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Materials Science and Engineering A 479 (2008) 365–372

Grain growth and particle pinning in a model Ni-based superalloy

Kai Song, Mark Aindow ∗Institute of Materials Science, University of Connecticut, Storrs, CT 06269-3136, USA

Received 10 February 2007; received in revised form 20 June 2007; accepted 26 September 2007

bstract

An experimental study has been performed on the grain growth in a model Ni-based superalloy, with particular emphasis on the pinning effect ofhe second-phase particles. Extensive annealing experiments were performed, and the microstructural development was evaluated in detail usingcanning and transmission electron microscopy. It was found that grain growth was strongly inhibited by the pinning effect of both the coarse �′

′ ◦

hase and the inert precipitates. For samples heat-treated at temperatures below the � solvus (1143 C), the limiting grain size was determinedy the size and volume fraction of the �′ phase. For samples heat-treated at super-solvus temperatures, the stability of the MC-type carbides andttrium oxides led to a nearly constant Zener limiting grain size over the temperature range 1143–1244 ◦C. Samples heat-treated at 1270 ◦C hadarger grain sizes due to the coarsening and/or dissolution of the MC-type carbides and yttrium oxides. 2007 Elsevier B.V. All rights reserved.

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eywords: Grain growth; Ni-based superalloy; Particle pinning; Limiting grain

. Introduction

In metallic alloys, dispersions of second-phase particles maynhibit grain growth by exerting a pinning force on migratingrain boundaries during thermal treatment. Since the drivingorce for grain growth varies with the grain size, grain growthill proceed until the grain size reaches a limiting value, where-pon the driving force is balanced by the pinning force. Thisffect was first described by Zener in the late 1940s [1] and isidely known as Zener pinning. Since then, numerous refine-ents of this model have been proposed in which the details

f the interactions between the grain boundaries and the parti-les are taken into account. These factors include: the degree ofontact between the boundary and the particles [2]; the shape ofhe pinned grain boundaries [3]; the heterogeneity of the grainize distribution [4]; the shape of the pinning particles [5]; thearticle-assisted motion of grain boundaries [6] and many more.ll of these factors may affect the grain size to some extent and

o the application of pinning theory to practical alloy systemsan be very challenging.

∗ Corresponding author at: Institute of Materials Science, 97 North Eaglevilleoad, Unit 3136, University of Connecticut, Storrs, CT 06269-3136, USA.el.: +1 860 486 2644; fax: +1 860 486 4745.

E-mail address: m.aindow@uconn.edu (M. Aindow).

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921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2007.09.055

Ni-based superalloys exhibit an attractive combination ofechanical properties and corrosion/oxidation resistance at high

emperature, leading to their use in a variety of gas-turbinengine components including blades and discs. Grain size playsn important role in controlling the mechanical properties ofhese superalloys, including their tensile strength [7], low cycleatigue life [8] and creep resistance [9]. Ni-based superal-oys generally contain a variety of different precipitates in aace-centered cubic �-Ni matrix [10]. The majority of these cor-espond to the L12 (Ni3Al) �′ phase, while inert precipitates likearbides and borides are present as minority constituents. Duringhe thermo-mechanical processing of the alloys, these second-hase particles could significantly retard the grain boundaryigration and limit grain growth. However, although there issignificant body of literature on Zener pinning, there is littleetailed information available about the pinning effect of therecipitates in Ni-based superalloys. This is presumably due tooth the complexity of the microstructures and the complica-ions associated with impurities and local inhomogeneities inommercial alloys.

In this study, the grain growth and particle pinning phe-omena have been examined in a model powder metallurgyP/M) Ni-based superalloy whose chemistry resembles that of

he matrix phase mixture in the commercial alloy IN100. Thislloy was produced as part of a program to develop analyticalodels for the mechanical behavior and microstructural devel-

pment in alloys such as IN100 [11], and was chosen for the

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tipfraction of the �′ phase in the AR material is around 40%, andthe distribution of this phase is complex with coarse recrystal-lized �′, finer unrecrystallized �′ and very fine �′ precipitatesthat form during slow cooling from the processing temperature.

