y‘ I II||II'.'IIIIV"Ir

 

THESlS

 

This is to certify that the

thesis entitled

WIGATICN OF SURFACE SHEINS IN
Fm TREE TURBINE BLADE M'IA'ICI‘MENI'S

presented by

Captain Joseph P. Marksteiner

has been accepted towards fulfillment
of the requirements for

AS°__degree in L

I I (
a Major professor
Date MM

0—7639 MS U i: an Aflirmative Action/Equal Opportunity Institution

 

 

 

MSU

LIBRARIES
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RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES will
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returned after the date
stamped below.

 

 

 

 

 

INVESTIGATION OF SURFACE STRAINS IN
FIR TREE TURBINE BLADE ATTACHMENTS

BY

Captain Joseph P. Marksteiner

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Metallurgy, Mechanics and Materials Science

1985

ABSTRACT

INVESTIGATION OF SURFACE STRAINS
IN FIR TREE TURBINE BLADE ATTACHMENTS

BY

Joseph P. Marksteiner

Surface strains in the fillet regions of test model
specimens of fir tree turbine blade attachments were
examined. The fir tree specimens are loaded under cyclic
tension-tension in the elastic range. The strains were
recorded with an interferometric.technique at the center and
near the edges of the exposed unloaded face of the fir tree.
Data were recorded for a total of over 700 load cycles on 23
different specimens. Two different load bearing surface
geometries were investigated. The effect of machining
tolerances were determined for both geometries. The load
split between the two sets of load bearing surfaces was
determined. Actual strains were compared to those predicted
by superposition of strain fields. Stresses computed from
the recorded strains were compared to photoelastic and

finite element analyses.

ACKNOWLEDGMENTS

This thesis project was funded by Garrett Turbine
Engine Company of Phoenix, Arizona. It was undertaken to
fulfill Master's Degree requirements for The Air Force
Institute of Technology.

I would like to thank my wife, Cathy, who supported me
through this entire project. Additionally, I'd like to
thank Michelle Ward for her help in typing this report and
Lonnie Lucas of Garrett for finite element analyses. And
finally, special thanks go to Dr. John Martin for his advice

and guidance.

ii

LIST OF
CHAPTER
CHAPTER
2.1
2.2
CHAPTER
3.1
CHAPTER
4.1
4.2

CHAPTER

5.4
CHAPTER
6.1
6.2
6.3

CHAPTER

TABLE OF CONTENTS

FIGURES . . . . . . . . . . . .
1. INTRODUCTION . . . . . . .
2. INTERFEROMETRIC STRAIN GAGE
Fundamentals of the ISG . . .
ISG Hardware and Software . .
3. LOAD TRAIN . . . . . . . .
Load Fixltures and Load Train
4. SPECIMEN PREPARATION . . .
Surface Preparation . . . . .
Indentation Placement . . . .
5. TEST PROCEDURES . . . . . .

Determining Young's Modulus .

Characterization of Effects Due to

Machining Tolerances . . . . .
Load Split Determination . . .
Superposition of Strain Fields
6. SPECIMEN ANALYSIS . . . . .
General Description . . . . .
Photoelastic Analysis . . . .
Finite Element Analysis . . .

7 0 CONCLUSIONS 0 O O O O O O 0

iii

Page

11
15
15
l7
17
20
22

22

24
31
34
50
50
54
60

64

APPENDIX 1.

REFERENCES

TABLE OF CONTENTS (Continued)

RIGID BODY MOTION EFFECTS ON THE

ISG

iv

Angular Displacement Effects

Rigid Body Motion Corrections

Rigid Body Motion of the Specimen

vertical Motion Effects on the ISG

Page

65
65
68
70
76
77

Figure
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.

45.

LIST OF FIGURES (Continued)

Load Split Data . . . . . . . . . .
Load Split Data . . . . . . . . . .
Load Split Data . . . . . . . . . .
Load Split Data . . . . . . . . . .
Load Split Data . . . . . . . . . .
Load Split Data . . . . . . . . . .
Superposition Determination . . . .
Superposition Data . . . . . . . .
Superposition Data . . . . . . . .
Superposition Data . . . . . . . .
Superposition Data . . . . . . . .
Superposition Data . . . . . . . .
Superposition Data . . . . . . . .
Specimen Specification . . . . . .
Fixture Specifications . . . . . .
Specimen Asymmetry . . . . . . . .
Neck Stress Parameters . . . . . .
Point Load Resolution . . . . . . .
Inner Hook Stress Parameters . . .
Outer Hook Stress Parameters . . .
Finite Element Analyses . . . . . .
Finite Element Analyses . . . . . .
Stress Comparisons . . . . . . . .

Specimen Vertical Motion . . . . .

vi

Page
36
37
38
39
40
41
43
44
45
46
47
48
49
51
52
53
55
55
57
59
61
62
63
66

Figure

46.

47.
48.
49.

50.

LIST OF FIGURES (Continued)

Angular Displacement of Specimen and

Fixture . . . . . . . . . .
ISG vertical Motion Test .
Angular Displacement Error
ISG Signal Distortion . . .

