high temperature, slow strain rate forging of adwanced

NASA / TM--2001-210901

High Temperature, Slow Strain Rate Forging

of Adwanced Disk Alloy ME3

Timothy P. Gabb and Kenneth O'Connor

Glenn Research Center, Cleveland, Ohio

National Aeronautics and

Space Administration

Glenn Research Center

August 2001

Acknowledgments

The authors wish to acknowledge the many helpful discussions with David Mourer at General electric Aircraft

Engines. The tests were performed at Wyman-Gordon Forgings, Houston R&D lab, by mike Powell, while the

subsequent heat treatments were performed by Jim Smith, under the direction of William Konkel.

NASA Center for Aerospace Information7121 Standard Drive

Hanover, MD 21076

Available from

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at ht_://gltrs.grc.nasa.gov/GLTRS

High Temperature, Slow Strain Rate Forging ofAdvanced Disk Alloy ME3


National Aeronautics and Space AdministrationGlenn Research Center

Cleveland, Ohio 44135

Introduction

The advanced disk alloy ME3 was designed in the HSR/EPM disk program to

have extended durability at 1150-1250F in large disks. This was achieved by designing

a disk alloy and process producing balanced monotonic, cyclic, and time-dependent

mechanical properties, combined with robust processing and manufacturing character-

istics. The resulting baseline alloy, processing, and supersolvus heat treatment produces

a uniform, relatively fine mean grain size of about ASTM 7, with as-large-as (ALA) grain

size of about ASTM 3 (ref. 1 ).

There is a long term need for disks with higher rim temperature capabilities than

1250F. This would allow higher compressor exit (T3) temperatures and allow the full

utilization of advanced combustor and airfoil concepts under development. Several

approaches are being studied that modify the processing and chemistry of ME3, to

possibly improve high temperature properties. Promising approaches would be applied

to subscale material, for screening the resulting mechanical properties at these high

temperatures. An obvious path traditionally employed to improve the high temperature

and time-dependent capabilities of disk alloys is to coarsen the grain size (ref. 2, 3). A

coarser grain size than ASTM 7 could potentially be achieved by varying the forging

conditions and supersolvus heat treatment (ref. 4).

The objective of this study was to perform forging and heat treatment experiments

("thermomechanical processing experiments") on small compression test specimens of

the baseline ME3 composition, to identify a viable forging process allowing significantly

coarser grain size targeted at ASTM 3-5, than that of the baseline, ASTM 7.

Material and Procedure

Specimen machining, testing, and heat treatments were performed by Wyman-

Gordon Forgings, Houston, Texas. A 1.1" thick cross-section of extrusion SMK05398

was removed using an abrasive disk saw. Specimen blanks were then electrodischarge

machined along a 4.5" diameter circle centered in the cross section. Twenty right circular

cylinder (RCC) specimens having a diameter of 0.50" and length of 0.75" were then

machined. Six double cone (DC) specimens were also machined according to Fig. 1 (ref.

5). The matrix of test conditions for the RCC and DC specimens is shown in Table 1.

RCC specimens were tested at 3 temperatures 2025, 2050, and 2075F using 3 strain rates

of 0.0001, 0.0003, and 0.001 sec L, after being pre-soaked at the test temperature for

times of either 1 or 10 h. This represented a 3x3x2 full factorial statistical test matrix.

Additional RCC tests were performed at the mid temperature 2050F and strain rate

0.003 sec-_: after a pre-soak of 5h to represent the centerpoint of the test matrix, and after

NASA/TM--2001-210901 1

an extended pre-soak of 24h. All RCC tests were continued to an upset of at least 50%,

and true strain of 0.70. DC specimens were tested at the 2 extreme temperatures of 2025

and 2075F and 2 extreme strain rates of 0.0001 and 0.001 sec -1 after a 10h presoak,

giving a 2x2 test matrix. Additional DC tests were performed at the mid temperature

2050F and strain rate 0.003 sec -I after a pre-soak of 5h as for the RCC matrix centerpoint,

and after an extended pre-soak of 24h. All DC tests were continued to an upset of 50%.

After the tests, all specimens were sliced into four quarters. Single quarters of

each specimen were heat treated together on a tray in a resistance heated furnace using a

"direct heatup'" (DH) supersolvus heat treatment of 2140F/lh and then air cooled. Other

quarters were given a "pre-annealed" (PA) supersolvus heat treatment consisting of a

subsolvus pre-anneal of 2075F/lh, followed by an extended supersolvus treatment of

2140F/3h. Heat treated and as-forged quarters were then sectioned, metallographically

prepared, and swab etched for 3 minutes using Kallings reagent. Five fields near the

center of the forging specimen were measured to determine mean grain size in each case,

using a circular overlay grid according to ASTM El 12. The largest grain observed on

each metallographic section was measured for as-large-as (ALA) grain size according to

ASTM E930. Statistical evaluations of flow stress and grain sizes were then performed.The test datum of 2050F/0.0003s-l/24h presoak was not used in the statistical evaluations,

as it would unbalance the statistical matrix designed around presoak times of I and 10h.

Controlled variables were orthogonally scaled to standardized form in all cases using the

relationship Vi'=(Vi-Vme,_)/(0.5*(Vn_x-V_n)). This produced a range for each standardized

variable of-I to +1. This gave standardized variables for temperature (T'), presoak time

(P'), and log strain rate (log(R)') of:

T'=(T-2050)/25 P'=(P-5.5)/4.5 log(R)'=(log(R)+3.5)/0.5

After regression model equations were selected, major effects, residuals, and predicted

confidence intervals were examined for each response.

Results and Discussion

Forging Stress-Strain Response

Typical engineering stress-strain curves are shown for RCC tests, and load-

displacement curves for DC tests are shown in Fig. 2. Flow stress at a true strain of 0.5

for each RCC test was employed in detailed analyses. Scatter plots of this flow stress (S)

vs. temperature (T), pre-soak time (P) and strain rate (R) are shown in Fig. 3. Strong

dependencies of flow stress on temperature and strain rate are obvious. Reverse stepwise

selection linear regression of log(stress) on log(strain rate), temperature, pre-soak time,

and their interactive products were performed, using an F-to-enter=4. The resulting

linear regression equation was:

log(stress)=-.240553+0.041239T'+0.018252P'+0.554102log(R) ' (1)

with a correlation coefficient R2adj =.984 and rms error=O.03434. The complete statistical

output is included in Appendix A- 1. Plots of the resulting predicted and observed

log(stress) vs. pre-soak time and vs. log(strain rate) showed only random error. A plot

NASA/TM--2001-210901 2

of predicted and observed log(stress) vs. temperature is also shown in A-1. A systematic

divergence at intermediate temperature is obvious, suggesting a non-linear dependence

of log(stress) on temperature. Therefore, reverse stepwise selection regressions were

performed including the squares of each variable. The resulting nonlinear regression

equation was:

log(stress)=381.044539-0.371578T'+0.000091T'2+0.019031P'+0.5639071og(R)' (2)

with a higher correlation coefficient R2adj =.995 and lower rms error=0.0194. The plot of

predicted and observed log(stresst vs. temperature showed improved agreement (A-2).

This equation indicated flow stress generally increased with presoak time and strain rate,

but the dependence varied with temperature. In the temperature range of 2025 to 2050F,

flow stress only slightly increased with temperature. Such a temperature response would

be preferable in a production process. But at higher temperatures, flow stress increased

more sharply with temperature.

It is highly preferable that the alloy exhibit superplastic flow during a forging

process. This allows complete flow of the material into all forging die cavities with

uniform strain and strain rates in the disk alloy, and minimizes the buildup of stresses in

the dies. Superplastic flow is present when a material exhibits high strain rate sensitivity

(m), as usually defined by the relationship _=K(dv_Jdt) n_. A material is considered

superplastic in deformation conditions where a strain rate sensitivity m of at least 0.3 is

observed. The strain rate sensitivity m was determined by fitting a second order

polynomial to the log(stress) data as a function of log(strain rate) for each temperature

and pre-soaks of 1 and 10h. The first derivative was then taken and evaluated at each

tested strain rate. It should be cautioned that only three strain rates were tested for each

temperature and pre-soak. Therefore, the second order polynomial fit used three data

points to estimate 3 constants, resulting in 0 degrees of freedom and a perfect fit through

the data. This did not allow an estimate of the remaining rms standard deviation between

the experimental data and the curve fit. The resulting equation constants are in Table 2,

and strain rate sensitivities are included in Table 1. The material exhibited superplastic

flow for all conditions evaluated.

Grain Size Response

1. As-For_;ed

Images of the typical microstructures observed in all specimens in the as-forged

state are compared in Fig. 4-9. Macrostructures appeared uniform in all cases. Scatter

plots of as-forged mean grain size (AFG) versus temperature (T), pre-soak time (P), and

log(strain rate) (R) are shown in Fig. 3. Dependencies of grain size on temperature and

strain rate are obvious. Reverse stepwise linear regression of mean ASTM grain size

number on temperature, pre-soak time, log(strain rate), and their interactive products

were performed, using an F-to-enter--4. The resulting linear regression equation was:

AFG= l 1.294737-0.416667T'

with a correlation coefficient R2adi =0.6598 and rms error=0.2408. The complete

statistical output is given in Appendix B. Plots of the resulting predicted and observed

NASA/TM--2001-210901 3

meangrain sizevs.pre-soaktimeandvs.log(strainrate)showedonly randomerror(A-3). Theaccompanyingplot of predictedandobservedmeangrainsizevs.tempera-tureshoweda systematicdivergenceatintermediatetemperature,suggestinga non-lineardependenceof meangrainsizeon temperatureasobservedfor flow stress.Therefore,additionalreversestepwiseregressionswereperformedincludingthe squaresof eachvariable. Theresultingnonlinearregressionequationwas:

AFG=11.486292-0.415313T'-0.0772181"+0.091960R'-0.100000T'P'+0.088773T'R'-0.301556(T')2 (3)

with ahighercorrelationcoefficientR-'._dj=0.9072andlowerrmserror=0.1258.Theplotof predictedandobservedgrainsizevs.temperatureshowedimprovedagreementwithrandomremainingerror. Theseresultsmirroredtheflow stressanalysisin therespectthatwithin atemperaturerangeof 2025-2050F,as-forgedgrainsizedid not stronglyincreasewith temperature.This wouldbea favorabletemperatureresponserangeforproductionconsiderations.

2. Direct Heatup (DH) vs. Pre-Annealed (PA) Heat Treatment Response

Images of the typical macrostructures and microstructures observed in all

specimens after DH and PA heat treatments are compared in Fig. 10-29. During forging,

disks could have significant localized variations in strain rate, based on forging shape and

material flow characteristics. During solution heat treatment, disks could have significant

localized variations in solution time at temperature and subsequent cooling rate based on

forging section thickness and mass, along with production practices. The microstructures

are therefore compared at constant forging temperature and pre-soak time, to inspect the

variations in grain size due to forging strain rate and solutioning time. Macroscopic

variations of grain size with location are obvious for long presoaks, slow strain rates, and

higher temperatures, especially at 2075F. Some of the variations in grain size were

localized near the surface and might be machined away from a disk forging. However,

the grain size variations for higher temperatures extended nearly across the entire

specimen cross section. The RCC and DC specimens tested at 2075F often had over

100% larger grains in the center of the specimen, than near the sides. This excessive

grain growth, while not classifiable as true critical grain growth at high strain rates

(ref. 5), was definitely not conducive to a uniform supersolvus heat treatment grain size

response desired in this study.

Grain sizes were consistently measured near the center of the cross section of

each specimen. Scatter plots of averaged DH and PA mean grain size and ALA grain

size are shown versus temperature (T), pre-soak time (P), and log(strain rate) (R) are

shown in Fig. 30. Dependencies of grain size on temperature and strain rate are obvious.

Regression analyses were therefore employed.

Two approaches were used to analyze this data. The first approach C evaluated

the stability of grain size response with the Constraint that the two solution heat treat

types DH and PA could be used to simulate expected random cause heat treatment

process variations. The average and standard deviation between DH and PA mean grain

sizes and the average between DH and PA ALA grain sizes were first analyzed in

NASA/TM--2001-210901 4

approach C. The C analyses therefore had 19 data points for each of averaged grain size,

standard deviation of grain size, and averaged ALA grain size.

