The purpose of this program is to develop life prediction models for coated anisotropic materials used in gas turbine airfoils. In the program, two single crystal alloys and two coatings are being tested. These include PWA 1480, Alloy 185, overlay coating (PWA 286), and aluminide coating (PWA 273). Constitutive models are also being developed for these materials to predict the time independent (plastic) and time dependent (creep) strain histories of the materials in the lab tests and for actual design conditions. This nonlinear material behavior is particularly important for high temperature gas turbine applications and is basic to any life prediction system. Some of the accomplishments of the program are highlighted

Meyer, T. G.

Nissley, D. M.

Swanson, G. A.

English

NASA Technical Reports Server

ORIGINAL PAGE IS
OF POOR QUALITY
LIFE PREDICTION AND CONSTITUTIVE MODELS FOR ENGINE HOT SECTION
ANISOTROPIC MATERIALS PROGRAM*
G.A. Swanson, T.G. Meyer, and D.M. Nissley
United Technologies Corp.
Pratt & Whitney
INTRODUCTION
The purpose of this program is to develop life prediction models for coated
anisotropic materials used in gas turbine airfoils. In the program, two single
crystal alloys and two coatings are being tested. These include PWA 1480, Alloy
185, overlay coating (PWA 286), and aluminide coating (PWA 273). Constitutive
models are also being developed for these materials to predict the time independent
(plastic) and time dependent (creep) strain histories of the materials in the lab
tests and for actual design conditions. This nonlinear material behavior is
particularly important for high temperature gas turbine applications and is basic to
any life prediction system. This report will highlight some of the accomplishments
of the program this year.
SINGLE CRYSTAL CONSTITUTIVE MODEL
Two separate unified constitutive models for single crystal PWA 1480 have been
formulated and are in the final stages of development. The first model, the
"microscopic model", computes the inelastic quantities on the crystallographic slip
systems. This model achieves the required directional properties as a consequence
of resolving the summed slip system stresses and strains onto the global coordinate
system. The second model, the "macroscopic model", uses global stresses and strains
directly and employs anisotropic tensors operating on global inelastic quantities to
achieve the required directional properties. The two models offer a trade between
accuracy and physical significance and computing time requirements. The microscopic
_odel is more accurate and is more physically significant in its formulation than
ti_e7acroscopic model. However the macroscopic model is more computationally
efficient, because integration of the evolutionary equations is required only for
the six global stress/strain quantities rather than for each of the slip systems.
Cyclic stress/strain data at 871C (160OF) will be used to illustrate the behavior of
the models. Figures l and 2 show test data from uniaxial bars oriented in three
_rystal directions: <OOl>, <lll_, and <Oil >. These three orientations represent the
_treme ends of the possible crystal orientations.
Work performed under NASA contract NAS3-23939.
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The tests were conducted under controlled strain rates ranging from 0.001%per
second to 1.0%per second.
The microscopic model models deformation on both the octahedral slip systems and the
cube slip systems. The importance of including both slip systems can be shownby
examining the results of inactivating the cube system terms. The model, thus
_odified, was fit to the <OOl> data and subsequently used to predict the<Ill>
behavior. Figure 3 shows the correlation with the <OOl>data is quite good, but the
prediction for the <Ill> data is poor. The good correlation with the <OOl> data
could have been expected since for a tensile bar in this orientation, only the
octahedral slip systems have nonzero resolved shear stresses. The resolved shear
stress on the cube slip systems is zero for this orientation. In contrast, a
tensile bar oriented in the <Ill> direction has nonzero shear stresses on both the
octahedral and the cube slip systems. Whencube slip terms are included in the
_odel, the correlation with the <Ill> and <OOl>data is quite good as seen in Figure
4. The model constants in this case have been determined to best fit both the <OOl>
and the <Ill> data. The accuracy of the full model is illustrated in Figure 5 by a
prediction of data from a third orientation: the <Oil> orientation. Comparisonwith
the test data in Figure 2 shows the prediction is very good. The maximumdifference
seen between the micro model and test data for all three orientations, for stress
ranges up to 2100 MPa(305 ksi) and over three orders of magnitude of strain rate is
less than 62 MPa(9 ksi).
