A comparative study of solidification features in nickel-base superalloys: microstructural evolution and microsegregation

Materials Science and Engineering, A145 ( 1991 ) 223-232

223

A comparative study of solidification features in nickel-base superalloys: microstructural evolution and microsegregation V.A. Wills and D. G. McCartney Department of Materials Science and Engineering, University of Liverpool, P.O. Box 147, Liverpool L 69 3BX (U.K.)

(Received September 26, 1990; in revised form January 14, 1991)

Abstract The solidification behaviour of four nickel-base superalloys has been studied using the technique of

quenched directional solidification. Three of the alloys are designed for use as single crystals whereas the fourth, MAR-M002, is used in directionally solidified form. Freezing begins in all alloys with the formation of ),-Ni dendrites and is terminated by a ~,+ )" eutectic reaction. In MAR-M002, MC-type carbides form, with a Chinese-script morphology, in the interdendritic liquid behind the dendrite tips. Phase transformation temperatures were measured, together with the evolution of fraction solid with temperature. The behaviour of MAR-M002 is significantly more complex than that of the single-crystal alloys. Primary and secondary dendrite arm spacings correlate with solidification parameters and are relatively insensitive to alloy constitution. Measurements of elemental partitioning at the start of freezing show that aluminium, hafnium, molybdenum, tantalum and titanium always segregate to the liquid, cobalt and vanadium segregate to the dendrite core, and the segregation direction of chromium and tungsten depends on alloy constitution.

1. Introduction

Nickel-base superalloy turbine blades are extensively produced, for high temperature gas turbine engines, in both single-crystal (SC) and directionally solidified (DS) forms by investment casting techniques [1-3]. DS turbine blades possess a number of columnar grains which are generally oriented with a (100) crystallographic direction parallel to the heat flow direction. In order to manufacture SC blades either a seed crystal or a spiral grain selector is included at the base of the shell-investment mould. High angle grain boundaries are thus eliminated, leading to the formation of a dendritic monocrystal oriented parallel to the heat flow direction. References 1-3 provide detailed descriptions of the casting of nickel-base superalloys into SC or DS form. Alloys used for DS blades differ little in composition from conventionally cast alloys as they need to contain elements which strengthen both the grains and the grain boundaries. It is the presence of grain-boundary-strengthening elements such as carbon (leading to the formation of MC-type 0921-5093/91/$3.50

carbides) which generally prevent a complete solution heat treatment and so limit mechanical properties [4-6]. The extension of the DS technique to SC casting allows the development of alloys, virtually free of grain-boundary-strengthening elements, which can be solution heat treated to give a microstructure in which the intermetallic y' precipitate of Ni3(AI, Ti) is uniformly distributed within the 7-Ni (f.c.c.) matrix [4-6]. Gas turbine engines present, in addition to turbine blades, a wide range of applications for other SC components [7] and this has led to the recent development of a family of alloys whose compositions are chosen to meet particular property requirements. In Table 1 the nominal compositions of three such SC alloys are listed together with that of the DS alloy MAR-M002. SRR99 is designed to replace MAR-M002 as a high strength blade alloy. RR2000 is for low density or high impact resistance blades, and RR2060 is a nozzle guide vane alloy where good corrosion resistance is required [7]. The main objective of the present work was to carry out a comparative study of the solidification © Elsevier Sequoia/Printed in The Netherlands

224

characteristics of the alloys listed in Table 1. Features of particular interest were: (i) the evolution of fraction solid with temperature within the mushy zone, (ii) the dependence of dendrite arm spacings on solidification parameters, (iii) the solute partitioning during growth of the primary 7-Ni and (iv) the temperatures of formation of solidifying phases. An important reason for carrying out the above study was to provide information on fundamental aspects of the solidification of these complex alloys, and to provide essential data for numerical heat flow modelling of the complex investment casting process [8].