66 K. Song, M. Aindow / Materials Scienc

resent study because it contains low levels of impurities, hashighly homogenous microstructure and has a fine initial grain

ize. The samples were heat-treated over a range of temper-tures corresponding to those at which Ni-based superalloysre typically processed for gas-turbine engine applications, andicrostructures were characterized using electron microscopy

echniques. These data were used to elucidate the effects of thearious second-phase particles on the grain growth behavior inhis alloy.

. Materials and experimental methods

The composition of the alloy is Ni–20.3Co–14.8Cr–4.6Al–.9Mo–3.7Ti–0.08Zr–0.08C–0.02B–0.011Y (all in wt.%). Thelloy was heat-treated at elevated temperatures to study therain growth behavior. First, small coupons of the alloy, aroundcm × 2 cm × 0.2 cm, were cut from the bulk material. The

mall sample size was chosen so that the sample could be heatedr cooled as quickly as possible. The samples were inserted intopre-heated tube furnace, and held under flowing Ar for times

anging from 2 min to 4800 min. The heat-treatments were con-ucted at temperatures between 1087 ◦C and 1270 ◦C: since theolvus for the �′ phase is around 1143 ◦C, samples heat-treatedbove and below this temperature are referred to as super-solvusnd sub-solvus, respectively. At the end of each heat-treatmenthe sample was removed from the furnace quickly and thenater-quenched to minimize any microstructural changes upon

ooling.The grain structure was characterized using scanning elec-

ron microscopy (SEM). The surfaces of the coupons were firstrepared using standard metallographic grinding and polishingechniques. The grain boundaries (GBs) were then revealed bymmersion-etching the sample in waterless Kalling’s solutionor a period of 1–3 min, while the locations of the �′ particlesere defined by etching the sample in Glycerygia for around0 s [12]. The Glycerygia etch preferentially attacks the �′ phaseesulting in deep etching of larger �′ particles where these areresent in the microstructure. Secondary electron (SE) imagesere obtained from these samples using a JEOL 6335F field-

mission SEM operating at an accelerating voltage of 15 kV.he � grain size was evaluated by measuring the mean linear

ntercept while the �′ size was measured by tracing the outlinef the particles and calculating the equivalent radius. The vol-me fraction of the �′ particles was determined using the pointount method. For each sample, an average of 300 interceptsere measured to determine the mean grain size.The inert precipitates were revealed by using a hybrid repli-

ation method developed by the present authors [13]. First, theample surface was electro-polished by suspending it from at wire in a solution of 10% HCl, 89% methanol and 1% citriccid held at a temperature of −45 ◦C, and applying a potential of5 V dc between this and a Ta foil cathode. Immediately after thelectropolish the sample was immersed in water-less Kalling’s

olution at room temperature for 3 min (for sub-solvus samples)r 12 min (for super-solvus samples). The specimen surface washen replicated by evaporating ≈30 nm of carbon onto the etchedample. The carbon replicas were released by electro-etching

Fms

Engineering A 479 (2008) 365–372

sing the same electrolyte as for the initial electro-polish, but at–10 ◦C under current control at a density of 0.03–0.05 A/cm2.he replicas were examined in a JEOL 2010 TEM operating at00 kV, and equipped with an EDAX Phoenix atmospheric thinindow energy-dispersive X-ray spectrometer (EDXS). The

ypes of precipitates were identified by determining the chem-stry and/or crystal structure of the particles. The former waschieved by using EDXS and the latter by using selected arealectron diffraction. The sizes of the particles were measuredirectly from bright field TEM micrographs.

