The purpose is to develop life prediction models for coated anisotropic materials used in gas temperature airfoils. Two single crystal alloys and two coatings are now 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 plastic and creep strain histories of the materials in the lab tests and for actual design conditions. This nonlinear material behavior is particularily important for high temperature gas turbine applications and is basic to any life prediction system

Swanson, G. A.

English

NASA Technical Reports Server

N88- 11175.
LIFE PREDICTION AND CONSTITUTIVE MODELS FOR
ENGINE HOT SECTION ANISOTROPIC MATERIALS PROGRAM*
G. A. Swanson
United Technologies Corporation
Pratt & Whitney
INTRODUCTION
The purpose of this five-year program is to develop life prediction models for
coated anisotropic materials used in gas temperature airfoils. In the base program,
now underway, 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
plastic and 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
A literature survey was conducted to identify constitutive models and modeling
approaches that are applicable to single crystal materials. Two distinct approaches
were identified. The first attempts to model the anisotropic behavior by using micro-
mechanical processes which occur during deformation as a basis for the mathematical
formulation. The second approach ignores the micromechanical processes and attempts
to describe the bulk behavior through macroscopic quantities which are functions of
material orientation. While some of the earlier macroscopic models can be considered
"fully developed", no complete micromechanical model can be considered fully devel-
oped.
Three candidate models have been identified for further evaluation. Two of these
models use the macroscopic continuum approaches. These are the classical Hill model
(ref. l) and a unified viscoplastic formulation by Lee and Zaverl, et al (ref. 2).
The third model uses a micromechanical approach which is currently being developed
by Dr. Kevin Walker. This model is showing the most promise and, therefore, is dis-
cussed in detail in this report.
The micromechanical model is based on slip system stresses and strains and is
imbedded in Walker's unified viscoplastic formulation (ref. 3). The viscoplastic
constitutive formulation based on crystallographic slip theory can be written in the
form:
Yr = Krp (rr - :r ) [rr - :r [p-I
*Work done under NASA Contract NAS3-23939.
341
https://ntrs.nasa.gov/search.jsp?R=19880001793 2020-03-20T08:33:42+00:00Z
where _r is the shear strain rate resolved on a particular slip system; T, Tr is
the shear stress resolved on that system; and _r and Kr are evolving constants
analogous to the back stress and drag stress. The term Kr accounts for the activa-
tion of slip systems other than the specific resolved one, that contribute to the
shear strain.
A preliminary evaluation of this model has been made using the 982°C (1800°F)
data obtained from PWA 1480. Predicted behavior differs depending on whether the
model assumes activity on octahedra] slip systems or on cubic slip systems, as shown
in figure I(A) through l(C). Figure I(A) shows the experimental cyclic hysteresis
loops at 982°C (1800OF) for the <OOl>, <llO>, and <Ill> orientations. For assumed oc-
tahedral slip, figure I(B), the variation of peak stress response with direction is
reasonable, but the theoretical hysteresis loop in the [OOl] direction is "fatter",
i.e., displays a more inelastic response, than the correspondin 9 experimental loop.
At this strain range, viz. + 0.3 percent, the experimental [OOlJ loop is almost be-
having elastically. At higher strain ranges, the response exhibits an inelastic be-
havior and the loop becomes "fatter".
Figure l(C) shows the corresponding predicted loops at a lO-3 per second strain
rate in the [OOl], lOll] and [lll] directions using the cube slip formula. The same
constants were used here for the cube slip response as were used for the octahedral
response, simply to see the variation of cube slip constitutive response with direc-
tion. The material constants are clearly inappropriate but suffice to show that no
inelastic response is predicted in the [OOlJ direction. Even for large strain ranges,
no inelastic response is predicted in the [OOl] direction due to the fact that the
resolved shear stress _r is zero in each of the six slip directions when the bar
specimen is pulled in t_e [OOl] direction. Clearly a mixture of octahedral and cube
slip wi l improve correlation between the theoretical model and the experimental
results! the
COATING CONSTITUTIVE MODEL
Knowledge of coating constitutive behavior is essential to the life prediction
of coated materials for a number of reasons. Coatings, as will be shown below, are
very often the sites of crack initiation and, therefore, the time for a crack to
initiate and progress into the substrate is very important in the overall life of
the component. Secondly, the coating is effectively a structural component and its
stress-strain history will affect the stress-strain history of the substrate-coating
interface.