2. Experimental procedure Nominal compositions of the alloys used in the study are given in Table 1. Specimens in the form of rods 180 mm long and 8 mm in diameter were directionally solidified in recrystallized alumina crucibles for a length of approximately 50 mm and then rapidly quenched during growth. These quenched directional solidification (QDS) experiments were performed in a modified Bridgman type of furnace in which the sample was pulled from a hot zone directly into a water-cooled water bath [9]. The temperature of the sample was recorded during growth using a single Pt-6%Rh/Pt-30%Rh thermocouple, sheathed in an alumina tube, which moved with the sample. The wire diameter was 0.35 mm, the outer sheath diameter 2.0 ram, and the thermocouple assembly was inserted axially from the top of the sample to a depth of approximately 100 mm. The sample was heated under argon until the top 140 mm was molten and allowed to equilibrate. It was then withdrawn at a known pulling rate, and

steady state growth was terminated by rapid quenching after the eutectic front had grown past the thermocouple. The thermocouple's output was recorded as a function of time with a resolution of about 0.5 K, and its calibration was carried out in the apparatus using high purity nickel with a freezing temperature of 1454 °C. Careful experimental measurements [10] showed that the pulling rate of the sample and growth rate of the dendritic front were of equal magnitude for all growth rates employed. The majority of samples were frozen at 4 mm min-~ with a liquid temperature gradient just ahead of the dendrite tips of about 6 K m m - l . However, to obtain a range of dendrite arm spacings in samples of SRR99 and MAR-M002, growth rates in the range 1-30 mm min- ~ and gradients up to 13 K m m - t were employed. Each QDS sample was sectioned longitudinally, polished and etched to reveal the dendritic and eutectic growth fronts (and in the case of MAR-M002 the carbide precipitation front). The microstructure of a QDS sample in the vicinity of the quenched dendritic front is shown in Fig. 1. The distances from the thermocouple bead to the eutectic and dendritic fronts were measured and used to determine growth front temperatures

TABLE 1 Nominal alloy compositions (wt.%) °

Element RR2000

RR2060

SRR99

AI C Co Cr Hf Mo Ti Ta W V Ni

5.0 0.015 5.0 15.0 -2.0 2.0 5.0 2.0 -Remainder

5.5 5.5 0.015 0.15 5.0 10.0 8.5 9.0 -1.5 --2.2 1.5 2.8 2.5 9.5 10.0 --Remainder Remainder

5.5 0.015 15.0 10.0 -3.0 4.0 --1.0 Remainder

MAR-M002

Fig. 1. Optical micrograph showing the microstructure of a q u e n c h e d directionally solidified sample of M A R - M 0 0 2 in the vicinity of the q u e n c h e d dendritic front (longitudinal section).

225

from the temperature vs. time data. In MARM002 the carbide precipitation temperature was also calculated in this way. A conventional point-counting method [10, 11] was used to measure the volume fraction of quenched liquid f as a function of temperature within the mushy region as follows. Transverse sections were cut at various distances from the dendrite tips (hence at different temperatures) and, after appropriate polishing and etching, optical micrographs were prepared. A regular hexagonal grid of points was then applied to ten micrographs from each transverse section and an average value of remaining fraction liquid calculated for each section (or temperature). The carbide volume fraction in MAR-M002 was measured somewhat differently because of the small size of the features concerned. The carbides were imaged on a scanning electron microscope using the backscattered electron signal which provided good contrast against the matrix. The image, at an appropriate magnification, was transferred to a Quantimet 970 image analysis system and average carbide volume fractions obtained [10] by analysing numerous separate fields. Primary dendrite arm spacings were measured on etched transverse sections taken from within the mushy region after quenching. The number of primary arms n in a known area A was counted and the primary arm spacing 2p = ( A / n ) °5 was calculated. To measure secondary dendrite arm spacings longitudinal sections were prepared so that the whole length of a primary arm could be seen within the mushy zone, i.e. the arm axis was parallel to the plane of the section. The width of a group of four secondary arms was measured and an average spacing calculated. Then the distance of the midpoint of the group from the dendrite tip was measured and converted into a local solidification time [12]. Electron probe microanalysis (EPMA) was used to measure the composition of the primary phase close to the tip of a primary dendrite arm in longitudinally sectioned QDS samples grown at 4 mm min- 1. Samples were lightly etched and point analyses performed every 0.05 mm along a dendrite core from its tip to about 1.0 mm from the tip. A portion of a typical analysis line is shown in Fig. 2. Wavelength-dispersive analysis was employed with an accelerating voltage of 15 kV and pure elements as standards. K a X-ray lines were used for aluminium, chromium, cobalt, nickel, titanium and vanadium with La lines for

hafnium, molybdenum, tantalum and tungsten. A standard Z A F correction programme was applied to the raw data to give normalized weight percentages of each of the elements. Using the same analysis procedures composition profiles across primary dendrite cores were also determined on selected transverse sections from the same samples. As discussed in detail later, an effective partition coefficient for each solute element k'/ was calculated, and this required the bulk quenched liquid composition of each of the microprobeanalysed QDS samples to be measured accurately. Inductively coupled plasma emission spectrometry was employed for this purpose using samples 2 mm thick and 8 mm in diameter which were cut transversely from the quenched liquid portion of specimens. 3. Results 3.1. Temperature measurements

