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Analysis of low cycle fatigue properties of single crystal nickel-base turbine blade superalloys

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Title:
Analysis of low cycle fatigue properties of single crystal nickel-base turbine blade superalloys
Creator:
Orozco Smith, Evelyn M. ( Dissertant )
Arakere, Nagaraj K. ( Thesis advisor )
Place of Publication:
Gainesville, Fla.
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University of Florida
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Copyright Date:
2006
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English

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Subjects / Keywords:
Crystals ( jstor )
Fatigue ( jstor )
Heat resistant alloys ( jstor )
High pressure ( jstor )
Hydrogen ( jstor )
Materials fatigue ( jstor )
Power laws ( jstor )
Room temperature ( jstor )
Shear stress ( jstor )
Single crystals ( jstor )
Dissertations, Academic -- UF -- Mechanical and Aerospace Engineering
Mechanical and Aerospace Engineering thesis, M.S
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bibliography ( marcgt )
non-fiction ( marcgt )
theses ( marcgt )
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United States--Alabama--Huntsville

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Abstract:
The superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities of single-crystal Ni-base superalloys PWA 1480/1493 and PWA 1484 over polycrystalline alloys make them excellent choices for aerospace structures. Both alloys are used in the NASA SSME Alternate Turbopump design, a liquid hydrogen fueled rocket engine. The failure modes of single crystal turbine blades are complicated and difficult to predict due to material orthotropy and variations in crystal orientations. The objective of this thesis is to perform a detailed analysis of experimentally determined low cycle fatigue (LCF) data for a single crystal material with different specimen orientations in order to determine the most effective parameter in predicting fatigue failure. This study will help in developing a methodical approach to designing damage tolerant Ni-base single crystal superalloy blades (as well as other components made of this material) with increased fatigue and temperature capability and lay a foundation for a mechanistic based life prediction system. ( , )
Subject:
blade, crystal, cycle, fatigue, low, PWA1480, SC7, single, superalloy, turbine
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Includes vita.
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Thesis (M.S.)--University of Florida, 2006.
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Includes bibliographical references.
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Text (Electronic thesis) in PDF format.

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ANALYSIS OF LOW CYCLE FATIGUE PROPERTIES OF SINGLE CRYSTAL
NICKEL-BASE TURBINE BLADE SUPERALLOYS














By

EVELYN M. OROZCO-SMITH


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2006
































Copyright 2006

by

Evelyn M. Orozco-Smith



































To my loving parents, Alvaro E. and Elizabeth Orozco, for always believing in me and to
my husband, Andrew P. Smith, for always being there for me.
















ACKNOWLEDGMENTS

The author is thankful for the guidance given by Dr. Nagaraj Arakere and Dr.

Gregory Swanson at the NASA Marshall Space Flight Center.

The author also gratefully acknowledges the NASA Graduate Student Research

Fellowship for its financial and technical support.




















TABLE OF CONTENTS


page

ACKNOWLEDGMENT S .............. .................... iv


LIST OF TABLES .........__.. ..... .__. ..............vi....


LIST OF FIGURES .............. ....................vii


AB STRAC T ................ .............. ix


CHAPTER


1 INTRODUCTION ................. ...............1.......... ......


2 MATERIAL SUMMARY ................. ...............3.................


Elastic M odulus .............. ...............4.....
Tensile Properties .............. ...............5.....
Creep Properties............... ...............

3 FAILURE CRITERIA ................. ...............7............ ....


Fatigue Failure Theories Used in Isotropic Metals............... ...............9.
Application of Failure Criteria to Uniaxial LCF Test Data ................. ................ ..10

4 LCF TEST DATA ANALYSIS ................. ...............18........... ...


PWAl 493 Data at 12000F in Air.......................... ......................1
PWAl493 Data at Room Temperature (750F) in High Pressure Hydrogen...............28
PWAl1493 Data at 14000F and 16000F in High Pressure Hydrogen ................... .......32
SC 7-14-6 LCF Data at 18000F in Air............... ...............36..


5 CONCLU SION................ ..............4


REFERENCE S .............. ...............41....


BIOGRAPHICAL SKETCH .............. ...............43....

















LIST OF TABLES


Table pg

3-1 Direction cosines of material (x, y, z) and specimen (x', y', z') coordinate
system s. .............. .. ...............11........_ ......

3-2 Direction cosines for example. ........_................. ...............15 ....

4-1 Strain controlled LCF test data for PWAl493 at 12000F for four specimen
orientations. .............. ...............26....

