y’ FORMATION IN A NICKEL-BASE DISK SUPERALLOY
Timothy P. Gabb*, Daniel G. Backman**, Daniel Y. Wei**, David P. Mourer **, David Furrer***, Anita Garg*, and David L. Ellis****
*NASA Glenn ResearchCenter
**General Electric Aircraft Engines
***Ladish Co., Inc.
****Case WesternReserveUniversity
Abstract
advanceddisk superalloy. The model describesand predicts the
nucleation, growth, and coarseningof y’ precipitates during the
heat treatmentprocess. However, it was designedto be simple
and streamlined,in order to speedup calculations and facilitate
linkage to finite elementthermal and structural codes.
Standardizedexperimental methodswere employed to calibrate
and initially validate the microstructure model. The model was
then further validated using an oil quencheddisk. y’ precipitate
morphologies were extensively quantified as functions of
thermal histories and comparedto model predictions. Model
calibration and validation efforts describedhere were focussed
on the primary cooling y’ precipitates,which form during the
first (primary) burst of nucleation during the solution quench.
A streamlined,physics-basedkinetic model was formulated,
calibrated, and validated on a nickel-base superalloy. It was
designedto be simplified and streamlined,to speedup
calculations and facilitate linkage to finite elementmodeling
thermal codes. The model describesand predicts the formation
of y’ precipitates during the heat treatmentprocess.
Standardizedexperimental methodswere employed to calibrate
and initially validate the microstructure model. The model was
then validated on an oil-quenched generic disk. Predictions of
primary cooling y’ size and areafraction agreedwell with
experimental measurementsover a large range of values and
cooling rates.
Model Formulation
Introduction
During the quench of a nickel-base superalloy from solution
temperatures,supersaturationof y’ phasesolutesbuilds up in the
y phase. When the supersaturationbuilds up to a sufficient
degree,a burst of nucleation of new y’ precipitates occurs. This
greatly reducesthe supersaturationof y’ solutes. Both the new
and prior precipitates continually grow by interface-diffusion
controlled growth. The precipitates also undergo coarsening,
where smaller precipitates dissolve to provide solute for larger
precipitatesto grow. A precipitation model of the y’ phasein
nickel-basesuperalloys had been previously developedby
General Electric Aircraft Engines (6) using classical nucleation
and diffusion controlled growth. That model encompassesthe
full consideration of thermodynamic excessfree energy,
supersaturationbuildup, nucleation, growth and coarsening. In
contrast,the presentwork was focused on a precipitation model
that is fast-acting such that it can be integrated with finite
elementmodel thermal analyses. However, this precipitation
model must still encompassthe entire precipitate physics
including supersaturationbuildup, nucleation, growth and
coarsening,to ensurethe streamlined model is capableof
predicting the y’ structure under the full spectrumof heat
treatmentconditions.
Many mechanical properties of nickel-base superalloys are
strongly influenced by the morphology of the strengtheningy’
precipitates (I,2 ). Both the sizes and areafractions of different
populations of precipitates are influential and therefore needto
be quantified and modeled. These microstructural
characteristics are strongly affected by the heat treatmentsa
componentundergoes(3-5). Previous work has often modeled
precipitate size through heat treatmentsusing cubic coarsening
equations(5). For physically accuratetreatments,it is necessary
to describethe kinetics of nucleation and subsequentgrowth and
coarseningof y’ precipitates as theseprocessesoccur within a
given heat treatment. This requires tracking multiple
populations of precipitates through heat treatmentscontaining
multiple steps.
The NASA-industry Integrated Design and ProcessAnalysis
Technologies (IDPAT) program had the objective of developing
computational tools that could be applied togetherto improve
the product and processdevelopmentcycle for aircraft engine
components. It was recognized that this required a “fast-acting”
y’ precipitation model for superalloy components,which could
rapidly perform the necessarycomputationswhile integrated
with material processingand mechanical property models. This
would enable prediction of y’ precipitate microstructure and
resulting mechanical properties from the processing. This paper
describesthe work performed in developmentof this fast-acting
y’ precipitation model.
