Work to develop fatigue life prediction and constitutive models for uncoated attachment regions of single crystal gas turbine blades is described. At temperatures relevant to attachment regions, deformation is dominated by slip on crystallographic planes. However, fatigue crack initiation and early crack growth are not always observed to be crystallographic. The influence of natural occurring microporosity will be investigated by testing both hot isostatically pressed and conventionally cast PWA 1480 single crystal specimens. Several differnt specimen configurations and orientations relative to the natural crystal axes are being tested to investigate the influence of notch acuity and the material's anisotropy. Global and slip system stresses in the notched regions were determined from three dimensional stress analyses and will be used to develop fatigue life prediction models consistent with the observed lives and crack characteristics

Anton, D. L.

Bak, Joe

Favrow, L. H.

Mccarthy, G. J.

Meyer, T. G.

English

NASA Technical Reports Server

N90-28643
CONSTITUTIVE AND LIFE MODELING OF SINGLE CRYSTAL
BLADE ALLOYS FOR ROOT ATTACHMENT ANALYSIS
T. G. Meyer and G. J. McCarthy
United Technologies, Pratt & Whitney
400 Main street
East Hartford, Connecticut 06108
and
L. H. Favrow, D. L. Anton and Joe Bak
United Technologies Research Center
Silver Lane
East Hartford, Connecticut 06108
ABSTRACT
This paper describes work in progress under a NASA contract
(NAS3-23939) to develop fatigue life prediction and constitutive
models for uncoated attachment regions of single crystal gas turbine
blades. At temperatures relevant to attachment regions, deformation
is dominated by slip on crystallograhic planes. However, fatigue
crack initiation and early crack growth are not always observed to be
crystallographic. The influence of natural occurring microporosity
will be investigated by testing both hot isostatically pressed and
conventionally cast PWA 1480 single crystal specimens. Several
different specimen configurations and orientations relative to the
natural crystal axes are being tested to investigate the influence of
notch acuity and the material's anisotropy. Global and slip system
stresses in the notched regions have been determined from three
dimensional stress analyses and will be used to develop fatigue life
prediction models consistent with the observed lives and crack
characteristics.
INTRODUCTION
The attachment regions of turbine airfoils are geometrically complex
with a variety of notched features at the interface with the turbine
disk and in the transition to the blade platform. These features lead
to stress concentrations which are potential fatigue crack initiation
sites. In single crystal components, the critical regions can have a
variety of local material orientations depending upon the location of
the notch and the crystallographic orientation in which the component
is cast.
510
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This paper describes a three year combined analytical and
experimental program intended to develop constitutive and fatigue life
prediction models for single crystal attachment regions. The work is
a part of NASA contract NAS3-23939, "Life Prediction and Constitutive
Models for Engine Hot Section Anisotropic Materials ". The contract
is divided into two parts with the Base Program focussed on developing
models for the coated airfoil regions of turbine blade and the Option
1 Program addressing the lower temperature uncoated attachment
regions. This paper is confined to the second part of the contract and
presents results from the first year of the effort.
DISCUSSION
Over 150 constitutive and fatigue tests will be conducted on single
crystal PWA 1480 specimens in three notched configurations and in
several crysatllographic orientations. All tests are being conducted
isothermally and will be limited to temperatures below 1600F.
Conventionally cast and heat treated PWA 1480 is used in the bulk of
these tests, but some tests will be conducted on hot isostatically
pressed (HIP'd) PWA 1480 to investigate the influence of microporosity
on fatigue life, since fatigue initiation sites are commonly
associated with pores in conventionally cast material.
Double edge notched plates with two different sized notches as shown
in Figure 1 are being used in the program. The gage section thickness
of the sharp notched specimen is 0.050 inches while the mild notched
geometry will be tested two thicknesses; 0.050 and 0.200 inches. To
completely describe the orientation of a notched specimen, both
primary orientation (i.e. the loading direction) and secondary
orientation (i.e. the direction normal to the notch) must be specified
as illustrated in Figure 2. The orientations are designated by a pair
of Miller indices, <HKL><PQR>, which define the primary and secondary
orientations respectively. Six different crystallographic
orientations have been selected for the notched specimens; <001><i00>,
<001><210>, <i01><i0[>, <I01><I_-2i>, <III><011> and <213><451>. These
orientations were selected to span the full range of possible crystal
orientations in the attachment region while minimizing the
out-of-plane distortions that can occur in nonsymmetrically aligned