The second approach U used solution time as a fourth Unconstrained process

variable. From a practical standpoint, solution time variations could be due to furnace

run-to-run dwell time variations, material location in a disk, and location of a disk on a

tray of multiple disks within a furnace. Note that approach U ignored the contribution of

the pre-anneal step of the PA heat treatment on resulting grain size. Approach U

assumed that the grain size differences between DH and PA heat treatments were

primarily due to only solution time, which for a disk can be measured with embedded

thermocouples and modeled as a function of location for any disk shape. The U analyses

therefore had 38 data points for each of mean grain size, standard deviation of grain size,

and ALA grain size. The evaluations below indicated solution time did not significantly

affect mean grain size, ALA grain size, and standard deviation of grain size.

Reverse stepwise selection linear regression of mean grain size (G) on the

standardized variables and their interactive products were performed, using an F-to-

remove=3.9. The resulting linear regression equations (A-4C and A-4U) were:

G=3.577042-1.008333T'-0.325844P'

G=3.550790-1.000000T'-0.314903P'

R2adj =0.8251, rms error=0.403 (4C)

R2adj =0.7394, rms error=0.5077 (4U)

These equations both indicated ASTM grain size number decreased (grain size increased)

with increasing temperature and presoak time.

Linear regression of ALA grain size on the standardized variables and their interactive

products were also performed, using an F-to-remove=3.9. The resulting linear regression

equations were:

ALA=-0.499171 - 1.066667T'-0.428152P'+0.197674R" R2adj =0. 87O0, (5C )mas error--0.3756

ALA=-0.496379-1.062500T'-0.425361 P'+0.206261R'-0.179167 T'P' (5U)

R-'adj =0.8467, rms error=0.4122

The complete statistical output is given in Appendix A-5C and A-5U. Plots of the

resulting predicted and observed mean and ALA grain size vs. temperature, pre-soak time

and vs. log(strain rate) showed only random error. The equations both indicated that

ALA grain size coarsened with increasing temperature, presoak time, and decreasing

strain rate. Equation 5U indicated an additional interactive contribution of combining

high temperature and long presoak times gave coarser ALA grain sizes.

The regressions of standard deviation of supersolvus grain size (SDG) gave mixed

results:

9

SDG=-.357895 R-adj =0.0000, rms error=-0.2969 (6C)

Log(SDG)=- 1.172359+0.394899T'-0.192353R'-0.259390T'R' R2,_dj=0.4186 (6U)nns error=0.4417

NASA/TM--2001-210901 5

The complete statistical output is given in Appendix A-6C and A-6U. Plots of the

resulting predicted and observed standard deviation of grain size vs. temperature, pre-

soak time and vs. log(strain rate) showed only random error. While the rms error was

larger using approach 6U, this equation did provide guidance in what variables controlled

SDG. The standard deviation of grain size increased with temperature and decreased

with strain rate, with their additional interactive contribution decreasing standarddeviation.

Selection of Modified Forging Conditions

The equations generated to describe flow stress, mean as-forged grain size, as

well as supersolvus heat treated mean, standard deviation, and ALA grain sizes could

now be used to allow selection of modified forging conditions. It was clear that the target

grain size of ASTM 3-5 could easily be attained using various combinations of

temperature, presoak, and strain rate. The flow stresses were all acceptably low, and the

material remained superplastic in all conditions evaluated. However, the uniformity goal

was a key discriminator. The variation in grain size observed across the TMP specimens

and across specimens with varied strain rates and presoaks clearly increased with

temperature. Further, the ALA grain size coarsened unacceptably at high temperatures.

These trends all pointed to the lower temperature of near 2025F as preferable. Flow

stress and as-forged grain size was relatively stable between 2025 and 2050F. Heat

treated grain size and ALA grain size only moderately increased with increasing presoak

time at 2025F, as opposed to the larger changes at 2050 and 2075F. ALA grain size

became finer with increasing strain rate.

The statistical software was used to determine optimal conditions for minimized

ALA grain size in equ. 5C and 5U, and for minimized standard deviation of heat treated

grain size in equ. 6U. The optimal conditions were 2025F/lh presoak/0.001 s -_ strain

rate. However, a constant presoak time of lh would not be possible in a section greater

than 1" thick, due to variations in heat up time in a furnace. Heat up times can vary by

1 hour between a surface and midsection. So a longer presoak time would be necessary

to allow for such heat up effects. An intermediate presoak of 5h was selected for several

reasons. This time should minimize the effects of the above heat up time variations

according to the regressions, and therefore be practical to use as an aim in a variety of

forging shapes. A 5 h presoak time would also fit best into the statistical test matrix

design, giving a tightened full factorial of two temperatures 2025 and 2050F by 3 presoak

times of 1, 5, and 10h. The conditions of 2025F/5h presoak/0.001 s-_ were therefore

entered into the above equations.

The resulting regression equation predictions of flow stress, as-forged grain size,

mean supersolvus grain size, standard deviation of supersolvus grain size, and ALA

supersolvus grain size are listed for the selected conditions of 2025F/5h presoak/0.001 s-j

with 95% confidence intervals in Table 3. The predictions and confidence intervals were

all judged acceptable and will be compared to experimental results when these conditions

are employed to forge and heat treat 20 pound subscale pancakes.

NASA/TM--2001-210901 6

Summary and Conclusions

A series of forging experiments were performed with subsequent supersolvus heat

treatments, in search of suitable forging conditions producing ASTM 3-5 supersolvus

grain size. High forging temperatures of 2025F to 2075F and slow strain rates of 0.0001

to 0.00Is -_ were used, after presoaks of lh to 24h. Two supersolvus heat treatments were

then used having solution times of lh or 3h. The findings can be summarized as follows:

1) The material displayed superplastic response under all tested conditions.

2) Forging flow stress increased with strain rate, but did not significantly increase

with temperature from 2025-2050F.

3) As-forged grain size coarsened with decreasing strain rate and increasing presoak

time, but did not significantly vary with temperature from 2025 to 2050F.

4) Heat treated mean and ALA grain size coarsened with increasing temperature,

presoak time, and decreasing strain rate.

5) The forging temperature of 2075F gave very nonuniform supersolvus grain sizes.

6) The forging conditions of 2025F/5h presoak/0.001 s_ strain rate were selected,

based on grain size uniformity, standard deviation, ALA, and processing window,

for evaluations on subscale pancakes.

It can be concluded from this work that:

1) Forging at high temperatures of 2025-2050F at moderately slow strain rates can

produce consistent supersolvus grain sizes of ASTM 4-5 in ME3 disk alloy.

2) The supersolvus grain sizes do not significantly vary with solution times of 1 to

3h or with the introduction of a subsolvus pre-anneal before solutioning.

3) The forging temperature of 2075F should be avoided for this alloy if uniform

grain size is desired.

References

1. Enabling Propulsion Materials Program Final Technical Report, Vol. 5: Task K -

Long Life Compressor/Turbine Disk Material, Contract NAS3-26385, NASAGlenn Research Center, May 2000.

2. K.R. Bain, "Development of Damage Tolerant Microstructures in Udimet 720",Superalloys 1984, ed. M. Gell, et. al., The Minerals, Metals, and Materials

Society, Warrendale, PA, 1984, pp. 13-22.3. J. Gayda, R. V. Miner, T. P. Gabb, "On the Fatigue Crack Propagation Behavior

of Superalloys at Intermediate Temperatures", Superallo_s 1984, ed. M. Gell, C.S. Kortovich, R. H. Bricknell, W. B. Kent, J. F. Radavich, The Minerals, Metals,

and Materials Society, Warrendale, PA, 1984, pp. 733-742.

4. M. Soucail, M. Harry, H. Octor, "The Effect of High Temperature Deformationon Grain Growth in a P/M Nickel-Base Superalloy", Superalloys 1996, ed. R. D.

Kissinger, et. al., The Minerals, Metals, and Materials Society, Warrendale, PA,

1996, pp.663-666.

5. E.Huron, S. Srivatsa, E. Raymond, "Control of Grain Size Via Forging Strain

Rate Limits for R'88DT", Superalloys 2000, ed. T. M. Pollock, R. D. Kissinger,R. R. Bowman, K. A. Green, M. McLean, S. L. Olson, J. J. Schirra, The

Minerals, Metals, and Materials Society, Warrendale, PA, 2000, pp. 49-58.

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NASAJTM--2001-210901 38

Appendix A- 1

Least Squares Coefficients, Response LS, Model DESIGN__AUTO__J.S

0 Term 1 coeff. 2 Std. Error 3 T-value 4 signif, 5 Transformed Term

1 1 0.240553 0.0078802 ~T O. 041239 0.009913 4.16 0. 0008 ((T-2.05e+03)/2.5e+01)3 ~P 0.082134 0.008091 10.15 0.0001 ((P-5.5)/4.5)4 -LSR O. 277051 0.009909 27.96 0.0001 ((LSR+3.5)/5e-01)

NO. cases - 19 R-sq. - 0.9836Resid. df - 15 R-sq-adj. = 0.9804- indicates factors are transformed.

RMS Error - 0.03434Cond. No. - 1.022

Least Squares Summary ANOVA, Response LS Model DESIGN__AUTO_LS

0 Source 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio S Signif.

i Total(Corr.) 18 1.0815452 Regression 3 1.063857 0.354619 300.70 0.00003 Residual 1S 0.017689 0.001179

R-sq. = 0.9836R-sq-adj. _ 0.9804

Model obeys h_erarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

Least Squares Components ANOVA, Response LS Model DESIGN_AUTO__LS

0 Source 1 df 2 sum Sq. 3 Mean sq, 4 F-Ratio 5 Stgnif. 6 Transformed Term

1 Constant I 1,0528702 ~T I 0.020408 0.020408 17.31 0.0008 ((T-2.05e+03)/Z.Se÷O1)3 ~P 1 0,12150S 0.121505 103.00 0.0000 ((P-S.S)/4.S)4 -LSR 1 0.921797 0.921797 781.70 0.0000 ((LSR+3.5)/Se-OI_5 Restdual 15 0.017689 0.001179

~ indicates factors R-sq. - 0.9B36are transformed. R-sq-adj. - 0.9804

Default sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

NASA/TM--2001-210901 39

Appendix A-1 (cont.)

Nul reg _ExFrMPONULREG, Model DESIGN_UTO__LSMain Effects on Response LOGSTRESS

(w_th 95% confidence Znterva]s)

T: 2025 to 2075

P: I to 10

LSR; -4 to -3

L....... D-.... _;

i '- -i

I ' _

0.0 0.1 0.2 0.3 0.4 0.5 0-6

Increase in LS

LOGSTRE$S vs TFJ4P, Adjusted for Remaining Predictorsusing Mulreg GEX_ULREG, Mode] DESIGN___TO_S

0.35-

AL

do 0.30jGu ss T 0.25t R

• E 0.20_'dsS b

2030 2035 2040 2045 2050 2055 2060 2065

TEMP

_J Adjusted Data ValuesAdjusted Fitted Curve

p, • |

2070 2075

0.4"

ALdO

JGo. 3-uS

STtReE0.2-

dS

0. I_1

LOGSTRESS vS PRESOAK, Adjusted for Re_tnfng PredictorsUsing Nu]reg _EXPTMP_NULREG, Mode] DESIGN__AUTO_LS

2 3 4 5 6 7 8 9

PRESOAK

i.: Adjusted Data ValuesAdjusted Fitted Curve

i

10

NASA/TM--2001-210901 40

Appendix A- 1 (cont.)

LOGSTRES$ vS LOGSTRART, Adjusted for Remaining Predictorsusi no _ulreg eEXFrTMPi_MULREG, Mode] DES_GN_.__UTO__LS

AL j_-_

dO 0.4jG

ST 0.2 __._-_'tR

eEdS 0.

4.2 t _--- _- -_ _ _ ..... l --) ) .......... 4-4.0 -3.9 -3.8 -3,7 -3.6 -3.5 -3.4 -3.3 -3.1 -3.1 -3.O

..-J

LOGSTRART

Adjusted Data valuesAdjusted Fitted Curve

.

e

s 0idu -1-a

-2"

Case Order Graph of Residuals of LSusing Studentized Residuals in wodel DESIGN_..AUTOjLS

÷ + +

+

+

+ 1.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Case Number

17

÷ 1.

18I, I

lg 2O

Re$i

Residuals of LS vs Fitted V_luesusing studentized Residuals in _odel DESIGN._AUTO__LS

+ 4"

+ ÷

4-+ 4-

',F

aU]__.i0!