The fast-acting y’ precipitation model has two basic
requirements:i) to generatehigh-fidelity predictions and provide
explanations for subtle but important relationships betweeny’
size distribution and the heat treat schedule,and ii) to provide a
computationally efficient algorithm that can be easily matedto
FEM thermal codeswithout burdening the overall computational
effort.
The objective of this work was to model y’ precipitation for the
caseof a powder metallurgy disk superalloy. A physics-based
kinetic model was formulated, calibrated, and validated on an
405
Superalloys2ooo
Fdk-d by T.M. Pollock, R.D. Kissinger,R.R. Bowman,
K.A. Gmn, M. McLean, S. Olson, aadJ.J.Schima
TMs CrheMinerals, Metals
&Materials Society), 2000
Each of the model’s elementsis elucidated in the following:
The fast-acting precipitation model includes the following
elementsto meettheserequirements:
A pseudo-binary solvus formulation that describesthe
a
solvus curve for the y’ formers.
b.
A kinetic model that predicts the minimum size of nuclei
as a function of supersaturation. This model employs a
simple kinetic criterion to determinethe onsetof
nucleation in lieu of a sophisticatedthermodynamic model
to computethe free energy and strain energy for
nucleation.
Classical nucleation expressionsthat predict nucleation
C.
rate as a function of supersaturationand time.
A precipitate growth relationship basedon an asymptotic
d.
solution that accountsfor diffusive transport driven by the
interfacial concentration gradient. These gradientsform
becauseof the concentration difference betweenthe
supersaturatedmatrix and the precipitate.
Particle coarseningrelationships that predict changesin
e.
the averageparticle size of a size distribution basedon the
functional dependencyof particle solubility upon particle
radius.
a. Equilibrium y’ solvus
The solvus line in a binary systemof limited terminal solubility
can be expressedby the following equation (7)
where:
The lever rule can be statedas:
c,=
These elementswere integrated into a computer codethat
numerically integratesthe effect of theserelationships as a
function of time and tracks mean size as shown in Figure 1 in
contrastto a conventional approach. For eachtime step,the
calculation startsby invoking maSsconservation to calculate the
supersaturation. If sufficient supersaturationis present,
nucleation of new y’ precipitates occurs, and theseprecipitates
are addedto the size distribution. Precipitatesare allowed to
grow, driven by interface diffusion basedon the level of
supersaturation. Coarsening is then allowed to modify the
existing particle size distribution through mean size and y’
volume conservation. This mechanismallows someprecipitates
to dissolve, removing them from the distribution.
INPUT
uclei Size
Empirical Coarsening Constant
Cooling Curve
MODEL
4
Cubic Coarsening
Law
4
Free Energy +
OUTPUT
Pre;ti cts:
- Mean y’ Size
(2)
Y.-l
c 0 (I-exp(-@&,,
v,. =
R T
Lw
(3)
c 7’-c 0q&l-1,)
R T I;nhur
The y’ composition was consideredindependentof temperature.
Therefore, a seriesof measurementsof equilibrium 7’ volume
fraction at temperaturesup to the y’ solvus was usedto correlate
the constantQ and approximatethe solvus line of y’ formation
C, as a function of temperature.
