Herng-Jeng Jou

QuesTek Innovations LLC, Evanston, Illinois 

Microstructure Modeling of 

Third Generation Disk Alloys

Final Report

NASA/CR—2010-216748

July 2010
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Herng-Jeng Jou

QuesTek Innovations LLC, Evanston, Illinois 

Microstructure Modeling of 

Third Generation Disk Alloys

Final Report

NASA/CR—2010-216748

July 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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NASA/CR—2010-216748 iii 

Microstructure Modeling of Third Generation Disk Alloys 

Final Report 

Herng-Jeng Jou 

QuesTek Innovations LLC 

Evanston, Illinois 60201 

Executive Summary 

The objective of this program was to model, validate, and predict the precipitation microstructure 

evolution, using PrecipiCalc (QuesTek Innovations LLC) software, for 3rd generation Ni-based gas 

turbine disc superalloys during processing and service, with a set of logical and consistent experiments 

and characterizations. Furthermore, within this program, the originally research-oriented microstructure 

simulation tool was to be further improved and implemented to be a useful and user-friendly engineering 

tool. 

In this report, the key accomplishments achieved during the third year (2009) of the program are 

summarized. The activities of this year included: 

• Further development of multistep precipitation simulation framework for γ' microstructure 

evolution during heat treatment 

• Calibration and validation of γ' microstructure modeling with supersolvus heat treated LSHR 

• Modeling of the microstructure evolution of the minor phases, particularly carbides, during 

isothermal aging, representing the long term microstructure stability during thermal exposure 

• The implementation of software tools. 

During the research and development efforts to extend the precipitation microstructure modeling and 

prediction capability in this 3-year program, we identified a hurdle, related to slow γ′ coarsening rate, with 

no satisfactory scientific explanation currently available. It is desirable to raise this issue to the Ni-based 

superalloys research community, with hope that in future there will be a mechanistic understanding and 

physics-based treatment to overcome the hurdle. In the mean time, an empirical correction factor was 

developed in this modeling effort to capture the experimental observations. 

The established modeling capability and software tools at the end of this program represent state-ofthe-art precipitation modeling and simulation for Ni-based aeroturbine disk superalloys under complex 

industrial heat treatment. While model calibration/validation was mainly established with data of 

NASA’s LSHR alloy, the resulting models and tools provide a solid foundation to model other disk 

alloys. Currently, further application to Rolls-Royce’s RR1000 alloy is underway. We expect these 

models and tools, through use and testing by materials engineers, to be further improved in the future. By 

utilizing these tools, novel process and microstructure optimization can be virtually and effectively 

developed for the 3rd generation gas turbine disc alloys to enable accelerated material development. 

 
 
NASA/CR—2010-216748 v 

Contents 

Executive Summary ..................................................................................................................................... iii

Introduction ................................................................................................................................................... 1

Task 2—Development of Calibration and Validation Data .......................................................................... 2

Task 3—γ' Precipitation Modeling ............................................................................................................... 2

Interaction of Secondary and Tertiary γ' in Isothermal Aging ............................................................. 2

Multistep PrecipiCalc Simulation Framework for γ′ Precipitation ....................................................... 4

Calibration and Validation of γ' Microstructure Modeling for Supersolvus LSHR ............................. 5

γ' Microstructure Modeling and Misfit Prediction with JMATPro ...................................................... 8

Task 4—Precipitation Modeling for Embrittling Phases .............................................................................. 9

Summary of Experimental Results ....................................................................................................... 9

Thermodynamics Investigation .......................................................................................................... 11

Multiphase PrecipiCalc Simulations of Carbides ............................................................................... 13

Task 5—Software Implementation and Dissemination .............................................................................. 15

γ' Precipitation Simulation Tool ......................................................................................................... 15

Carbide Precipitation Simulation Tool ............................................................................................... 16

Conclusions ................................................................................................................................................. 16

References ................................................................................................................................................... 17

 
 
Introduction 

Predictive science-based computational materials modeling and tools have great potential to accelerate 

process optimization of 3rd generation Ni-base superalloys in gas turbine disk applications. By extending the 

DARPA-AIM methodology, previously demonstrated in disc alloys IN100 and R88DT (Refs. 1 and 2), this 

NASA Aviation Safety Program aimed to establish logical calibration, validation and user-friendly 

implementation of PrecipiCalc, a multicomponent multiphase precipitation simulation software, for four 3rd

generation nickel-based disk superalloys: ME3 (also called René104), LSHR (Low-Solvus, HighRefractory alloy developed by NASA), Alloy 10 (developed by Honeywell), and RR1000 (developed by 

Rolls-Royce). The nominal compositions for these alloys are listed in Table 1. 

TABLE 1.—NOMINAL COMPOSITIONS OF THE FOUR THIRD GENERATION 

DISC ALLOYS, IN wt%, STUDIED UNDER THIS PROGRAM 

wt% Ni Cr Co Mo W Al Ti Nb Ta Hf C B Zr 

ME3 Bal. 13.1 20.0 3.8 1.9 3.5 3.6 1.1 2.3 – 0.040 0.030 0.05 

LSHR Bal. 13.0 21.0 2.7 4.3 3.5 3.5 1.5 1.6 – 0.030 0.030 0.05 

Alloy10 Bal. 10.2 14.9 2.7 6.2 3.7 3.9 1.9 0.9 – 0.030 0.030 0.10 

RR1000 Bal. 15.0 18.5 5.0 – 3.0 3.6 – 2.0 0.5 0.027 0.015 0.06 

The program was completed at the end of 2009, and this report summarizes the key results in the third 

year (2009) of this program. The major activities conducted in 2009 are shown in the Gantt chart (see 

Figure 1). The project team includes NASA Glenn Research Center (GRC), QuesTek, AFRL (as scientific 

advisor), Rolls-Royce (as industrial advisor), and University of Cambridge. Regular monthly 

teleconferences among the project team and monthly reports were facilitated to enhance communication. 