. Results and discussion

.1. Microstructural evolution and grain growth

A typical example of a SEM image showing the microstruc-ure exhibited by the alloy in the as-received (AR) state is shownn Fig. 1a. The darker areas correspond to the �′ phase that wasartly etched out during the preparation process. The volume

ig. 1. Microstructure of the alloy in the as-received condition: (a) SE SEMicrograph showing the overall phase distribution and (b) BF TEM micrograph

howing the four types of inert particles (a, M3B2; b, M23C6; c, MC; d, Y2O3).

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K. Song, M. Aindow / Materials Sci

he lighter areas are the � grains that were etched to a lesserxtent. The � grain boundaries are resistant to the etchant sohey appear as bright protruding ridges on the sample surface.he mean � grain size for the AR material was measured as.3 �m. The white particles are inert precipitates, which are notffected by the etching. The character of these inert precipitatesas investigated using extraction replicas and a representativeF TEM image from one such replica is shown in Fig. 1b.our different types of inert precipitates were identified from

uch images: Cr/Mo-rich M3B2-type borides with tetragonal3Si2 structure (arrow a); Cr-rich M23C6-type carbides with

ubic Cr23C6 structure (arrow b); Ti-rich MC-type carbides with

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ig. 2. Examples of EDXS spectra and SADPs obtained from each of the four typesu peaks arise from the support grid for the TEM specimen.

and Engineering A 479 (2008) 365–372 367

ubic NaCl structure (arrow c); and yttrium oxides, Y2O3 (arrow). Typical examples of the corresponding EDXS spectra andelected-area electron diffraction patterns obtained from theseour types of precipitates are shown in Fig. 2a–d, respectively.

Typical examples of SEM images showing the microstruc-ures exhibited by the alloy after sub-solvus and super-solvuseat-treatments are shown in Fig. 3a and b, respectively. Theub-solvus samples contain significantly lower volume fractionsf the �′ phase than the AR material due to the higher sol-

bility of the various alloying elements in the � phase at theeat-treatment temperature. These microstructures are also lessomplex due to the preferential dissolution of the finer �′ precip-

of inert precipitates: (a) M3B2; (b) M23C6; (c) MC; (d) Y2O3. In each case the

368 K. Song, M. Aindow / Materials Science and

Ft

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ihttitfirgtoTTslowly with T from 1087 C to 1127 C, but I then increasesmore markedly as the solvus temperature is approached (i.e.T = 1127–1143 ◦C). For the super-solvus samples, however, thegrain size attained after 300 min is nearly constant over a wide

ig. 3. SE SEM micrographs showing typical microstructures of samples heat-reated for 30 min at: (a) 1127 ◦C and (b) 1177 ◦C.

tates and unrecrystallized �′ during heat-treatment, and there issmall increase in the grain size. For the super-solvus samples

here is no �′ phase; the microstructures consist only of � grainsnd inert particles; and the grain growth is more pronounced.

ig. 4. BF TEM micrograph obtained from a replica of the sample heat-treatedt 1127 ◦C for 30 min, showing the distribution of the inert precipitates.

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Engineering A 479 (2008) 365–372

ig. 4 shows a representative image of a replica obtained from aub-solvus sample heat-treated at 1127 ◦C for 30 min. All ofhe particles in Fig. 4 were identified to be either MC-typearbides (large blocky particles) or the yttrium oxides (smallound particles). Similar results were obtained from replicasf the other heat-treated samples indicating that the M23C6-ype carbides and the M3B2-type borides were unstable andissolved at all of the heat-treatment temperatures used in thistudy.

In this study the � grain size was evaluated by determin-ng the mean linear intercept, I. Values of I are plotted againsteat-treatment time, t, in Fig. 5 for seven different tempera-ures between 1127 ◦C and 1270 ◦C: for clarity the data fromhe sub-solvus and super-solvus treatments are shown separatelyn Fig. 5a and b, respectively. At each of these temperatures,he � grain growth is rapid initially, then slows down, andnally stagnates at a stable grain size. This latter value iseferred to as the limiting grain size, DLim, since further grainrowth is negligible. For these seven heat-treatment tempera-ures the samples reach DLim after around 300 min. As such,ne can see how DLim varies with heat-treatment temperature,, from Fig. 6, which is a plot of I against T for t = 300 min.he figure shows that initially the grain size attained increases

◦ ◦

ig. 5. Variation of the mean grain size, I, with heat-treatment time, t, for sampleseat-treated at various temperatures: (a) sub-solvus treatments and (b) super-olvus treatments.