b.-c. Nucleation
The classical solid statehomogenousnucleation theory (8-12)
defines the free energy AG* required for a spherical nucleus as:
1
I
-c
Mass Conservation ~1
+
v,.c; -c,
where V, is they’ volume fraction. Equation (1) can be restated
Ci.5:
Current
Approach
+
Allov Comuosition
Physical Properties
Cooling Curve
Conventional
Approach
(1)
CY=C 0exp(-e(L’
R T iii’
C, = y solubility
Co= initial composition of y’ former (e.g., Al + Ti +
Ta)
Q = excessfree energy per mole of y’ former in y
solution
R = gas constant
Tsolvus
= solvus temperature
(4)
4
Transient
Nucleation
AG, = volume free energy
AG, = induced strain energy in the precipitates
CJ = precipitate/matrix interfacial energy
where:
i+
Diffusion Driven
Growth
I
Coartening
4
Predicts:
- Mean y’ Sizes
- y’ Volume Fractions
- y’ Number Densities
For the casewhere AG,, AG,, and o are independentof radius,
the critical radius r* of nuclei can be expressedas:
I
I
20
‘*=(AG,+AG,)
I
(5)
I
In the fast acting model, this time-intensive thermodynamic
calculation was avoided. The critical size r* of surviving y’
Fig. 1. Flowchart of model approachcomparedto a
conventional approach.
406
nuclei was defined to satisfy the following stability criterion
employing an adjustablenucleation scaling factor S:
The number of nuclei AN, at time interval At and available
volume V(t) is then:
AN,,=f
2ov
s
r* =m
RT ln(CY</C,)
I
Once a precipitate nucleates,its rate of growth in a
supersaturatedmatrix is determinedby [13-171:
dr
z=
t)
D V2C= E/c%
c,v-c,,v,,v,
cs@)
= (V-v,q,>
(13)
(14)
at any instant, where C, (t) is the solute composition in the
matrix, V is the total volume consideredin the simulation, q is
the solute composition in the precipitates,V.,+is the total volume
of precipitatesat any instant, Vr is molar volume ratio between
matrix and precipitate, and Co is the total solute composition in
the alloy.
The solute concentration C!.),at the r/y’ interface for a precipitate
with radius r can be determinedusing the equation:
(8)
20 v
CyIyIIo=C, exp(*)
where h = a& is the atomic spacing, D the diffusion coefficient
of the rate limiting speciesin the matrix, and r* was determined
before. The Zeldovich factor was calculated using:
Z=[AG*/(3nkT)l”2
(12)
Now total solute massconservationrequires:
(7)
in which N is the density of active nucleation sites per unit
volume, Z is the Zeldovich non-equilibrium factor which
correctsthe equilibrium concentration of critical nuclei for the
loss of nuclei to growth and thus to the concentrationpresentat
steadystate, S* is the rate of atomic attachmentto the critical
nuclei, AG* is the activation energy for the formation of a
critical nucleus as defined above,k and T have their usual
meaning, and ‘c is the incubation time to form embryosbefore
nucleation. However, to keep the entire calculation manageable
in the fast-acting model, the latter incubation effect was instead
related to r*. For an f.c.c. or LIZ lattice, the frequency factor
S* was defined as:
/3* = (C, D /n4) 4 zY2
(C,, - Crlrrr )
where the varying concentration field in the matrix is
determinedby solving the diffusion equation with abovemoving
boundary:
Formally, the isothermal nucleation rate J* is given by
nucleation theory as (11):
exp(-AG* I kT)exp(-rl
(11)
d. Growth
where C, is the saturatedsolute concentration in the y matrix, Ce
is the equilibrium solute concentration in they matrix and V,,,=
a3/4 is the averageatomic volume in the y’ precipitate using a,
the lattice parameter. The interfacial energy cr and nucleation
scaling factor S in equation 6 are determinedthrough iterative
estimation of these constants,followed by comparisonto
measurementsfrom calibration heat treatments. For eachtime
stepin the precipitation model algorithm, r* is first calculated
using equation 6. r* is then used in equation 5 to obtain
(AG”+AG,). AG* is then obtained from equation 4.
J*=NZ$
AtV(5)
(6)
(15)
where R is the gas constantand Vm is precipitate molar volume
per atomic site.