4-2 Maximum values of shear stress and shear strain on the slip systems and normal
stress and strain values on the same planes. ................. .....___............... ..27

4-3 PWAl493 LCF high pressure hydrogen (5000 psi) data at ambient temperature. ..31

4-4 PWAl493 LCF data measured in high pressure hydrogen (5000 psi) at 14000F....36

4-5 PWAl493 LCF data measured in high pressure hydrogen (5000 psi) at 16000F....36

4-6 LCF data for single crystal Ni-base superalloy SC 7-14-6 at 18000F in air. ...........39

















LIST OF FIGURES


Figure pg

3-1 Primary (close pack) and secondary (non-close pack) slip directions on the
octahedral planes for a FCC crystal [6] ....._.._.. ..... ...._. ...._.._ ..........

3-2 Cube slip planes and slip directions for an FCC crystal [6] ........._.._.. .................8

3-3 Material (x, y, z) and specimen (x', y', z') coordinate systems. .............. .... ...........11

4-1 Strain range vs. cycles to failure for LCF test data (PWAl493 at 12000F). ............20

4-2 [ Tmax+ E ] vs. N .............. ...............21....


4- + r n noE vs. N ............... ...............22...





4.4 [ (1+k n )y vs. N............... ...............23...




4-5. (a m ax ) vs. N ................. ...............24.......... .....


4-6 Shear stress amplitude [A zmax ] vs. N ................. ...............25........... .

4-7 LCF data for PWAl493 at room temperature in 5000 psi high pressure
hydrogen: strain amplitude vs. cycles to failure ......... ................. ...............29

4-8 Shear stress amplitude (Almax) vs. cycles to failure for PWAl493 at room
temperature in 5000 psi hydrogen. .............. ...............30....

4-9 LCF data for PWAl493 at 14000F in 5000 psi high pressure hydrogen: strain
amplitude vs. cycles to failure ................. ...............32........... ...

4-10 LCF data for PWAl493 at 16000F in 5000 psi high pressure hydrogen: strain
amplitude vs. cycles to failure ................. ...............33........... ...











4-11 Shear stress amplitude (Almax) vs. cycles to failure for PWAl493 at 14000F in
5000 psi hydrogen. ............. ...............34.....

4-12 Shear stress amplitude (Almax) vs. cycles to failure for PWAl493 at 16000F in
5000 psi hydrogen. ............. ...............35.....

4-13 LCF data for SC 7-14-6 at 18000F in air: strain amplitude vs. cycles to failure.....37

4-14 Shear stress amplitude (Almax) vs. cycles to failure for SC 7-14-6 at 18000F in
air ................ ...............38.................
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

ANALYSIS OF LOW CYCLE FATIGUE PROPERTIES OF SINGLE CRYSTAL
NICKEL-BASE TURBINE BLADE SUPERALLOYS

By

Evelyn M. Orozco-Smith

August 2006

Chair: N. K. Arakere
Major Department: Mechanical and Aerospace Engineering

The superior creep, stress rupture, melt resistance, and thermomechanical fatigue

capabilities of single-crystal Ni-base superalloys PWA 1480/1493 and PWA 1484 over

polycrystalline alloys make them excellent choices for aerospace structures. Both alloys

are used in the NASA SSME Alternate Turbopump design, a liquid hydrogen fueled

rocket engine. The failure modes of single crystal turbine blades are complicated and

difficult to predict due to material orthotropy and variations in crystal orientations. The

obj ective of this thesis is to perform a detailed analysis of experimentally determined low

cycle fatigue (LCF) data for a single crystal material with different specimen orientations

in order to determine the most effective parameter in predicting fatigue failure. This

study will help in developing a methodical approach to designing damage tolerant Ni-

base single crystal superalloy blades (as well as other components made of this material)

with increased fatigue and temperature capability and lay a foundation for a mechanistic

based life prediction system.















CHAPTER 1
INTTRODUCTION

In the aerospace industry turbine engine components, such as vanes and blades, are

exposed to severe environments consisting of high operating temperatures, corrosive

environments, high mean stresses, and high cyclic stresses while maintaining long

component lifetimes. The consequence of structural failure is expensive and hazardous.

Because directionally solidified (DS) columnar-grained and single crystal superalloys

have the highest elevated-temperature capabilities of any superalloys, they are widely

used for these structures. Understanding how single crystal materials behave and

predicting how they fatigue and crack is important because of their widespread use in the

commercial, military, and space propulsion industries [1, 2].