The main activities in 2009 are Tasks 2 to 5, and the subsequent sections of this report summarize the 

activities and results. Due to a change in the priority focus of this program, the resource originally planned 

for Task 6—“Microstructure Variation and Optimization” was shifted to other higher priority Tasks, 

particular Tasks 4 and 5. 

Figure 1. —Gantt chart of the third year of this program. 

NASA/CR—2010-216748 1 
Task 2—Development of Calibration and Validation Data 

The focus of Task 2 was to develop necessary experimental data for the calibration and validation of 

models established in Task 3 and 4. Two previous annual reports (Refs. 3 and 4) summarize the data 

development in the first two years (2007 and 2008) of this program. In 2009, the experimental study 

focused on the following two areas. 

• γ/γ' Misfit Measurement—in addition to the misfit measurement by x-ray diffraction conducted at 

GRC (summarized in Ref. 4), University of Cambridge has conducted synchrotron and neutron 

diffraction characterization of both LSHR and Alloy10 samples. The LSHR data will be discussed 

in the Task 3 effort. 

• Carbide Microstructure Characterization—carbides, and other minor phases, in LSHR samples 

were studied by GRC under different aging conditions. The results will be discussed in detail in 

Task 4. 

Task 3—γ' Precipitation Modeling 

Ni-based aeroturbine disk superalloys rely on a multiscale γ' precipitate microstructure to achieve a 

suitable combination of mechanical properties. As heat treatment has a substantial impact on the γ' 

microstructure, the capability of simulating γ' size and fraction evolution is strongly desirable for disk alloy 

development. Continuing the efforts in the first two years of this program, the focus of the last year was the 

development and calibration/validation of the multistep PrecipiCalc framework. 

Interaction of Secondary and Tertiary γ' in Isothermal Aging 

The mean field approximation and theory used in PrecipiCalc models for computational efficiency 

have limitations, which have been identified in the DARPA AIM initiative (Ref. 5) in addition to this 

program. Under the mean field assumption, every particle interacts with all other particles instantaneously 

through common mean matrix compositions. This assumption is reasonable for single modal randomlyarranged precipitate distribution under nucleation, growth, or coarsening. For a multimodal distribution, 

such as γ' precipitates in Ni-based aeroturbine disk superalloys, number density variation and spatial 

arrangement limits the diffusional interaction and the particle coarsening kinetics deviate from that 

predicted by the mean field theory. This subsection describes a semi-empirical modeling approach to 

correct the results obtained from predictions using the mean field approximation. 

With a multimodal distribution, a single large particle (low number density) is typically surrounded by 

many small particles (high number density), see Figure 2(a) for a schematic illustration with one secondary 

particle surrounded by many tertiary γ' particles. The aforementioned approach also applies to the primary 

and the secondary γ' particles. The large secondary γ' particle can only interact diffusionally with the tertiary 

particles within a region represented by a spherical radius, RS, which is larger than the radius representing 

precipitate free zone, RPFZ. Due to the interaction with large secondary γ', the tertiary γ' within the shell 

region (RPFZ <R< RS) are dissolving to feed the growth of the larger particle. But the growth rate of 

secondary particle is lower than that predicted by mean field theory, see Figure 2(b) for a schematic 

illustration. Tertiary γ' particles away from the shell region, on the other hand, do not experience the field of 

large secondary particle, and coarsen as if there are only tertiary particles. 

NASA/CR—2010-216748 2 
 

RPFZ

Rs

2nd

•

R

R2nd

Coarsening

Zone

Dissolution

Zone

dt

dR

R 0

RC

Mean Field

2nd 3 γ’ rd γ’

Actual

(a) (b)

Figure 2.—Schematic diagrams of (a) a large secondary γ' particle surrounded by many 

tertiary γ' particles, and (b) particle growth rate versus particle radii comparing mean field 

prediction and actual growth rates under coarsening. 

Under the DARPA AIM initiative (Ref. 5), an approach involving multistep PrecipiCalc and freezing 

large γ' particles was utilized to overcome the mean field limitation, which had caused overgrowth of the 

large γ' particles during cooling and coarsening. This approach involves a series of multiple PrecipiCalc

calculations, removal of large γ' particles, and subsequent coarsening simulations considering only smaller 

γ' particles. By freezing out the large particles and prohibiting communication between the two populations 

of particles, the growth potency of the large γ' particles are suppressed during isothermal aging. However, 

GRC’s experimental evidence did indicate that ignoring the growth of large γ' particles is not a good 

assumption. In this program, we have further refined and extended the approach developed under AIM to 

account for the communication of multimodal distributions under coarsening. 

The new approach to incorporate the interaction between secondary and tertiary γ' particles during 

isothermal aging was formulated by post-processing the results obtained by considering only tertiary γ' 

coarsening (with secondary γ' removed from the calculation). Based on the mean size ( R ) and mean field 

growth rate ( R nd,2 MeanField  ) at the beginning of coarsening (denoted t=0), the actual growth rate, R2nd

 , of 

supercritical secondary γ' was semi-empirically derived in the following equations: 

( ) ( ) ( )

( )tR

tR R Rt t

RCR

RCR

S

PFZ

2nd

2nd

nd,2 MeanField nd,2 MeanField

2 2nd

1 2nd

0 0 = = =

=

=

 

( )( ) ( )

( ) ( )

( ) ( ) ( )

Constant [ ] ( ) 0 ( ) 0

3

410 ~ 0

0

1 ~

2nd nd,2 MeanField 2nd

3 3

2

2nd

2nd

nd,2 MeanField

rd3

 inside and rd3

MeanField 2 nd,22nd

×= =×=

⎥

⎦

⎤ ⎢

⎣

⎡ − π ⎥

⎦

⎤ ⎢

⎣

⎡

⎥

⎦

⎤ ⎢

⎣

⎡ = =

=

R R tRt

RR

tR R

tR R t

tN

N

R

RR t

s PFZ

PFZ

R

PFZ

S

 





 (1) 

NASA/CR—2010-216748 3 
This allowed us to reduce the correction down to a single fitting parameter. With calculations for the 

growth rate of secondary γ', the corresponding changes to the volume fractions of secondary and tertiary γ' 

could be determined through geometric corrections: 

( ) ( )

( ) ( ) ( )

() ( ) ( ) [ ] ( )tftftftf

NtRtf

tRtRtR

3rd 2nd 3rd 2nd

2nd

3

2nd 2nd

2nd 2nd 2nd

0 0

3

4

0

−=+==

π =

×+== 

Note that the mean size of the tertiary particles was already determined by the coarsening simulation of 

the tertiary particles alone. 