In the SC alloys freezing began with the formation of primary y dendrites and was terminated by a y - y ' eutectic reaction. One would naturally expect (from thermodynamic considerations) the L-" ~,+ y' binary eutectic to occur over a range of temperatures and compositions, but in practice it was found to be completed in a temperature interval of no more than 5 K. In MAR-M002 freezing again started with the growth of primary dendrites. Then MC-type carbides began to form, in the interdendritic liquid, at a temperature Tc approximately 20 K below the dendrite tip temperature. Freezing was terminated, as in the other alloys, by a y + y ' eutectic reaction.

Fig. 2. Longitudinal section through the core of a primary dendrite arm near its tip. A typical portion of a line along which EMPA measurements were performed is shown in the optical micrograph.

226

Thermodynamically neither of these reactions in MAR-M002 is invariant because of the multicomponent nature of the alloy. However, the final eutectic reaction was spread out over only 5 K approximately, and the reaction involving Y and MC-type carbides was completed within 5 K of Tc. In Table 2 the temperatures at which the various solidification reactions began are listed. These are average values taken from four samples of each alloy. In all cases the growth rate was 4 mm min- 1 with a temperature gradient of about 6 K ram-~. It should be emphasized that the measurements were obtained directly from QDS samples containing a calibrated noble metal thermocouple. The error of + 5 K for each absolute temperature measurement reflects experimental limitations associated with the following: (i) the determination of freezing front positions on a longitudinal section, (ii) the finite size of the thermocouple bead in a steep temperature gradient and (iii) calibration errors of the thermocouple against pure nickel. Despite these limitations it has been shown [13] that these temperature measurements taken directly from QDS samples are in good agreement with values obtained by both direct and differential thermal analysis of the same alloys. 3.2. Fraction solid evolution within the mushy region With the point-counting method employed it was more convenient to measure the fraction of (quenched) liquid f on a transverse section rather than the fraction solid f~ formed. Hence the graphs in Figs. 3(a)-3(d) show the results of volume fraction liquid vs. temperature measurements for QDS samples grown at 4 mm min-L The first three plots (Figs. 3(a)-3(c)) are for SC

alloys whereas Fig. 3(d) is for the DS alloy MARM002. Experimental points are indicated by error bars whose magnitudes correspond to two standard deviations from the mean. Errors are larger towards the dendrite tips because in this region it is more difficult to distinguish "asgrown" solid from quenched liquid. The full lines correspond to best-fit analytical relationships as discussed in Section 4. In the case of all the SC alloys there is a smooth monotonic decrease in fraction liquid with decreasing temperature within the mushy region. The majority of solid is seen to be deposited within the first one-third of the freezing range and freezing is terminated by essentially isothermal growth of 7-7' eutectic. The DS alloy MAR-M002 behaves somewhat differently as can be seen from Fig 3(d). Very clearly there is a sudden decrease in fraction liquid at about 22 K below the dendrite tip temperature which coincides with the formation of the Chinese-script MC-type carbides (see Table 2). This abrupt decrease in fraction liquid was found to be principally due to the formation of a large amount of 7-Ni phase, which accompanied carbide precipitation in the interdendritic liquid, since the carbide volume fraction was revealed by image analysis to be only 0.02 in the fully solidified alloy. Again freezing is terminated by ~-y' eutectic. 3.3. Dendrite arm spacings Measurements of primary (2p) and secondary (2s) dendrite arm spacings were performed on the alloys MAR-M002 and SRR99. Samples were solidified at steady state with growth rates V of 1, 4, 10 and 30 mm min -~ and liquid temperature gradients G~(measured just ahead of the dendritic growth front) of between 4 and 14 K m m - t In the case of primary dendrite arms the empirical expression 2p = Kp C, n V m

