac-rostructures are very similar for both Al–3% Si and Al–7%Si, the concentrations of inoculant required are nearly anorder of magnitude larger in the Al–7% Si alloy. This effectmight be caused by Si poisoning of the TiB2 inoculant par-ticles, which is an effect discussed in the literature on grainrefining of Al–Si alloys, but shown within the context ofthe CET for the first time in the present work.

The liquidus isotherm velocity and the temperature gra-dient and average cooling rate at the isotherm decreasealong the ingot during solidification. The isotherm velocity,however, reaches a minimum value, increasing thereafter.At the position where columnar grains are completelyblocked the values of these parameters are referred to as“critical” values. The critical average cooling rate displayedthe lowest variation between experiments, being 0.42 K s�1

for the Al–3% Si alloy and ranging from 0.18 to 0.25 K s�1

for the Al–7% Si alloy.The solidification paths, which are curves of the liquidus

isotherm velocity as a function of the temperature gradientat that isotherm, are very similar in all experiments, but dif-fer when plotted on dimensionless growth maps. These dif-ferences reveal different potentials to induce columnar,equiaxed, or mixed columnar–equiaxed growth. Withoutinoculant addition the paths are located in the lower partof the maps and cross a relatively thin mixed columnar–equiaxed region when instantaneous nucleation is assumed.This is in agreement with the relatively thin CET regionobserved in the present ingot macrostructures. When inoc-ulant is added, however, the nucleation undercooling

decreases and the paths are shifted upwards, where themixed region is wider, favoring the simultaneous growthof columnar and equiaxed grains. This is also in agreementwith the increase in the length of the CET region, in whichcolumnar and small equiaxed grains coexist, observed inthe macrostructures with inoculant additions. Althoughqualitative predictions of growth maps agree with the mac-rostructures in the present work, some discrepancy exists inquantitative terms. The growth maps indicate that theupper limit of the CET region, where columnar grainsare completely blocked by equiaxed grains, should be clo-ser to the ingot base than experimentally observed. Onepossible source of this discrepancy might be the hypothesisof steady-state solidification conditions adopted to con-struct the growth maps, but which is inapplicable to thepresent experiments.

Acknowledgements

The authors thank the Fundac�ao de Amparo a Pesquisado Estado de Sao Paulo and Conselho Nacional de Desen-volvimento Cientıfico e Tecnologico, grants 03/08576-7and 475451/04-0, for financial support.

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