Multistep PrecipiCalc Simulation Framework for γ' Precipitation 

To enable the freezing and post-processing correction discussed in the previous subsection, a sequential 

multistep PrecipiCalc simulation framework was required. Simulation structure for a thermo-mechanical 

and heat treatment cycle with two aging steps required a total of six sequential PrecipiCalc simulations, as 

shown in Figure 3. During the two isothermal aging steps (nos. 3 and 5), the communication between 

secondary and tertiary γ' (or primary and secondary γ') was captured using the framework discussed in the 

previous section. This sequential operation involved tedious mass balance and careful setup of PrecipiCalc

calculations. Hence, it has been automated in a software wrapping program, which will be discussed in 

Task 5. Temperature,

T

Time (t)

2000°F

Powder

Compaction

and Forging

2200°F

Supersolvus

Solution

Treatment

1200°F

Aging

Treatment

Optional 2nd

Aging

Treatment

20hr

10°F/s

10°F/s 10°F/s

PrecipiCalc #1:

Formation of P γ’ until S

(for subsolvus) or T (for

supersolvus) γ’

nucleation occurs

#2:

Freez‐

ing P

or S γ’

#3:

Freezing

P or S γ’,

consider

commun‐

ication

between

P‐S or  S‐

T

P: Primary

S: Secondary

T: Tertiary

#5:

Freezing

P or S γ’,

consider

commun

‐ication

between

P‐S or  S‐

T

#4:

Freez‐

ing P

or S γ’

#6:

Freezing

P or S γ’

Figure 3.—Schematic multistep PrecipiCalc simulation framework with respect to the heat treatment history. 

NASA/CR—2010-216748 4 
Calibration and Validation of γ' Microstructure Modeling for Supersolvus LSHR 

A portion of the microstructure characterization results published in the NASA study of supersolvus 

LSHR (Ref. 6) was selected, see Table 2, to calibrate the multistep PrecipiCalc framework established 

earlier. The setup of the multistep PrecipiCalc simulation is summarized below. 

• LSHR lookup table data was generated based on Ni-3.4Al-12.9Cr-21.3Co-3.67Ti-2.66Mo-4.3W1.35Nb-1.66Ta-0.048Zr-0.024C-0.03B (in wt%) with carbides and borides eliminated; 

• Two controlled cooling rates after the supersolvus treatment were 202 °C/min (3.67 °C/s) and 

72 °C/min (1.2 °C/s), according to the NASA study (Ref. 6). Only the fast cooling (202 °C/min) 

data (as in Table 2) were used for calibration purposes; 

• The cooling rate after the aging was assumed to be 11 °C/min (0.183 °C/s) for all samples; 

• The heating rate to solution treatment or aging was assumed to be 10 °F/s (5.56 °C/s) for all 

samples; 

• All non-isothermal heating and cooling were assumed to be linear for all samples, though in reality 

the cooling were more likely Newtonian; and 

• Simulations started from the heatup to the solution treatment (without forging/extrusion portion 

illustrated in Figure 3) and no γ' particles were assumed to exist at the start of the simulations. This 

is a valid assumption as the subsequent 1171 °C/4 hr supersolvus treatment eliminates primary γ' 

particles anyway. 

TABLE 2.—SELECTED γ' MICROSTRUCTURE FROM SUPERSOLVUS 

TREATED LSHR (REF. 6) USED FOR MODEL CALIBRATION 

Solution treat Age 1 Age 2 

1171 °C + 202 °C/m 0 0 

1171 °C + 202 °C/m 815 °C/3 hr 0 

1171 °C + 202 °C/m 815 °C/8 hr 0 

1171 °C + 202 °C/m 855 °C/1 hr 775 °C/8 hr 

1171 °C + 202 °C/m 855 °C/4 hr 775 °C/8 hr 

1171 °C + 202 °C/m 855 °C/8 hr 775 °C/8 hr 

The calibration facilitated the determination of the following three main parameters: 

• Surface energy was determined to be 0.025 J/m2 which is within the range 0.0225 to 0.0315 J/m2 

determined in earlier single sensor DTA (SSDTA) nucleation study (Refs. 4 and 7); 

• The single constant parameter for the interaction between the secondary and tertiary γ' particles (Eq. 

(1)), as discussed earlier was determined; 

• An adjustment for the tertiary γ' coarsening rate was found to be needed in order to avoid particle 

size over-estimation (by a factor of about 2, which is consistent with the slow isothermal coarsening 

kinetics for γ' particles discussed in the 2008 annual report (Ref. 7)). 

Figure 4 shows the γ' microstructure evolution results from one of the calibration calculations (the last 

condition shown in Table 2). During isothermal aging steps, secondary γ' size and fraction (green) 

increased, while tertiary fraction decreased, demonstrating the secondary/tertiary interaction. Without this 

regulated interaction, the mean field assumption would cause a complete dissolution of tertiary γ' too 

quickly. Note that there was an increase of tertiary γ' size during cooling right after the 855 °C aging. 