Single crystal materials are used extensively in applications where the prediction of

fatigue life is crucial and their anisotropic nature hampers this prediction. Single-crystal

materials are different from polycrystalline alloys in that they have highly orthotropic

properties, making the orientation of the crystal lattice relative to the part geometry a

main factor in the analysis. In turbine blades the low modulus orientation is solidified

parallel to the material growth direction to acquire better thermal fatigue and creep-

rupture resistance [3, 4]. There are computer codes that can calculate stress intensity

factors for a given stress field and fatigue life for isotropic materials; however, assessing

a reasonable fatigue life for orthotropic materials requires that material testing data be

altered to the isotropic conditions. The ability to apply damage tolerant concepts to









single crystal structure design and to lay a foundation for a mechanistic based life

prediction system is critical [5].

The obj ective of this thesis is to present a detailed analysis of experimentally

determined low cycle fatigue (LCF) properties for different specimen orientations.

Because mechanical and fatigue properties of single crystal materials are highly

dependent on crystal orientation [2, 6-12], LCF properties for different specimen

orientations are analyzed in this paper. Fatigue failure parameters are investigated for

LCF data of single crystal material based on the shear stresses, normal stresses, and strain

amplitudes on the 30 possible slip systems for a face-centered cubic (FCC) crystal. The

LCF data is analyzed for PWAl493/1480 at 12000F in air; for PWAl493/1480 at 750F,

14000F, and 16000F in high pressure hydrogen; and for SC 7-14-6 (Ni-6.8 Al-13.8 Mo-6)

at 18000F in air [2, 8]. Ultimately, a fatigue life equation is developed based on a power-

law curve fit of the failure parameter to the LCF test data.















CHAPTER 2
MATERIAL SUMMARY

Single crystal nickel-base superalloys provide superior creep, stress rupture, melt

resistance and thermomechanical fatigue capabilities over their polycrystalline

counterparts [3, 5-6]. Nickel based single-crystal superalloys are precipitation

strengthened, cast monograin superalloys based on the Ni-Cr-Al system. The

microstructure consists of approximately 60% by volume of y' precipitates in a y matrix.

The y' precipitate, is based on the intermetallic compound Ni3Al, is the strengthening

phase in nickel-base superalloys, and is a face centered cubic (FCC) structure. The base,

7, is comprised of nickel with cobalt, chromium, tungsten and tantalum in solution [5].

Single crystal superalloys have highly orthotropic material properties that vary

significantly with direction relative to the crystal lattice [5, 13]. Currently the most

widely used single crystal turbine blade superalloys are PWA 1480/1493, PWA 1484,

CMSX-4 and Rene N-4. These alloys play an important role in commercial, military and

space propulsion systems. PWAl493, which is identical to PWAl480 except with tighter

chemical constituent control, is currently being used in the NASA SSME alternate

turbopump, a liquid hydrogen fueled rocket engine.

Single-crystal materials differ significantly from polycrystalline alloys in that they

have highly orthotropic properties, making the position of the crystal lattice relative to the

part geometry a significant factor in the overall analysis. Directional solidification is

used to produce a single crystal turbine blade with the <001> low modulus orientation

parallel to the growth direction, which imparts good thermal fatigue and creep-rupture









resistance [3, 5-6]. The secondary direction normal to the growth direction is random if a

grain selector is used to form the single crystal. If seeds are used to generate the single

crystal both the primary and secondary directions can be selected. However, in most

turbine blade castings, grain selectors are used to produce the desired <001> growth

direction. In this case, the secondary orientations of the single crystal components are

determined but not controlled. Initially, control of the secondary orientation was not

considered necessary [7]. However, recent reviews of space shuttle main engine (SS1VE)

turbine blade lifetime data has indicated that secondary orientation has a significant

impact on high cycle fatigue resistance [3,8].

The mechanical and fatigue properties of single crystals is a strong function of the

test specimen crystal orientation [2, 3, 5-8, 13]. Some of the properties and the effect of

orientation on those properties, which are used for design purposes, are discussed below.

Elastic Modulus

For single crystal superalloys, the elastic or Young's modulus (E) can be expressed

as a function of orientation over the standard stereographic triangle by Equation (2. 1) [9]:

El = Sir [2(Sll S12) S441[COS2 ~(Sin2 Sin2 8 COS2 COS2 6)] (2.1)

where 6 is the angle between the growth direction and <001> and $ is the angle between

the <001> <110> boundary of the triangle. The terms Sil, S12 and S44 are the elastic

compliances. Since the <001> orientation exhibits the lowest room temperature modulus,

any deviation of the crystal from the <001> orientation results in an increase in the

modulus. The <1 11> orientation exhibits the highest modulus and the modulus of the

<1 10> orientation is intermediate to that of the <001> and <1 11> directions.