The survey of candidate constitutive models for this program was limited to iso-
tropic formulations. Data to measure any anisotropy inherent in the actual applica-
tion would be well beyond the scope of this program. Models selected for evaluation
have included a classical model (ref. 4), Walker's viscoplastic formulation (ref. 3),
Stowell's model (ref. 5), and Moreno's simplified version (ref. 6).
Experimental data on the aluminide coating is not yet available. The testing pro-
cedures are complex and are in the development stage. For the overlay coating some
cyclic-creep relaxation data have been obtained, using both hot isostatically pressed
and plasma sprayed specimens, to partially evaluate the models. Comparison of cyclic-
creep relaxation data against the classical model and the Walker model is shown in
figure 2. In this test the classical model matches the data almost as well as
Walker's model. For longer tests and/or more complex cycles, the Walker model's bet-
ter accuracy may become very important.
342
LIFE PREDICTION MODEL
The selection process for life prediction models has not yet been focused to the
extent of that for the constitutive models. However, an extensive list of candidates
has been developed, and they generally fall into three broad c]assifications: 1)
phenomenological models, 2) cumulative damage models, and 3) crack growth mode]s.
In general, a11 of the phenomenological models have the advantage of simplicity
and a rather direct relationship to data bases. A drawback, however, is that they
are not very amenable to accounting for significant interaction effects when differ-
ent damage mechanisms (cyclic creep, fatigue) operate either simultaneously or se-
quentially as a result of complex high temperature loading patterns. The cumulative
damage (ref. 7-8) approaches assume that the plastic and creep components of inelas-
tic strain cause damage which can be explicitly predicted and which define the state
of the material. Damage is considered to be zero in the initial undamaged state and
failure occurs when a critical level or limit is reached due to plastic, cyclic creep
or monotonic creep deformations. A number of different definitions of damage and ap-
proaches for counting damage are used. Nearly a11 of these require use of a consti-
tutive model to determine the portion of damage caused by a particular load condi-
tion. Life prediction models which use this approach are: Linear Time and Cycle
Fraction, Ductility Exhaustion, Continuous Damage, Strain Range Partitioning, and
Cyclic Damage Accumulation.
The model development will follow closely the results of low cycle fatigue and
thermal mechanical fatigue tests.
LIFE PREDICTION TESTS
From the initial test results, the importance of the coating in influencing the
substrate life is demonstrated both by the metallography of the failures and the num-
ber of cycles to failure. Comparing the fracture surface photographs in figures 3 and
4, note that the diffusion coated specimens cracked almost uniformly around the cir-
cumference, whereas the overlay coated specimens developed families of thumbnail
cracks around the circumference. Also, note in figure 5 that the diffusion coated
specimen is more sensitive to strain range than the overlay coated specimens.
Replica data taken during thermal mechanical fatigue tests, shown in figure 6,
demonstrate that cracks in the diffusion coating grow relatively quickly around the
circumference and uniformly into the single crystal, while cracks in the overlay
coating penetrate the coating quickly but stop at the coating-substrate interface
for an "incubation" period before proceeding into the substrate. A life prediction
model must account for these differences in crack initiation behavior between coat-
ings.
Since airfoils pass through complex thermal mechanical cycles,, the life predic-
tion model must address the variation in temperature and strain through each cycle.
Various thermal mechanical fatigue cycles are being tested. One interesting result _
is shown in figure 7. Two cycles were run with the same end points and, despite the
differences in cycle shape, the lives were nearly the same. Other cycle shapes are
likely to give significantly different lives.