Next we applied the calibrated parameters to the entire available dataset of supersolvus LSHR discussed 

in Reference 6. Both experimental data and predictions are summarized in Table 3 and graphically in 

Figure 5. In Table 3, both experimental median and mean (3–D) particle sizes are listed. For multistep 

PrecipiCalc predictions, 3–D mean sizes are reported. For tertiary γ' particles, the sizes at the end of the last 

aging step (before subsequent final cooling) and at the end of the simulation (after final cooling) are 

reported. It was observed the final cooling could increase the tertiary size by growth, or decrease it by 

NASA/CR—2010-216748 5 
nucleation (generation of smaller γ' particle into the same tertiary distribution). In both cases, the volume 

fraction of tertiary γ' precipitates increased during the final cooling step. This could represent the potential 

microstructure variation due to the approximation of cooling rate during the final cooling. The green and 

red colors are used for slow and fast quenching from supersolvus solution treatment, respectively, in both 

Table 3 and Figure 5. The symbols in the last column of Table 3 represent the plot symbols used in 

Figure 5. That is, triangles for as solution treated condition, diamonds for single step aging conditions, and 

squares for double step aging conditions. 

TABLE 3.—CALIBRATION AND VALIDATION RESULTS OF γ' MICROSTRUCTURE FOR SUPERSOLVUS TREATED LSHR 

Experiments Prediction 

Secondary Tertiary Secondary Tertiary 

Solution treat Age 1 Age 2 Median 

radius 

(nm) 

Mean 

radius 

(nm) 

Volume

fraction 

(%) 

Median 

radius 

(nm) 

Mean 

radius 

(nm) 

Volume

fraction 

(%) 

Radius 

(nm) 

Fraction 

(%) 

Radius 

(nm) 

Volume 

fraction 

(%) 

1171 °C + 72 °C/m 0 0 135.1 132.1 50 4.4 6.3 8 134.7 44.5 7.0 7.4 ∆

1171 °C + 72 °C/m 775 °C/8 hr 0 115.4 111.0 52 6.1 6.5 6 135.1 44.9 7.3/7.7 7.3/8.1 

1171 °C + 72 °C/m 815 °C/8 hr 0 115.1 111.6 57 9.9 10.3 1 136.0 45.7 8.0/8.9 5.5/7.0 

1171 °C + 72 °C/m 855 °C/1 hr 0 134.0 133.6 53 10.8 10.9 5 135.2 44.9 8.1/9.9 4.9/7.8 

1171 °C + 72 °C/m 855 °C/8 hr 0 116.0 112.1 57 14.6 14.8 1 139.1 48.9 10.6/14.5 1.0/2.1 

1171 °C + 72 °C/m 855 °C/1 hr 775 °C/8 hr 119.7 118.2 54 9.1 9.3 4 135.3 45.0 9.8/10.5 7.2/7.5 □

1171 °C + 72 °C/m 855 °C/4 hr 775 °C/8 hr 155.0 142.0 51 13.2 14.0 7 136.9 46.6 11.7/12.3 5.6/5.6 □

1171 °C + 72 °C/m 855 °C/8 hr 775 °C/8 hr 139.2 140.0 57 15.3 14.5 1 142.2 52.3 15.4/0.8 0/2 □

1171 °C + 202 °C/m 0 0 75.6 75.2 54 2.7 3.5 4 75.2 45.0 4.0 6.4 ∆

1171 °C + 202 °C/m 775 °C/8 hr 0 61.2 61.0 55 5.1 5.2 3 75.3 45.2 5.0/5.3 7.0/8.1 

1171 °C + 202 °C/m 815 °C/3 hr 0 77.5 77.3 57 6.8 7.4 1 75.4 45.2 5.8/6.6 5.9/7.8 

1171 °C + 202 °C/m 815 °C/8 hr 0 89.4 89.1 57 9.4 9.6 1 75.7 45.9 7.1/8.0 5.3/6.9 

1171 °C + 202 °C/m 855 °C/1 hr 0 70.3 71.4 54 8.1 8.1 4 75.3 45.2 7.2/9.2 4.6/7.6 

1171 °C + 202 °C/m 855 °C/8 hr 0 70.4 70.9 58 15.0 14.2 0.1 77.4 49.0 12.1/16.0 0.9/1.9 

1171 °C + 202 °C/m 855 °C/1 hr 775 °C/8 hr 96.7 97.1 56 10.5 11.0 2 75.4 45.3 9.1/9.8 6.9/7.3 □

1171 °C + 202 °C/m 855 °C/4 hr 775 °C/8 hr 62.9 62.4 55 11.0 11.3 3 76.1 46.5 11.8/12.3 5.7/5.8 □

1171 °C + 202 °C/m 855 °C/8 hr 775 °C/8 hr 78.5 78.9 56 14.5 15.4 0.1 79.1 52.3 16.9/4.7 0/0 □

Figure 4.—An example calculation results are shown below for the case with a treatment condition: 1171 °C/4 hr + 

72 °C/m + 855 °C/8 hr + 775 °C/8 hr. 

NASA/CR—2010-216748 6 
In the plot of secondary particle size in Figure 5(a), experimental measurements are shown to have a 

larger variation than the model prediction. However, there was no correlation in experimental values with 

respect to the heat treatment parameters (Ref. 6). Hence, the prediction of secondary γ' sizes were 

considered accurate. There was a consistent discrepancy that experimental secondary γ' fractions are higher 

than the prediction, as shown in Figure 5(b). Several possibilities have been discussed, including 

experimental artifacts (etching and 3–D effects) and thermodynamics database inaccuracy, but no definite 

reasons have been concluded. This deserves further investigation to determine the cause of discrepancy. 