K. Song, M. Aindow / Materials Science

Fig. 6. Variation of the limiting grain size, DLim (from the average grain size, I,for the samples heat-treated for 300 min), with heat-treatment temperature, T.

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ig. 7. SE SEM micrograph obtained from the sample heat-treated at 1132 ◦Cor 30 min showing examples of grain boundaries pinned by the �′ particlesblack arrows) and by the inert precipitates (white arrows).

ange of T (1152–1244 ◦C), and only increases significantly for= 1270 ◦C.

.2. Effect of the γ ′ phase on grain growth

As shown in Section 3.1, stagnation of � grain growth was

bserved when the alloy was heat-treated at elevated tempera-ures. This is consistent with what one would expect for Zenerinning of the � grain boundaries by the second-phase particlesnd clear evidence for this was observed in both the SEM and

φ

ai1

able 1icrostructural data obtained from the alloy samples heat-treated at various sub-solv

(◦C) 1087 1093 1099 1104 1110 1116(�m) 3.7 3.8 3.8 4.3 4.5 5.2(�m) 2.8 2.8 2.9 3.2 3.4 3.9

(%) 26.1 23.1 17.4 12.8 9.3 8.2(%) 1.8 1.8 1.6 1.3 1.1 1.1(�m) 0.78 0.88 0.91 0.72 0.58 0.61

0.90 0.86 0.84 0.78 0.73 0.65

R 0.84 0.92 0.94 0.67 0.51 0.47

grain size (mean linear intercept), I; mean equivalent grain radius, R; volume frache �′ phase, r; and area fraction of the �′ phase at � grain boundaries, φ. The theoromparison.

and Engineering A 479 (2008) 365–372 369

EM images obtained in this work. One example is shown inig. 7, which is an SEM image obtained from a sample heat-

reated for 30 min at 1132 ◦C. The most obvious pinning eventsre indicated by arrows in this figure: the black arrows showositions where the � grain boundaries are pinned by the �′,hile the white arrows indicate places where the boundaries areinned by inert particles. From such images it is clear that for theub-solvus heat-treatments the �′ particles play the major rolen pinning the grain boundaries. This is mainly because the vol-me fractions of the �′ particles are generally much higher thanhose of the inert precipitates in the sub-solvus samples. More-ver, the �′ particles tend to be located preferentially at the grainoundaries and so they pin the boundaries more effectively.

The data obtained from samples heat-treated for 300 min atarious sub-solvus temperatures were used to perform a quan-itative analysis of the pinning phenomena, and these data areresented in Table 1. The table includes values for: I, whichere taken to be equivalent to DLim; the mean equivalent area �rain radius, R, that one would obtain if the grains of this sizeere spherical; the volume fraction of the �′ phase, f; the mean

quivalent area �′ particle radius, r; and the area fractions of the′ phase at grain boundaries, φ. The parameter φ is defined asBP/AP, where ABP is the total area of the �′ particles in con-

act with grain boundaries on a 2D cross section while AP ishe total area of all the �′ particles on the same cross-section.hus φ will adopt values between 1 (all �′ particles in contactith � grain boundaries) and 0 (no contact between particles

nd boundaries). For comparison, the value of φ for a randomistribution of �′ particles, φR, is also given in this table. Valuesf φR were obtained using Doherty’s estimate [14]. Assumingpherical grains of radius R and spherical particles of radius r,he area of grain boundaries per unit volume, SV, is equal to/2R. Any particle whose center is within 2r of the grain bound-ry will be in contact with the grain boundary. Thus, the fractionf particles on the grain boundaries, φR, can be written as