Rigid Body Motion Correction

vii

Page

67
69
71
73

76

CHAPTER I

INTRODUCTION

In recent years there has been an increased demand
placed upon aircraft powerplant manufacturers to provide
more efficient engines. A major part of this effort has
been dedicated to investigating the limitations of the
materials and structures used, especially in the "hot
section" of the engine (l)*. Hot section components include
the combusters, turbine blades, vanes, and disks. All
operate under extremely high temperatures and severe loads
even at low engine power.

Improvements in design result from testing existing
components and with those data, developing new and better
materials and structures to cope with the adverse operating
conditions involved. Prior to implementing any new design,
extensive testing is required to determine whether it is
better than its predecessor and if so, how much.

Design criteria for turbine blades are based on the
expected operating temperature and cyclic loading
conditions. Figure 1 shows a typical stress-range diagram

for a turbine blade material. The turbine blade itself

 

*Numbers in parentheses refer to references listed in the
reference table. Numbers in brackets refer to equations.

0 end.
bine Blade

\
Ucyclic 0 \
Attatclment

O" steady Cult.

 

Figure 1 Stress Range Curve

Outer Hooks

Inner Hooks

 

Figure 2 Fir Tree Attatclment

3
operates on the limit of the curve, so that it will theore—
tically fail near its design life. The attachment however,
is usually designed so that it falls somewhere within the
limits of the curve (2). Recently, however, advancements in
turbine design and coating technology have made the blade
attachment region the life limiting factor (3).

A modified two tang fir tree turbine blade attachment
of directionally solidified MAR 247, which a nickel based
super alloy, is in the initial stages of testing and is
being compared to the current design of the same material.
The basic design of the fir tree attachment is shown in
Figure 2. It consists of two sets of tangs or "hooks". The
designation of inner or outer refers to the position the set
occupies in relation to the center of the turbine disk. The
indicated load bearing surfaces are planes in both the fir
tree and turbine disk for the current design geometry.
Theoretical data compiled by Garrett Turbine Engine
Company** using finite element methods (4) based on contact
stress studies conducted by J. 0. Smith and C. K. Liu (5),
indicate a possible 10 fold increase in fatigue life for a
crowned geometry of the fir tree load bearing surfaces.

Both the initial finite element model used by Garrett
and predictions based on photoelastic theory are two
dimensional in nature. The fir tree attachment however,
approximates a right cylinder with the loads applied on the

lateral boundary, and no assumed deformation along the axis

 

**A division of Garrett Corporation, Phoenix, Arizona.

4
of the cylinder. This, according to Sokolinikoff (6) falls
into the class of plane strain problems. The two
dimensional approach is justified by Durelli and Wiley (7)
by assuming that separate slices of the blade attachment are
essentially two dimensional and that the load carried by
each slice is different. Data collected in photoelastic
studies on thin sheets compared very well with actual test
results and validated this assumption.

The actual stress state in the fir tree attachment is
extremely complex. The complexity is due not only to the
geometry of the attachment but to the loads appled to it.
Stresses are due to the bending and twisting moments that
result from the aerodynamic forces on the blade and are
superimposed on the stresses caused by centrifugal tension
in the fir tree.

The purpose of this study is to directly determine the
actual surface strains on the face of the fir tree specimens
under tensile load conditions. This will simulate the
centrifugal forces on the blade attachments in the engine.
Strain measurements will be made with an interferometric
strain measuring technique. These data will be used for
three purposes. The first will be to characterize the
effects of machining tolerances on load distribution.
Second, the load split between the two sets of load bearing
surfaces will be determined. Third, it will be determined
whether the principle of superposition of strain fields

accurately predicts surface strains. Finally, surface

5
stresses calculated from the strain data will be compared to

photoelastic studies and finite element model analyses.

CHAPTER 2

INTERFEROMETRIC STRAIN GAGE

2.1 Fundamentals of the ISG
An Interferometric Strain Gage (ISG), which is a

noncontact laser device, was used to measure surface strains
(8-11). The ISG is able to measure strains over very small
gage lengths, typically 100 microns. The device measures
strains by monitoring the position of interference fringe
patterns generated by pyramidal indentations in the surface
of the specimen. These indentations are made with a
Vicker's Micro Hardness Tester and measure approximately 25
microns across. Figure 3 shows a schematic diagram of the
indents and the incedent laser light. Interferring rays of
light are out of phase by d sin a where a is the angle
between the incedent laser beam and the reflected
interferring rays. Whenever the following relationship is
satisfied:

d sin a = nA (n = 0,1,2,...) [1]

where A = wavelength of the laser light

The reflected rays are constructively in phase and a bright
spot in the fringe pattern will be caused. Figure 4 shows a
typical fringe pattern. Due to symmetry, two identical
fringe patterns will be created, Figure 5. When observed

from any stationary point, defined by dog any movement of

6

Incident Laser Beam

A
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Figure 3 Indent and Laser Scha'natic (8)

 

Figure 4 Interference Fringe Patterns

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11

the indentations is seen as a fringe shift. For any single
fringe in the pattern, dsin a is a constant determined by
the order n, in equation [1]. An increase in d (tensile
strain) will cause the fringe patterns to shift toward the
incedent laser beam, while a decrease in d (compressive
strain) will shift the fringe patterns away from it. For
rigid body motion along the same axis as the indentations
and fringe patterns, one set of fringes will move toward the
laser beam while one set will move away. If these motions
are assigned positive and negative signs respectively, then
averaging them will cancel rigid body motion.