For the tertiary γ' microstructure in Figure 5, only the prediction at the end of last aging (before final 

cooling) was used. The tertiary γ' size, Figure 5(c), showed a good correlation between experiments and 

prediction. The multistep PrecipiCalc framework predicted the correct trend and reasonable values of 

tertiary radii with respect to the heat treatment condition. The predicted volume fraction of tertiary γ' had a 

scattered correlation with the experimental data, but was well within the correct range of phase fraction. 

With the higher potential variability in experimental volume fraction measurement, the prediction was 

considered satisfactory. 

(a) (b)

(c) (d)

Figure 5.—Correlation plot of γ' microstructure for supersolvus treated LSHR samples. (a),(b) for secondary and (c),(d) 

for tertiary γ'. (a),(c) for mean radii and (b),(d) for volume fraction. The diagonal dash lines represent perfect 

correlation. 

0

30

60

90

120

150

0 30 60 90 120 150

Measured Secondary γ'Mean Radius

(nm)

Predicted Secondary γ'Mean Radius(nm)

40%

45%

50%

55%

60%

40% 45% 50% 55% 60%

Measured Secondary γ' Fraction (%)

Predicted Secondary γ' Fraction (%)

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

Measured Tertiary γ'Mean Radius(nm)

Predicted Tertiary γ'Mean Radius(nm)

0%

1%

2%

3%

4%

5%

6%

7%

8%

0% 1% 2% 3% 4% 5% 6% 7% 8%

Measured Tertiary γ' Fraction (%)

Predicted Tertiary γ' Fraction (%)

NASA/CR—2010-216748 7 
γ' Microstructure Modeling and Misfit Prediction with JMATPro 

An LSHR sample was sent to University of Cambridge for analyses by synchrotron/neutron diffraction 

to measure γ/γ' room temperature misfit, and a value of +0.026 percent was estimated. This subsection 

summarizes an attempt to predict misfit by combining PrecipiCalc and JMATPro (Sente Scientific) 

software tools. 

Based on a simulated temperature profile provided by NASA (see Figure 6) at the location where the 

LSHR misfit sample was taken, a PrecipiCalc quenching simulation was conducted. Final secondary γ' was 

predicted to be 47 percent, in good agreement with the 45 percent estimated by neutron diffraction. Based 

on the PrecipiCalc simulation results, two temperatures (1094 and 956 °C, representing 50 and 90 percent 

secondary γ' completion) were used by GRC for predicting the associated γ and γ' compositions, and room 

temperature misfit, using JMATPro-Ni 5.0 software (Ref. 2), to compare with the misfit measurement. 

The JMATPro results shown in Figure 7 indicate that the room temperature misfit prediction using the 

compositions at 50 and 90 percent completion does bracket the experimental measurement (thick arrows). 

JMATPro results also indicate fairly strong composition dependency in misfit. This brings up a 

consideration of significance for location-specific misfit driven by varying γ' microstructure and 

compositions. 

Figure 6.—PrecipiCalc simulation for LSHR sample used in misfit measurement. 

NASA/CR—2010-216748 8 
Figure 7.—JMATPro misfit prediction for an LSHR sample and comparison with experimental measurement 

indicated by the large blue arrows. 

Task 4—Precipitation Modeling of Minor Phases 

Several minor precipitate phases in Ni-based aeroturbine disk alloys, including carbides, borides and 

intermetallics, can nucleate or evolve during the long term thermal exposure during service. These minor 

phases can affect the performance of the disk component, and thus is desirable to model the precipitation 

evolution of the aforementioned phases during thermal exposure. 

Summary of Experimental Results 

GRC conducted experimental characterization of minor phases in LSHR—carbides (including MC and 

M23C6), boride (M3B2) and topological close packed TCP (σ) phases. LSHR samples having different 

process histories were investigated, including extrusion, forging, supersolvus solution treatment at 1199 °C 

(followed by water quench or furnace quench), and one single aging step at three isothermal aging 

temperatures (760, 843 and 927 °C) for three different hold times (10, 100 and 1000 hr), spanning heat 

treatment to prolonged service conditions. SEM/EDS and TEM were used at GRC to identify the phase and 

microstructure of the precipitates. The detailed experiment and analysis procedures will be published by 

GRC researchers. Table 4 summarizes the mean radii and volume fraction of the minor phases in 

characterized LSHR samples. Figure 8 presents the data with the thermal history on the x-axis. 

NASA/CR—2010-216748 9 
TABLE 4.—A SUMMARY OF GRC EXPERIMENTAL MINOR PHASE 

CHARACTERIZATION ON LSHR HEAT TREATED UNDER DIFFERENT CONDITIONS 

MC M23C6 M3B2 σ

ID Conditions <R>, 

μm 

vf, 

% 

<R>, 

μm 

vf, 

% 

<R>, 

μm 

vf, 

% 

<R>, 

μm 

vf, 

% 

1 As Extruded 0.137 0.08 0 0 0.256 0.351 0 0 

2 1 + Forging 0.155 0.1 0 0 0.299 0.121 0 0 

3 2 + 1199 °C/1 hr + F. Cool 0.186 0.196 0 0 0 0 0 0 

4 2 + 1199 °C/1 hr + WQ 0.173 0.161 0 0 0.178 0.002 0 0 

5 4 + 760 °C/10 hr+ WQ 0.163 0.161 0 0 0 0 0 0 

6 4 + 760 °C/100 hr + WQ 0.173 0.189 0.104 0.015 0.364 0.033 0 0 

7 4 + 760 °C/1000 hr + WQ 0.179 0.217 0.171 0.148 0.18 0.054 0 0 

8 4 + 843 °C/10 hr + WQ 0.194 0.259 0.077 0.003 0.077 0.001 0 0 

9 4 + 843 °C/100 hr + WQ 0.198 0.219 0.144 0.095 0 0 0.196 0.058 

10 4 + 843 °C/1000 hr + WQ 0.195 0.184 0.288 0.418 0.383 0.042 0.265 0.327 

11 4 + 927 °C/10 hr + WQ 0.196 0.162 0.147 0.136 0.46 0.0005 0.174 0.053 

12 4 + 927 °C/99 hr + WQ 0.187 0.126 0 0 0.6 0.0005 0.191 0.024 

13 4 + 927 °C/1000 hr + WQ 0.198 0.3 0 0 1.139 0.827 0 0 

(a) (b)

0.23% for MC, >840°C

for M23C6, <750°C

(c) (d)

0.4% for M3B2, <1050°C

Figure 8.—Graphical representation of the minor phase microstructure data in Table 4. Carbides microstructure is 

shown in (a) and (b), while microstructure of boride and σ phases are shown in (c) and (d). The black horizontal lines 

in (a),(c) represent the equilibrium phase fraction predicted by PrecipCalc using the Ni-Data v7 database. 