(9)
The interface kinetics are likely to be rate limiting during the
very early stageof growth, since the diffusion distancetends to
be negligible. However, diffusion is likely to becomedominant,
asthe precipitatesgrow larger. For the growth of spherical
precipitates,an invariant size approximation solution can be
statedas:
where AG* was determinedas previously describedfrom
equation 4. A volume-related time dependentnucleation rate
was derived, given that as nucleation proceeds,a portion of the
volume will have been transformedinto y’ precipitates. Within
this volume and its neighborhood further nucleation is not
possible. Therefore, it was assumedthat the stationary
nucleation rate can proceedonly in the remaining (non-depleted)
volume, using the expression:
V(t)=V,-~4/3an,(r,+Br,)3
i=I
where h is a non-dimensional parameterrelated to growth rate
and Q is a saturation index factor. The saturation index factor R
where V0 is the total volume considered,k is the number of
nucleation bursts, and V(t) the remaining non-depletedvolume.
407
describesthe level of supersaturationof y’ formers in the matrix,
driving both nucleation and growth:
determinethe equilibrium areafraction of y’ as a function of
temperature,in order to calibrate the solvus formulation. Other
small specimenswere supersolvussolution heat treated, cooled
to temperaturesbelow the solvus for short dwells of up to 20
minutes, and then rapid quenchedin water to determinethe
kinetics of y’ formation near the solvus, for the kinetic model.
Theserapid quencheswere accomplishedvia a drop quench
furnace, where a specimenwas directly droppedfrom the hot
zone of the furnace into a chamberof water for a transfer time of
lessthan 1 second. StandardizedJominy bar end quench tests
and sampling techniqueswere adaptedto establish a uniform
and reliable test for the kinetics of y’ formation in rapid
quenching conditions. One end of thermocoupledbars 25.4 mm
in diameterand 63 mm in length was quenchedwith water.
Sectionsof the bars were extractedusing precision numerical
controlled electro-dischargemachining and preparedfrom three
locations selectedto spanthe range of cooling rates expectedin
oil quencheddisks. Other small specimenswith attached
thermocoupleswere cooled in a programmedfurnace to assess
slower cooling ratesthan that achieved in the Jominy bars.
2(C, -G)
sz=(C/-C,)
(17)
The resulting growth rate relationship is then defined as:
I Ar = 2 h (D At)“’
where D is estimatedas describedbefore, R and h are
determinedthrough equations 16 and 17.
e. Coarsening
Particle coarseningis driven by the higher solubility of small
particles, which tend to dissolve as solute diffuses to larger
particles. The driving potential is provided by the reduction of
total interfacial energy while conserving the total volume
fraction of precipitates. From coarseningtheory (18-23), the
general form of precipitate coarseningcan be written as:
I
I
dr
2DC, oV,
dt=RTr(C,,,
-C,)
(&i)(l+6r)
r r
The model was further validated on a generic disk via measuring
gammaprime sizes at specific locations where cooling rates
were measuredby thermocouples. Disks were subsolvus
solution heat treated at 1149W2h, and then quenchedin oil.
Thermocoupleswere embeddedwithin one disk to gather
accuratetemperature-timedata at selecteddisk locations during
the oil quenching process. Another disk was then heat treatedin
the sameprocesswith no thermocouplesattached.
Microstructural specimenswere excised from bore and rim
locations of the seconddisk.
(19)
where C, is the equilibrium solute content, and b is correction
factor for the casewhere volume fraction of precipitatesis high
(19,20). The correction factor b tendsto broadenthe precipitate
size distribution, which is not tracked by the current mean size
approximation. So this correction factor was neglectedduring
the coarseningcalculation. All other terms in this equation had
previously been estimated.
Specimensevaluatedin the SEM were first metallographically
polished and then electrolytically etchedto leach away the y
matrix to exposey’ particles. Specimensevaluated in the TEM
were electrochemically thinned. At leasttwo TEM foils were
examinedfrom each selectedspecimen. Multiple weak beam
dark field imageswere consistently taken from near the [OOl]
zone axis, selecting grains which required tilting of less than
30”. Precipitate size measurementsincluded major and minor
axis widths, equivalent circle (feret) diameter, and several shape
parameters.Size-frequencyhistogramswere then generatedfor
primary cooling and tertiary y’ precipitates. Over 100
precipitateswere measuredto estimateeach distribution.