Tensile Properties

The tensile properties of superalloys are primarily controlled by the composition

and the size of the y' precipitates [10, 11]. Single crystal superalloys with the <001>

orientation deform by octahedral slip on the close packed {111} plannes andl exhibit yield


strengths similar to those of the conventionally cast, equiaxed, polycrystalline

superalloys. Lower yield strengths and greater ductilities are reported for samples with

<110> orientations. The <111> oriented samples exhibit the highest strengths but have

the lowest ductilities at all test temperatures.

Single crystals with high modulus orientations (i.e., <110> and <111>) can exhibit
lower strengths as a result of their deforming on {100} cuben plannes whichr have a Ilowr


critical resolved shear stress. Tensile failure typically occurs in planar bands due to

concentration of slip that is characteristic of y'-strengthened alloys. The planar,

inhomogeneous nature of slip results in concentrated strains and ultimately slip plane

failure with the formation of macroscopic crystallographic facets on the fracture surface

of tensile samples that appear brittle. At test temperatures above 9000C, deformation

becomes more homogeneous and the facets become less pronounced. In addition to

being a function of orientation, the yield strength of single crystals is also a function of

the type of loading [1l]. The tensile and the compressive yield stresses are not equal.

Creep Properties

In general, the creep properties of single crystal alloys are anisotropic, depending

on both orientation and y' precipitate size and morphology. In addition, the test

temperature has an effect on the orientation anisotropy and the dependence of creep

strength on y' precipitate size [13, 14].










At intermediate temperatures (7500C 8500C), the creep behavior of Ni-base single

crystal superalloys is extremely sensitive to crystal orientation and y' precipitate size [16,

17]. For a y' size in the range of 0.35 to 0.5Clm, the highest creep strength is observed in

samples oriented near <001>. Samples with orientations near the <111> <110>

boundary exhibited extremely short creep lives.















CHAPTER 3
FAILURE CRITERIA

This chapter depicts the development of the formulas that govern single crystal

fatigue theory by using failure parameters of polycrystalline materials.

The development requires an understanding of the behavior of the single crystal

material. Slip in metal crystals often occurs on planes of high atomic density in closely

packed directions. The four octahedral planes corresponding to the high-density planes

in the FCC crystal are shown in Fig. 3-1 [6]. Each octahedral plane has six slip directions

associated with it. Three of these are termed easy-slip or primary slip directions and the

other three are secondary slip directions. Thus there are 12 primary and 12 secondary

slip directions associated with the four octahedral planes [6]. In addition, there are six

possible slip directions in the three cube planes, as shown in Fig. 3-2. Deformation

mechanisms operative in high y' fraction nickel-base superalloys such as PWA

1480/1493 and SC -7-14-6 with FCC crystal structure are divided into three temperature

regions [5]. In the low temperature regime (260C to 4270C, 790F to 8000F) the principal

deformation mechanism is by (111)/<110> slip; and hence fractures produced at these

temperatures exhibit (111) facets. Above 4270C (8000F) thermally activated cube cross

slip is observed which is manifested by an increasing yield strength up to 8710C (16000F)

and a proportionate increase in (111) dislocations that have cross slipped to (001) planes.

Thus nickel-based FCC single crystal superalloys slip primarily on the octahedral and

cube planes in specific slip directions.












Plane 1
Primary:r, r, r3
Secondary: r'3 r, r'S







S100


Plane 2
Primary: r r, r6
Secondary: r' r' r'






100


Plane 3
Primary: r r8, r9
Secondary: rl9, 20O 21







100


Plane 4
Primary: r'o, r", r
Secondary: rZZ, as3 24


010


Figure 3-1. Primary (close pack) and secondary (non-close pack) slip directions on the
octahedral planes for a FCC crystal [6].


Plmne 1


010 1 Plne 2


Plmne 3


Figure 3-2. Cube slip planes and slip directions for an FCC crystal [6].









Fatigue Failure Theories Used in Isotropic Metals

Four fatigue failure theories used for polycrystalline material subj ected to

multiaxial states of fatigue stress were considered towards identifying fatigue failure

criteria for single crystal material. Since turbine blades are subjected to large mean

stresses from the centrifugal stress field, any fatigue failure criteria chosen must have the

ability to account for high mean stress effects.

Kandil et al. [15] presented a shear and normal strain based model, shown in

Equation (3.1), based on the critical plane approach which postulates that cracks nucleate

and grow on certain planes and that the normal strains to those planes assist in the fatigue

crack growth process. In Equation (3.1) y;;a is the max shear strain on the critical plane,

En the normal strain on the same plane, S is a constant, and N is the cycles to initiation.