The relationship between fringe movement and strain
causing indentation motion is:

_ A
Ad - m Am [2]

Where 'm' is the number of fraction of fringes passing the
fixed observation point defined by do. The average motion
of the two generated fringe patterns is:
Aml + Amz
A

- < >
Ad ‘ ears; 2 [3’

 

2.2 ISG Hardware and Software

A schematic diagram of the ISG is shown in Figure 6.
Two servocontrolled mirrors are positioned in the
interference fringe patterns defining the angle 00. These
mirrors sweep a portion of the fringe pattern across the

face of the photomultiplier tubes (PMT's). Each tube is

12

8 4

PMT 6‘

Reading 4
(volts) 41
24

 

 

T

50 80 :57) 260 250 360

Mirror Position

Figure 7 PMI‘ Voltage vs. Mirror Position

l3
masked by a cover with a narrow slip parallel to the bars of
light in the fringe patterns, so that only one bright fringe
can shine through at a time. The sweep of the mirrors is
governed by a ramp generator and a plot of time versus
voltage output from the ”PMT‘s has a sine wave appearance,
with higher voltage corresponding bright spot in the fringe.
A minicomputer divides this data into 256 locations and
stores the PMT output voltage for each one, as shown in
Figure 7. During loading of a test specimen, the shift of
fringes is updated every 100 milliseconds. Any change in
fringe position is converted to an analog voltage by the
computer that is directly proportional to strain at the
indentations. This output voltage is determined by the
strain and preset parameters in the controlling program and
obeys the following equation:

mv = (e s d sin a (9.76) gain)/A [4]
where e = strain, s = average spacing between peaks in
Figure 7, d = distance between indents, gain is a computer
parameter between 2 and 8.

For a given strain the output voltage can easily be
computed. This voltage is then run through an analog
computer and is used to calibrate recording equipment. The
ISG output is fed through the analog circuit and to the

recorder and can be read directly as strain.

 

14

 

 

Figure 8 Test Specinen & loading Fixture

CHAPTER 3

LOAD TRAIN

3.1 Load Fixtures and Load Train

Test specimens and loading fixtures supplied by Garrett
are shown in Figure 8. The design of the loading fixtures
and the specifications of the test program required a
multicomponent load train. The load fixtures were mounted
in modified compression grips, designed to accommodate the
button heads on the test fixtures. Universal joints were
used to attach the compression grips to the hydraulic ram
and the load cell. The universal joints were needed to
allow for orientation changes between the fir tree and the
loading fixture. Orientation changes would result from
shifting and slipping of the contact surfaces predicted by
Heywood (12). The complete load train is depicted in Figure

9.

15

16

Load Cell

0 L Universal Joint

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

..J
Carpressicn Grip
1 \

j

_ g Loading Fixtures
and Specimen

.J

/ X
0
Hydraulic Ram

Figure 9 Oarplete Load Train

CHAPTER 4

SPECIMEN PREPARATION

4.1 Surface Preparation

The specimens supplied by Garrett were prepared in the
same manner as the actual turbine blade attachments. The
shape of the fir tree was produced by very accurately shaped
grinding wheels. To inhibit crack initiation the entire
surface was shot peened. This greatly reduced the
reflectivity of the specimen and consequently would have
added to the difficulty of producing data with the ISG.

The shot peened face of the crowned specimens was
polished with progressively finer abrasives until it was
highly reflective. The specimens with the flat load bearing
geometry were supplied with a very large bevel on the edges.
On several of the specimens, the bevel extended
approximately 25% across the small fillet region, Figure 10.
The faces of the flat specimens were ground down until the
remaining bevel was the same as the crowned specimens. This
grinding reduced the cross-sectional area of the flat
specimens approximately 1%. In all direct comparisons
between the crowned and flat geometries, this area reduction

was accounted for.

17

l8

 

Figure 10 Flat Speciuen Edge Bevel

l9

Centerline

 

 

 

 

 

 

 

Figure 11 Indent Locations

20
4.2 Indentation Placement

Indentations for the interferometric strain measure-
ments were made on the polished faces of the specimens with
a Vicker's Microhardness Tester. Three sets of indentations
were placed along a horizontal line joining the innermost
edges of each fillet region, Figure 11. They were placed in
the center of each fillet and 50 microns from the inside
edge of the bevel.

The indentation locations were chosen in the fillet
region for several reasons. First, the material was
directionally solidified along the radial or Y axis of the
fir tree. Young's modulus data was available only for this
axis. Second, the principal stresses in the fillet region
were nearly identical to the radial or Y-direction stresses
in two separate finite element analyses conducted by Garrett
(3 and 4). Additionally, the Y axis of the specimen, the
tensile axis and the strain measurement axis of the ISG were
all aligned in the same direction. Finally, the micro
hardness tester used to make the indentations was not
equiped with a rotating table. Placement of indentations
along any axis other than vertical or horizontal would have

been innacurate and inconsistent.