Precipitateswere then grouped into 3 classesfor areafraction
measurementsby point counting: remnanty’ particles > 1.0 pm
in diameterthat were not solutioned during subsolvus solution
heat treatments,cooling y’ precipitatesbetween 0.05 and 1.0 pm,
and tertiary y’ precipitates less than 0.05 urn in diameter.
Summarizing, these elementsand associatedequationswere
integrated into a computer codethat numerically integratesthe
effect of theserelationships as a function of time and tracks
meansize as shown in Figure 1. For eachtime step,the
calculation startsby invoking massconservation (eq. 14) to
calculate the supersaturation. Nucleated particles (eq. 6) are
then addedto the size distribution if sufficient driving force (eq.
4) is present. Precipitatesare allowed to grow basedon the level
of supersaturation(eq. 17) using the growth relationship (eq.
18). The coarseninglaw (eq. 19) is finally applied to modify
the existing particle size distribution through mean size and y’
volume conservation. This did allow small precipitatesto
dissolve, removing them from the distribution.
Results and Discussion
Experimental Procedure
Model Calibration
The powder metallurgy nickel-base disk superalloy CH98 (24)
was selectedfor evaluation. This alloy has a nominal
composition in weight percent of 4A1-0.03B-0.03C-18Co-l2Cr4Mo-3.8Ta-4Ti-O.O3Zr-bal.Ni. Alloy powder was atomized,
then hot compacted,extruded, and isothermally forged. A
variety of heat treatment experimentswere first performedon
the alloy to help formulate, calibrate, and initially validate the y’
model. Small cube specimenswere heatedto a variety of
temperaturesand soakedfor a sufficient period of time to
After formulation, the model had to be initially calibrated with
heat treatmentexperiments. Equilibrium y matrix solubility was
determinedaspart of the kinetic model calibration. Specifically,
the solubility curve for the y/y’ pseudobinary systemwas
correlatedagainstvalues of y’ volume fraction measuredat
severaltemperaturesup to the solvus temperature. This
solubility relationship was usedto model y’ solubility for
temperaturesthat ranged from the solvus temperaturedown to
408
Model calibration and validation efforts were focused on the
primary (larger) cooling y’ sizes. The model’s cooling rate
responsewas calibrated using cooling curve and microstructural
measurementsfrom a programmedfurnace cooling experiment
run at a cooling rate of 1.l”C/s. A seriesof size estimatesat
intermediatetimes during the quench were also generatedby
both the fast-acting and full thermodynamic model (6) after
initial calibrations. This was performed to model the thermal
path dependenceof they’ microstructure. A non-linear
regressionanalysis was then conductedto obtain the values of
the four kinetic parametersin the fast-acting model that gave the
best data fit and most reasonablepredictions of intermediate
sizes.
870 OC. The empirically derived solubility curves were then
usedto compute the solute supersaturationlevels in they matrix.
These experiments indicated a y’ solvus of approximately a
12OO’Cfor CH98.
The objective of the rapid quench coupon testswas to determine
the time to onset and resulting fraction of y’ precipitation within
the temperaturerange between the alloy solvus temperatureand
80 ‘C below the solvus. All sampleswater quenchedin these
testshad a ‘cbackground))quantity of y’ precipitates lessthan
0.015 pm in size. These were presenteven in specimens
directly water quenchedin lessthan 1 sec. This indicated that
nucleation could not be fully suppressedhere in this alloy.