anisotropic bodies.
The prediction models must properly account for crystallographic
orientation in the notch. Life parameters based on slip system
quantitltes will be among those investigated since deformation (and
presumably damage) is known to occur by sllp in specific crystal
directions at temperatures in the regime of interest. Such models can
be expected to account for orientation effects in an implicit manner.
More conventional life parameters such as maximum principal stress or
511
IO
0.125"---_+ _
0.75 0.55
I
0
_ 3.5" _-_
O 0_5 I'V _ 0
_'-- .050 _'
FIGURE 1 MILD AND SHARP NOTCH SPECIMEN GEOMETRIES
[0011
PRIMARY ORIENTATION [HKL]
[PQR] SECONDARY ORIENTATION
[010]
I100]
FIGURE 2 PRIMARY AND SECONDARY ORIENTATIONS OF SPECIMENS
512
strain also account for orientation through proper anisotropic stress
analysis. Three dimensional stress analyses are being used to
determine the local stresses and strains in each configuration and
orientation. In someorientations the location of maximumstress does
not occur at the minimum section as would be expected in isotropic
specimensof the same shape. Global and slip system stresses and
strains have been determined as a function of location in the notch.
See Figure 3. Finite element results for the thin, mild notched
specimen in the <001>, <i01> and <iii> primary orientations are shown
in Table i. The values presented are at the element integration
points closest to the notched surface. Figure 4 shows the finite
element meshused in the analysis. Additional analyses using a more
refined finite element meshas well as boundary element analyses are
being conducted to provide more accurate stresses and strains on the
notch surface. The boundary element code being used is the BEST3D
(Boundary Element Stress Analysis Technology - Three Dimensional)
which was developed by Pratt & Whitney and SUNY-Buffalo as part of
NASA contract NAS3-23697. For convenience, the stresses and strains
in Table I have been normalized by the net section stress or strain to
give a stress or strain concentration factor.
_,SLIP SYSTEM
SHEAR STRESS
<1(
O'p PRINCIPAL STRESS
B : SLIP DIRECTION
<010>
e
n : SURFACE NORMAL
AT
FIGURE 3 GLOBAL AND SLIP SYSTEM STRESSES IN THE NOTCH
513
Orientation
Primary Secondary
<001> <I00>
<001> <210>
<I01> <10i>
<101> <I_i>
<iii> <01i>
TABLE 1
Global and Slip System Parameters
for Thin, Mild Notched Specimens
Principal Principal
Strain Stress
Maximum Slip System
Shear Stress
0 TIs B •n
0 1.5 23 1.8
0 1.5 23 1.8
0 1.9 0 2.0
0 1.9 0 2.0
0 2.0 0 2.0
23 .76 .28
23 .79 .00
0 .77 .48
0 .72 .17
16 .57 .22
0 = anglular location in the notch measured
from the minimum section (degrees)
S = net section stress
E = net section strain
O = maximum principal stress in the notch
6 = maximum principal strain in the notch
T = shear stress on the most highly stressed
octahedral slip system
B = slip direction of the most highly stressed
octahedral slip system
n = surface normal
• \ • % • 1 •
• _ ° ° °
i,i
_ ° ! • ° .
_ ° i ° ° "
.1..•,
• i • • •
FIGURE 4 THREE DIMENSIONAL FINITE ELEMENT MESH USED IN SPECIMEN ANALYSIS
514
The location of the maximum principal stress and the maximum strain do
not coincide for all orientations being tested. In addition, the
maximum slip system shear stress and the maximum principal stress do
not change in constant proportion from one orientation to another and
do not even occur at the same location in the notch for the
<111><015> orientation.
The results shown in Table 1 are from elastic finite element analyses.
However at the stress levels of interest to this program, the region
around the notch yields. The test data clearly shows slip lines being
formed at the fatigue loads. A constitutive model for this nonlinear
material behavior is being developed to permit nonlinear stress
analysis. Such a model was developed in the Base Program with emphasis
on high temperature behavior (Swanson et. al., 1987), and will be
refined as necessary for the lower temperature regime of interest in
this program. This model uses the unified approach for computing all
inelastic strains simultaneously rather than the conventional approach
of separating plastic and creep strains. Global stresses are resolved
onto the twelve octahedral and six cube slip systems and then used in
a viscoplastic formulation to calculate inelastic strains on each slip
system. The strains in the global coordinate system are then obtained
by summing the slip system 8hear strains. The model constants were
determined from approximately forty cyclic constitutive tests on
uniaxial strain controlled specimens tested at several temperatures
between 800F and 2200F. Specimens were oriented in the <001>, <i01>,
<iii> and <213> directions. These test showed that the material is
only moderately strain rate sensitive at 1400F and is very insensitive
at 1200F and below.
Fatigue tests have just recently begun on thin, mild notched
specimens. Tests have been conducted at room temperature, 1200F and
1400F at 1 cycle per second under load control. There is insufficient
data to date to report clear life versus stress trends, however some
information regarding crack initiation sites and crack morphology is
available. In general, cracks were found to initiate from casting