$ -

-- r

2

I-

÷

-4-

,' ; "r I t I t t

-O.l 0.0 0.1 0.2 0.3 0.4 0.5

Fitted Values

0.6 0.7

NASA/TM--2001-210901 41

O, 99-

C O.95-u 0._

m 0.8-

HPro O. 2=

b 0.1_0.05

O. O_


No_a] Probability Plot of Residuals of LSUsing studentized Residuals in Model DESZGN___UTOmLS

Csample size = 19)

_____..... .-._r--¸

÷

: _ F I tS -2.0 -1.5 -1.0 -0.5 0.0

÷

4. + 4.

0.5 1.0 1.5

Residuals of Ls

,

Fre4-quen 2-cY

H_stogr_ of Residuals of LSusing student_zed Residuals in Model DESZGN.__UTO_LS

(Sample size = 19)

Residuals of LS

m_

t

, !i t

I , _, s [ t '; '10.6 0.8 1.0 1.2 1.4 1.6

0 Factor, Response 1 Range 2 Zn_tta] 3 Optima1or Formula Setti ng Value

1 Factors2 TEMP3 PRESOAK4 LOGSTRART56 Responses7 LOGSTRESS

2025 to 2075 2050 20251 to 10 5.5 1.0004-4 to -3 -3.5 -3.9974

N_N -0.15841

converged to a, tolerance of 0.000077 after 109 Steps.

NASA/TM--2001-210901 42

O, 99

C 0.95u 0.9

m 0.8-

1PPo 0.2-b 0.1-

0.OS-

0.0__2


Normal Probability Plot of Res_duaTs of LSUsing studentized Residuals in Model DESIGN___UTO__L$

CSamp]e size = 19)

÷

÷

.--_@

+

S -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Residuals of LS

.

Fr

e 4'qU

en 2"¢Y

Histogra_ of Res_dua]s of LSusing Student_zed Residuals _n Node] DESIGN_.AUTO__LS

(sample s_ze = 19)

1

I

r ........................ i - ........I,J

I.......... i , , t ,1 I _ !

Residuals of LS

0 Factor. Response 1 Range 2 In_¢tal 3 Optimalor Formula Se_cing Value

1 Factors2 TEMP 2025 to 2075 2050 20253 PRESOAK 1 to 10 5.5 1.00044 LOGSTRART -4 to -3 -3.5 -3.9974S6 Responses7 LOGSTRESS M_N -0,1$841

converged to a _olerance of 0.000077 after 109 steps.

NASA/TM--2001-210901 43


LOGSTRESSPRESOAK = 1.0004

-3.0'

LOGST -3.5,RART

-4,C2025

' ' ' ......... U 4_...... 0,35 .............. - ........................... 0.4 ............ _ .... " :_------

................... 0.3 ........... - .....................................--o.25 .......... ........................ 0.3..................:-.................... 0.35 .......... 0 2 ---0, 25 ..............

_ _'_.............................. 0 2 .......................... 0.25 ........... U" L_ ............ " ............. . ......................

r_....... _ ....................... O. 15_ ....... - ........................--o ._s.i_i_...__i._................................... o.z--Z.:i-±-.i_................. ,o.15........

• -........... o.o5.................. -.............--S'-_L- ........... 0 ................................... 0 ........ ' .................... _). 05 ....---o.o_ .......................................... 0.05 .......... "........

........................ ,0 1 ........ ........ 0.05--.--..... ," : ------:-_-. ......... - :-.- .-------._-r, -9__ .1 .... ,,..... i 4 --- ,

2030 2035 2040 2045 2050 2055 2060 2065 2070 2075

TEMP

....... LS

1C"

P 8-R

E 6"SOA 4"K

LOGSTRF_RSLOGST_ ,, - 3.9974

r _ .......... : : .-rb. 04 ¢ I

__.__0 , 02 .2_ .......... _ ................ 0 " 0_ .......

:--°.°6,_ -......o.o -0.04_

................. ' ............... 0. 1 .._ --'- --0o 0_,

2 .......... 01.14. _ _ ..........:.._..... -0.12 .... . ............ T--0,1 .... "---0.08 ..

2025 2030 2035 2040 2045 2050 2055 2060 2065 2070

................ --'0.04 .......

-_-_0.02 ............

2075

TEMP

......... LS

LOGSTRESSTE_ ,- 2025

-3.0' " ......... b, 4._L.:_. : t _ I i _ f .......... ,L .................................. -0.4 ...... ' ................... " ..... -' -----'-0.5 -'------

O ................... -0,3 .......... - .............. "............... '.................. 0.4 .....

G ........................ 0.3

S .................. _). 2 ,. '............................................ O. 3 .....T -3.5,_ ...... - ...................................... 0.2 ............. -

R , -.............. _3,1 .... ........... ' ................................... 0.2 ......A .................... 0.1 ........R ..................... 0 ...... "--................. ............................ 0.1T ......... .....

-4.o,-...._.........._......i........_--o._t....., , , , , . .... ...... , , _.....,..o.__z.o 1.s 2.0 2.s 3.0 3.s 4.0 4.5 5.0 5.5 6.0 _.5 7.0 7.s 8.0 8.s 9.0 9.5 10.0

PRESOAK

....... LS

NAS A/TM--2001-210901 44

Appendix A-2

Bisquare coeffScients, Response L5, model DESIG_UTO_S

0 Term 1 coeff. 2 Std. Error 3 T-value 4 Signif, 5 Transformed Term

1 1 0.207982 0.0073352 ~r 0.046337 0.005602 ((T-2.05e÷03)/2.Se+01)3 _P 0.085639 0.004572 18.73 0.0001 ((P-5.5)/4.5)4 -LSR 0.281954 0,005600 50.35 0,0001 ((LSR+3.S)/Se-01)5 ~T**2 0.056926 0.009229 6.17 0.0001 ((T-Z.05e+03)/2.Se+01)**

No. cases = 19 R-sq, _ 0.9953Resid. df m 14 R-sq-adj, = 0.9940~ indicates factors are transformed.

RMS ErrOr - 0.0194cond. No. _ 2.958

Bisquare Summary ANOVA, Response LS Model DESIGlq_UTO_LS

0 Source 1 df 2 SUm Sq. 3 Mean Sq, 4 F-Ratio 5 sign_f.

1 TotalCcorr.) 18 1,1336312 Regression 4 1.128359 0.282090 749.20 0.00003 Linear 3 1.114033 0.371344 986.20 0.00004 Non-linear 1 0.014326 0.014326 38.04 0.00005 Residual 14 0,005272 0.000377

R-Sq. - 0.9953R-sq-adj, = 0.9940

Node1 obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

0 Source

Bisquar_Compor_nts ANOVA, Response LS Model DESIGN_.AUTO_LS

1 df 2 sum Sq, 3 Mean sq, 4 F-Ratio 5 Signif. 6 Transformed Term

1 Constant 1 1,0824062 ~T 1 0.025765 0.025765 68.43 0.0000 ((T-2.0Se+03)/2.Se+0I)3 ~P 1 0.132090 0.132090 350.80 0.0000 ((P-5.5)/4.5)4--LSR 1 0.954705 0,954705 2535.00 0.0000 ((LSR+3,5)/Se-01)5 -T**2 1 0.014326 0.014326 38.04 0,0000 ((T-2.05e+03)/Z.Se+01_**6 Residual 14 0.005272 0.000377

~ indicates factors R-sq, - 0.9953are transformed. R-sq-ad_. = 0.9940

Defmult sum of squ_res.Model obeys hierarchy, The sum of squares for each termis computed assuwing higher order terms are f_rst removed.

NASA/TM--2001-210901 45


Mulreg gEXPTMP_AtULREG, Model DESIGN__AUTO.__LSMain Effects on Response LOGSTRESS

(with 95% Confidence Intervals)

T: 2040 to 2075

P: 1 to 10

LSR: -4 to -3

I ! I t :

; t I0.0 0.1 0.2 0.3 0.4

Zncrease in LS

O.S 0.6

ALdoJGu ssTt R• Eds

S

O. 35_

O. 30

O.25

I

0.20_'_--_'----

_S02 ........ :O. 5 2030

LOGSTRESS vs TEMP, Adjusted for Remaining PredictorsUsing Mulreg _-XPTMP_IULREG, Mode] DESIGN._AUTO__LS

2035 2040I .I t ...... t

2045 2050 2055 2060

TEMP

'_ Adjusted D_ta ValuesAdjusted Fitted curve

.....I " I2065 2070 207S

ALdO

jGuSs TtReEdS

$

LOGSTRESS vs PRESOAK, Adjusted for Remaining PredictorsUsing blulreg 8EXFTMI_tULREG, Model DESIGN__AUTO_.L5

0.35

0.30

0.25

0.20

0.10 2 3 4I I I _ t I5 6 7 8 g I0

PRESOAK

Adjusted oata valuesAdjusted F_tted Curve

NASAITM--2001- 210901 46


LOGSTRESS VS LOGSTRART, Adjusted for Remaining Predictors

USing Mul reg _EXPTMPgNULREG, Model O_SIGN_..AU_LS

~

J

AL 0"iIdO 0.jG

°' tsT 0.2-

dS O. -_-_

S-0.2-L I J

-4.0 -3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2

LOGSTRART

iZ Adjusted Data values---- Adjusted Fitted Curve

• -L ........ I-3.1 -3.O

Case order Graph of Residuals of LSUsing Studentized Residuals in Mode] DESIGN__AUTO__LS

2TR ÷

d

a -2

1

_.- P I _0 1 2 3

÷ +

+ 4- ÷ +

+ ÷

4 5 6 7 8 9 10 11 ].2 13 14 15 16 17 18 1.9 ZO

Case Number

2T

R 1-

es Oid -iua -2-1

s _}

÷

Residuals of LS vs Fitted values

using studentized Residuals in Model DESIGN__AUTO_LS

+ ÷

÷

÷

++

t

÷ q-

4-

I t t

2 -0.1 0.0 0.1 0.2 0.3

Fitted values

0,4 0.5 0.6 0.7

NASA/TM--2001-210901 47

0.99'

¢ 0.95-u 0.9.

m 0.8.

Hro 0.2,b 0.1

0.05

0.01


Normal Probability Plot of Residuals of LSUsing studentized Residuals in _odel DESIGN__AUTO_L$

(Sample size = 19)

+

j"

f_

,/

', : _ : : ;-3 -2 -I 0 1

/ +/

Residuals of LS

B

1.0 isqu

r

.S •

et

g

3.0 h2

s

.

Fr_equ 4-enc 2,Y

0"; " :-4.0 -3.5

Histogram of ResSduals of LSUsing studentized Residuals _n Model DESIGN__AUTO_LS

(sample size - lg)

Ft

; .......... _........... i t-3.0 -2.5 -2.0 -1.5

F ....................

ii

I

i

-1.0 -0.5 0.0

Residuals of LS

I ..... _ - I :0.5 1.0 1.S 2_0

0 Factor, Response 1 Range 2 Initial 30p_imalor Formula Setting Value

1 Factors2 TEWP 2025 to 2075 2050 2039.33 PRESOAK 1 to 10 5.5 1.05124 LOGSTRART -4 to -3 -3.5 -3,99995

6 Responses7 LOGSTRESS _N -0.16798

Converged to a tolerance of 0.000077 after 71 steps.

NASA/TM--2001-210901 48

0.00-

LO -0.O5-GST -0.10-

RES -0.15-S

-0.20


Predictions and 95% simultaneous confidence intervalsfor mean responses of LOGSTRESS using model DESIGN_..AUTO__LS

P - 1.0512, LSR = -3.9999

Lr 4 b i

2025 2030 2035 2040

r-

-F

I

J

2045 2050 2055 2060 2065 2070 207_

TEMP

------- Curve I

0_1"

L

o 0.0GST -0.1-RE

S -0.2-5

-0.3

Predictions and 95% simultaneous confidence intervalsfor mean responses of LOGSTRESS usin9 model DESIGN__AUTO_LS

LSR = -3.9999, T = 2039.3

.... _ .... L

}1 2 3 4 5 6 7 8 9 10

PRESOAK

----F_-- Curve ]L

0-6"

L 0.4"O

GS 0.2-T

R O.O-

SS -0.2-

Predictions and 95% simultaneous confidence intervals

for mean responses of LOGSTRESS using model DESIGN__AUTO__LST = 2039.3, P = 1.0512

. ...