21

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CHAPTER 5

TEST PROCEDURES

5.1 Determining Young's Modulus

To test the alignment of the load train and the
accuracy of the ISG, the tensile modulus of the specimen in
the longitudinal direction was Obtained. Indentations were
placed in the center portion of a test specimen equidistam;
from each of the fir tree ends. ISG strain versus load data
were produced. The center of the specimen was assumed to be
analogous to a smooth bar with a rectangular cross sectional
area (0.32 square inches). From the strain versus load data
Figure (12), and the previous assumption, a modulus of 15.8
x 106 for the tensile direction of the specimen was
computed. The Young's modulus was reported at 15.92 x 106
(13).

All test specimens were initially tested at relatively
low loads (4500 lbs) compared to the actual fatigue loads
(11,750 lbs) that were used in later stages of the test
program. The low loads were chosen to prevent any plastic
deformation and to ensure that rigid body motion of the
specimen did not move the indents out of the area
illuminated by the laser. Rigid body motion effects are

discussed in detail in Appendix 1 of this report.

22

30388 8.3 2 6.53m

 

24
5.2 Characterization of Effects Due to Machining

Tolerances

Photoelastic studies indicate that stress imbalances as
high as 50,000 psi may result from the misfit produced by
allowable machining tolerances between the fir tree and the
disk (7).

Load versus strain data were produced for six locations
on the unloaded face of the fir tree on each end of the
specimen as shown in Figure 13. Because of the symmetry of
the ends of the specimens, this produced two data sets per
specimen.

These characterization data revealed some trends that
were completely unforeseen. On some specimens the load
versus strain data is very linear at all locations. It
qualitatively reflects stress and strain distributions that
would be expected across the fillet region as shown in
Figure 14. These data also fit the predicted stress
distribution produced by the finite element studies and
photoelastic distributions for similar shapes.

Even though the specimens were loaded in cyclic
tension-tension, a large number of the strain plots showed
compression. The data, initially seemed illogical. The
first specimen to show this tendency was removed from the
loading fixtures, reindented, and then retested.. But the
same data resulted. The opposite face of the specimen was
indented and tested, and the results agreed with the

previous data. The data from the three sets of indents

25

 

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8 .P. ' _ . . .
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Figure 14 Photoelastic Stress Distribution (13)

 

Resultant
Strains

26

 

 

 

 

 

Fillet

 

 

 

 

amin

 

 

 

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Figure 15 Compressive
Figure 16 Superposition of Strains

/ +
Tensi
Strains

27
across the inner fillet in Figure 15 illustrate this
phenomenon. It was assumed that the combined effects of
machining tolerances at the four load bearing surfaces could
cause a bending stress field across the fillet region.
Figure 16 demonstrates how a pure bending stress distribu-
tion superimposed on a tensile stress distribution would
produce the observed load versus strain data. With the much
smaller cross sectional area and moment of inertia at the
inner fillet, any bending stresses that were produced by
machining effects would show prominently in this area. If
the bending moment caused by machining tolerances is assumed
to be equal in each of the fillet regions, then a simple
calculation of the relative stresses can be made. The
following calculation compares the maximum stresses due to

bending at the inner and outer fillet regions.

 

 

M
o = Ty, OI M(.0914/2) 3 = 898 M,
_1_ (.8)(.09l4) [5]
12
do _ M(.234/2) 3 = 137M
1_ (.3)<.234)
12

Bending stresses in the inner fillet were clearly exhibited
in 10 of 16 crowned specimens and 4 of 7 flat specimens.

Some of the data exhibited a cyclic pattern as shown in
Figure 17. The figure shows the load versus strain plots
for the right edge, center, and left edge of the inner

fillet, respectively. The arrows shown how the load was

28

 

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Cyclic Strains

Figure 17

29
changing during that portion of the plot. The center plot
indicates that the stress at that point is linearly changing
with load. The two edge plots indicate two values of strain
for the same load, depending on whether the load was
increasing or decreasing. The general shape would suggest a
hysteresis loop, but the loading is strictly tensile. The
cyclic shape can be explained by slipping of the contact
surfaces as predicted by Durelli & Wiley (7). On the linear
side of each loop, the point of load application is not
changing. The nonlinear side indicates that there is
slipping of the contact surfaces during the loading cycle.
It was also noted that when there was slipping of the
contact surfaces, one surface remained fixed while the other
shifted. For the crowned geometry specimens, slipping will
not affect the point of load application in the fir tree.
An analysis of the fixture similar to that carried out for
the fir tree shows that a change of load position on the
fixture will change the magnitude of the load applied to the
fir tree.

Additionally, the surface strains for the given loads
indicated that in all the specimens only a very small
percentage of the total load was carried by the material
near the surface of the unloaded face. The problem was
further complicated by the fact that the specimens had a fir
tree at each end. Reactions at one end of the specimen that

caused some change in alignment between the fir tree and the

30

 

 

 

 

Figure 18 Partial Fixtures

31
fixture, could not be separated from the reactions at the

other end.

5.3 Load Split Determination

To simplify the problem of determining the load split
between the inner and outer set of hooks, a set of loading
fixtures were cut as shown in Figure 18. One fixture would
only apply load to the inner set of hooks, while the other
fixture would only apply load to the outer set. Three
specimens from each geometry were run in the partial
fixtures. Both ends of the specimens were tested in each
cut fixture. This generated two data sets for each end of a
specimen.