micropores in un-HIP'd material and at locations corresponding to the
maximum principal stress rather than the maximum principal strain.
For the orientations tested to date this initiation site also
coincides with the maximum slip system shear stress, so that it is not
possible to conclude which of these two paramters is more important.
Figure 5 is an overall view of a <001><I00> specimen cycled between 6
and 115 Ksi. nominal stress at 1400F. Life to failure was 2976 cycles.
Fatigue cracks initiated in both notches near the maximum stress
location and in the latter stage of growth, progressed along a {iii}
plane intersecting the specimen surface at an angle of 48 degrees from
a line connecting the notch centers. For a perfectly aligned
<O01><lO0> specimen, the slip system with the highest shear stress
intersects the specimen surface at 45 degrees from a line connecting
515
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the notch centers. Figure 6 shows the initiation sites in the primary
crack in more detail. Cracks initiated from two separate pores which
were located at angles of 22 and 30 degrees from the minimum
specicimen dimension. The maximum stress location in this orientation
is calculated to be 23 degrees from the notch bottom. The crack planes
near the initiation sites were perpendicular to the maximum stress
direction rather than along a single {iii} plane. However a closer
examination of similar pore initiated cracks by Anton in 1987 showed
that the crack plane was formed by crack growth along several
intersecting octahedral planes. So even though the general plane of
the crack is perpendicular to the principal stress, it cannot be
concluded that the principal stress is the controlling fatigue
paramenter. The three dimensional stress state in the vicinity of the
pore will lead to several slip systems having high stress and may
promote cracking on more than one plane at a time. In a similar
fashion, the transverse "constriction" stress in the thick specimens
to be tested may lead to multiple plane cracks.
After an initial region of "non-crystallographic" growth, the cracks
turn abruptly and proceed along a single {Iii} plane. Critical crack
sizes for this transition are being determined. Detailed crack growth
measurements in the early stages of crack growth are being taken in
room temperature tests to provide additional data for model
development. Figure 7 shows crack growth data obtained by periodic
inspection at 100X magnification with the specimen unloaded.
Hot isostatlc pressing eliminates microporosity so that the initiation
processes and lives are expected to be different than in the un-HIP'd
specimens. Fatigue studies in superalloy single crystals by Giamei and
Anton (1986) showed that cracks initiated due to slip steps formed at
the intersection of slip planes and the surface. In the absence of
micropores, surface initiation is anticipated. In anticipation that
slip step height may be an important initiation parameter in HIP'd
material, two of the secondary orientations were chosen to vary the
angle at which the most highly stressed slip system intersects the
notch surface. The angle of intersection with the notch surface can
be quantified by the dot product of a vector in the slip direction, B,
and a vector normal to the surface, _. A dot product of 1 indicates
that the sllp direction is perpendicular to the surface (resulting in
a large sllp step) while a dot product of 0 indicates that the slip
direction is parallel to the surface (producing no slip step). Table
1 shows how this parameter varies with secondary orientation in the
<001> and <I01> primary orientation specimens.
517
O., CRACK
LENGTH, IN
0.007
0.006
0.005
0.004
0.003
0.002
0.001 w
-_ I I I 1 I I I
1500 2000 2500 3000 3500 4000 4500
CYCLES
l
5000
FIGURE 7 FATIGUE CRACK GROWTH FROM MICROPORE
CONCLUS IONS
The analytical and test program described above is a multiyear effort
intended to develop constitutive and fatigue life prediction models
for single crystal materials with application to the lower temperature
uncoated and notched regions of turbine airfoils. Specimen
configurations and orientations have been chosen to span the range of
possible attachment configurations while testing possible fatigue
paramenters in a systematic way. Initial test indicate that the in
thin un-HIP'd notches fatigue cracks are initiated at casting
micropores near the maximum stress location. This preliminary data
suggests that the maximum strain is not the best fatigue parameter.
REFERENCES
Anton, D. L., 1984, "Low Cycle Fatigue Characteristics of
" Acta Metall
Randomly Aligned Superalloy Single Crystals,
No. i0, pp. 1669-1679.
<001> and
Vol. 32,
Giamei, A. F. and Anton, D. L., 1985, "Plastic Strain Localization in
Superalloy Single Crystals," United Technologies Resaerch Center final
report, Air Force Office of Scientific Research contract
F49620-83-C-0104.
Swanson, G. A., Linask, I., Nissley, D. N., Norris, P. P., Meyer, T.
G., and Walker, K. P., 1987, "Life Prediction and Constitutive Models
for Engine Hot Section Anisotropic Materials," NASA CR-179594.
518


Constitutive and life modeling of single crystal blade alloys for root attachment analysis

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