In the macroscopic model being developed, a single set of evolutionary equations are
written using the global stresses and strains directly (i.e. not resolving them onto
slip systems). The orientation dependenceis achieved by including anisotropic
tensors in the evolutionary equations for both inelastic strain and back stress. If
the anistropic tensor is included only in the equation for inelastic strain, the
best correlation with <OOl>and<Ill> data resulted in a maximumstress error 2.5
times that achieved in the slip system based model. However, as shownin Figure 6,
when the back stress componentsare allowed to evolve anisotropically, correlation
of the <OOl>and <Ill> test data is comparable to that achieved with the slip system
based model. The ability of the macroscopic model to predict other orientations is
currently under investigation.
COATING CONSTITUTIVE MODEL
Five isotropic constitutive models were evaluated based on ability to correlate
isothermal overlay coating behavior during stress relaxation and ability to predict
thermomechanical behavior. The models evaluated were a classical formulation (e.g.
Ref.l), Walker's isotropic formulation (Ref.2), a simplified form of Walker's
isotropic formulation where back stress was assumed equal to zero, the Stowell model
(Ref.3), and Moreno's Simplified Unified Approach (Ref.4).
Zarly evaluation of model correlation ability indicated little differences between
-be models. Additional isothermal cyclic stress relaxation tests were subsequently
conducted to determine whether kinematic terms were necessary. To accomplish this,
5 _inute strain hold initiating at zero stress after unloading was incorporated
into the test history. Experimental results from the test conducted at 649C (120OF)
is presented in Figure 7. The positive relaxation observed during the 5 minute
strain hold indicated that kinematic hardening was necessary to accurately represent
the overlay coating response. As such, the 3 models which do not contain kinematic
i_rJening formulations (i.e. classical, simplified Walker, and Stowell) were dropped
from consideration.
386
ORIGINAL PAGE IS
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Correlation of the isothermal stress relaxation information was best accomplished
using the Walker model. The Moreno model as applied was generally unable to
correlate the observed positive relaxation response largely as a result of the
assumed back stress evolution equation:
/k_= Ep_ Gin + _in_Ep
where : _ = back stress increment
Ep = strain hardening slope in uniaxial tensile test
._cin = inelastic strain
_in = inelastic strain increment
Ep = change in Ep (with respect to temperature)
_,breno in his work on Hastelloy X (Ref.4) utilized a less rigorous back stress
formulation which relied on a set of rules. This was considered cumbersome and,
hence, the above formulation was adopted.
Prediction of an out-of-phase overlay coating hysteresis loop by the Walker and
_reno models is presented in Figure 8. Clearly, the Walker model is the more
accurate, but the Simplified Unified Approach does predict the gross behavior and is
also quite easy to apply, since only simple hand calculations are required.
Aluminide diffusion coating isothermal stress relaxation tests are in process.
Because diffusion coatings depend largely on the substrate material, tests are
conducted on 2 thicknesses of PWA 1480 material .13 and .25 mm (.005" and .OlO").
Initially, the overlay constitutive model (i.e. Walker) will be applied to both
thicknesses and each material constant will then be plotted vs. PWA 1480 thickness
_nd extrapolated to zero PWA 1480 thickness to obtain the "effective" coating
material constants.
LIFE PREDICTION TESTS
Tests concentrated on gaining insight to coating/PWA 1480 substrate interactions
during thermomechanical loading conditions. Critical fatigue experiments conducted
on <001> and <Ill> PWA 1480 specimens with either overlay or aluminide coatings have
_hown that thermomechanical fatigue life is significantly influenced by the presence
of a coating, coating structure (overlay or diffusion), substrate orientation, and
strain-temperature-time path. Test results supporting these conclusions are
presented in Figures 9 through 12. All lives are relative to specimen separation
life, except in Figure 12 where coating cracking lives are also provided. Although
not shown, coating cracking lives generally follow the same trends. Isothermal
Fatigue tests were primarily limited to overlay coated <OOl> PWA 1480 and were
designed to provide initial life data for exercising life models. This particular
coating/substrate orientation combination was chosen because it is the most
_nderstood from previous experience and material behavior standpoints.