Ymax + S ,, = f(N) (3.1)

Socie et al. [16] presented a modified version of this theory, shown in Equation

(3.2), to include mean stress effects. Here the maximum shear strain amplitude (Ay) is

modified by the normal strain amplitude (AE) and the mean stress normal to the

maximum shear strain amplitude (Uo,).


+ n no f(N) (3.2)


Fatemi and Socie [17] have presented an alternate shear based model for multiaxial

mean-stress loading that exhibits substantial out-of-phase hardening, shown in Equation

(3.3). This model indicates that no shear direction crack growth occurs if there is no

shear alternation.









ny ~max~
(1+ k n ) = f (N) (3.3)
2 e~

Smith et al. [18] proposed a uniaxial parameter to account for mean stress effects

which was modified for multiaxial loading, shown in Equation (3.4), by Banantine and

Socie [19]. Here the maximum principal strain amplitude is modified by the maximum

stress in the direction of maximum principal strain amplitude that occurs over one cycle.


( a) = f(N) (3.4)


Two other parameters were also investigated: the maximum shear stress amplitude,

A ma,, and the maximum shear strain amplitude, Anax on the 30 slip systems. These

parameters seemed like good candidates since deformation mechanisms in single crystals

are controlled by the propagation of dislocation driven by shear.

Application of Failure Criteria to Uniaxial LCF Test Data

The polycrystalline failure parameters described by Equations (3.1) through (3.4) will be

applied for single crystal uniaxial strain controlled LCF test data. Transformation of the

stress and strain tensors between the material and specimen coordinate systems (Fig. 3-3)

is necessary for implementing the failure theories outlined. The direction cosines

between the (x, y, z) and (x', y', z') coordinate axes are given in Table 3-1.






























Figure 3-3. Material (x, y, z) and specimen (x', y', z') coordinate systems.

Table 3-1. Direction cosines of material (x, y, z) and specimen (x', y', z') coordinate
sy stem s.
xyz





The components of stresses and strains in the (x', y', z') system in terms of the (x,

y, z) system is given by Equations (3.5) and (3.6) [20]

a )= [Q']{a) ; ( = [Q ]{} (3


{e)= [cL''Y {ei = [al l'f; ') [' Y W) =10.1') (3.(


v <010>


z <001>


x <100>


5)


6)


where


(3.7)


o, ~x
v v

Z Z
vz vz
Z, Z,,
z z
v v


E, E,
E E

EZ E,
~d f~)= v
Yvz ~/vz
Y, Y,
: :
Yxy Yxy











a,2
~2





ra, ~


a
2


#22
722
a22


af
P2
32
Y33



33 3


2a3 2
2f3 2
273 2
23~y 32 P~
23za 32 Ya








Y32


3 (2Y3 3Y2
3 (2 3 Y3 2
S(a2P 3 3 2


2a a3
2# #3
27 73
13~y 31 y
13a 31 a,
13,P 31 P




13 ,
~3
1 3
13~y 31 P~
1Ya 3 3sa 1
1 (,3 3 1 ~


2a2 1
2P2 1
272 1
12~y 21Py
12~a 21ya
12,P 21aP




21a
P2P
2Y1
12~y 21~y
1ya 2 2 1,
1 2aP 2 1P~


(3.8)


2
1
~2

2Py


27,a,
2a, A


2


2
72
2P22
272 2
2a2 2


2


2
Y3
2Pf3
273 .
2a, f


(3.9)


The transformation matrix [Q] is orthogonal and hence [Q]~ = [Q]T = [Q']. The

generalized Hooke's law for a homogeneous anisotropic body in Cartesian coordinates

(x, y, z) is given by Equation (3.10) [20].


(s)= a (o-) (3.10)


where [aij] is the matrix of 36 elastic coefficients, of which only 21 are independent, since

[aij] = [aji]. The elastic properties of FCC crystals exhibit cubic symmetry, also described

as cubic syngony. Materials with cubic symmetry have three independent elastic

constants derived from the elastic modulus, Exx and E,,, shear modulus, Gyz, and Poisson

ratio, vyx and vxy. Therefore, Equation (3.10) reduces to Equation (3.11).