NASA/CR—2010-216748 10 
Figure 9.—Phase fractions in LSHR (denoted as NP) at 

equilibrium as functions of temperature, predicted by 

ThermoCalc using the Ni-Data version 7 database. 

Thermodynamics Investigation 

Equilibrium predictions of phase fractions versus temperature are shown in Figure 9. It is worth noting 

that, M3B2 is not stable during extrusion/forging/solution treatment, and replacement of MC with M23C6 was 

predicted below 841 °C. When all TCP phases are suspended in the calculation, M23C6 solvus temperature 

increased by 10 °C. The σ and μ phases appeared to have high equilibrium fraction, but are usually limited 

by slow formation kinetics. When both σ and μ are suspended in the calculation, P phase appeared in a 

similar temperature range with a similar phase fraction as that of μ phase. 

Within 700 to 900 °C where isothermal aging was conducted for LSHR samples, the predicted phase 

compositions (in atomic fraction) are: 

σ Cr0.50Co0.30Ni0.10Mo0.07W0.01 

μ Co0.30Mo0.22Cr0.17Ni0.15W0.14 

P-phase Cr0.28Co0.20W0.18Mo0.17Ni0.16 

M3B2 Mo0.38-Cr0.21-W0.01-B0.40

M23C6 Cr0.60-Mo0.09-Co0.05-W0.01-C0.21

MC Ti0.12-Nb0.16-Ta0.15-Zr0.08-C0.49 

The major components in the individual phases were mostly in agreement with GRC’s experimental 

observation. One major exception is M3B2, where there was experimental evidence of high W content. In 

addition, GRC’s experiments found that, in some aging conditions, a very small amount of a Mo,Ti, and Crrich phase appeared with cylindrical morphology. However, there were no Mo, Ti, and Cr rich phases 

predicted. More quantitative experimental composition measurements would be beneficial to confirm the 

current measurements and to clarify the composition discrepancy between experiments and predictions. 

Comparing Figure 9 and Figure 8, several inferences can be made: 

• Prior to aging, MC phase fraction was increasing towards the equilibrium predicted phase fraction. 

There was no M23C6 found in the as-quench condition prior to aging treatments. 

NASA/CR—2010-216748 11 
• At 927 °C, MC fraction increased while amount of M23C6 decreased, which was compatible with 

thermodynamics predictions. However, the observed M23C6 at 10 hr aging might be formed during 

heat up to 927 °C. 

• At 843 °C, replacement of MC by M23C6 occurred. This indicates that M23C6 had higher thermal 

stability than predicted by the thermodynamics. However, MC fraction at 10 hr was higher than the 

equilibrium value, which was unexpected. 

• At 760 °C, fraction of both carbides increased but were still below their equilibrium values at 1000 

hr. According to thermodynamics, the amount of MC carbides will eventually decrease to feed 

additional M23C6 formation. 

• Overall effect of aging time on MC size was smaller than that on M23C6 size. Several higher than 

equilibrium fractions were observed experimentally. The simulations, however, are not expected to 

capture those high volume fractions. 

• M3B2 dissolves prior to aging, which was compatible with equilibrium prediction. During the 

dissolution of M3B2, there was no experimental observation of MB2 phase. It is desirable to 

determine whether boron stays in solution, or less probably in few large MB2 particles which are 

difficult to find. 

• M3B2 amount increased during aging, with a fast transformation kinetics at 927 °C. M3B2 amount 

was in general far from equilibrium, except at 927 °C/1000 hr. 

• σ phase amount increased at 843 °C, while dissolving at 927 °C, again compatible with equilibrium 

prediction. But overall, σ phase amount was far from equilibrium, and precipitation kinetics of σ

phase was extremely slow at 760 °C. 

The three plots in Figure 10 summarize the precipitation trajectory of MC and M23C6 carbides based on 

an unstable equilibrium fraction-supersaturation relationship. This information helped us understand the 

precipitation path along the thermodynamic supersaturation, and provided calibration input for multiphase 

simulation. 

760°C 843°C 927°C

Figure 10.—Trajectory evaluation of carbides at the three isothermal aging temperatures. Driving force of MC (M23C6) is 

shown in the X- (Y-) axis. The stars represent the experimentally observed carbide fractions. The precipitation 

trajectory is formed by connecting the stars. 

NASA/CR—2010-216748 12 
Multiphase PrecipiCalc Simulations of Carbides 

This subsection summarizes the application of PrecipiCalc software to simulate the concurrent MC and 

M23C6 carbide microstructure evolution during isothermal aging. As discussed in the equilibrium study 

above, several unexpected phase fractions were observed, and PrecipiCalc simulations were not expected to 

capture those observations quantitatively. Hence, our key simulation objective was to capture the qualitative 

trend while attempting to capture the quantitative values as much as possible. In order to achieve a 

manageable simulation complexity, the simulations focused on the carbides by assuming that: 

• γ' reaches equilibrium a lot faster than carbides (for example, γ' volume fraction is fairly constant 

after 1 hr aging at 775 °C γ' by simulation)—this allowed us to remove the γ' phase at ~53 percent 

phase amount, and focus on the remaining 47 percent of the carbides precipitation in FCC 

simulation. 