_-- ---_

_ _----

-0.4 -4,0 -3_,9 -3.8 -3'.7 -3,6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0

LOGSTRART

--r_ _.... Curve 1

NAS A/TM--2001- 210901 49

Appendix A-2 (cont.)LOGSTRESS

LOGsTRART = -3.9999

P

R

E

S

0

A

K

10'

8

6-

2-

2025

............................................... o ............. ............_ ........oo4.- .i- ............-0.06..........................-0.°6?......-.-i............-I"-Co.o2."....

......... 0,12 ........................... - ........... . -0,04 "-

2030 2035 2040 2045 2050 2055 2060 2065 2070 Z075

TEMP

.... L5

LOGSTRESS

PRESOAK - 1.0512

-3.O

L

0

G

S

T -3.5,R

A

R

T

-4.C2025

...... _, f .... I ,, _, - -0_ ............::: -_.i i.......O._S__ :

......... O. 35 ........................................................... _ .... _. "'_-----.

7_o-7_¢:_-7---TL---7_--Z---.---.--7.-_--Z.o_i-CT_" "..........--o._s.....'_-:

............o.i........ _" •............ --o.ls......"-0.05 ................................ 0,0S ................. ....

................ -o ............................. o ............... _................. o o5 "--o.o5...........................................o.os...............-.................." ........

.... -_'_ ........ _-,,'--T-------r ............._, __7-/ ....... ::7"-° z :?7 7 .os......zo_ 203s 2040 204s zo50 20s5 2060 206s 2070 zon

TEMP

....... LS

LOGSTRESSTEMP - 2039.3

-3.0

LO

G

S

T -3.R

A

RT

_4 ..... ( U _ " _ • I l t t I t_L_.:.. I I I I ! J

....... - ...................................0.4 ........ - " - - 0.5 .... |I........... -u . :_...................... ................... -.0.4 .... [

.................-0.3...... 0................O.Z......................................-0.2-.

:................ -0.1 .................... ................... 0.2 ..................... -0.1 ......

......................0 ..... "....................._--0. I....

............. i-7i .....:,:,::_--0. a....... : . _...... ,...... T.... -r-°--.'--4. _L40 ; ....• z.s _.0 2.s 3.0 3.s 4.0 4.s s'.o s:s 610 6:.s ,'.0 ,.s 8.0 s.s 9.0 _.s zo.o

PRESOAK

.......... LS

Predictions and 95_ stmult&neous confidence intervals

for r_n responses of LOGSTRF_S using mode] DESIGN__AUTO._.J.S

LSR - -3

P T-2025

Lower 0.4534585 Predicted 0.491009

Upper 0.528560

NASA/TM--2001-210901 50

Appendix A-3C

Least Squares Coefficients, Response A_GS, Model DESIGN._.AUTO__AFGS

O Term l coeff. 2 std. Error 3 T-Value 4 Signif. 5 TransFormed Tern

1 1 11.294737 0.0552552 -T -0.416667 0.069527

No. cases = _9 R-sq. = 0.6787Resid. df _ 17 R-sq-adj, = 0.6598~ indicates factors are transformed.

-5.99 0.0001

RM5 Error = 0.2408cond. No. = 1

((T-2.05e÷03)/2.Se+01)

Least Squares Summary ANOVA, Response AFGS Mode] DESIGN__AUTO_FGS

0 Source I df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio 5 signif,

I Total(Corr,) 18 3.0694742 Regression 1 2.083333 2.083333 35.91 0.00003 Residual 17 0.986140 0.058008

R-Sq. = 0.6787R-sq-adj, = 0.6598

Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

Least Squares Components ANOYA, Respoltse AFGS Model DESZG_O_FGS

0 Source 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio S Signif. 6 Transformed Term

1 Constant 1 24242 ~T 1 2.083333 2.083333 35.91 0.0000 ((T-2.0Se+O3)/2.Se+O1)3 Residual 17 0.986140 0.058008

~ indicates factors R-sq. = 0.6787are transformed. R-sq-adj. = 0.6598

DefauIt sum of squares.t4odel obeys hierarchy. The sum of squares for each termis computed &ssuming higher order terms are first removed.

NASA/TM--2001-210901 51

Appendix A-3C (cont.)Mulreg _IEXPT_MULREG, Model DESIGN_UTO__AFGS

Main E_fects on Response ASFORGEDGS(w_th 95% confidence Intervals)

Ii

ttrt

-0.5

Xncrease in AFGS

A _'°T

flF ij o lz.sJ_uR [

tE II,eo

dG j

S i0 5 2030

ASFORGEDGS vs TEMP, Adjusted for Remaining Predictorsusing Nulreg @EXPT_I_ULREG, Model DESZGN_UTO_.J_FGS

....( _ ....2035 2040

r-'

t '- I , I J2045 2050 2055 2060

TEMP

i;:! Adjus%ed Data values_, Adjusted Fitted curve

.p , f2065 2070 2075

Case Order Graph of Residuals of AFGSusing student_zed Residuals _n Model DESIGW___UTO._AFGS

+ +

÷

+

+

2TJ

l

° la

1I

-2!0

÷ ÷

+ +

-Ih ÷

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 _8 19 20

Case Number

NASA/TM--2001-210901 52

2TI

Rle +

s

id 0 + ....u I +

1 -1

i.- _ e - io_,9

Appendix A-3C (cont.)Residuals of AFGS VS Fitted Values

Using 5tudentized Residuals in Model DESIG___AUTO__AFGS

-t-

÷

4-

11.0 11.1 11.2 11.3 11,4 11, S 11.6 ll.l 11.8

Fitted values

Normal Probability Plot of Residuals of AFGSUsing Studentized Residuals in Node] DESIGN._.AUTO___AFGS

(Sample size = 19)

0.ggT0.95

m

"!:_i._ J_--_ _...........p ._ .__¢_.... ;k _'- ""

o _T --b ....._.- -"

0+

-2.0 -1.S -1.0 -0.S O.0 O. S

Residuals of AFGS

1.0 1.5 2.0

Histogram of Residuals of AFGSUsing Studentized Residuals in Model DESIGN.,_AUTO_.A_GS

(Sample size - 19)

r I

• 41tq

n - ..................

c ! i i

1.o"-_. ' ' ' _ '_.'_ .... _....... i _ ; ' _ ; i I • _ ,-t _ 2 1.4 1.6 1.8 2"0-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8

Resiclua]s of AFGS

NAS A/TM--2001-210901 53

Appendix A-3C (cont.)

0 Factor, Response 1 Range 2 Initial 3 Optima]or Formula setting Value

1 FaCtOrS2 TENP 2025 TO 2075 2050 20253 PRESOAK 1 TO 10 5.5 7,7S4S Responses6 ASFORGEOGS MAX 11. 7117 AVGS_ALA 3.969g

converged to a tolerance of 0.00012 after 46 steps.

Predictions and 95% simu]taneous confidence _nterva)sfor mean responses ot= ASFORGEDGS using mode] DESIGN.__UTO__AFG5

_"°T T

A ._ .....S i ----

F 11.5 t ± " -O

R 1G FDE li. O_-

GS

I0.5 _ _ '.2025 2030 2035 2040 204S 2050

L

2055 2060 2065 2070 2075

TEMP

NASA/TM--2001-210901 54

Appendix A-3U

Least squares coefficients, Response AFGS, Model DES_GN___UTO_..AFG5

0 Term 1 coeff. 2 Std. Error 3 Tovalue 4 SSgnif. 5 Transformed Term

1 1 11,486292 0.0475562 -T -0,415313 0-0363223 _o -0.077218 0.0295434 --LSR 0,091960 0.0363015 -T*P -0._00000 0.0363156 -TWLSR 0.088773 0.0444627 -'1"*'2 -0,301556 0.059832

NO. cases = 19 R-sq. = 0.9381Resid, df = 12 R-sq-adj. = 0.9072~ indicates factors are transformed.

-2.75 0.01752.00 0.0691

-5.04 0.0003

((T-Z.05e+03)/2,$e'_ll._

((_-5.s)/4.s)((LSR+3.5)/Se-01)((T-2.05e+03)/Z.5e+01_*(((T-2.05e+O3)/2.Se+01)*(((T-2.05e_03)/Z.Se+01_**

t_5 Error = 0.1258cond. No, - 2.958

Least Squares sun_nary/U_OVA, Response AFGS Model DESIGN__AUTO__AFGS

0 source 1 df 2 sum Sq. 3 Mean Sq. 4 F-R_tio 5 s_gnif.

1 Total(corr.) 18 3.0694742 Regression 6 2.879564 0.479927 _0.33 0.00003 Linear 3 2.294470 0.764823 48,33 0,00004 Non-_inear 3 0.585094 0.195031 12.32 0,0006

5 Residual 12 0.189909 0.015826

R-sq. = 0.9381R-sq-adj. _ 0.9072


Least Squares Components ANOVA, Response AFGS Model DESIGtC_AUTO___APGS

0 Source t df 2 sum sq. 3 Mean sq, 4 F-Ratio 5 Stgn_f. 6 Transformed Term

1 constant 1 24242 ~T 1 2.083333 2.083333 I31.60 0.00003 ~P I 0.107391 0.107391 6.79 0,02304 ~LSR 1 0.101557 0.101557 6.42 0.02635 ~T*P 1 0.120000 0.120000 7,58 0.01756 -T*LSR 1 0.063089 0.063089 3.99 0.06917 -T**2 1 0.402005 0.402005 25.40 0.00038 Residual 12 0.189909 0.015826

(O'-2.05e._3)/Z.Se+0_((p-5. s)/4, 5)CCLSR÷3.5)/5e-0 I)((T-2.05e+03)/2.5e+01)*(C(T-2.05e+03)/2.5e+.Ol)* C((T-2.05e+0 3)/2.5t+O_**

~ indicates factors e-sq. - 0.9381are transformed. R-sq-adj, = 0.9072

Default sum of squares.Mode_ obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are f_rst removed.

NASA/TM--2001-210901 55

Appendix A-3U (cont.)

_u]reg @EXPT_4ULREG, Mode] DES_GN_AUTO__AFG5Main Effects On Response AS_OllGEDGS

{w_th 95_ Confidence Intervals)

T: 2033 ¢o 2075

P: lto20

LSR: -4 ¢o -3

-1.2

,_ ', ; _

-1.0 -0.8 -0.6 -0.4 -0.2 0.O

Increase in AFG5

0.2 0.4

Mu]reg _EXPT_LREG, Model DESZGN__AUTO_.AFGS2nteraction Effeccs of TEMPwith LOGSTRART

on Respoflse ASFORGEDGS

LS_ = -3 t- _ _ ' I

LSR: -4 1:O -T 2025T = 2050

T = 2075 _ 4 _ :. a-1.5 -1.0 -O.S 0,0 0.5

95% confidence IntervalsFor Increase in ASFOP_EDGS

1.O

Mu]reg OEXFrT_MULREG, Model DESIGN___AFGSInteraction Effects of TEMPwtth PRESOAK

On Response ASFORGEDGS

T. zo2s } !T = 2050 _ ,_-

T - 2075 ! !

-Z.4 -1.2 -1.O -0.8 -0.6 -0.4 -0.2 O.O 0.2 0.4

gs_ Confidence IntervalsFOr Zncrease in ASFORGEDGS

NASA/TM--2001-210901 56

A 12._A SdF --j o ii.S-uRs G

t E li._• Dd_

$i0°5 -;

202 2030


ASgORGEDGS vs TEMP, Adjusted for Remaining Predlctorsu,:i ng Mul reg OEX_ULREG, Model DESTGN.__U_FGS

2040 2045 2050 2055 2060 2065 2070 2075

TEMP

Adjusted Data ValuesAdjusted F_tted Curve

AASdFjouRsGtEeDdG

S

ASFORGEDGS vs PRESOAK, Adjusted for Remaining Predictorsusing Mulreg _EXPT_IULREG, _odel DESIGN__AUTO__AFGS

11.6_,

zz.

11.2-

11.0-

_0. g2

_D

3 4 5 G 7 8 ,9 10

PRESOAK

Adjusted Data valuesAdjusted Fitted curve

ASdF .jo

sG 1.1..2

eD 11.

S 10.