TABLE 2 Initial freezing temperature Tf, onset temperature for Y-7' eutectic freezing T~ and onset temperature for carbide precipitation Tc Alloy

L (°C)

L (°C)

L (°C)

SRR 99 MAR-M002 RR2000 RR2060

1379 1369 1335 1347

1309 1254 1240 1217

-1347

All temperature measurements were obtained from QDS samples grown at 4 ram rain- 1 and are accurate to + 5 K,

where Kp is a constant for a given alloy, has been widely used to correlate the data [3, 9, 14, 15]. However, in this instance there were insufficient data points to warrant a regression analysis. Figure 4 illustrates simply that the data for both alloys are consistent with the relationship ,~p = KpG1-0.5 V-O.25

(which has been predicted theoretically [16, 17]) and are approximately described by a common straight line.

227

/a/

1.0

/

1.0

(b)

/

0.8

0.8 RR2000

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._ET J 0.6

=

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,

,

,

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•

g

*604

t~ u 0.4 u-

u_

0.2

0.2

o.o

0.0

220

1240 1250 1260 1270 1280 1290 1300 1310 1320 1350 1340

1240

Temperature(°C)

1260 1280 1300 Temperature(°C)

J

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0.8

0.8

k

g 0.6

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SRR99

o

.

• MAR-MOO2 k=0.59,0.63,0.67

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(d)

1.0

(c)

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0.2 0.0

/~

k=o.9,o ~.2o8o

, , , ,Jl ~ 1300 1310

1320

.... i . , -- e . . . . L.... i .... 1330 1340 1350 1360 1370 1380 Temperature(°C)

.

0,0 1260

1280

1300 1320 T e m p e r o t u re(°C)

1340

.

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L

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1360

Fig. 3. Plots of fraction liquid in the mushy zone v s . temperature for (a) RR2000 (k = 0.77, 0.79 and 0.83), (b) RR2060 (k = 0.79, 0.82 and 0.85), (c) SRR99 (k=0.72, 0.75 and 0.78) and (d) MAR-M002 (k=0.59, 0.63 and 0.67): - - - , best-fit analytical expressions according to eqn. (2). The experimental points are indicated with error bars.

d 0 = a MAR-M246(ref.14) =. MAR-M002(ref. 14) • SRR99 • MAR-M002

25O

3E~2oo

/ A /

~"

[] /

where d is the distance of the group of secondary arms from the primary dendrite tip and V the steady state growth rate. In Fig. 5(a) ~s is plotted against 0 for SRR99 and Fig. 5(b) is a similar plot for MAR-M002. As expected itSincreases with increasing 0 and linear regression analysis was used to determine the value of the coefficient n in the widely used equation [ 18]

co 1 5 0

~' I O 0 E n

50

0

.00

. . . . . . . ' * . . . . = . . . . 0.05 0.1 0 0.1 5 G ~ / - - ¢ = (K-~sO.=mO.~)

V

0.20

F i g . 4. P r i m a r y d e n d r i t e a r m s p a c i n g p l o t t e d v s . t h e p a r a m e t e r G I o5 V o25 f o r t h e a l l o y s M A R - M 0 0 2 (A) and SRR99 ( • ) used in this work, including additional points taken from ref. 1 4 f o r M A R - M 0 0 2 (A) and MAR-M246 (r3): - a p p r o x i m a t e b e s t fit c o m m o n t o all t h e d a t a p o i n t s .

As described in Section 2 secondary dendrite arm spacings were measured within the mushy region of QDS samples, and local solidification times 0 were calculated according to the equation

Z~ = KsO"

where K s is a constant for a given alloy. For SRR99 n = 0.47 with a correlation coefficient of 0.88 and for MAR-M002 n = 0.46 with a correlation coefficient of 0.84. Thus the value of n is much larger than either that of 0.33 predicted by simple coarsening theory for a binary alloy or that of 0.39 measured in the A1-Cu alloy system [12, 18]. Furthermore there was no indication in MAR-M002 that ;tS changed discontinuously at the MC-type carbide precipitation temperature.