az, al2 "12 0 0 0
al2 "11 "12 0 0 0

ar;= =1 1 1 (3.11)
0 0 0 a44 0 0
0 0 0 0 a44 0
0 00 0 0a4

where the elastic constants are

1 1 V, V
az, a44 a12 (3.12)
E, G, E E

The elastic constants in the generalized Hooke's law of an anisotropic body, [a,], vary

with the direction of the coordinate axes. In the case of an isotropic body the constants

are invariant in any orthogonal coordinate system. The elastic constant matrix [a',] in the

(x', y', z') coordinate system that relates {8': } nd{ r' }~ is given by the +t-ranfrmation


Equation (3.13) [20].



m=1 n=1 (3. 3)
(i, j=1, 2,......,6)

Shear stresses in the 30 slip systems, shown in Figures 3-1 and 3-2, are denoted by z ,

22. 230. The shear stresses on the 24 octahedral slip systems are shown in Equation

(3.14) [6].









z' 1 0 -1 1 0 -1 23 -1 2 -1 1 -2 1
0 -1 1 -1 1 0 4' 2 -1 -1 1 1 -
1 -1 0 0 1 -1 2 -1 -1 2 -2 1 1
24 -1 0 1 1 0 -1 cl6 -1 2 -1 -1 -2 -1 exx
-1 1 0 0 -1 -1 o,. r" -1 -1 2 2 1 -1 o,
zu6 1 0 1 -1 -1 -1 0 o, 2'8 1 2 -1 -1 -1 1 2
S1-1 0 0 -1 -1 4. 9 ]z~3J -1 -1 2 2 -1 1 l1On
r" 0 1 -1 -1 1 0 ox pa 2 -1 -1 -1 -1 -2 Ex,
r9 1 0 -1 -1 0 -1 -1 2 -1 -1 2 1 o4
z'a 0 -1 1 -1 -1 0 /" 2 -1 -1 1 -1 2
r" -1 0 1 -1 0 -1 -1 2 -1 1 2 -1
r'" -1 1 0 0 1 -1 94 -1 -1 2 -2 -1 -1

The shear stresses on the six cube slip systems are shown in Equation (3.15) [6].

r2 0 0 0 1 1 0 ax
v26 0 0 0 1 -1 0 a,
r7 1000O1 0 1 a
r2 0J~I 0 0 1 0 -1
v29 0 0 0 0 1 1 ax
r" 0000 O-1 1 aRv

Engineering shear strains on the 30 slip systems are calculated using similar kinematic

relations.


15)


As an example a uniaxial test specimen is loaded in the [111] direction (chosen as

the x' axis in Fig. 3-3) under strain control. The applied strain for the specimen is 1.219

%. The material properties are Exx = 1.54E-7 psi, Gvz = 1.57E-7 psi, and vyx = 0.4009.

The problem is to calculate the stresses and strains in the material coordinate system and

the shear stresses on the 30 slip systems.

The x' axis is aligned along the [111] direction and the y' axis is chosen to lie in

the xz plane. This yields the direction cosines shown in Table 3-2.


>(3 14)










Table 3-2. Direction cosines for example.
x y z
x' la=0.57735 1~(=0.57735 1 }=0.57735
y` 1 =-0.70710 1 A=0.0 1 =0.70710
z 1 a=0.40824 P3=-0.81649 y3=0.40824

The stress-strain relationship in the specimen coordinate system is given by Equation

(3.16)


(&} a\ (0-'}


The [a',] matrix is calculated using Equation (3.13)

(All of the elements in [a'lj] have units of psi- .)

2.552E- 8 6.326E- 9 -6.326E- 9

6.326E- 9 3.537E- 8 -1.618E- 8

~=- 6.326E- 9 -1.618E- 8 3.537E 8


0 2.787E- 8 -2.787E- 8

0 0 0


(3.16)


and is shown as Equation (3.17).


0 0

0 2.787E 8

0 -2.787E-

1.031E -7 0

0 1.425E 7

5.574E 8


8 0

5.574E 8


0 1.425E- 7


(3.17)


The uniaxial stress, ox', is the only nonzero stress in the specimen coordinate system and

is show in Equation (3.18).


E' 0.01219
0-' x 4.776E5 psi
az', 2.552E 8

Use of Equation (3.10) yields the result for (r') shon~x in Equatio n (3. 19).


Ex 4.776E5 0. 01212
( 0 9. 059E 4

(E'} = = aO < >
7r 0 ~ 1. 785E 3685-
7 OI 4.815E- 3

rYx 0 (6. 435E 3


(3.18)









(3.19)










The stresses and strains in the material coordinate system can be calculated using

Equation (3.6) as shown in Equation (3.20).