ASFORGEDGS vs LOGSTRART, Adjusted for Remaining predic_corsusing Mulreg _F.XPTO_JLREG, Mode] DESTGN._AUTQ__AFGS

H

-3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3,2 -3.1 -$.0

LOGSTRART

:-2 Adjusted Data va]uesAdjusted Fitted Curve

NASA/TM--2001-210901 57

2-

R 1e

s Oidu -1-a1

--2"

-3 o


Case order Graph of Resiflua]s of AF_using studencized Residuals in Mode] OESIGN_UTO___FGS

+ ++

+ + +

÷ ÷ +

+ +

÷ ÷ ++

+

i 2 3 4 s 6 7 s 9 zo lz lz z3 z4 is 16

Case Number

! -I'- ! -

17 18 I9 Z0

.

R

S

i 0d

u_ 1 +a

1s -2,

_.o.4 .0.6

Residuals of AFGS vs Fitted ValuesUsing studentized Residuals in Mode] DESTGN__AUTO__AFGS

÷

÷

+

÷

ar

', ; I I10.8 11.0 11.2 11.4

Fitted Values

+

q11.6

|11.8

0.99"

c 0.9_u 0,9m 0.

r

0 O.b 0.1"

O.OS"

o._

Nomal Probability Plot of Residua]s of AFGSUsing Studentized Residuals in Model _ESZGN__UTO__AFGS

(Sample size _ 19)

f ..----

_._ *--- Jr

J

+

,5 -2.0 -1.5 -1.0 -0.5 0,0

Aesiduals of AFGS

4-

/

+ : : :O.S 1.0 1.$ Z.O

NASA/TM--2001-210901 58


Histogram of Residuals of AFG$Using Studertt_zed Residuals in Model DESZGN__AUTO.._AFGS

(sample size = 19)

Fr• 4-quen 2-c

Y ,- ....... 7I

-2.5 -2.O

I

-1'.5 -I.0 --O.5

i ! ! 'o_o o.5 1_o z.s 2.0

Resi dual s of AFGS

0 Factor, Response 1 Range 2 Initial 3 optimalor Formula Setting Value

1 FaCtOrS2 TEMP 202S to 207S 2050 2040.33 PRESOAK i to 10 5.5 1.0024 LOGSTRART -4 to -3 -3.5 -3.001S6 Responses7 ASFORGEDGS MAX 11.6988 LOGSTRESS O. 39439

converged to a tolerance of 0.00012 after 4S steps.

1_°0"

ASF

11. S"ORG

E 11.ODGS

Predictions and 95_ s_multaneous confidence intervals

for mean responses of ASFORGEDG5 using model DESZGN_TO__AFGSP _ 1,002, LSR - -3.001

T

i

•- ,' t ] I ,I t -2025 2030 2035 2040 2045 2050 20SS

TEMP

2O6O

.4.

2065 2070 2075

-- iS---curve ].

NASA/TM--2001-210901 59


Predictions and 95% simultaneous confidence intervalsfor mean responses of A_FORGEDGS using model DESIGN__AUTO_.AFGS

LSR _ -3.001, T - 2040.3

5 12.0F

° 11.87 ;_R ............ :.................

°°fE ll.

D

sG 11.4_ .k

ii 2 .... _ ' '1 2 3 4 5 6

', : I , i,,7 g 9 10

PRESOAK

---C_--- Curve I

12.2-

AS 12.0

F

0 ll.&R

GE 11.6-

0

G 11.4-S

11.2

predictions and 95_ simultaneous confidence intervalsfor mean responses of ASFDRGEDGS using model DESIGN_AUTO_.AFGS

T = 2040.3, P _ 1.O02

Td

i/

1

|

!

/ I" I-4.0 -3.9 -3.8

1-

I

I I : - _ I ,' ,' - I'-"-3.7 -3.G -3,5 -3.4 -3.3 -3.2 -3.1 -3.0

LOGSTRART

-,- .--C---- Curve 1

PRESOAK

10"

8-

6

4-

\

2025 2030L t .

2035 Z040

ASFORGEDGSLOGb"TRART - -3.001

.... i .......

\• ,...

x

_1.6

i ab

2045 2050

%

" % il

% ", N "\

\ "a. _ \,.. ,. 11.I

\

1"1.5 11.4 11.3 X ".,'x• \

- _!-,! 12-., "_.2055 2060 2065 2070

TEMP

.........AFGS

2075

NASAffM--2001-210901 60

-3.0"

L IO

GS

T -3,5,R

ART

2025


ASFORGEi_S

PRESOAK - 1.002

1

If.st

; .... !.... i • I $

\ x1,6\

20_0 Z035 204O

- o-_, ++

: / -'--./ ,./(

2045 2050 2055

TEMP

/

/ /

; / /,/ ]"

e " •

• -" /," .1 /f :

• / • , .

:: /.'" ,/ / /"

/" " J t " "/ ..I"

II._ II.} ll.'i 1£"" I0.!

/ l" f _/'1• _ -" l-'-" " : /"

2060 2065 2070 2075

....... AFGS

ASFORGEDGS

TEMP - 2040.3

-3.0

L

0

G

S

x -3.5.R

A

R

T

........................ ..Ii. 6 .........

_- ---- ii.58 -

"" ..... II.6 .... --""- "

.......... il. 5S .... zz. 56- iil. 6

I1, 52 .......... :

-4"_L_0 1.5 2.0 2.5 3.0 3:5 4.0 415 $:0 5:5 6+.O-+25 710 7:5 6:0 B.5 9.0 9.$ 10.0

PRESOAK

........ AFGS

Predictions and g5_ simultaneous confidence intervals

for mean responses of _FORGEOGS using model DESI_TO._.AFGSLSR _ -3

P 1--2025

SLower 11.249138

Predicted 11.600705Upper 11.952272

NASA/TM--2001 -210901 61

Appendix A-4C

Least Squares coefficients, Response AVG, Model DESZGN___UTO_VG

0 Term 1 coeff. 2 std. Error 3 T-Value 4 Signif. 5 Transformed Term

1 1 3.577042 0.0924532 ~T -1,008333 0.116332 -8.67 0.00013 -P -0.325844 0.094954 -3.43 0.0034

NO. cases - 19 R-sq. - 0.8445 RNS Error - 0.403Resid. df - 16 R-sq-adj. = 0.8251 Cond. No. - 1.006~ indicates factors are transformed.

CCT-Z.05e+03)/2.Se+01)CCP-5.S)/4.S)

TABLE:49296 3R x 5C

Least squares Summary ANOVA, Response AVG Node1DESIGN__AUTO__AVG

0 source 1 df 2 SUm sq. 3 Mean Sq. 4 F-Ratio 5 Signif.

1 Total (Corr.) 18 16.711582 Regression 2 14.11321 7.05661 43.45 0,00003 Residua] 16 2.59836 0.16240

A-sq. - 0.8445R-sq-adj. - 0.8251

Nodel obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

16-SEP-ZO00 21:12 Page 1

Least Squares Components ANOVA, Response AVG Nodel OESIG_O__J_VG

0 Source i df 2 Sum Sq. 3 Mean sq. 4 F-Ratio 5 Signtf. 6 Transformed Term

1 Constant 1 243.36B422 ~T 1 12.20083 12.20083 75.13 0.00003 ~P 1 1.91238 1._123B 11.78 0.00344 Residual 16 2.59836 0.16240

~ indicates factors R-s;. = 0.8445are transformed. R-sq-adj. - 0.B251


((r-2.05e-_.O3)/2.Se-t.O1.)(Cp-s.s)/4.s)

NASA/TM--2001-210901 62

Appendix A-4C (cont.)Mulreg @EXPT_MULREG, Wodel DESIGN__AUTO_j_VG

Main Effects on Response AVGS(with 95% confidence Intervals)

T: 2025 to 2075

P: 1 to 10I

-3.0

¢ t ) i I

+ ............. • .............. !

42.5 -2.0 -1.5

Increase in AVG

I°1.0

I-0.S 0,0

d

uvsGtSed

2030

AVGS VS TEMP, Adjusted for Remaining Predictorsusing Mulreg OEXPTt_NULREG, Model DESIGN__AUTO__AVG

2035 2040 2045 2050 2055 2060

TEMP

_: Adjusted Data Values---- Adjusted Fitted Curve

2065 2070 2075

4.s

j A _'u v l:s G 3.5_

de 3,50_,

AVGS vs PMESOAK, Adjusted for Remaining PredictorsUsing Mu|reg @EXPTQMULREG, Model DESIGN__AUTO_.AVG

1 2 3 4 5 6 7 8

PRESOAK

_: Adjusted Oata ValuesAdjusted F_tted Curve

NASA/TM--2001-210901 63

3

2

1-

0

-20

Appendix A-4C (cont.)case order Graph of Residuals of AVG

Using studentized Residua]s in _lodel DESIGN_UTO__AVG

+

+ +

÷

++ +

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Case Number

++

16 17 18

+

19 2O

R 2"e

s

i 1"d

u 0a

1s -1.

Residuals of AVG v$ F_tted Valuesusing student_zed Residuals in Mode] D£SIG_I_AUTO_J_VG

++

+

+J.

+

t-

•4- + +

+ 4-+

I f t ,_ I 1

2.5 3.0 3.5 4.0 4.5 S.O

Fitted values

o.99T

m 0.8-1-

0 " -

b O.1-O.OS-

0.01

Normal Probability Plot of Residuals of AVGusing Student_zed Residua]s in Mode] DESZGhL_AUTO__AVG

(sample s4ze - 19)

.0

i

Jf

+

t I- . f t-1.5 -1.0 -0.5 0.0

_..,.-. .,Ib. "-"

0.5 1.0 1.5 2.0 2.5

Residuals of AVG

NASA/TM--2001-210901 64


Histogram of ResSduals of AVGUsing Studentized Restdua)s in Node1DESZGN__AUTO_._VG

Csamp]e s_ze - 19)

Fr

• 2-

qUenc

Y

IJ

-O.

I

I

I;

-0_2.0 -1,5 -I.0 5 0.0 0.5 1.0 I_5I

2.0 2.5

Residuals of AVG

0 Factor, Response 1 Range 2 Initial 3 optimalor FOrmula setting Value

I Factors2 TE_P 2025 to 2075 2050 20253 PRESOAK 1 tO 10 5.5 1.006545 Responses6 AVGS MAX 4.9106

Converged t_ a to]erance of 0.0OO36 after 39 steps.

Predictions and 95_ simultaneous confidence intervalsfor mean responses of AVGS using model DESIGN___UTO_._AVG

P _ 1.OO65

..... ,-..

. - : --% .....2 2025 2030 2035

4..

2040 2045 2050 2055 2060 206S 2070 2075

TEMP

.... -: .... Curve i

NASA/TM--2001-210901 65

AVGs


Pred_ ctions and 95% simultaneous confidence _ ntervals

for mean responses of AVGS us1 ng mode] DESZGN._.AUTO_.AVGT ,, 2025

5-5

5,0"

4,_"

4.0-

T

_i.

3.5 _ " - _ - -; .... _ ' "q1 2 3 4 S

-- ....... i

r t I I I6 7 8 9 10

PRESOAK

--E--_ Curve 1

AVGS

PRES0AK

10'

8-

6-

2-

2025

_.6 4.4

2030

\.

4z

2035 2040

! _ . .I

2055

"4 3.8

2045 2050

TEMP

..... AVG

--,,%

_.6

i

- %

3.4

"" ''""" I "_""",I2060 2065

... , ;_.

_ 2.6

3.2 3_ _'_.

[

2070 2075

Predictions and 95_ simultaneous confidence interval s

for mean responses of AVGS ustng model DESIGN_.AUTO__AVG

p T-2025

Lower 4.1573425 Predicted 4,621580

upper 5,085819

NASA/TM--2001-210901 66

Appendix A-4U

Least Squares Coefficients, Response AVG, Mode] DESIGN_AUTO_VG

0 Term I Coeff. 2 std. Error 3 T-value 4 Signif. 5 Transformed Term

1 1 3.550790 0.082366

2 ~T -1.000000 0.103639 -9.65 0.0001 ((T-2.05e+03)/2.Se+01)3 ~P -0.314903 0.084594 -3.72 0.0007 ((p-5.5)/4.5)

NO. cases = 38 R-sq. - 0.7534Resid. df - 35 R-sq-ad_. = 0.7394~ indicates factors are transformed.