228

3.4. Dendritic microsegregation

Figure 2 shows a typical line along which solute concentrations were measured. It lies along the core of the dendrite and begins very close to its growing tip. Figure 6 illustrates the results obtained for MAR-M002. There is obviously very little variation in solute concentrations along the dendrite core for distances up to about 1 mm from the tip, and thus a reasonable approximation to the dendrite tip composition can be obtained by averaging the analysed values shown in Fig. 6 for each solute element. Table 3 summarizes the data on average dendrite tip compositions Ct for each of the alloys investigated, and also includes measurements of average bulk liquid compositions C~ obtained by chemical analysis.

Elemental partitioning can now be described in terms of the effective partition coefficient for each solute element k/where

the subscript i indicating that ki' is the ratio of Ct to CI for the solute element i. The values of k" calculated from the results in Table 3 are given in Table 4 and are best regarded as effective partition coefficients at the beginning of solidification. It is apparent that the effective partition coefficients of aluminium, cobalt, titanium and molybdenum vary little with alloy composition whereas tantalum and tungsten exhibit significant variations. Hafnium is the most strongly segregating element in all the alloys, and the k' value of 0.06 is not dissimilar to previously reported measurements on the alloy M A R - M 2 0 0 + H f [19J.

SRR99

4. Discussion

n=0.47

E & "~ ~00 .E

4.1. Evolution offraction solid

•m •

mm i

o

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In a binary alloy the evolution of fraction solid (or decrease in fraction liquid) within the mushy semisolid region can be modelled using either the Scheil equation or a modified Scheil equation which takes account of solid state backdiffusion

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5 10 50 100 Local Solidification Time(s)

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5 10 50 100 Local Solidification Time(s)

3

~00

Fig. 5. Secondary dendrite arm spacing plotted vs. local solidification time for the alloys (a) SRR99 and (b) M A R M002: - - . , determined by linear regression analysis with (a) n = 0.47 and (b) n = 0.46.

......

0.0

~- • . ~ . - . t . ' ' t ' " t - "

0.1

0.2

0.3

'~- . . . . .

0.4

•

0.5

......

0.6

Y"t

0.7

distance (mm) Fig. 6. Electron microprobe measurements of solute element concentrations plotted vs. distance from the dendrite tip in the alloy M A R - M 0 0 2 . Measurements were made along the core of a primary dendrite arm.

229

[20]. When written in terms of temperatures and assuming a constant partition coefficient k and straight liquidus and solidus lines on the phase diagram the Scheil equation can be written as

( 7~,,--Tlil';k-I'

f=lTm_ T,}

(2)

where f is the fraction liquid at temperature T, Tm is the melting point of the pure material, T~ is the liquidus temperature of the alloy and k is the equilibrium partition coefficient. Physically it is reasonable to expect the fraction liquid in the mushy zone to decrease with temperature in a similar fashion in a multicomponent alloy provided that the mushy zone consists of primary dendrites plus interdendritic liquid. This is the case for the three SC alloys whose fraction liquid vs. temperature measurements are plotted in Figs. 31a)-3(c). The full lines shown on these figures have been obtained using the Scheil equation and adjusting the value of k in eqn. (2) to give a best fit with the experimental results. The values of k used are shown in the figure caption. Obviously there is now no direct physical interpretation of the parameter k but choice of an appropriate value leads to an analytical f(T) relationship which fits the experimental results for all the alloys remarkably well. The analytical equation is terminated at the eutectic temperature. The f ( T ) relationship for the DS alloy MARM002 shown in Fig. 31d) is very different from that of the SC alloys. The formation of MC-type carbides about 20 K below the dendrite tips is accompanied by the formation of a large fraction of y-Ni phase, which suggests the occurrence of a divorced eutectic-type reaction. The MC-type