• Slow kinetics for borides and TCP—this allowed us to ignore these phases. 

The starting microstructure at the beginning of the simulation had no M23C6, and the amount of MC was 

assumed to be 0.161 percent at a mean size of 0.163 μm, corresponding to the as-quenched microstructure. 

A normal distribution with a standard deviation of 0.02 μm was used to describe the initial MC particle size 

distribution. In addition, a homogeneous nucleation (intragrain) model was used for MC, while grain 

boundary heterogeneous nucleation model was used for M23C6. By investigating the M23C6 morphology 

observed by NASA, see Figure 11 as an example, a grain size of 32 μm and a wetting angle of 32° were 

used. The LSHR overall composition used was Ni-3.4Al-12.9Cr-21.3Co-3.67Ti-2.66Mo-4.3W-1.35Nb1.66Ta-0.048Zr-0.024C-0.03B (in wt%). 

By calibrating to experimental data, key precipitation parameters were determined: 

• MC/FCC surface energy: 0.8 J/m2 for all three temperatures 

• M23C6/FCC surface energy: a linear dependency with temperature, see Figure 12, provided the best 

overall fit to experimental data 

• Diffusion scaling of 0.2 (to account for slower coarsening rate), and additional diffusion scaling of 

0.005 for M23C6 due to its limited interaction with MC 

Figure 11.—A processed LSHR SEM micrograph showing 

blue M23C6 grain boundary carbides. Figure 12.—M23C6 surface energy was taken to linearly 

depend on temperature consistent with positive surface 

entropy. 

LSHR

843°C

1000hr

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

700 750 800 850 900 950

M23C6/FCC Surface Energy (J/m2)

Temperature (°C)

NASA/CR—2010-216748 13 
The results of the simulation are summarized in Figure 13. The overall microstructure evolution 

features were captured through simulation. However, several discrepancies, including small M23C6 size and 

faster MC dissolution near 1000 hr (driven by mass balance of carbon), demand further investigation in the 

future. The ignoring of γ', boride and TCP phases in these simulation could play some role in the 

discrepancies observed. In addition, the observed M23C6 at 927 °C/10 hr could be due to heating to aging 

temperature, which was not simulated as we only considered isothermal aging. Though they lack absolute 

accuracy for material engineering optimization, these simulation capabilities can already provide valuable 

insights into the carbide microstructure evolution. 

 

0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000

Phase Fraction (%)

760°C Aging Time (hr)

MC

0

50

100

150

200

250

300

1 10 100 1000

Mean Radius (nm)

760°C Aging Time (hr)

MC

M23C6 M23C6

 

0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000

Phase Fraction (%)

843°C Aging Time (hr)

MC

0

50

100

150

200

250

300

1 10 100 1000

Mean Radius (nm)

843°C Aging Time (hr)

MC

M23C6

M23C6

 

Figure 13.—Comparison of LSHR carbide microstructure evolution between experiments and 

predictions. NASA experimental results are in square points and PrecipiCalc simulation results are 

in solid curves. MC carbides are in blue and M23C6 carbide are in red. 

0

50

100

150

200

250

300

1 10 100 1000

Mean Radius (nm)

927°C Aging Time (hr)

MC

0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000

Phase Fraction (%)

927°C Aging Time (hr)

MC

M23C6 M23C6

NASA/CR—2010-216748 14 
Task 5—Software Implementation and Dissemination 

Driven by the need to minimize the steep learning curve of PrecipiCalc software, this Task focused on 

producing user friendly precipitation simulation tools, based on PrecipiCalc, for aeroturbine disk material 

engineers. There were two software tools, one for γ' precipitation microstructure during heat treatment, and 

another for carbide precipitation microstructure during isothermal holding. Both set of software shared similar 

features: graphical user interface (GUI) for user friendly pre- and post-processing operation, cross platform 

implementation (using Java and Python) for easy transfer to other operating systems (tested on Microsoft 

Windows XP/7 and Linux), based on PrecipiCalc simulation software. Alpha and beta versions of the software 

were distributed during 2009, and the final version of the software was released at the end of 2009. 

γ' Precipitation Simulation Tool 

The detailed operating instruction of the software is described in a separate software manual. Here we 

summarize the key features of the software in relationship to the Task 3 modeling efforts described in the 

above Section. Figure 14 provides an overview of the software architecture, which includes three levels: 

1. Graphical User Interface (GUI)—containing four separate modules of operation. Lookup table module 

allows user to input alloy composition and generate a lookup table file. Preprocessing module collects 

heat treatment conditions and material properties. Computing module starts and monitors calculation 

and post-processing module provides facility to view and plot results. GUI is written in Java (Sun 

Microsystems, Inc.) (http://www.java.com/) and PLPlot library (http://plplot.sourceforge.net/). 

2. CALPHAD-based Programs—including PrecipiCalc, lookup table generation software, and a software 

for composition calculation with phases removal. These command line-based tools often use ThermoCalc and were written in C/C++. 

3. Wrapper Programs—these take the information provided by the GUI and operate the CALPHAD-based 

programs (no. 2 above) according to the developed algorithm, such as the multistep γ' simulation 

framework discussed in Task 3. The wrapper programs were command line-based and were written in 

Python (Python Software Foundation) (http://www.python.org/). In addition, wrapper programs can 

also be operated by a software robot (like iSIGHT) to enable large scale simulations. 

Preprocessing

Module

Computing

Module

Postprocessing

Module

GraphicalUser Interface

Rj(t)

fj

(t)

Ci— overall

composition

T(t) —

temperature

profile

σ — surface

energy

PpC .........