RMS Error - 0.5077Cond. No. - 1.006

Least Squares Summary ANOVA, Response AVG Model DESIGN___UTO__AVG

0 SOurce 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio 5 Signif.

1 Total(Corr.) 37 36.594742 Regression 2 27.57221 13.78611 53.48 0.00003 Residual 35 9.02253 0.25779

R-sq. = 0.7534R-sq-adj. = 0.7394


Least Squares Components ANOVA, Response AVG Model DESIGN__AUTO_YG

0 Source 1 df 2 sum $q. 3 Mean sq. 4 F-Ratio 5 signif. 6 Transformed Term

1 Constant 1 479.60526

2 ~T 1 24.00000 24.00000 93.10 0.0000 ((T-2.05e+03)/Z.Se+01)3 _ 1 3.57221 3.57221 13.86 0.0007 (CP-5.S)/4.S)4 Residual 35 9.02253 0.25779

~ indicates factors R-sq, _ 0.7534are transformed. R-sq-adj. - 0.7394


NASA/TM--2001-210901 67

Appendix A-4U (cont.)blulreg _EXPT_MULREG, Model DESIGN__AUTO_VG

Nain Effects on Response AVG5(w_th 95% confidence Intervals)

!

T: 2025 to 2075 l/

P: 1 tO I0

I _ .......

I-2.5

.... i

-2.0 -1. S -1.0 -0.S

Increase in AVG

0.0

AVGS vs TEMP, Adjusted for Remaining Predictorsusing Nulreg _EXPT_MULREG, Model DESIGN___UTO__.AVG

6TJ

A S_d

jA4_-----------_

SGt$ 3

'td 2

5 2030 203S 2040 2045

:.-%

2050 20S 5 2060 2065

"I'EMP

Adjusted Data Values-- Adjusted Fitted Curve

2070 2075

ST_

dA4-_

u v !:

AVGS vs PRESOAK. Adjusted for Remaining PredictorsUsing Nulreg @EXPT_ULREG, wodel DESIGN__AUTO_AVG

sG

etS 3,id

1.0 1.5

L.

3.0 3.5 4.0 4.5 5.0 5.5 6.0

PRESOAK

Z_

6.5 7.0 7.5 8-0 8.5 9.0 9.5 1.0.0

Adjusted Data values-- Adjusted Fitted Curve

NASA/TM--2001-210901 68

3T

1 -2_

-310


Case order Graph of Residuals of AVGUsing Studentized Residuals in Mode] DESZGN_UTO_JWG

+

+

2 4 6

+

4-

__+__.

+

.I- +

I0 12 14

+

+

+

+

+ +

+

+

+

+

+

+

+

'1 '- t 't' t _ I J , _ i "-I-- _ I -

16 18 20 22 24 26 28 30 32 34 36 38

Case Number

3-

R 2'e

s 1.

i

d 0U

a -1

I

s -2-

-I!o

Residuals of AVG vs Fitted values

using studentized Residuals in Model DESIGN__JWTO__AVG

+

÷

++ +

+ ÷ :1:,+ _ + ;

÷ +

+

. t+

+

+

2.5 3.0 3.5 4.0 4.5

Fitted Values

l1

S,O

C 0.9

uiII1

P .

t

o 0.2

b

0.% o

Normal Probability Plot of Residuals of AVGUsing studentized Residuals in _I DESIGt4,..AUTO,__VG

(sample size- 38)

/•w f

-2.5 -2,0

° _ _-r-f ¢

1+.-t%

I I | I I t I ' I .... _,

-1,5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2,5

Residuals of AVG

NASA/TM--2001-210901 69

15-

Fr

• I_clU

e

c

y

Appendix A-4U (cont.)HiStogram of Residuals of AVG

using S_udeN1;_zed Residuals in Node1 DESZGN__AUTO___AVG(Samp]e size = 38)

_

r---_ !

-3.0 -2.5 -2.0 -1.5 -1.0

, i

, !i !

;

, _ • , .-0.5 0.0 0.5 Z.0

Resi duals of AVG

1

1.5 2.0 Z.$

0 FaCtOr, Response 1 Rangeor Formula

2 Initial 3 OptimalSett-i ng Value

1 Factors2 TEMP 2025 to 2075 20503 PRESOAK 1 to 10 S. S45 Responses6 AVGS K_X

2025.11.0088

4. 8616


predtcttons and 95_; simultaneous conf_ dence interval sfor mean responses of AVGS using model DESIGN__AUTO_.AW;

P - 1.0088

6T

V ..... _ ._

-_,- ! I2025 2030 2035 2040 20'45 20'50 20:55 2060 2065 2070 2075

TEMP

.... V_._-- Curve I

NASA/TM--2001-210901 70

Appendix A-4U (cont.)Predictions and 95_ simultaneous confidence intervals

for mean responses of AVGS using model OESIGhI__AtrrO.._AVGT I, 2025.1

S. ST

.°lik .... _ .... _ ......... _

V 4 . S * _ .................................

G I

4.

13.51 - _ -_- , : --_-- _ --_-

1 2 3 4 $ 6 7

T

8 9 10

PRESOAK

-_--- Curve I.

AVGS

4.4

2030 2035 2040

'4 ,_

2045

3.8

\

2050

-- _ --,'-

• \

%

3,6

"k\

*x. 2.6

"x

2055

2.8

3.4 3.2 "3 ""

-_, "" P "" -- I2060 2065 2070

TEMP

.......... AVG

2075

NASA/TM--2001-210901 71

Appendix A-5C

0 Term

LeaSt Squares coefficients, Response AVA, Node1 DESIG___AUTO__VA

I coeff. 2 Std. Error 3 T-Value 4 sign_f. 5 Transformed Term

1 1 -0.499171 0.0861902 -1 -1.066667 0,108427 -9,84 0,0001 ((T-2.0Se+03)/2.Se+01)3 ~P -0,428152 0.088S01 -4.84 0.0002 ((P-5.5)/4.5)4 ~LSR 0.197674 0.108385 1.82 0.0882 ((LSR+3.S)/Se-01)

NO. cases - 19 R-sq. - 0.8917Resid. df - lS R-sq-adj. = 0.8700- indicates factors are transformed,

RMS Error - 0.3756cond. No. = 1.022

Least squares Sunuary ANOVA, Response AVA Model DESZGN__AUTO_VA

0 Source I df 2 Sum Sq. 3 Mean Sq. 4 r-Ratio 5 S_gnif.

I xotalCcorr.) t8 19.540002 Regression 3 17.42385 5.80795 41.17 0.00003 Residual 15 2.11815 0,14108

R-sq. - 0.8917R-sq-adj. = 0.8700

14odel obeys hierarchy, The sum of squares for each term_s computed assuming higher order terms are first renoved.

Least squares Components ANOVA, Response AVA M4odel DESIGIq_AUTO_VA

0 Source i df 2 Sum sq. 3 Mean Sq. 4 F-RatiO S signif. 6 Transformed Term

i Constant 1 4.75000

2 ~T 1 13.65333 13,65333 96.78 0.00_ ((T-2.0Se+O3)/2.Se+O1)3 _P 1 3.30180 3,30180 23.40 0.0002 ((P-5.$)/4.5)4 --LSR 1 0.46926 0.46926 3.33 0.0882 ((LSR+3.S)/$e-01)$ Residual 15 2.11615 0.14108

- tnd4cates factors R-sq. - 0.8917are transformed. R-sq-adj. - 0,8700

Default sum of squares.Model obeys h_erarchy. The sum of squares for each term_s ,computed assunring higher order terms are first removed.

NASA/TM--2001-210901 72

Appendix A-5C (cont.)Mulreg _q_Xlrl_LREG, Node_ DESIGH__A_VA

Ma4n Effects on Response AVALA(With 95X confi dence Interval s)

T: 2025 to 2075

P: 1 to 10

LSR: -4 tO -3

4

J . . ., lI

+ _ _, 4 +-___-___-3.0 -2.5 -2.0 -1.S -1.0 -0.5 0.0 0.5 1.0

Increase in AVA

o.s]

dA O.

jv

u A -0.5_s L

tA

• -I._d

-1,5a-4.0

AVALA vs LOGSTRART, Adjusted for Remaining PredictorsUsing Mu]reg _EXPT_IMULREG, Model DESIGN_UTO__AVA

2

;5;

-3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0

LOGSTRART

_ljusted Data Values--- Adjusted Fitted Curve

AdAjvu As LtAed

AVALA VS TEMP, Adjusted for Remaining Predictorsusing Mulreg OEXPTOMULREG, Model DESIGN__AUTO._JWA

1T

O

-1

--2-

_I

2025p - I

2030 2035

i-_,

' - I - - _ _ t : " I r2040 2045 2050 2055 2060 2065 2070 2075

TEMP

Adjusted Data Values---- Adjusted Fitted curve

NASA/TM--2001-210901 73


AVALA vs PRESOAK, Adjusted for Remaining Predictors

Using Nulreg _EXPT(_ULREG, Mode] DESIGN__AUTO_VA

A 1TdA !"

uA _SL L

t A -i[d

I-t.o 2 d'z .5 3J5

,.&__

4.0 4.5 5.0 5.5 6.0 6_5 7.0 7.S 8.O

PRESOAK

Adjusted Data values

-- Adjusted F_tted Curve

0

: ..T : :8.5 9.0 9.5 I0.0

2-

R _e

s (>id

U -1]

0

÷

3. 2 3

Case order Graph of Residualsof AVA '

Using studentized Residuals in Model DESIGN._AUTO._.AVA

÷

÷

4-

4 S 6 7 B 9 10 11 12 13 14 15 16 17

Case Number

,, pI8

÷

!19

!

2O

e

si Od

U -]La

1S -2

Residuals of AVA vs Fttted V_lues

Vstng studenttzed Residuals in Node1 OESZGN...AUTO__AVA

÷4-

÷

<.

4- ÷ 4"

4- 4-

+ 4- ÷ ++

4-

- .5 -2.0 -1.S_. I ! I

-1.0 -O.5 O.0 O.5

Fitted Values

÷

1.0 1.S

NASA/TM--2001-210901 74

C09

m 018+

0 * '

b 0.1-0.05-

0.0_ -- ,0 -2.5

Appendix A-5C (cont.)Normal probability Plot of Residuals of AVA

using 5tuclentized Residuals in Model DESIGN_._AUTO__.AVA(sample size = _Ig)

.J

t4

._...

-2.0 -1.5 -i,0 -0,5 0.0 0,S 1.0

Residuals of AVA

f

f

t1.5

I2.O

Histogram of Residuals of AVAUs4 ng studen_i zed Residuals i n Flodel DESIGN.._UTO_AVA

(sample s_ze - 19)

r

e

qu 4-e

n

c 2_.-

Y :I

...................... s

o.o 0.5

i..................

• i

1.0 1.5 2.0

Residuals of AVA

0 Factor, Response 1 Range 2 Initial 3 _i_1or Fornmla Setttng Value

1 Factors

2 TEWP 2025 TO 2075 2050 20253 PRESOAK 1 TO 10 5.5 1. 0001

4 LOGSTRART -4 TO -3 -3.5 -3.001556 Responses7 AVALA MAX 1.1916

converged _o a tolerance of 0.0004 after 65 steps.

NASA/TM--2001-210901 75

A

V

A

L

A


Predictions and 95% simultaneous confidence intervalsfor mean responses of AVALA using model DESZGN__.AUTO_..AVA

P - 1.0001, LSR = -3.0015

2TT

0

202S 2030 2035 20_ 204S 2050 2_5 2060 2065 2070 207S

-......

W _|

TEMP

---_ Curve 1

A

V

A

k

Predictions and 9_ sfmultaneous confidence _r_ervalsfor mean responses of AVALA using model OESTGN.._AUTO_._AVA

LSR m --3.0015, T = 2025

°11 2

I --I _ I I I3 4 S 6 7 8

T

II

i

9 I0

PRESOAK

_--- Curve I

2.0 T

It 5 N "_"

A

V

A 1.0-

L

A

0.S-

0,_ ,' I

-4.0

Predictions and 95% simultaneous confidence _ntervals

for mean responses of AVALA using model DESIGN__AUTO_..AVAT = 2025, P- 1.0001

TI

!t

i!

i

l .... I ' I I '" I - t !-3.9 -3.8 -3.7 -3,6 -3.S -3,4 -3,3 -3.2

LOGSTRART

-3.I -3.0

.... ?::--*-curve I

NASA/TM--2001- 210901 76

Appendix A-5C (cont.)AVALA

LOGSTRART ,, -3,0015

10_' 0. _._, '- - 0 .1

p 8_ "- .........