Ex





7,
: :


2. 049E 3
2. 049E 3
2. 049E 3
5. 0 70E -3 I
5. 070E 3


(3.20)


The shear stresses on the 30 slip planes are calculated using Equations (3.14) and (3.15)

as shown in Equation (3.21).


1
Z
z
r
/
Z6
r
r
r9
r "

7"
T


0
0
0
0
- 1.3E
-1.3E
- 1.3E
0
- 1.3E
-1.3E
-1.3E
O


0
0
0
-1.501E + 5
7.505E + 4
7.505E + 4
- 1.501E + 5
7.505E + 4
7.505E + 4
7.505E + 4
-1.501E + 5


S26


r2 I
r29
Z"


2. 252E
0
2. 252E


2. 252E

0


(3.21)


The engineering shear strains on the 30 slip planes are shown in Equation (3.22).


Ux 1.592E +5
S1. 592E + 5
a 1.592E +5
z 1.592E+5

zv 1 592E +5
z 1.592E+5









yl1 10 713 0
72 0 714 0
73 1 0 Y'5 0
74 0 716 9.561E- 3 2 0.014
6 1 8.28EO3 77 4.780E -3 72
76 1-8.28EO3 y'8 4.780E- 3 2 0.014
7 8.28EO3 719y 4.780E -3 72
78 0 72 I -9.561E-3 729 II0.014
79 8.28EO3 72 4.780E -3 73
710 8.28EO3 722 4.780E- 3
y" 8.28EO3 723 4.780E- 3
712 0 724 i -9.561E-3

The normal stresses and strains on the principal and secondary octahedral planes are

shown in Equation (3.23).

a" 4.776E5 0.012
a" 5.307E4 e -1.331E- 3
can 5.307E4 1 n -1.331E- 3
a" 5.307E4 e -1.331E-3I.EEE34(.3

The normal stresses and strains on the cube slip planes are simply the normal

stresses and strains in the material coordinate system along (100), (010), and (001) axes.

This procedure computes the normal stresses, shear stresses, and strains in the material

coordinate system for uniaxial test specimens loaded in strain control in different

orientations.















CHAPTER 4
LCF TEST DATA ANALYSIS

This chapter illustrates the application of the four theories introduced in Equations

(3.1) through (3.4) in Chapter 3 as well as A Tmax, and Anax to measured fatigue data for

PWAl493 and SC 7-14-6 specimens. Initially, all of the theories are applied to strain-

controlled LCF data for PWAl493 in air at 12000F. The theories are then reduced to one

that shows good correlation. This is then applied to various sets of measured strain-

controlled LCF data to see how they compare for PWAl493 specimens in air at room

temperature, for PWAl493 specimens in high-pressure hydrogen (5000 psi) at 14000F

and 16000F,and for SC 7-14-6 specimens in air at 18000F [13].

PWA1493 Data at 12000F in Air

Strain controlled LCF tests conducted at 12000F in air for PWAl480/1493 uniaxial

smooth specimens for four different orientations is shown in Table 4-1. The four

specimen orientations are <001>, <111>, <213>, and <011>. Figure 4-1 shows the plot

of strain range vs. cycles to failure. A wide scatter is observed in the data with poor

correlation for a power law fit. The first step towards applying the failure criteria

discussed earlier is to compute the shear stresses, normal stresses, and strains on all 30

slip systems for each data point for maximum and minimum test strain values, as outlined

in the example problem. The maximum shear stress and strain for each data point for

minimum and maximum test strain values is selected from the 30 values corresponding to

the 30 slip systems. The maximum normal stress and strain value on the planes, where

the shear stress is maximum, is also calculated. These values are tabulated in Table 4-2.









Both the maximum shear stress and maximum shear strain occur on the same slip system

for the four different configurations examined. For the <001> and <011> configurations

the maximum shear stress and strain occur on the secondary slip system (214, 14 and z1 ,

y respectively). For the <111> and <213> configurations maximum shear stress and

strain occur on the cube slip system (225, 25 and 229, 9 TOSpectively). Using Table 4-2

the composite failure parameters highlighted in Equations (1-4) can be calculated and

plotted as a function of cycles to failure.

Figures 4-2 through 4-5 show that the four parameters based on polycrystalline

fatigue failure parameters, Equations (3.1)-(3.4), do not correlate well with the test data.

This may be due to the insensitivity of these parameters to the critical slip systems. The

parameter that gives the best correlation is a power law fit to the maximum shear stress

amplitude [A Tmax] shown in Fig. 4-6. The parameter A Tmax is appealing to use for its

simplicity; its power law curve fit is shown in Equation (4.1).