carbides contain principally hafnium, tantalum, titanium, tungsten and carbon [10] and are virtually free of aluminium, chromium and cobalt. Table 4 shows that titanium, tantalum and hafnium all segregate to the liquid during freezing and so the MC-type carbides will form in the interdendritic liquid once it has become sufficiently enriched in these positively segregating elements. The carbide and y-Ni phase then grow simultaneously, leading to a decrease in fraction liquid of about 0.4 over a narrow temperature interval. However, the overall volume fraction of carbide formed is only of the order of 0.02. Thus the f ( T ) relationship for this alloy can be considered to consist of three regions as follows. Above 1347 °C solidification occurs by the growth of the y-Ni phase. Between 1349 and 1345°C f changes from approximately 0.55 to 0.15 by the simultaneous growth of y-Ni and MC-type carbides with a Chinese-script morphology. Below 1345 °C both y-Ni and MC carbides continue to increase their volume fraction. However, most of the change in fi is associated with growth of the y-Ni phase, and the carbide fraction remains approximately constant at about 0.02. The final fraction of y - y ' eutectic is about 0.05. Only the initial formation of primary y-Ni can be analysed using a Scheil-type equation giving best-fit k values of between 0.59 and 1/.67 as shown in Fig. 3(d). Measurements of phase transformation temperatures and fraction solid evolution are essential for the development of numerical finite difference or finite element heat flow models of alloy solidification during casting. It is in this context that analytical expressions for fraction liquid

TABLE 3 Average dendrite tip (C,) and bulk liquid (Ct) solute concentration (wt.%) ELement

RR2000

AI Co Cr Hf Mo Ti Ta W V

5.28 15.52 111.90 -2.95 2.45 --1.09

RR2060

5.42 14.40 9.94 -3.04 4.10 --0.96

4.87 5.41 15.99 -1.80 1.27 2.97 1.68 --

SRR99

5.14 4.93 15.12

MAR-M002

5.53 5.45 8.42

5.51 5.01 8.83

1.44

2.12 2.81 9.56

5.57

5.60

11.64

10.06

8.61 0.06

9.07 1.07

1.98 1.95 5.08 2.1)8

1.46 10.17

0.78 1.18

11.27

1.30 2.65 9.98

230

(or solid) as a function of temperature in multicomponent alloys are valuable. Moreover, the accurate incorporation in a heat flow model of complex fraction solid evolution, such as that exhibited by MAR-M002, is important if reliable predictions of isotherm migration rates in a casting are to be achieved [ 10].

4. 2. Dendrite arm spacings The primary dendrite arm spacings measured in this work and displayed in Fig. 4 agree well with previous measurements on MAR-M002 [14] which are also shown in this figure. Data from MAR-M246 [14], an alloy of similar composition to SRR99 and MAR-M002, also lie close to the common straight line. Although 2_ has been plotted in Fig. 4 against G l - ° s V -°'~5 a n d fits this relationship, there is an insufficient spread in the results to enable the parameters m and n in the equation ~,p = Kp Glm V n

to be determined with any degree of certainty. However, Taha et al. [15] have shown that in multicomponent steels the exponents m and n are close to - 0 . 5 and - 0 . 2 5 respectively as predicted by theoretical models of binary systems [16, 17]. Therefore it appears probable that the variation of 2p with solidification parameters in the complex nickel-base superalloys studied is adequately accounted for by these binary alloy models [16, 17]. Following Flemings [18] it has become customary to relate the secondary dendrite arm spacing ;t~ to local solidification time 0 as shown in Fig. 5. In both alloys studied there is a strong correlation between 2 s and O" with n ~ 0.46. The constant K s is almost identical for the two alloys which is to be expected, given that they are of very similar TABLE 4 Values of effective partition coefficient ki' for solute elements in the alloys studied Element

RR2000

RR2060

SRR99

MAR-M002

AI Co Cr Hf Mo Ti Ta W V

0.97 1.08 1.10 -0.97 0.60 --1.13

0.95 1.10 1.06 -0.91 0.65 0.58 0.81 --

1.00 1.09 0.95 --0.68 0.52 1.06 --

0.99 1.16 0.95 0.06 -0.60 0.45 1.12 --

composition. The value of n is much larger than either that of 0.33 predicted by simple coarsening theory for a binary alloy [18, 20] or that of between 0.31 and 0.39 measured in binary A1-4.5wt.%Cu alloys [12, 18]. It is not altogether clear why this should be so, although it must be noted that exponents ranging from 0.17 to 0.55 have been measured in other multicomponent alloys [15, 21-23].