T(t), σ

Ci(t), R(t),

f(t)

PpC

T(t), σ

Ci(t), R(t),

f(t)

PpC

T(t), σ

Ci(t), R(t),

f(t)

Multistep PrecipiCalcWrapper

Lookup Table

Module

Ci

Lookup

Table

Gene‐

ration

Carbide

/boride

removal

Lookup Table File

Figure 14.—Software implementation architecture for multistep PrecipiCalc (PpC) γ' microstructure 

simulations of heat treatment. 

NASA/CR—2010-216748 15 
Preprocessing Computing Postprocessing

GraphicalUser Interface

Rj(t)

fj

(t)

Ci— overall

composition

T — aging

temperature

PpC

γ’

removal

Carbide PrecipiCalc

Wrapper

Figure 15.—Schematic diagram of the carbide precipitation simulation software. 

Carbide Precipitation Simulation Tool 

Like the γ' simulation tool, the carbide precipitation simulation tool, capturing the carbide simulations 

discussed in Task 4 of this report, also contains three levels of software—GUI, CALPHAD-based tools and 

wrapper programs. It has simpler GUI module and wrapper components than those in the γ' simulation 

program. 

Conclusions 

At the conclusion of this third year NASA program, extensive development of precipitation 

microstructure evolution was made for Ni-based disk superalloys in the following areas: 

• γ' Precipitation Modeling

– Successful development of multistep PrecipiCalc framework to eliminate mean field limitation 

– Reasonable calibration and validation of multistep PrecipiCalc framework against supersolvus 

treated LSHR with systematic discrepancy in phase fraction comparison 

– Implementation of the framework into a user friendly software tool 

– Slow γ' coarsening rate calibrated, but deserves further study by the Ni-based superalloys 

research community in order to determine a physics-based mechanism 

• Carbide Precipitation Modeling

– Equilibrium study identified mismatches between experimental results and thermodynamics 

database 

– Successful demonstration of multiphase PrecipiCalc simulation for concurrent MC and M23C6

carbide microstructure evolution during long term aging 

– Qualitative carbide microstructure features with complex interaction were predicted 

– Implementation of software into a user friendly software tool 

• Software Dissemination—the software components developed under this program was delivered 

to NASA and project collaborators at the end of this program. 

Though model calibration/validation was mainly established with data of NASA’s LSHR alloy in this 

report, the tool can be used to support modeling efforts for other alloys, such as Rolls-Royce’s RR1000 

alloy. 

NASA/CR—2010-216748 16 
NASA/CR—2010-216748 17 

References 

1. A.M. Wusatowska-Sarnek, G. Ghosh, G.B. Olson, M.J. Blackburn, and M. Aindow, J. Materials 

Research, 18 (2003) 2653–2663. 

2. N. Saunders, Z. Guo, X. Li, A.P. Miodownik, J-Ph. Schille, Superalloys 2004, eds. K.A. Green, T.M. 

Pollock, H. Harada, T.E. Howson, R.C. Reed, J.J. Schirra, and S. Walston, (2004) 849–858. 

http://www.sentesoftware.co.uk/jmatpro-version-50-released.aspx 

3. H.-J. Jou, Microstructure Modeling of 3rd Generation Disk Alloys—1st Annual Report, December 2007, 

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080021187_2008019927.pdf 

4. H.-J. Jou, Microstructure Modeling of 3rd Generation Disk Alloys—2nd Annual Report, December 2008. 

5. H.-J. Jou, P. Voorhees and G.B. Olson, Superalloys 2004, eds. K.A. Green, T.M. Pollock, H. Harada, 

T.E. Howson, R.C. Reed, J.J. Schirra, and S. Walston, (2004) 877–886. 

6. T. Gabb, J. Gayda, J. Telesman, A. Garg, Superalloys 2008, eds. R.C. Reed, K.A. Green, P. Caron, T.P. 

Gabb, M.G. Fahrmann, E.S. Huron, and S.A. Woodward, TMS (The Minerals, Metals, & Materials 

Society), (2008) 121. 

7. G.B. Olson, H.-J. Jou, J. Jung, J.T. Sebastian, A. Misra, I. Locci and D. Hull, Superalloys 2008, eds. 

R.C. Reed, K.A. Green, P. Caron, T.P. Gabb, M.G. Fahrmann, E.S. Huron, and S.A. Woodward, TMS 

(The Minerals, Metals, & Materials Society), (2008) 923–932. 

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20090004682_2009001242.pdf
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4. TITLE AND SUBTITLE

Microstructure Modeling of Third Generation Disk Alloys 

Final Report

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NNC07CB01C 

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6. AUTHOR(S)

Jou, Herng-Jeng 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The objective of this program was to model, validate, and predict the precipitation microstructure evolution, using PrecipiCalc (QuesTek 

Innovations LLC) software, for 3rd generation Ni-based gas turbine disc superalloys during processing and service, with a set of logical and 

consistent experiments and characterizations. Furthermore, within this program, the originally research-oriented microstructure simulation 

tool was to be further improved and implemented to be a useful and user-friendly engineering tool. In this report, the key accomplishments 

achieved during the third year (2009) of the program are summarized. The activities of this year included: Further development of multistep 

precipitation simulation framework for γ' microstructure evolution during heat treatment; Calibration and validation of γ' microstructure 

modeling with supersolvus heat treated LSHR; Modeling of the microstructure evolution of the minor phases, particularly carbides, during 

isothermal aging, representing the long term microstructure stability during thermal exposure; and the implementation of software tools. 

During the research and development efforts to extend the precipitation microstructure modeling and prediction capability in this 3-year 

program, we identified a hurdle, related to slow γ′ coarsening rate, with no satisfactory scientific explanation currently available. It is 

desirable to raise this issue to the Ni-based superalloys research community, with hope that in future there will be a mechanistic 

understanding and physics-based treatment to overcome the hurdle. In the mean time, an empirical correction factor was developed in this 

modeling effort to capture the experimental observations. 

15. SUBJECT TERMS

Gas turbine engines; Rotating disks; Heat resistant alloys 

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