When the inner hooks were loaded, the exact strains
across the neck for a given load (4500 lbs) were determined.
The inner hook strains resulted from the neck stress and the
superimposed hook stress field. The strains across the
outer fillet were also recorded. These strains were the
result of tensile neck stresses, without the superimposed
hook stress field. Typical plots for strains in the neck
regions are shown in Figuresl9 and 20. When the outer hooks
were loaded, the recorded strain versus load plots reflect
both neck and hook stress fields.

The mean stress in the outer fillet was the same
whether the inner or outer hooks were loaded. The stress
distribution as expected for each of these cases was
different. The most noticeable difference was in the center

of the fillet. When loaded at the outer hooks, the

shadow 83.me Heep-am 888 x8: 8,5 2 253m

 

33

3.25m mania Han-8m omen x8: 885 on ESE

 

34

average strain in the center is nearly zero. For the mean
stress across the cross section to be the same, an increase
in the stress concentration at the edge of the fillet is
required. This indicates that hook loading has a greater
contribution to stress concentrations in the fillet than
neck loading.

It was assumed that if a given load on the inner hooks
produced a certain strain in the partial fixture data, then
that same strain would indicate the same load on the inner
hooks during the high load tests. Data were compared for
the three indent locations across the fillet and averaged to
compute the load carried by the inner hooks. By simple
subtraction the remaining load carried by the outer hooks
was computed. Figure 21 shows this process and Figures

22-27 graph the actual data.

5.4 Superposition of Strain Fields

The principle of superposition is widely used to
simplify problems with combined stress fields (6). The
strains measured at the edge of the outer fillet were used
for the superposition testing. These strains were large in
magnitude than the center strains which improved the
accuracy of the measurements. To eliminate errors caused by
bending stresses, the average value of these strains was
used in the computations. To determine if the principle
held, the process depicted in Figure 28 was followed.

First, with the load split previously determined, the outer

35

 

InnerHookloadvsStrainData

 

 

QOuter Hook load
:3 B- A
5.
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A Total load

Figure 21 load Split Determination

 

 

 

 

 

 

 

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Figure 22

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load Split Data

37

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Figure 24 Load Split Data

39

 

 

 

Figure 25 Load Split Data

 

 

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'Ibtalload: . g . :' ;......

load Split Data

41

 

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Figure 27 Load Split Data

42

fillet strains due to the load carried by the inner hooks
were determined from the corresponding partial fixture data.
The calculated load carried by the outer hooks was compared
to the partial fixture data taken when only the outer hooks
were loaded. A strain in the outer fillet due to the load
on the outer hooks was determined. The sum of these two
calculated strains were compared to the actual outer fillet
strain. Based on the above calculations the principle of
super-position did not hold for strains in the outer
fillet.

The data produced by the preceeding process is shown in

Figures 29-34.

43

 

/ \. /
\ /
Outer Hook Load vs Strain Data
A_
B- ' .
CA-B)—
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' 62 ‘ ‘ ‘ e. ' " 6.
f Actual Strain Superposition Strain
(62+ 63 H Q
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Figure 28 Superpositicn Determination

 

 

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Figure 30

Superposition Data

 

 

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Figure 31

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Figure 32

'1le Load

Superposition Data

 

 

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Figure 33

--TotalLoad

Superposition Data

49

 

 

 

 

 

 

 

 

 

 

 

 

‘Ibtalload

Figure 34 Superposition Data

CHAPTER 6

SPECIMEN ANALYSES

6.1 General Description

The two tang fir tree test specimens and loading
fixtures to simulate the turbine disk were provided by
Garrett Turbine Engine Company. The fir tree specimens are
made of directionally solidified MAR 247, and the loading
fixtures are Astroloy. Diagrams and specifications of the
specimens and fixtures are contained in Figures 35 and 36.
The two test specimen geometries are identical with the
exception of the load bearing surfaces. The flat geometry
specimens have plannar load bearing surfaces, while the
crowned specimens have load bearing surfaces that are
sections of a large radius circle as noted in the
specifica-tions. The specimens and test fixtures are
asymmetric about the Y axis. The reason for the assymetry
vis to provide an extended shoulder of supporting material
for the trailing edge of the turbine blade as shown in
Figure 37. The load bearing geometry of the loading
fixtures had to accommodate the test specimens, and is
necessarily axymmetrical too. The hooks on the fir tree,
however are symmetrical.

Stresses in the blade attachment can be considered to

result from two superimposed stress fields. Tensile

50

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Specimen Specifications

 

 

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CONTACT'PLANE

 

 

52

 

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Top View

 

 

 

 

 

Front View

Figure 37 Specimen Asymmetry

S4
stresses in the neck fillet region are due to the notches
between the tangs. Another stress field arises from the
bending of the tangs themselves. The neck stresses are
expected to be greatest in the narrowest cross secton of the
fillet, and the tang bending stresses are greatest where the
tang joins the neck. The total stress anywhere in the

attachment is a combination of the two fields.

6.2 Photoelastic Analyses

Photoelastic studies and data compiled by Heywood
provide equations for the analysis of the stress in turbine
blade attachments (12). The mathematics are simplified by
the fact that the specimens are to be loaded in tension
only. Thus the bending and twisting moments due to the
aerodynamic loads on an actual turbine blade are not
present. The equations are empirical in nature and were
derived to give the best agreement with actual test results.
Angular values used in the computations were calculated from
the provided specimen dimensions. Distances that could not
be easily calculated were measured on large scale drawings.
For simplification of the initial problem, it was assumed
that the load on the specimens was equally split between all
four load bearing surfaces.