Samplesquenchedbefore nucleation took place in the nearsolvus dwell periods exhibited no coarsey’, whereassamples
quenchedfollowing nucleation near the solvus had coarse
primary y’. Coarsey’ precipitateswere observedafter 1200s
dwells at 1160°Cor lower temperatures,and after 180 s dwells
at 1150“C or lower. The morphology of y’ precipitatesformed
near thesetemperatureshad a roughly cuboidal morphology,
with somedendritic growth of the cube comers. Precipitates
agedat lower temperatureexhibited a more cuboidal
morphology. These observationsare consistentwith y’
morphological transitions reportedin the literature (13). The
results of these experimentswere then mappedon to a y’ timetemperature-transformationdiagram shown in Figure 2 for
CH98. These observationsare essentialto calibrate the
nucleation portion of the kinetic model.
0.1
0.09
0.08
c 0.07
3 0.06
i 0.05
.g 0.04
j 0.03
Wull
Therm0Model
,I,.
The fast acting model contains four additional adjustablekinetic
parametersthat also required calibration:
the nucleation scaling factor S which is assumedto be
9
temperatureindependent,
ii)
the value of the y/y’ interfacial energy cr.
iii)
the diffusion activation energy Q of y’ former%
iv)
the diffusivity D for the y’ formers.
1220
1
c
800
900
1000
1100
1200
Temperature(C)
Fig. 3. Saturation levels predicted using the models.
1 -Model
Curve
-Solvus
-m-m--
1160
800
900
1000
1100
1200
Temperature (C)
1140
1
10
100
1000
10000
Fig. 4. Primary cooling y’ size predicted by the models.
Time (set)
Fig. 2. Time-temperature-transformationdata and model curve
near the y’ solvus temperature,open symbols indicate no coarse
y’was present,solid symbols indicate the presenceof coarsey’.
409
Figures 3 and 4 show the calibration results, comparing fast
acting model and full scalethermodynamic predictions for
CH98. Figure 3 shows good agreementof predicted
supersaturationlevels, as indicated by the saturation index Sz,
during quench for the full scaleand fast acting models. As can
be clearly observed,the fast-acting model is capableof tracking
the balancebetweennucleation and growth in accordancewith
the predictions of the full scalemodel for the primary burst of
cooling y’ nucleation. There is room for further improvements
in predictions of subsequentbursts of precipitate nucleation.
However, predictive capability for the subsequentprecipitation
bursts was not a prime goal for the fast acting model. Figure 4
comparesthe primary cooling y’ sizes generatedby the two
models. Excellent agreementwas achievedbetweenthe
experimental measurements,the fast acting model predictions,
and full scalemodel calculations. The full scalemodel has
previously been demonstratedto provide good agreementwith
experimental observationson other alloys.
r
l
0
.
0
mw -Disk
0
200
CalibrationRun
Slow Cool
JominyBar (1.9cm)
JominyBar (5.7cm)
Disk (Bore)
(Rim Edge)
400
600
Time (set)
800
1000
Fig 5: Comparisonof representativecooling curves from heat
treatments.
Model Validation
of primary cooling y’ at bore, web, and several rim locations are
comparedin Fig. 10 - 11. The model predicted the trend of the
measurements,but predicted consistently lower sizes for these
cases. This may be due to the lack of any calibration
experimentsfor aging effects.
The model was initially validated using controlled cools of other
small specimensand standardizedJominy bar end-quenchtests.
Cooling curves from the various validation experimentsare
comparedin Fig. 5. The Jominy end quench testswere usedto
initially validate the model for fast cooling conditions in CH98.
A slow programmedfurnace cooling heat treatmentwas used to
validate the model for slow cooling paths. They’ distributions
produced in the Jominy bar at distancesof 1.9cmand 5.7cm
after water quenching from supersolvussolutioning are
comparedto the slow furnace cooling casein Fig. 6.
Histograms illustrating the primary cooling y’ size distributions
for thesecasesare also shown. The size distributions were
considerednormally distributed and a normal curve fit is shown.
The mean size of the primary cooling y’ slightly increasedwith
decreasingcooling rate, while the areafraction remained
comparable. Excellent agreementwas obtained between
predicted and experimentally measuredmean sizes of the
primary cooling y’ particles for thesecases.