E 6 - "--• ", ,,S "" , ,

A 4_ " .......K

2-" '1. "0.8

2025 2030

" -,, ....... " " " . '1.4

..... '" " "" L1 "

"1_1. _ .... '0.. -_1 Z --0.4 --0.6 --0 o8 """,.

. - _ ".

2040 2045 2050 2055 2060 2065 2070 2075

"'0",6 0.4

, I2035

TEMP

....... AVA

AVALA

PRESOAK - 1.0001

L - 3" Oil .'/I /O

GS

TR -3.5 IA ,,

R i 'T "/

-4. o_,-:2025

I I

O.8

/:

/"

0.6

/

-i2030

q p ,

/ / I ¢

:: .., //

.-: ./. .,,"

. ..1

: / /

/ '" .

J / 1/ I ,,

•" o.2 /' -o.20.4 , O

i ,/

/'t / i .J ik

2035 2040 2045 2050

; 3

s . /.. .¢

, i i /::': : I /

,'., /; i /

,: ,' : ,

i /

: /

-o.'4 -o.'6 -o.s -z :'1• " . j . -" /..

/ ' / ,•

2055 2060 2065 2070 2075

TEMP

...... AVA

AVALATEMP = 2025

-3 .-, . / _ .l- .... _ t _ _ r- .... "" 0.4.L 1 ' 0.9 0,8" 0.7 0.6 0.S 0.3"

• ..- .."" ,..

GO If "" "" ........... " "'" " ""'-" "'"'"J ....... "" "-" ""'- ,_-" " " """'. " " " "- "" ""

T -3.5_(" ,.'/'" "'" -..... -'"'"' - . ' i" ...."" .--'"_" '

TAR il " " '"'" ": '"'" ....' 0.3"" 0.2 "'" 0.1 """,.0.8 "' 0.7" " 0.6" 0.5"" 0,4"

-4.0, . , I ,,, _ _ i . - , ,--'"_ _ .-_ t, -4 I .<" ,I.1,0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.S 8.0 8.5 9.0 9.5 10.0

PRESOAK

....... AVA

Predict-ions and 95_ simultaneous confidence intervals•For mean responses Of AVALA uslng mode] DESZGN__AUTO...AVA

LSR = -3

P 1"-2025

Lower O.lg3091S Predicted 0.812742

upper 1.432393

NASAfl'M--2001-210901 77

Appendix A-5U

Least Squares coefficients, Response AVA, Model DESIGN_.AUTO..J_VA

0 Term 1 coeff. 2 std. Error 3 T-value 4 Signif. 5 Transformed Term

I 1 -0. 496379 0.0668842 ~T -1.062500 0.084141 ((T-Z. 05e+03)/2. Se+01)3 ~P -0. 425361 0.068678 ((P- 5.5)/4.5)4 ~LSR 0.206261 0,084108 2.45 0.0197 ((LSR+3,5)/Se-01)5 ~T*P -0.179167 0.084141 -2.13 0.0408 ((T-2.05e+03)/2.Se+01)*(

No. cases - 38 R-sq. = 0.8633Restd. df = 33 R-sq-adj. x 0.8467~ indicates factors are transformed.

RMS Error = 0.4122cond. No. = 1.022

LeaSt Squares sur_maryANoVA, Response AVA Mode] DESIGN__AUTO_VA

0 Source 1 df 2 sum Sq. 3 Mean Sq. 4 F-Ra_io 5 Signif.

1 Total(Corr.) 37 41.009742 Regression 4 35.40267 8.85067 52.09 0.00003 Linear 3 34.63225 11,54408 67.94 0.00004 Non-linear 1 0.77042 0.77042 4,53 0.04085 Residual 33 5.60707 0.16991

R-sq. - 0.8633R-sq-ad_. = 0.8467

Node1 obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

Least Squares Components ANOVA, R_porlSe AVA Model DESZGN__AUTO._AVA

0 source I df 2 Sum Sq. 3 Mean $q. 4 F-RatiO 5 Signif. 6 Transformed Term

1 Constant 1 9.400262 ~T 1 27.09375 27.09375 159.50 0.0000 ((T-2,0$e+03)/Z.5e+01_3 -P 1 6.51780 6.51780 38.36 0.0000 ((P-5,5)/4.5)4 ~LSR 1 1.02183 1.02183 6.01 0.0197 ((LSR+3.5)/Se-O1)5 -T*P 1 0.77042 0.77042 4.53 0.0408 ((T-2.05e÷O3)/2.Se+01)*(6 Residual 33 5.60707 0.16991

- _nd|cates f&ctors R-sq. = 0.8633are transformed. R-sq-adj, = 0.8467

Def&ul¢ sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

NASA/TM--2001-210901 78


Mulreg _EXPT_IMULREG, Mode] DES_GN,._AUT'O.._AVAMain Effects on Response AVALA

(with 95_ Confidence Intervals)

T: 2025 to 2075

P: 1 to 10

LSR: -4 _O -3

t t I '

L

-2.5 -2.0 -1.5 -1.0 -O.S O.O 0.5 1.O

Increase in AVA

Mulreg @EXPTOMULREG, Mode] DESIGN__AUTO_VAInteraction Effects of TERP with PRESOAK

on Response AVALA

T: 2025 to 2075iP-1 tP =' 10 I

P: i to I0

T = 2025T ,,, 2075

-3.0

I .f , • i

I: I

-2.5 -2.0 -1.5

! t

--- . ...... !

It J J

-1.0 -0.5

95_ confidence InteevalsFor Increase in AVALA

0.0

AdA

jvuAs LtAed

0-

-1

--2'

2030

AVALAvS TEMP, Adjusted for Remaiaing Pred_c¢orsusing Mulreg _qEXPT_b4ULREG, Mode] DESIC4_L_.AUTO_._AVA

• i

2035 2040 2045 2050 2055 2060

TEMP

_ Adjusced Data Values-- Adjusted Fitted Curve

2065 207'0 Z075

NASA/TM--2001-210901 79

A 0.dA

jvu A -0.5 -_s L

t A -1.O_ed -I.5

-2. !1 2


AVALA vs PRESOAK, Adjusted for Remaining Predictorsusing Mulreg @EXPT_ULREG, Model DESIGN_._AUTO_..AVA

Et

I b I ÷ _

3 4 S 6 7 8

PRESOAK

Adjusted Data values_- Adjusted Fitted Curve

5

: I9 IO

AdA . kjvu A 5-_s L -0.

"id

-4.0

AVALA vs LOGSTRART, Adjusted for Reclining Predictorsusing Mulreg_EXPT_LREG, Model DESZGN_J_JTO___VA

LJ

'ii.

-3.9

G

El I -_ ...... l,,, I , _ - I

-3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2

LOGSTI_RT

Adjusted Data Va]ues_- Adjuszed Fitted Curve

•, !-3.1 -3.0

3-

2-

R

e 1-S

idU

a "zL1

--2

0 2

4-

+

Case O_der Graph of Restdua]s of AVAUsing Student_zed Residuals _n Mode] DESZGN__AUTO__AVA

4- +

÷ + +

T

t I r q t4 6 8 10 12

+ ÷ ÷

.f.

÷

÷÷

÷ -F +

+ 4.+ + 4- +

4,

+ 4- ÷

_ - _ _ .... _ t ' I' ' " _ : " : : I

14. 16 18 20 22 24 26 28 30 3,?. 34 36 38

C_se Number

NASA/TM--2001-210901 80

3 ^

R 2e

S 1id 0tl

a -1 _] ÷

s -2 +

--2.s

÷ ,F

++


Residuals of AVA VS Fitted ValuesUsing student_zed Residua]s in Model DESIGN__AUTO___AVA

"4- +

÷ ÷

+ % + ÷

÷ + ÷-F

+ +

++

-2.0 -1.5 -1.0 -0.5 0.0 0.5

Fi tted Values

+

q-

÷

t

1.0I

1.5

Normal probabiIfty Plot of Residuals of AVAUsing studentized Residuals in _odel DESIGN___UTO__AVA

(sample size _ 38)

0.99-

C 0.95-u 0._m 0.8-

o 0._b 0.1"

0.05-

0.01_ ''_-f-2.5 -2,0

j,p-'

-1.5 -1.0 -0.5 0.0 0,S 1.0 1.5

I. j +f

- _ : -I2.0 2.5 3.0

Residuals of AVA

10'

Histogram of Residuals of AVAusing studentized Residuals in Node1 DESZGN...AUTO...AVA

(sasmple size = 38)

,m .........

t

S.

f

• i

-,_5 -2.0 -I, 5 -I,0 -0.5 0.0

.......... i

1 ; i

r

...... _

0'5 l_O Z._ 2.0 2.5 3.0

Residuals of AVA

NASA/TM--2001-210901 81


0 Factor, Response 1 Range 2 Initial 3 Optimalor Formula Setting Value

1 Factors

2 TEMP 2025 to 2075 2050 20253 PRESOAK 1 to 10 5.5 1,00164 LOGSTI_.RT -4 to -3 -3.5 -3.000356 Responses7 AVALA MAX 1.0176


AVALA

Predictions and 95% s_multaneous confidence interv_]sfor mean responses of AVALA using mode] DESZG_UTO_..AVA

P - 1.0016, LSR - -3.0003

-1

T

±

I 2

2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075

TENP

--_ Curve 1

AVALA

Predictions and 95% simultaneous confidence intervalsfor mean responses of AVALA using mode] DESIGN_AUTO.._AVA

LSR - -3.0003, T - 2025

2°I1.5 !

1.0 -_ ..................

o.sI L0.0

O5-- o ,,i 2 I - _ - ) ; ' '1 t ___ l

3 4 5 6 7 8 9

PRESOAK

T

1

10

.... U.- Curve 1

NASA/TM--2001-210901 82

Appendix A-5U (cont.)Predictions and 95_ simultaneous confidence intervals

for mean responses of AVAI.A USirlg mode] DESIGN___AUTO...AVAT = 2025, P - 1.0016

Z.O

1.5"

Av 1.0-

A

L 0.5-A

O°0"

T"

!

....................... .........

[

F.... ........ _,_-t. _- --

i

4.

-0,5 t I ' - I I .F. _ _ 1 I • ; :-4.0 -3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3,1 -3.0

LOGSTRART

.... _ ..... Curve I

-3.0'

LO 0.8"

S .//

T -3.5:R

/A "

R 0.6T /

/

-4.0 "2025

AVALAPRESOAK = 1.0016

//

j_

/

/

/

,../

0.4 O. 0

I t z_ I -- :"2030 2035 2040

,. .."

, .e

7 / . ./": 7 •-"

,e :k ./ .." ;/

" -o, _ -o. a -o. g/ / •

/. s .,

." * / p . :l (.2045 2050 2055 2060 2065

//

jr

• .t

-O.g -1

, i I ,2070 2075

TEMP

........ AVA

i0 _ : _ m ,_.- .

:If2025

0.6 o. 4\I " 4 ,, t "',

2030 2035 2040

AVALALOGSTRART ,, -3.0003

. F

-0.4

0.2 '0 -0.2

I _ ,_ ' '2045 2050 2055

' _" i _ ...... : .

" ", .... . ', "_ -1.2 '"

"'-0.8 "'

-0.4 ~0.6 .........._ : "'-_.: "_. "_

2_0 2065 20_ 2075

TEIaP

....AVA

NASA/TM--2001-210901 83


AVALATEMP = 2025

-3.0-" f : ', ', _'-- t t I _ 4 _ _ 1._ i _ i 0 6 t_ I 4 "P'

°[ Is 3 5 .....'" ....... " ...... -- 0,6 .......... 0.5 ........ 0.4 .... "'_

T-.,, m..... ..0.7.... .....-.... ,.... ._ ........... j.._.Tm

R ....0,6 ".......... -...... "...... "..... "J'"T .... yn. 5 '- ".... 0.4""" "" . .0.3...... '- 0.2 ....-4.0_-.":F-_...._ , ,_ , _ _ -"i _ .', ',_ , _- -.- _"_ , • , ,

1,0 1.5 2,0 2.5 3.0 3.5 4,0 4.5 5,0 5.5 6,0 6.S 7.0 7.5 8.0 8,5 9.0 9.5 10.0

PRESOAK

............ AVA

Predictions and 95_ simultaneous confidence intervalsfor mean responses of AVALA u$i no model DESIGN__AUTO__AVA

LSR = "3

P T=2025

Lower O. 312069S Predicted 0.799737

Upper 1.287406

NAS A/TM--2001-210901 84

Appendix A-6C

Least squares Coefficients, Response SDG, Model DESIGN__AUTO__SDG

0 Term 1 Coe_. 2 Std. Error 3 T-value 4 signif.

1 i 0,35789S 0,068105 5,26 0,0001

No. cases - 19 R-sq. = 0.0000 RMS Error = 0.2969Resid. df = /8 R-sq-adj. = 0.0000 Cond. No. = 1

Least Squares Summary ANOVA, Response SDG Model DESIGN__AUTO__SDG

0 source 1 df 2 Sum Sq. 3 _ean Sq. 4 F-Ratio 5 signif.