The remainder of specimen coating/substrate orientation combinations are intended to
obtain anisotropy and coating structure effects.
LIFE PREDICTION MODELS
3_sed on observed speciT,lencracking lives obtained from multiple acetate
_.eplications of each specimen, life must be separated into coating and substrate
387
componentssuch as provided in the following equation:
Nsep = Nci + Nsi + Nsp
where: Nci = !lumber of cycles to generate a crack through the
coati ng.
Nsi = Additional cycles for coating crack to penetrate a
small distance into the substrate. Initially
defined as .13 mm(.005").
Nsp = Additional cycles to grow crack to critical size.
Nsep = Specimenseparation life (50% stress range drop).
Initially, simple correlations of overlay coating cracking life (Nci) were
considered: Coffin-Manson, Ostergren, actual tensile hysteresis energy, and another
hysteretic energy approach based upon the concept of effective temperature (Ref.5).
In the latter approach, effective temperature was assumedto be the midcycle
temperature of the loading condition (i.e. (Tmin+Tmax)/2). These four correlations
are presented in Figure 13. In each case, the overlay coating correlating
parameters were determined by analysis using a one-dimensional 2-bar mechanism. The
correlation lines shownin the figure represent a "hand-fit" curve passing through
all the out-of-phase TMFtest conditions and are intended to serve as a reference to
qualitatively judge the correlations. Of the four, the tensile hysteretic energy
model is best able to correlate the lives of the varied test conditions.
P'4A1480 substrate life modeling dependsupon what is considered crack initiation
vs. propagation. The methodology applied in this program initially defines
substrate crack initiation as a crack which has penetrated .13 mm(.005") into the
P'4A1480. Assuming a penny-shapedcrack, this is consistent with a .15 to .25 mm(.006" to .OlO") surface crack. To verify the relationship between acetate replica
observations and actual substrate cracking, substantial optical and Scanning
Electron Microscopy (SEM)fractography has been conducted. Such investigations have
indicated that overlay coating cracks do not penetrate into the PWA1480 substrate
_uring tests conducted at high temperature. Figure 14 is a schematic of the
_emarkation between temperatures where coating cracks do or do not penetrate into
the PWA 1480.
TI4Fof a coated specimen (or component) is particularly complex because thermal
growth mismatch between coating and substrate introduce biaxial stresses and strains
during thermal cycling. Final model(s) will consider such biaxial conditions and
lore rigorous statistical evaluations of the model(s) will then be performed.
FUTURE
in the coming year, additional cyclic tests are planned to assist in life prediction
_,]Jel development. Also, in Option l of the program, life model development will be
__xtended to airfoil root attachment temperatures, stress levels, and notch stress
concentrations.
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ACKNOWLEDGE_NTS
The authors wish to recognize some of the individuals contributing to the progress
of the program. Dr. Kevin P. Walker, of Engineering Scientific Software, Inc.,
originator and developer of the single crystal constitutive models and one of the
coating constitutive models. At P&W, Messrs. Paul P. Norris, Indrik Linask, and
many others are continuing to develop constitutive and life prediction models and
overseeing and interpreting specimen tests; also, Messrs. Frank X. Ashland, Phillip
D. Retzer, William A. Murphy, and Larry E. Durey for their support in specimen
procurement and testing.
l ,
•
.
4.
,
REFERENCES
Kraus, H.: "Creep Analysis", John Wiley & Sons, Inc., New York,
Chapter 2, 1980.