To better understand the behavior of the coating on the substrate in a thermal
mechanical fatigue cycle, a two element model was developed with one element repre-
senting the overlay coating and the other the substrate. This simple structure, uti-
343
lizing the Walker constitutive model for the coating, and a simple constitutive model
for the substrate, was analytically run through three cycles• As shown in figure 8,
the coating mechanical strain-stress history is considerably different from that of
the substrate. In each cycle the coating stress relaxes to zero stress at maximum
temperature conditions due to the coating's high creep rate at these conditions. The
resulting hysteresis loop should provide important parameter data for a coating
cracking model•
FUTURE WORK
In the coming year, additional cyclic tests are planned to: l) develop the con-
stitutive model, 2) assist in the life prediction model formulation, and 3) evaluate
constants for the models. Also, assuming Option l of the program is exercised, model
life development will be extended to airfoil root attachment temperatures, stress
levels, and notch stress concentrations.
l •
.
REFERENCES
Hill, R.: "A Theory of the Yielding and Plastic Flow of Anisotropic Metals,"
Proc. Royal Society of London, Ser. A, Vo1. 193, pp. 281-297, 1948.
Lee, D.; Zaverl, F., Jr.; Shih, C. F.; and German, M. D.: "Plasticity Theories
and Structural Analysis of Anisotropic Metals," Report No. 77CRD285, General
Electric Corporate Research and Development Center, Schenectady, New York, 1977.
3. Walker, K. P.: "Research and Development Program for Nonlinear Structural Model-
ing With Advanced Time-Temperature Dependence Constitutive Relationships," NASA
CR-165533, November, 1981.
4. Kraus, H.: Creep Analysis, John Wiley & Sons, Inc., New York, Chapter 2, 1980.
5. Stowell, E. Z., et al: "Predicted Behavior of Rapidly Heated Metal in Compres-
sion," NASA TR R-59, 1960
. Moreno, V.: "Development of a Simplified Analytical Method for Representing Ma-
terial Cyclic Response," NASA CR-168100, January, 1983.
7. Lemaitre, J.; and Chaboche, J. L.: "A Non-Linear Model for Creep Fatigue Damage
Cumulation and Interaction," Mechanics of Viscoplastic Media and Bodies, J. Hult,
Ed., Springer-Verlag, pp. 291-30I, 19/5.
8. Lemaitre, J.; and Plumtree, A.: "Application of Damage Concepts to Predict Creep
Fatigue Failures," J. Eng. Materials and Technology, Vol. lO, ASME, pp. 284-292.
1 Swanson, G. A.; and Bill, R. C.: "Life Prediction and Constitutive Models for En-
gine Hot Section Anisotropic Materials," AIAA-85-1421, AIAA/SAE/ASME 21st Joint
Propulsion Conference, Monterey, California, 1985.