Neck stress concentrations were calculated from formula

[6], with the paramteres as defined in Figure 38.

_ 1 h .65 _ N-e 1+2.4 /R/h
KT ’ 1 + [.8+5.6(h/a) ' ii] [1 180-5) 1 [6]

55

THH

 

/ /
/ - ...!
/ / /
./ /
/ /
/
/
N /
E
/ :
I ’ —*<
I V \\
l 1 R
1 \
\
\ I
‘\
\ —-—- -
\ .
\ :
\

 

 

Figure 38

 

 

 

 

 

 

Figure 39

Neck Stress Parameters

Point Load Resolution

56
When these calculations were carried out for both inner and
outer paires of hooks, the stress concentration factors
were:

KT (inner hooks) = 1-44 KT (outer hooks) = 1-57
These stress concentration factors combined with the assumed
equal distribution of load yield maximum neck stresses of:
0 (inner fillet) = 116 kSi 0 (outer fillet) = 104 kSi

The parameters used in the above calculation are the
same for both flat and crowned specimens.

To compute the stresses associated with bending of the
tangs themselves, the distributed load along the load
bearing surface must be resolved to a point load. For the
crowned geometry, this is simply the middle of the load
bearing surface. For the flat specimens, however, the load
location must be computed using the following formula [7]
and Figure 39.

l 1

‘II.

E Ed hd [7]

Where Eb and Ed refer to the modulus of the blade and disk

 

CT
53'

material, respectively. The modulus of the blade material
was measured on a test specimen under tensile load with
interferometric equipment. The modulus for astrology, the
fixture material, was provided by Garrett. The length l was
computed from the specimen and fixture specifications. For

nominal tolerances in the flat geometry case, the resultant

5'7

 

 

 

 

Figure 40 Inner Hook Stress Parameters

58
loads act at the following points on the load bearing
surfaces of the hooks.
inner hook 1b = .0155 in outer hook lb = .0135 in
The inner hook stresses are computed using formula [8]
with the dimensions and angles from Figure 40.

1.5' 0.36 l . w
0 ='—’fl + (1 + — Sin y) [8]
t ((3 JEe 4 )

cos (8+8' "Y)

 

An assumed frictional coefficient of l/3 between the
blade and disk yields an angle of 20 degrees for y, and
Heywood specifies w as 30 degrees for the inner hook of
multiple projection fir trees. Completing these
calculations yield nominal stresses at point A of:

In a similar manner, the stress for the outer set of
tangs is computed using the same formula and Figure 41, with
0 equal to five degrees.

A hook stress concentration factor formula [9],
empirically derived by Heywood is applied to the calculated
hook stresses,

Kt = l + .26 (%)'7 [9]

This yields hook stresses of:

Flat Geometry Crowned Geometry
inner hooks 71,000 psi 71,700 psi
outer hooks 120,000 psi 120,000 psi

This coincides well with the partial fixture data taken
at the outer set of hooks. The mean stress at the outer
fillet was the same when the inner hooks were loaded and

when the outer hooks were loaded. Higher maximum strains

 

Figure 41

Outer Hook Stress Parameters

center

 

60
were recorded in the outer fillet when the outer hooks

carried the load.

6.3 Finite Element Analysis

Finite element data generated by Garrett (3 and 4)
produced the stresses resulting from the superimposed neck
and hook stress fields as shown in Figures 42 and 43. The
data were based on a maximum tensile load of 11,750 pounds
and a frictional coefficient of 1/3. The Garrett data
included stress plots for nominal and 1/2 worst case
tolerances, with a friction coefficient of 1/3. In the two
finite element studies, the radial or Y direction stresses
and the principal stresses are almost the same in the fillet
region.

The similar nature of the separate stress plots
indicate that the principal stress in the neck region runs
in the radial direction parallel to the Y axis of the
specimen.

Figure 44 shows the comparisons between the stresses
generated by the photoelastic analyses and the finite
element stresses. Hook stresses from the photoelastic
equations, however do not fit the Garrett finite element
data. Anisotropy of the specimen material is not accounted

for in the photoelastic equations.

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Neck Stresses Hook Stresses
Inner Outer Inner Outer

Photoelastic Computaticns

Crowned 116 ksi 104 ksi 72 ksi 120 ksi

Flat 116 ksi 104 ksi 71 ksi 120 ksi
Finite Element Method #1
Figure 42 100 ksi 120 ksi 138 ksi 280 ksi
Finite Element Method #2
Figure 43

Crowned 95 ksi 183 ksi

Flat 100 ksi 237 ksi

Figure 44 Stress Carparisicns

CONCLUSIONS

Characterization of the effects due to machining
tolerances produced two very noticeable phenomena. First,
compressive strains were recorded in the inner fillet
region. These compressive strains result from bending
moments caused by the slight mismatch between the fir tree
and the loading fixutre. Nearly 2/3 of the tested specimens
showed some bending in the inner fillet. Cyclic strain data
indicated that slippage of contact surfaces was occuring as
load changed. 1

Load split determinations were performed. For 11 of
the 12 data sets, a relatively even load split between the
inner and outer fillets was observed. With the load split
data the principle of superposition of strain fields was
tested. However, it did not hold for strains in the outer
fillet region.