Walker, K. P.: "Research and Development Program for Nonlinear
Structural Modeling with Advanced Time-Temperature Dependence
Constitutive Relationships", NASA CR-165533, November, 1981.
Stowell, E. Z., et al: "Predicted Behavior of Rapidly Heated Metal
in Compression", NASA TR R-59, 1960.
Moreno, V.: "Development of a Simplified Analytical Method for
Representing Material Cyclic Response", NASA CR-168100, January,
1983.
Pejsa, P. N. and Cowles B. A.: "Thermal Mechanical Fatigue Life
Prediction for Advanced Anisotropic Turbine Alloys", Journal of
Engineering for Gas Turbine and Power, vol. I08, July, 1986. ASME
no. 86-GT-124.
389
160000
96000
32000 --
Z
-32000 --
-96000 m
.,_0000 I I I I I
.140 .084 o28 028 0.84 14o
STRAIN IN PERCENT
FIGURE 1 EXPERIMENTAL LOOPS IN <001> AND <111> DIRECTIONS AT 871C {1600F) AT STRAIN RATES OF
A) .001% PER SEC, B) .0025% PER SEC, C) .01% PER SEC, D) .1% PER SEC, AND E) .5% PER SEC
_60000
'96000
32000
Z
m
U3
-32000 --
96000 --
-160000
-1.40
I DATA ,J
1 PSI = 6895 _PA /i
/' ,/
/
/
/
/
/
O84
1 I I I
-0.28 0,28 084 I 40
STRAIN IN PERCENT
FIGURE 2 EXPERIMENTAL LOOPS IN <011> ORIENTATION AT 871C (1600F) AT STRAIN RATES OF
A) 1.0% PER SEC, B) 0.1% PER SEC, AND C) 0.001% PER SEC
390
160000 --
96000
32000 --
Z
09
_n
-32000 --
-96000 --
-160000
-140
<111> RESPONSE PREDIC
BY MODEL WITH NO CUBE
SYSTEM TERMS
1 PSi = 6.895 kPA
I I I
-028 0 28 0,84 140
STRAIN INPERCENT
FIGURE 3 USING ONLY OCTAHEDRAL SLIP TERMS, THE <001> DATA IS CORRELATED WELL BUT
SUBSEQUENT PREDICTION OF <111> RESPONSE IS POOR. COMPARE TO DATA IN FIGURE1
160000 --
96000"
32soc,-
Z
_-32000 --
-96000 --
-160000
.' 40
1 PSI = 6 895 kPA
<111> <OO_>
I I I I I
-0 84 -0 28 0.28 0 84 1 40
STRAIN IN PERCENT
FIGURE 4 MICRO MODEL WITH BOTH OCTAHEDRAL AND CUBE SLIP TERMS CORRELATED TO
<111> AND <001> DATA. COMPARE TO DATA IN FIGURE1
391
160000
96000
32000 --
Z
-32000 --
U3
-96000 --
-1600OO
• 1 40
m
1 PSI = 6.895 kPA
/
/
/
/
/
/
/ / I"/
/ / I"//"
/ /
(iS I I I I
-084 -O28 0,28 O84 1 40
STRAIN IN PERCENT
FIGURE 5 PREDICTED LOOPS IN <011> ORIENTATION AT 871C (1600). COMPARE TO DATA IN FIGURE 2
160000 -
1 PSI = 6895 kPA
96000 -- , .
32000 --
-32000 -- /Z
96000 --
-16oooo I I I
-1.40 -0.84 0 84 1 40
I I
-O28 0.28
STRAIN IN PERCENT
FIGURE 6 CORRELATION OF <001> AND <111> DATA WITH ANISOTROPIC BACK STRESS MODEL
392
ORIGINAL PAGE IS
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E-O5
1 PSI = 6.895 kPA
1O0 A
0.80 /
U3060
///y //0.4(?