4.3. Dendritic microsegregation The segregation of alloying elements in these nickel-base superalloys has been measured in terms of effective partition coefficients at the beginning of freezing ki'. k i' is defined by eqn. ( 1 ) and is the ratio of the average solute level of the element i in the solid at the dendrite tip to the average solute level of i in the quenched bulk liquid. Since the solute undercooling at the dendrite tip is likely to be of the order of 5 K or less for the growth conditions used then the values of ki' listed in Table 4 will probably be close to the equilibrium partition coefficients ki at the beginning of freezing. It is important to emphasize that the results refer to the initial stages of solidification since Sellarnuthu and Giamei [19] have clearly shown that equilibrium partition coefficients in the nickel-base alloy MAR-M200 can vary significantly with the fraction solidified. In the alloy systems investigated the values of ki' for aluminium, cobalt, molybdenum and titanium show little variation with overall alloy composition. For example, cobalt has an effective partition coefficient of 1.08 in RR2000 and 1.10 in RR2060 despite the three-fold difference in cobalt composition between these two alloys. However, it is apparent from Table 4 that chromium and tungsten can segregate either positively (k i' < 1 ) or negatively (k i' > 1 ) at the beginning of freezing, depending on alloy constitution. The values of effective partition coefficients measured in this work are in reasonable agreement with measurements reported by LecomteBeckers [24]. The alloys used in ref. 24 had somewhat different compositions from those used in the present work, particularly with regard to the absence of tantalum and tungsten. However, the following ranges of values of k i' were obtained [24]: kAl' = 0.9-1.2 kcr' = 0.8-1.1

kMo' -~ 0.5-0.9

231

kco'= 1.0-1.15 kvi'-- 0.45-0.65 The main difference observed is thus in the much wider spread of values for aluminium, ranging from less than to greater than unity. Similarly there is reasonable agreement between the present results and the equilibrium partition coefficients at f , = 0 determined by Sellamuthu and Giamei [19] in the alloys MARM200 and MAR-200 + Hf. The former alloy is closest in composition to SRR99 and the latter to MAR-M002. In MAR-M200 they obtained partition coefficient values of 0.95, 0.85, 0.60 and 1.10 for aluminium, chromium, titanium and tungsten respectively, all of which are close to the values listed in Table 4 for SRR99. In the hafnium-modified alloy the values for the same elements were 0.96, 0.85, 0.83 and 1.2 which, apart from the somewhat larger value for titanium, agree well with the MAR-M002 measurements of the present work. They also obtained a higher value of partition coefficient for hafnium: 0.28 as opposed to 0.06. It seems probable that the greater error is in the present measurement, given the low level of hafnium in the alloy and the use of a pure element standard during EPMA. However, the partitioning of hafnium is extremely sensitive to alloy composition [19] and so the lower value measured in this work may simply reflect the different starting composition of the alloy compared with that used previously by Sellamuthu and Giamei [19]. For example, in binary Ni-Hf alloys one can estimate the equilibrium partition coefficient to be only around 0.1.

5. Summary Steady state QDS experiments have been performed on four nickel-base superalloys designed for high temperature aeroengine applications. A comparative study of the solidification characteristics was performed and the alloy MARM002, designed for use in directionally solidified turbine blades, solidifies very differently from the three alloys designed for SC use. A Scheil-type equation has been formulated to describe mathematically the evolution of fraction solid with temperature in the SC alloys. However, it cannot be applied to MAR-M002 in which the formation of MC-type carbides (about 20 K below the dendrite tip temperature) is accompanied by a large increase in the volume fraction

of the 7-Ni phase over a temperature interval of a few degrees. Primary dendrite arm spacings were measured and correlate satisfactorily with the parameter G-o.sV o.25 where G~ is the liquid temperature gradient and V the growth rate. For secondary dendrite arms the spacing ;t~ is related to local solidification time 0 through the equation 2~ = K~O~ with n = 0.46. Neither primary nor secondary dendrite arm spacings depend much on overall alloy composition. Effective partition coefficients have been calculated for all elements in each of the alloys investigated. Aluminium, cobalt, molybdenum and titanium show little variation in segregation behaviour with overall alloy composition. However, the alloy composition markedly influences the segregation behaviour of chromium and tungsten.

Acknowledgments The authors would like to acknowledge the help of K. McKindlay and W. Voice in performing EPMA and scanning electron microscopy respectively. We would also like to thank F. J. Horrocks for his support and advice throughout the course of the work. The project was supported by SERC and Rolls Royce plc through the provision of a CASE studentship to V. A. Wills. MAR-M is a Martin Marietta Company trademark. SRR99, RR2000 and RR2060 are alloys registered by Rolls Royce plc, U.K.

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