344
PWA 1480 STABILIZED LOOPS
1800°F, 10- 3 iN/IN/SEC
STRESS, KSI
75 __ 2'1111;
_ ?;23;
-o.oo3 -o.oo_/ / -0.002 -o.oo3
STRAIN, PERCENT50
75
,5F
<111>
45 <011>
< 001>
15
-15
-45
-7_ I I I
-o._ -o._1 -0.07 0.07 o._1 o._
STRAIN IN PERCENT
(A) Experimental Hysteresis Loops
for PW& 1480 at 982°C (1800°F)
at I0 -3 Sec -I Strain Rate
(B) Octahedral Slip Predictions of
Hysteresis Loops for PWA 1480 at
982°C (1800°F)
60
36
_/ ,12
Z
_) _12
-36
I
i
I I I
-0.21 -0.07 0.07
<011>
<TI 1>
<001 >
(c)
-60 I I
-o.3, o.21 o.3,
STRAIN IN PERCENT
Cube Slip Predictions of Hyster-
esis Loops for P_A ]480 at 982°C
(laOO°F)
Figure I
345
1101.2 
COATING CONSTITUTIVE I.XIDEL-DATA CCTPARIW 
CYCLIC - CREEP REW(ATIDi TEST AT 538°C (1OOO"F) . . - DATA 
d REORESSION FIT 
VI 
VI u
c 
CLASSICAL mlEL 
Figure 2 
LIALER KIDEL 
sox 6X 
(.A ) C i  rcumferenti a1 Cracking ( 6) Faint  Fati yue S t r i  dtioiis 
Figure 3 PbA 273 Coated PW 1480<100>; Specimen JB-22; Af te r  Being Thermal He- 
chanical Fatigue Tested a t  427-1038°C (800-1900°F) A E  = - +0.275%, 1 CPM, 
Out-of-Phase f o r  3772 Cycles 
346 ORIGINAL PAGE IS 
OF POOR QUALITY 
.ORIGINAL ?A-GE 1s 
.OF POOR QUALITY 
- E 
1 .O 
c7 z2 f
2 
2 
I- 
u) 
-1 
0 
1 ox 40X 
(A ) Mu1 ti p l  e Small T humbnai 1 i i ke 
Fat igue Cracks 
(B) F a i n t  Fat igue S t r i a t i o n s  
- 
PWA 286/OUT-OF-PHASE 
\ 
PWA 286IlN-PHASE - PWA 273/OUT-OF-PHAS€ 
- - 
- i \ 
PWA 273 ALUMlNlDE DIFFUSION 
PWA 286 NiCoCrALY OVERLAY 
F i g u r e  4 Pld 286 Coated PM 1480 <loo>; Specimen JB-9; A f t e r  Being Thermal Me- 
chanica l  Fa t igue Tested a t  427-1038°C (800-1900°F) A € =  - +0.4%y 1 CPiYY 
Out-of-Phase f o r  1878 Cycles 
0.1 1 I I 1 I I , , * I  1 1 I 1 I 1 1 , l  I 
100 1000 10000 
50% L O A D  DROP LIFE-(CYCLES) 
Figure  5 Thermal Mechanical Fat igue L i f e  Vs. S t r a i n  Range f o r  Coated P l d  1480 
427-1038°C (800-1900°F) 
34 7 
L
0 8.e5-
M
G
£
S
T 8.
0
B
S
E
R
U 8.
E
D
S
U 8.
R
F
A
C
E
8.81
C
R
A
C
K
e.ee-
i
N
PUA 1488 <188>
1988°F. ISOTHERMAL LCF
*..4X , 18CPM * I MIN. @ -.4_ (PC)
t.4_ , 18CPM ÷ 1 MIH. @ *.4X (CP)
PWA 286 OVERLAY
PWA 273 DIFFUSION
/
/
•P'-_ i,lJ
l T
i
J2] /J j
_J
jf
f
//
8 288 488 688 888 1888 1288 1408 1688 1888
188 388 588 788 988 1188 1380 1588 1788
CYCLES
Figure 6 Comparison of Crack Growth with Diffussion and Overlay Coatings
v
Z
CO
0,4
0,4 ¸
j 1900OF
Z
800°F
I--
0,4
19(]0.OF
800°F
COATING LIFE LIFE
ALLI,IINIDE.P4A 273 2.76CYCLES 580 CYCLES
OVERLAY.R.IA288 1847 1878
Figure 7 Coated PW_ 1480 ,Life Comparison: Two TMF Cycle Shapes
348
964.6 MPa
Overlay Coating
(PWA 286)-,,_
140 ksi
!
0.4
Mechanical Strain (%)
Figure 8 TMF Cycle - Coating and Substrate Stress-Strain History
Out of Phase Cycle
Temperature Range 427°C - I038°C (800°F - 1900°F)
Strain Range + 0.4 Percent
349


Life prediction and constitutive models for engine hot section anisotropic materials program

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server