00C
000 0 50 1 O0 1 50
STRAIN -- IN/IN
2 O0
E-02
FIGURE 7 649°C (1200°F) STRESS RELAXATION TEST OF UNEXPOSED, BULK HIP'PED PWA286
i_ 871! 1600,
I
427 _ ToC (OFi
L800i \
STRESS
KSII
' I DATA I PREDICTION
I l
STRESS
(KSI)
I
-04 0 3-02-0 1 0 0 7 ,.32 03 04 05
STRAIN %
FIGURE 8 WALKER AND MORENO MODEL PREDICTION OF OUT-OF-PHASE TMF TEST
393
PWA1480 <001>
C = ± .4%
E;
T (F) o
, /<,
80/ 19OO
T (F)
m
<
r,r
p-
C,3
.J
<
L.)
z
<
"I"
U
}
COATING
NONE 1 00 235
PWA273
N,AI
DIFFUSION
PWA286
N,CoCrAIY
OVERLAY
22 4.00 -
73 406
FIGURE 9 THERMAL MECHANICAl. FATIGUE LIFE DEPENDS UPON COATING
m
R
n
m
m
B
D
O"
100
PWA 1 480
PWA273 COATING
<TI 1>
<ol _>
<111>
.o--....__
I I I I ! I111 I I I I I 1111 1
1000 10.0oo
SEPARATION LIFE, CYCLES
FIGURE 10 THERMAL MECHANICAL FATIGUE LIFE DEPENDS UPON SUBSTRATE ORIENTATION
394
ORIGINAL PAGE IS
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mPWA1480 <111>
6= -+ .15%
80 o T (F)
cw
800 1900 T (F)
ORIGINAL PAGE IS
OF POOR QUALITY
CCW
BOO 19oo T(F)
COATING
PWA273
N,AI
DFFFUSION
1.0 116 4.75
PvVA286 I 0 I 23 3.85-
N,CoCrAIY
FIGURE 11 TMF LIFE DEPENDS UPON MECHANICAL STRAIN - TEMPERATURE PATH
6
48242 1900i
8O
--454
,850_
CO_TING CRACKS
PWA286 COATED PWA1480
6 = +-.25%
lO38 T °C (°F)
19ooi
<1 1 1>
6
ISOTHERMAL
T °C (°Fl
---..,, j
I IDENTICAL ]SPECIMEN HYSTERESIS
/ ",,,
>7130
2320 _NO CRACKS OBSERVED,
NSE_ 3532 >7;30
FIGURE 12 TMF LIFE DEPENDS UPON THERMAL CYCLE
395
;RiGINAL
OF
:N ,%
4" 427C (800°F) )421-1038C (800-1900°F, OuT OF-PHASE TMF
427 1038C _800 1900oF_ OTHER THAN OUT.OF P_ASE T'VPF
427-1149C (8OO-2100°F_ OuT-OF-PHASE TMF:
OSTERGREN
1 1
IC 3 _0 4
NC, 'C'r CLES=
3 S
':3IxdENSILE:-_l \ _: HYSTERETIC ENERGY ,o31 TENSILEAPPROAcHNYSTERETICBASEDoNENERGYTEFF
• IX,. _**
b 2x 2x
_32 103 104 105 102 103 104
NC, _CYCLES_ Nci _CYCLES_
J
_35
FIGURE 13 PWA286 OVERLAY COATING CRACKING LIFE CORRELATIONS
396
PWA286 OVERLAY PWA273 ALUMINIDE
n
c I
--4"I
I
I
--" I
_J
I l J I I
427 760 927 1038 1149
_800_ (1400)(17001t 1900t (21001
TEMPERATURE °C (OF)
SPECIMEN
ID
FAILURE
I
I
I_
I I I l l
427 760 927 1038 1149
(8001 11400) (1700) (1900) I2100_
TEMPERATURE °C (OF)
FIGURE 14 SCHEMATIC OF OBSERVED SPECIMEN FAILURES. AT HIGH TEMPERATURES PWA286 COATING
CRACKS DO NOT PENETRATE INTO PWA1480.
397



Life prediction and constitutive models for engine hot section

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