R = 2rSV = 3r

R(1)

The values of φ and φR are plotted against the volume fractionf the �′ phase, f, in Fig. 8. It can be seen that for f < 15% both

and φR increase with f, but that φ is always larger than φR

s expected. For f > 15%, however, the trends are less clear andndeed for f = 17.4% and 23.1% (whose standard deviations are.6% and 1.8%, respectively), φR > φ, which presumably results

us temperatures, T, for 300 min

1121 1126 1129 1132 1135 11385.8 6.4 9.0 11.8 15.7 18.74.4 4.8 6.8 8.9 11.8 14.07.5 5.8 3.2 1.7 1.1 0.51.0 0.8 0.6 0.6 0.3 0.30.67 0.64 0.68 0.76 0.76 0.770.60 0.66 0.75 0.72 0.65 0.560.46 0.40 0.3 0.26 0.19 0.16

tion of the �′ phase, f; standard deviation for f, σ; mean equivalent radius ofetical values of φ for randomly distributed particles, φR, are also included for

370 K. Song, M. Aindow / Materials Science and Engineering A 479 (2008) 365–372

Fig. 8. Variation of the area fraction of the second-phase particles at the grainb ′ ′to

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oundaries with � volume fraction, f: φ—experimental results for the � phase inhe sub-solvus Matrix alloy; φR—theoretical estimate for a random distributionf particles.

rom the use of inappropriate assumptions such as a sphericalorphology for the grains and particles. These data confirm the

nitial impression given by the SEM images that the �′ phaseends to be located preferentially at the grain boundaries for allf the specimens. This tendency is more apparent for small f,here the value of φ is several times larger than that of φR.his is also in broad agreement with previous reports by Liund Patterson [2] and Gao et al. [15].

The relationship between the limiting grain size and the par-icle dispersion has been studied extensively by many differentroups over the last five decades [1–6,14–20]. The majority ofhese investigators have shown that DLim can be expressed as3–6,16–20]

Lim = Cr

fn(2)

here r and f are the size and volume fraction of the second-hase particle, respectively, and C and n are constants whosealues differ from one model to another. Eq. (2) is valid for aaterial that contains a uni-modal distribution of second-phase

articles; for the alloy considered in this study, however, bothhe �′ phase and the inert precipitates contribute to pinning the �rain boundaries. Thus, it is necessary to adapt Eq. (2) to accountor the combined pinning effect. The procedure is as follows. Theverall pinning force can be assumed to be the sum of the pinningorces from each type of particles [4,17]. Considering the facthat the inert particles are rather stable for the sub-solvus heat-reatments, it is reasonable to assume that the pinning force fromhese particles will correspond to a constant in the expressionor the total pinning force. Thus the overall pinning force, PZ,an be written as

Z =∑

Pi = C1γSfn

r+ kγS (3)

In the above equation, γS is the � grain boundary energy,hereas C1γSfn/r and kγS represent the pinning forces exertedy the �′ phase and by the inert particles, respectively. Theriving force for normal grain growth, PD, is generally given

mpsd

ub-solvus heat-treatment temperatures. The line corresponds to Eq. (6), whichs the best-fit linear relationship obtained when the data points corresponding to> 15% are excluded.

y

D = C2γS

D(4)

here D is the mean grain size and C2 is a constant whosealue depends on the relationship between the grain size andhe boundary curvature. Normal grain growth stagnates whenD = PZ, and D = DLim, which yields:

1

DLim= C3f

n

r+ C4 (5)

here C3 = C1/C2 and C4 = k/C2. By using the least squaresethod with the data in Table 1, and assuming that I = DLim for

= 300 min, the best straight line fit between 1/DLim and fn/r wasbtained as

1

DLim= 0.45 f 0.56

r+ 1

51(6)

A plot of 1/DLim against f0.56/r is shown in Fig. 9. Theata show a clear linear relationship except for the speci-ens with f > 15%, where I is fairly constant at 3.7–3.8 �m