The photoelastic and finite element data agreed
qualitatively with the measured strain distribution across
the fillet region. When numerically compared to the
photoelastic and finite element data, the actual surface
strains were far below expected. This indicates that
somewhere in the attachment, strains and stresses are higher

than predicted.

64

APPENDIX 1

RIGID BODY MOTION EFFECTS ON THE ISG

1.1 Rigid Body Motion of the Specimen

During initial Shakedown runs of the system to test the
load train, ISG, recorders and controller, two significant
and unforeseen complications were noted. First,because of
the number and overall length of the load train components
there was a comparatively large and easily visible amount of
vertical motion of the specimen at high cyclic loads due to
elastic deformation. During triangular wave loading from
580 to 11,750 pounds the vertical motion at the specimen was
measured with a dial gauge at .050 inches, Figure 45.

In addition to the perceived vertical motion, the
specimen shifted in the loading fixture causing a change in
alignment of the fixture and specimen centerlines, Figure
46. This shifting resulted in an angular displacement
between initially coincidental specimen and fixture axes.
This displacement was measured from photographs at
approximately 8 degrees.

These two factors have a considerable effect on the

ability to produce accurate data with the ISG.

65

66

 

 

 

 

 

 

 

 

 

 

(5)5

 

 

 

 

 

 

 

Figure 45 Specimen Vertical thion

67

 

 

 

 

 

 

Figure 46 Angular Displacement of Specimen and Fixture

 

 

68

1.2 Vertical Motion Effects on the ISG

The ISG measures strain by comparing the phase shift of
two sets of interference fringe patterns produced by
reflecting laser light from two pyramidal indents on the
specimen surface. The ISG averages the phase shift of two
sets of fringes and compares this to an initial value. This
averaging allows the indents to translate along the same
axis as the ISG without producing erroneous data. The laser
used to illuminate the indentations on the specimen has a
beam width of approximately 2 cm. During high load tests
the indents would move out of the illuminated area and no
data would be produced. Even at lower loads there would be
considerable rigid body motion compared to the strains being
measured. It had to be determined whether a loss in
accuracy would result from the decreasing fringe pattern
strength as the indents moved toward the edge of the laser
illuminated area.

To evaluate this problem and determine the working
range of the ISG, the following experiment was performed. A
rigid bar was clamped to the base of the load train
extending upward toward the specimen. At the same level as
a test specimen, an indented specimen was clamped to the
bar, Figure 47. The ISG was aligned on the clamped specimen
and strain measurements were taken during various loading
cycles. Because no loads were being applied to the clamped
specimen, the ISG if operating correctly should show no

strain in the specimen as long as sufficient signal strength

69

ISG Vertical mticn Test

 

 

 

 

Figure 47

70
was available. The clamped specimen was rigidly attached to
the base of the load train, it underwent twice the vertical
motion of the actual test specimen held by the fixtures.
During cyclic test loads from 500 to 4500 pounds the ISG
output remained linear and showed no strain through
approximately 3/4 of the cycle. Some operator expertise was
required to align and properly adjust the ISG. Due to
operator experience there was a high degree of confidence
that the data obtained was not adversely affected by

vertical rigid body motion.

1.3 Angular Displacement Effects

In addition to vertical rigid body motion of the
specimen, that the ISG can accommodate without loss of
accuracy, there was the previously mentioned angular
displacement. The ISG, however was not designed to handle
angular deviations that would change the alignment of the
indentations on the specimen in relation to the initial.
alignment axis. As shown in Figure 48 an angular
displacement from the initial alignment would cause the
fringe patterns on the face of the mirrors to shift slightly
toward each other. This slight phase shift is interpreted
as tension by the computer system. For large strains and
very small displacement angles the effect might be
negligible.

The estimated displacement angle measured during

Shakedown runs was eight degrees. The following calculation

71

 

 

 

 

4
g -
£2 -———-—--—1--
Ad
I
d d
80
e‘ .21-

Figure 48 Angular Displaoexrent Error

 

 

 

72
[10] shows that an angular displacement of only one degree
would cause an indicated change in strain of

_ 0
strain = 39 = d(1 dcos 1 ) = .00015- [101

 

d

distance between indentations
This is a considerable error compared to the predicted and
measured surface strains.

Also, as the angular displacement increases the sine
wave signal generated by the mirror sweeping the fringe
pattern past the slit on the face of the photomultiplier
tube becomes distorted, Figure 49. This distortion results
in an extreme loss of accuracy in the ISG data, especially
as signal intensity is lost. Signal intensity decreases
rapidly when the indents move along the edge of the laser

illuminated area.

1.4 Rigid Body Motion Corrections

The distortion and loss of signal intensity were a
compound problem. As the top of the sine wave becomes
flatter, the computer has more trouble establishing the
location of the greatest value of each peak. By tracking
the phase shift of these peaks, the computer calculates the
phase shift and the resulting strain. Loss of signal
strength further flattens the sine wave and degrades the
data.

The following procedure was used to obtain the
indicated but not actually present strains caused by angular

deviations from the ISG axis.