Due to the promising results with the supersolvussolution heat
treatmentquench tests,subsolvus Jominy testswere also
performed. The precipitate distributions developedin the
Jominy bar after water quenching from subsolvus solutioning
conditions are comparedin Fig. 7. The subsolvus cases
producedmuch smaller primary cooling y’ sizes, aspredicted by
the model. Model predictions of precipitate sizes again agreed
well with observedresults.
Comparisonsof measuredand predicted primary cooling y’
precipitate sizes and areafractions for various validation
experimentsare shown in Fig. 10 and 11. The model gave good
predictions of primary cooling y’ size for the heat treat coupons,
jominy bar, and generic disks, over a very broad range of
precipitate sizes. The model’s predictions of areafractions of
primary cooling y’ were also reasonable,but showed room for
further improvements.
Differences betweenpredicted and measuredy’ sizes and
quantities can be attributed to model inaccuraciesas well as
measurementdifficulties. As can be seenin they’ imagesof
Fig. 4-6, several groupsy’ precipitates having different sizes and
morphologies can be presentin the samemicrostructure, as
predicted by the model. Also, tips and comersof the somewhat
rectangular precipitatescan be sectionedin a metallographic
section or TEM foil. This effect is most notable for slow cooled
primary cooling y’, where the cube corners show enhanced
growth (19). The size vs. frequency distribution of all these
precipitateswas combined together for measurements.
However, the size distributions of eachof thesegroups
sometimescould not be separatedor deconvoluted in the
combined measurements.Objective experimental analyseswere
capableof grouping precipitates into 3 classesfor size and area
fraction measurements:remnant y’ particles that were not
dissolved during subsolvus solution heat treatmentswhich were
greaterthan 1.Opm in diameter,cooling y’ precipitatesbetween
0.05 and 1.0 pm, and tertiary y’ precipitates less than 0.05 pm in
diameter. Attempts to subdivide and measurerelative quantities
and areafractions of each of several groups of cooling y’
A CH98 disk of generic shapeshown in Fig. 8 was then
subsolvus solution treatedand oil-quenched for further model
validation. Thermocouple temperatureversus time data
collected during the disk oil quenching from the bore, web, and
rim locations indicated the bore location clearly cooled slower
than the web and rim, which had similar cooling responses.The
temperature-timeresponseswere employed for model
predictions at several locations. Typical SEM imagesof bore
and rim edgemicrostructuresfrom an as-quencheddisk are
comparedin Fig 9. Predicted and measuredsizes of primary
cooling y’ at the bore hole, bore, and rim edge locations agreed
well, as shown in the comparisonsof Fig. 10.
Another disk was oil quenchedand then aged760W16h.
Typical microstructuresfrom the bore, mid rim, and rim edgeof
this disk are comparedin Fig. 9. Predicted and measuredsizes
410
Predicted
20
18
16
4
2
J
0
0
100
200
300
400
500
600
700
800
600
700
800
Feret Diameter (nm)
Predicted
0
100
200
300
400
500
Feret Diameter (nm)
Predicted
I
18
16
*Predicted by
Model
Gaussian Fit
0
100
200
300
400
In
CMeasurements
R
500
Feret Diameter (nm)
Fig. 6: Comparison of f microstructures and size histograms
after supersolvus heat treatments: (a) Jominy bar 1.9cm and (b)
Jominy bar 5.7cm from the quenched end, (c) slow furnace cool.
411
600
700
4
800
Fig. 7. Comparison of the y’ microstructures in subsolvus
solution heat treated Jominy bars: (a) 1.9cm and (b) 5.7cm from
the water quenched end.
\I
.AnalyizdLocations
/
Fig. 8. Generic disk shape used for further model validation.