1/DLim ≈ 0.27 �m−1). Since the � grain size does not dependn the �′ dispersion for these latter specimens, these microstruc-ures are presumably over-pinned such that any further increasen f does not give a corresponding decrease in I. If the dataoints for the two specimens with the highest f (i.e. T = 1087 ◦Cnd 1093 ◦C) are ignored, then regression analysis gives an R-quared value of 0.96 for Eq. (6). The value of 0.56 obtained forhe �′ phase volume fraction exponent in this analysis is muchloser to estimates in the literature for microstructures in whichll the particles are in contact with grain boundaries (n ≈ 0.515,18]) than those for random particle-boundary intersectionn = 0.87–1.00 [16,17]). This is consistent with our measure-

′

ents of φ, which show that the � phase tends to be locatedreferentially at the grain boundaries. A more detailed analy-is of the degree of contact and its effect upon microstructuralevelopment will be presented elsewhere [21].

K. Song, M. Aindow / Materials Science and Engineering A 479 (2008) 365–372 371

Fig. 10. Grain boundary pinning by inert precipitates: (a) SE SEM micrographshowing examples of � grain boundaries pinned by MC particles in a samplehas

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eat-treated for 30 min at 1152 ◦C; (b) BF TEM micrograph of a replica fromsample heat-treated for 30 min at 1177 ◦C showing a small � grain pinned by

everal particles.

.3. Effect of the inert precipitates on grain growth

As shown in Section 3.1, the inert precipitates observed inhe alloy after heat-treatment are MC-type carbides and yttriumxides. In the analysis presented in Section 3.2 it was shownhat these particles play only a minor role in pinning the �rain boundaries in the sub-solvus samples. For the super-solvusamples, however, there is no �′ phase present and the inert pre-ipitates are the only pinning particles in the microstructure.xamples of pinning events in super-solvus samples are pre-ented in Fig. 10. The SEM image in Fig. 10a was obtainedrom a sample heat-treated at 1152 ◦C for 30 min. The largerarticles in this figure are Ti-rich MC carbides and the finer onesre Y2O3. Two of the boundaries in Fig. 10a are pinned by MCarticles as indicated by the arrows. The BF TEM image pre-ented in Fig. 10b was obtained from a hybrid replica of a sampleeat-treated at 1177 ◦C for 30 min. The image shows MC and2O3 particles decorating the trace of a small � grain: the diam-

ter of this grain is only ≈2 �m, whereas the mean grain size is

23 �m, and so one would expect this grain to have been elim-

nated from the microstructure were it not for the pinning effectf the inert particles. The mean sizes of the MC and Y2O3 parti-les were measured from BF TEM images obtained from hybrid

ictp

ig. 11. Variation of the limiting grain size, DLim, and the sizes, r, of the MCnd Y2O3 particles with super-solvus heat-treatment temperature, T, for sampleseld for 300 min.

eplicas for each of the super-solvus samples with t = 300 min:hese values are plotted against T in Fig. 11, together with the

ean linear intercept values for the � grain size. Because theolume fractions of these inert particles are low (<1%) it is dif-cult to measure them accurately and reproducibly. If, however,ne assumes that the solubility of C in the � and �′ phases isegligible, so that all of the C in the alloy is present in the formf MC carbides, then the volume fraction of the carbides woulde approximately 0.65%. Similarly, if all of the Y in the alloyas oxidized selectively to Y2O3 then the volume fraction of

he oxides would be 0.09%. These values are broadly consis-ent with the estimates from the SEM and TEM images of theuper-solvus microstructures.