73

Normal Signal

 

 

8-:
P M T 6 ~ /
Reading ‘ ‘
(volts) 4‘
24
50 :00 :50 200 250 300
Mirror Position
8 ~ Distorted Signal
P M T 5 « /"\ /'\ /
Reading ‘1 / \ /
(volfa) 41 , \ ,
2: \/

 

so XE) :50 250 250 350

Mirror Position

Figure 49 Signal Distortion

74

First the test specimen was placed in the fixtures and
loaded to the median load of the test cycle. For high load
runs this was 4750 pounds, while for partial fixture and fit
characterization runs it was 2500 pounds. With the specimen
under tension the ISG was carefully aligned. During
allignment great care was taken to assure that the mirror
axis and the axis of the fringe pattern concided. This
effort was facilitated by the shape of the fringe patterns
themselves. The interference patterns generated by the
pyramidal indentations have an ”Eiffel Tower" shape with an
easily discernable axis.

On the test specimens all 12 sets of indentations were
parallel to each other and had the same relationship to the
axis of the specimen. This was ensured during the
indentation process by holding the specimen in a special jig
so there could be no motion but the horizontal and vertical
translation of the micropositioning table.

After test data were gathered on a specimen, rigid body
motion data was taken. A small indented block of material
was attached with double sided tape to the indented face of
the specimen away from any possible contact with the holding
fixtures. The two sided tape would prevent any specimen
strains from being transferred into the indented block.
Additionally, it was assumed that the surface strains
present in the test specimen would be small and evenly
distributed enough that the block would not change

orientation on the specimen during a loading cycle. No

75
No changes were made in the ISG position or orientation.
The indented block was adjusted so that its fringe patterns
lined up exactly on the ISG mirrors. Since no change had
been made in ISG position, the alligned fringe patterns
meant that the indentations on the block and the test
specimen were parallel and both had the same relationship to
the ISG. The test specimen was subjected to another loading
cycle. This time however, the only data generated came from
the motion of the indented block and not from actual
strains. The data from the rigid body motion runs was
subtracted from the specimen data runs to produce data free

from rigid body motion error, Figure 50.

76

0 Indicates Data Points Corrected for
:3 = =

. :

Rigid

6

Body thion

.'. 1.!

       
  

     

  

:
:
4

Figure 50 Rigid Body thion Correction

10.

11.

LIST OF REFERENCES

Signorelli, R. A., Glasgow, T. K., Halford, G. R. and
Levine, S. R., "Materials and Structures Technology,"
NASA Conference Publication #2092, May 1979, 150-162.

Macke, H. J., “General Analysis of Dovetail Blade
Attachments,” General Electric Technical Information
Series, December 1959.

Lucas, L. J., "Supporting Tests for Directionally
Solidified Blade Attachments," Garrett Turbine Engine
Co., 1984.

Denniston, W. E., “Comparison of Crowned and Uncrowned
Blade Attachment Stress,” Internal Report Garrett
Turbine Engine Co., June, 1983.

Smith, J. 0., Liu, C. K., "Stresses Due to Tangential
and Normal Loads on an Elastic Solid with Application
to some Contact Stress Problems,” Journal of Applied
Mechanics, June 1953, 99- 157-166.

Sokolnikoff, I. 8., ”Mathematical Theory of Elsticity,”
Robert E. Kreiger Publishing Company, Inc., 1983, pp.
24-55 0

Durelli, A. J., Wiley, W. F., "Introduction to
Photomechanics,” Prentice Hall, Inc., 1957, pp.
220-231.

Sharpe, W. N., Jr., ”The Interferometric Strain Gage,"
Experimental Mechanics 8, April 1968, PP. 164-170.

Sharpe, W. N., Jr., ”Interferometric Surface Strain
Measurement," International Journal of Non-Destructive
Testing 3, 1971, pp. 51-76.

Sharpe, W. N., Jr., "A Short Gage-Length Optical Gage
for Small Strain," Experimental Mechanics, 14, 1974,
pp. 373-377.

Sharpe, W. N., Jr., ”Development and Application of an

Interferometric System for Measuring Crack Displace-
ments,” Final Report on NSG 1148, June 1976.

77

12.

13.

14.

15.

l6.

17.

78

Heywood, R. 8., "Designing by Photoelasticity," Chapman
and Hall Ltd., 1952: PP. 167-169, 178-181, 210-244.

MAR-TEST Inc., "Cyclic Stress Strain Curve for
MM-247-DS at 1200F, R = 0.05,” DRF 922 F-109 Program,
December 1983.

Coker, E. G., Filon, L., "Treatise on Photoelasticity,"
Cambridge University Press, 1957, pp. 579-563.

Kawata, K., "Analyses of Yielding of Several Dovetail
Joint Designs," Proceedings of the International
Symposium on Photoelasticity at Illinois Institute of
Technology, Pergamon Press, 1963, pp. 224-229.

Ruiz, C., Boddington, P. H. B., Chen, K. C., ”An
Investigation of Fatigue and Fretting in a Dovetail
Joint," Experimental Mechanics, September 1984: PP.
208-217.

Peterson, R. E., "Stress Concentration Factors," John
Wiley and Sons, Inc., 1974, pp. 150—196.