1 Total Ccorr.) 18 1, 58631E2 Regression 0 0.0000003 Residual 18 1, 586316 0,088129

R-sq. - O.0Q00R-sq-adj, = 0,0000

Nodel obeys hqerarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

Least Squares coefficients, Response SDA, _de] DESIGN__AUTO_DA

0 Term 1 coeff. 2 std. Error 3 T-value 4 Signif.

I 1 0.247368 0.042830 5.78 0.0001

No. cases - 19 R-sq. - 0.O000 R4_S Error - 0.1867Resid. df - 18 R-sq-adj. = 0.0000 Cond. No. - 1

Least Squares summary ANOVA, Response 5DA Model DESIGN_AUTO_DA

0 Source i df 2 sum sq. 3 Mean Sq. 4 F-Ratio 5 signif.

1 Total(Corr.) 18 0.62736842 Regression O 0.00000003 R.sldual 18 0.6273684 0,0348535

R-sq. - 0.0000R-sq-adj. - 0.0000


NASA/TM--2001-210901 85

Appendix A-6U

0 Term

Bisqu_re coefficients, Response $log_SDG, Model DESIGN__AUTO__SDG

1 coeff. 2 std. Error 3 T-value 4 Signif. S Transformed Term

1 1 -1.172359 0.0716772 ~T 0.394899 0.0901873 ~LSR -0.192353 0.0901374 -T*LSR -0.259390 0.110399

No. cases . 38 R-sq. = 0.4657Resid, df = 34 R-sq-adJ. - 0.4186~ indicates factors are transformed.

-2.35 0.0247

RMS Error = 0.4417Cord. No. - 1.021

((T-2.05e+03)/Z.Se+01)((LSR+3.S)/Se-0_)((T-2.05e÷03)/Z.Se+01)*(

Bisquare summary ANOVA, Response $1og_SDG Model DESIGN_UTO_SDG

0 source 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio 5 signtf.

1 TotalCcorr.) 37 12.418842 Regression 3 5.78402 1.92801 9.88 0.00013 Linear 2 4.70673 2.3S337 12.06 0.00014 Non-llnear 1 1.07729 1.07729 5.52 0.0247$ Residual 34 6.63482 0.19S14

R-sq. - 0.46S7R-sq-ad_. - 0.4186

Mode_ obeys hierarchy. The sum of squares for each termis computed &ssuming higher order terms are first removed.

Sisquare Components ANOVAo Response $]og_SDG Model DESZGN_.AUTO__SDG

0 Source 1 df 2 Sum $q. 3 Mean Sq. 4 F-Ratio S Sign-if. 6 Transformed Terra

1Constant 1 51.939612 ~T 1 3.81805 3.81805 19.57 0.000I3 -LSR 1 0.88868 0.88868 4.55 0.04014 -T*LSR 1 1.07729 1.07729 5,52 0,02475 Restdual 34 6,63482 0.19514

~ indicates factors R-sq. - 0.4657are transformed. R-sq-adj. - 0.4186

Defau]t sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.

(CT-2.05 e+03)/2.5e+01)(CLSR+3. S)/5e-01)((T-2.05e_03)/2. Se+0!)* (

NASA/TM--2001-210901 86


Mulreg _EXPT_MULREG, Model DESIGN_AUTO__SDG_ain Effects on Transformed Response SDGS

(with 95% confidence Intervals)

T: 2025 to 2075

LSR: -4 to -3

-1.0

I t

F" -- ............. _ ...........

-0.5 0.0 0.5 1.0

Increase in Transformed SDG

1.5

Mulreg eEXPT_LREG, Model DESIGN__AUTO_._SDGZnteraction Effects of TEMP with LOGSTRART

on Transformed Response SDGS

/

T: 2025 tO 2075rLSR = -4LSR - -3

LSR, -4 to -3T - 2025T ,= 2075

-2.0

I

.t-1.5

t ? _ '- :

F I , I

, I', _ I T I

-1o0 -0,5 0.0 0,5 l,O _..5

95% Confidence IntervalsFor Increase in Transformed SDGS

2,0

TA rdajnu ssft o• rdm

ed

0"

S _1-'

DG

S -24

"2_z5 2030

SDGS vs TEMP, Adjusted for Remaining PredictorsUs|n 0 Mu]reg QEXPTtlMULREG, Mode] DESIGN_.AUTO__SDG

I=

, ,_ , ,

2035 2040 2045 2050 2055 2060

TEMP

Adjusted Data Values-- Adjusted Fitted Curve

2065 2070

J

2075

NASA/TM--2001-210901 87

Appendix A-6U (cont,)SOGS vs LOGSTRART, Adjusted for Remaining Predictors

using leulreg _EXPT_IMULREG. Model DESIGN__AUTO_SDG

rTj nS-" _i

u s D -1.0_ _s fG _.t o s -1. S_

d m -2.e

d -2 .- ' -:-4.0 -3.9

l

7

c

I t t .,. I.,- I I I ..... ! q-3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0

LOGSTRART

',j Adjusted Data V_luesAdjusted g_tted Curve

Case order Graph of Residuals of Transformed SO,;Using studenttzed Residuals in Model DESIGN_AUTO___SDG

2*

1-

R

e 0$id -1ua -21

-3

4-

+ +÷

+ ++ 4-

+

+ + + + _ ¢-" -":k -+

+ 4- + ÷

4-

0 2 4 6 8 10 12 1'4 16 18 20 22 2'4 26 2'8 30 32 34 36 38

case Number

2-

R 1-

es 0id-l"

Ua-2-]s -3"

Reslduals of Transformed SO(; vs Fitted Values

Using studenttzed Residuals in Model RSZGN__UTO_SOG

4-

÷ 4- ÷

+ ++ 4-+÷ +

÷ • -I"+ "P

+ + 4"

÷÷

-1.6 :1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2

Transformed Fitted values

NASA/TM--2001-210901 88

0.99-

C 0.95-u 0,9-m 0.8"

PP0 " "

b 0,1-0.05-

0.01"-'_.5

-+i-3.0

Appendix A-6U (cont)

Normal Probability Ploc of Residuals of Transformed SDGUsing 5tudentized Residuals in Model DESIGN__AUTO_SDG

(sample size = 38)

I/

/" +

/

_" _1-" 4"÷

/

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0,5 1.0 I,S

Residuals of Transformed SOG

B

-1.0 iS

qU

a

r

0.$ •

We

i

g

218.0 ths

lelO,quenc

Y

Histogram of Residuals of Transformed SDGUsing studentized Residuals in Model DESIGN__AUTO__SDG

Csample size - 38)

' t . . , ; "

03_ . - 1 .......... . , ' - , ;-3.0 -2.5 -2.0 -1,5 -1.0 -0.5 0.0

' I

0'.5 110 1.5

Residuals of Transformed SDG

2.0

0 Factor, Response 1 Range 2 Initial 3 olrcim_lor Formula Setting value

I Factors2 TEMP 2025 to 20753 LOGSTRART -4 to -345 Responses6 SDGS kiN

2050 2025-3.5 -3.9999

0.19518

Converged to a tolerance of 0.00009 after 43 steps.

NASA/TM--2001- 210901 89

1.5"

1.0"SDG

S0.5

0.1

0°5"

0.4 !

sD

0,3GS

o.z!

0.1

Appendix A-6U (cont.)Predictions and 95% simultaneous confidence intervals

for mean responses of SDG$ using mode] DESIGN_UTO_SDGLSR = -3.999g

T

2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075

TEMP

Predictions and 95_ simultaneous confidence intervalsfor mean responses of SDGS using model DESZGN_AUTO__SDG

T = 2025

(

T ti!

i

k

-3r

: I

F + I I .' t..... i _ 4- 4 -; ',-4.0 -3,9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0

LOGSTRART

SDGs

---__"..'-- Curve I

--_---- Curve I

-3,0'_

L0GST -3.5RART

-4,02025

--j .... : +

/

:

0._s:

/

I ') t /2030 2035 2040

+

0.3

_..i; _ _ l + "- -- ;- ---

+_0.3 ............t + ....... __0.35 ......

.... 0.4 .....

0.35 +_-+_+ .... +_ -"o.+"'G 7.1....0.4 0.55 ..-

• ]

+ '+'_ '+' '+ _,, + + I "-++ ' 'I *°+ " " i -"' "_2045 2050 2055 2060 2065 2070 2075

TEMP

$DG

Predictions and 95_Q simultaneous confidence intervals

1:or mea_ respol_ses of SINS using mo(_)l DE$IGN__AUTO__SOG

LSR T=2025

Lower 0.122143-3 Predicted 0.2230B1

Upper 0.407435

NASA/TM--2001- 210901 90

REPORT DOCUMENTATION PAGE FormApprovedOMB No. 0704-0188

Public reporting burden for this collectionof information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources.gathering and maintaining the data needed, and completing and reviewing the collection of information, Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports 1215 JeffersonDavis Highway, Suite 1204. Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

August 2001 Technical Memorandum

4. TITLE AND SUBTITLE

High Temperature, Slow Strain Rate Forging of Advanced Disk Alloy ME3

6. AUTHOR(S)


7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

9, SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

11. SUPPLEMENTARY NOTES

5, FUNDING NUMBERS

WU-714-04-10-00

8. PERFORMING ORGANIZATIONREPORT NUMBER

E-12778

10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

NASA TM--2001-210901

Responsible person. Timothy E Gabb, organization code 5120,. 16-43.-3.7_.

12a.

13.

DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified - Unlimited

Subject Category: 26 Distribution: Nonstandard

Available electronically at http://_ltrs.grc.nasa.gov/GLTRS

This publication is available from the NASA Center for AeroSpace Information. 301 _o21 _)390.

ABSTRACT (Maximum 200 words)

The advanced disk alloy ME3 was designed in the HSR/EPM disk program to have extended durability at 1150 to 1250 °F in large

disks. This was achieved by designing a disk alloy and process producing balanced monotonic, cyclic, and time-dependent mechanical

properties, combined with robust processing and manufacturing characteristics. The resulting baseline alloy, processing, and

supersoh, us heat treatment produces a uniform, relatively fine mean grain size of about ASTM 7, with as-large-as (ALA) grain size of

about ASTM 3. There is a long term need for disks with higher rim temperature capabilities than 1250 °E This would allow higher

compressor exit (T3) temperatm-es and allow the full utilization of advanced combustor and airfoil concepts under development. Several

approaches are being studied that modify the processing and chemistry of ME3, to possibly improve high temperature properties.

Promising approaches would be applied to subscale material, for screening the resulting mechanical properties at these high tempera-

tures, n obvious path traditionally employed to improve the high temperature and time-dependent capabilities of disk alloys is to

coarsen the grain size. A coarser grain size than ASTM 7 could potentially be achieved by varying the forging conditions and

supersolvus heat treatment. The objective of this study was to perform forging and heat treatment experiments ("thermomechanical

processing experiments") on small compression test specimens of the baseline ME3 composition, to identify a viable forging process

allowing significantly coarser grain size targeted at ASTM 3-5, than that of the baseline, ASTM 7.

14. SUBJECT TERMS

Forging; Superalloy; Disk; Grain size: Thermomechanical processing

17. SECURITY CLASSIFICATIONOF REPORT

Unclassified

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATIONOF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATIONOF ABSTRACT

Unclassified

15. NUMBER OF PAGES

9616. PRICE CODE

20. LIMITATION OF ABSTRACT

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18298-102

high temperature, slow strain rate forging of adwanced

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