It has been shown in Fig. 6 that the super-solvus samplesxhibit similar limiting grain sizes over a wide range of heat-reatment temperatures and that further significant coarseningoes not occur until 1270 ◦C. This is presumably because thenert precipitates exert a stable pinning force on the grain bound-ries. As shown in Fig. 11, the increase in the limiting grain sizet the highest temperatures occurs concurrently with increasef the particle size, particularly for the MC-type carbides: thiss what one would expect for Zener pinning, in which the lim-ting grain size is proportional to the particle size, see Eq. (2).his relationship between super-solvus grain growth and coars-ning of the MC carbides can be seen more clearly in Fig. 12and b, which are plots of mean grain size and MC particle sizegainst holding time for the samples heat-treated at 1177 ◦C and270 ◦C, respectively. In both cases the grain growth data followhe MC particle sizes closely. The only exception to this is theata for t = 2 min at each temperature. These latter data proba-ly correspond to the short initial transient period over whichhe super-solvus microstructure is established: the developmentf such microstructures involves the dissolution of the �′ and

3B2 phases, and the transformation of M23C6 carbides to theC structure.It is important to note that while the increase in the limit-

ng grain size and the coarsening of the MC particles occurs

oncurrently, the extent of the particle coarsening is not enougho account for all of the increase in the grain size. For exam-le, in the samples held at 1152 ◦C and 1270 ◦C for 300 min the

372 K. Song, M. Aindow / Materials Science and

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ig. 12. Variation of the grain size, I, and the carbide size, r, with holding time,, for heat-treatments performed at: (a) 1177 ◦C and (b) 1270 ◦C.

alues of the mean � grain size (I) are 22.8 �m and 33.2 �m,espectively, whereas the mean MC particle sizes are 0.27 �mnd 0.33 �m, respectively. This represents a 45% increase inrain size and a 22% increase in particle size. According to Eq.2), the grain size should scale linearly with the particle size at aonstant volume fraction of the pinning phase. The most likelyxplanation for the discrepancy is that the MC particles undergoartial dissolution at 1270 ◦C, which further decreases the totalinning force, but this has not yet been verified experimentally.

. Conclusions

The microstructures exhibited by a model Ni-based super-lloy in the as-received condition and after a series ofeat-treatments at different times and temperatures have beentudied using SEM and TEM techniques and the following pointsave been established:

1) The initial microstructure consists of � grains, a com-plex distribution of grains/precipitates of the �′ phase, andfour types of inert particles: M3B2-type borides, MC- andM23C6-type carbides, and Y2O3. The M3B2 and M23C6 par-ticles were eliminated during the heat treatments, as wasthe �′ phase for the super-solvus samples. The �′ phase wasretained at a lower volume fraction in the sub-solvus samples

with only the larger recrystallized particles being present.

2) Significant grain growth stagnation was observed for bothsub-solvus and super-solvus heat-treatments. The grain sizeincreases remarkably with temperature for the sub-solvus

[[[[[

Engineering A 479 (2008) 365–372

heat-treatments, but remains similar for most of super-solvus heat-treatments until around 1270 ◦C. The graingrowth stagnation is closely related to the pinning effectof the second-phase particles.

3) The �′ particles are located preferentially along the grainboundaries in the sub-solvus samples. This tendencybecomes more pronounced for the samples heat-treatedclose to the solvus temperature (1143 ◦C), which containsmall volume fractions of the �′ phase. The �′ particles playthe major role in inhibiting the grain growth in the sub-solvus specimens. The final grain size DLim is a function ofthe �′ phase volume fraction, f, and size, r, and is given as

1

DLim= 0.45 f 0.56

r+ 1

51

The latter term in this expression is due to the effects of theMC-type carbides and Y2O3 particles.

4) The MC-type carbides and Y2O3 particles are the onlypinning particles in the super-solvus samples. The stabil-ity of these particles leads to a value for DLim, which isconstant over almost the whole temperature range consid-ered. For samples heat-treated at 1270 ◦C, however, DLimincreases due to coarsening and dissolution of the MCparticles.

cknowledgements

This work was supported by DARPA/USAF under contracto. F33615-00-2-5216 with Dr. R. Dutton as technical monitor.he authors would like to thank Dr. Mike Savage of Pratt andhitney for providing the alloys used in this investigation.

eferences

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