Fig. 9. y’ microstructures produced in oil quench and aged
generic disk: a) bore, b) mid rim, c) rim edge
412
300
0
precipitatesbetween0.05 and 1.Opm in size would require more
subjective selectionsamongprecipitates. Yet, the model was
capableof predicting the precipitation of several groups of
cooling f, through later bursts of nucleation and subsequent
growth during the quench. Two groups of cooling y’ were in
fact predicted for the caseof the disk rim edge. There were
possible indications of this in the associatedmicrographs and
histograms,but this could not be fully proven due to the above
mentioned limitations. However, the model would benefit from
further refinementsin predictions of the formation of theselater
groups of secondarycooling y’ precipitates.
500
PredictedY’ Size (nm)
The ability of this model to track both size and quantity of
multiple distributions of y’ particles can be very important in
fully relating microstructuresto mechanicalproperties in disk
superalloys. Inspection of Fig. 9- 12 indicates the mean size of
the primary cooling y’ precipitates did not decreaselinearly with
cooling rate as often expected. However, their areafraction
decreasedin the web and rim, allowing a larger areafraction of
tertiary y’ precipitates <O.O2ymin size. Mechanical testing
underway indicates these subtle changesproduce a significant
increasein tensile and creepproperties of the rim and web, over
the bore. Both primary cooling and tertiary y’ needto be
quantified for mechanical property modeling in such cases
Fig. 10. Comparison of predicted and measuredprimary
cooling y’ sizes.
80 ,
Further model refinements are contemplatedto refine area
fraction prediction capabilities and enhancesecondaryy’
prediction capabilities. Further calibration experiments are
planned to improve the thermal path modeling and include more
effects of multi-step stressrelief and aging heat treatmentsused
on many disk alloys. Integration trials have already successfully
linked this model to typical processingcodesfor processing
sensitivity studies. This allows prediction of microstructures
and mechanicalpropertiesresulting from processinginputs,
This enhancedprediction capability allows reducing the forging
design cycle time and expandsmodeling capabilities to improve
the product and processdevelopmentcycle for aircraft engine
components.
80
Predicted+rArea Fraction (%)
Fig. 11. Comparison of predicted and measuredprimary
cooling y’ areafractions.
600
(
n SupersolvusPredicted
Summaryand Conclusions
1.
2.
3.
4.
1.0
2.0
3.0
AverageCooling Rate(C/s)
4.0
Fig. 12. Comparisonof predicted and measuredprimary
cooling f as a function of averagecooling rate from solution
temperatureto 870°C.
413
A streamlinedphysics-basedmodel describing the
evolution of y’ precipitates during the heat treatment
processwas formulated.
The resultant calibrated model gave reasonablepredictions
of primary cooling y’ size over a very broad range of
conditions, agreeingwell with measurementsfrom
experimentsrun on coupons,Jominy bars, and a generic
disk.
Improvements in predictions of primary y’ areafraction and
secondarysizes and areafractions are planned in future
work.
The streamlinedy’ model was successfully linked with a
commercialheat treat code enabling prediction of y’ sizes
and areafractions acrossa componentin a computationally
efficient manner.
12. W. F. Lange, III. M. Enomoto, and H. I. Aaronson,
“Precipitate Nucleation Kinetics at Grain Boundaries”, &&
Mat. Rev., 34(3) (1989), 125-150.
Acknowledgements
This work was sunoortedbv the NASA IDPAT Program,
managedby Douglas Rohn-andJohn Gayda The authors also
wish to acknowledgethe work of Howard Merrick, Honeywell
Engines and Technologies (Allied-Signal Engine Co.) and
Timothy Howson, Wyman-Gordon Forgings Co.
I.
13. R. ‘A. Ricks, A. J. Porter and R. C. Ecob. “The Growth
of-r’ Precipitatesin Nickel-Base Superalloy”, Acta Met. ,
31 (1983), 43-53.
14. H. I. Aaronson, “Atomic Mechanisms of Diffosional
Nucleation and Growth and Comparisonswith Their
Counterpartsin ShearTransformations”, Met. Trans. A, 24
(1993), 241-276.
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