Almax = 397,758 N-0.1598 (4.1)

Since the deformation mechanisms in single crystals are controlled by the propagation of

dislocations driven by shear, the A Tmax might indeed be a good fatigue failure parameter


to use.












Power Law Curve Fit (R2 = 0.469): As = 0.0238 170124


0.018


0.016


S0.014
LL

-~0.012


a 0.01

. 0.008


c 0.006

0.004


0.002


1 10 100 1000 10000 100000 1000000
Cycles to Failure
Figure 4-1. Strain range vs. cycles to failure for LCF test data (PWAl493 at 12000F).











Power Law Curve Fit (R2 = 0.130): [ynax + 4 ,] = 0.0249 Nam1


5I
8..0
UJ
+ ~o


1 10 100 1000 10000 100000 1000000
Cycles to Failure


Figure 4-2. [Tma + En ] vs. N







22



Power Law Curve Fit (R2 = 0.391):A e -o -000 -.0


0.010
S<001>

0.014-
-- <111>

e- A <213>
u. 0.012-

7~ 11+ <011>
S0.01-


co 0.008-


r~0.006-


S0.004-


S0.002-


1 10 100 1000 10000 100000 1000000
Cycles to Failure

Figure 4-3. +~ ~ n no vs. N
22E












Power L~aw Curve Fit (R2 = 0.3 83): (1+ k Un )] = 0.0342 N-0.14


0.2-

0.025






0.015




0.01


0.005


1 10 100 1000 10000 100000 1000000
Cycles to Failure
max
Figure 4.4. (1+ k ) vs. N









(mj""L)] = 334. N-0.209l


Power Law Curve Fit (R2 = 0.189):


1 10 100 1000 10000 100000 1000000
Cycles to Failure


Figure 4-5.


[ (emax") vs.N











Power Law Curve Fit (R2 =0.674): AT = 397,758 N-0.1598


350000


300000






m 150000




5 00000


1 10 100 1000 10000
Cycles to Failure
Figure 4-6. Shear stress amplitude [A Tmax ] vs. N


100000 1000000











Table 4-1. Strain controlled LCF test data for PWAl493 at 12000F for four specimen
orientations.
Specimen Max Min R Stann
to
Orientation Test Strain Test Strain Ratio Range
Failure
<001> .01509 .00014 0.31 .01495 1326
<001> .0174 .0027 0.16 0.0147 1593
<001> .0112 .0002 0.D2 0.011 4414
<001> .01202 .00008 0.31 0.0119 5673
<001> .00891 .00018 0.D2 .00873 29516
<111> .01219 -0.006 -0.49 .01819 26
<111> .0096 .0015 0.16 0.0081 843
<111> .00809 .00008 0.31 .00801 1016
<111> .006 0.0 0.0 0.006 3410
<111> .00291 -0.00284 -0.98 .00575 7101
<111> .00591 .00015 0 33 .00576 7356
<111> .01205 0.00625 0.52 0.0058 7904
<213> .01212 0.0 0.0 .01212 79
<213> .00795 .00013 0.D2 .00782 4175
<213> .00601 .00005 0.31 .00596 34676
<213> .006 0.0 0.0 0.006 114789
<011> .0092 .0004 0 04 Os.0088 2672
<011> .00896 .00013 0.31 .00883 7532
<011> .00695 .00019 0 33 .00676 30220
















Table 4-2. Maximum values of shear stress and shear strain on the slip systems and normal stress and strain values on the same
p anes.
Specimen ymax ymin Ay/2,, sma Emi, A/2 Imax ImZi. omax I omin AG3 Cycles
Orientation to
Failure
<001> 0.02 0.000185 0.0099075 0.00097 9.25E-06 0.0004804 1.10E+05 1016 1.08E+05 7.75E+04 719 7.68E+041 1326
0.023 0.0036 0.0097 0.0015 1.78E-04 0.000661 1.26E+05 1.96E+04 1.06E+05 8.93E+04 1.39E+04 7.54E+041 1593
Zmax = 14 0.015 2.64E-04 0.007368 7.34E-04 1.32E-05 0.0003604 8.13E+04 1452 7.98E+041 5.75E+04 1027 5.65E+041 4414
ma 14 0.016 0 0.008 7.94E-04 0 0.000397 8.73E+04 0 8.73E+041 6.17E+04 0 6.17E+041 5673
0.012 0 0.006 5.89E-04 0 0.0002945 6.47E+04 0 6.47E+041 4.57E+04 0 4.57E+041 29516
<111> 0.014 -7.06E-03 0.01053 2.05E-03 -1.01E-03 0.00153 2.25E+05 -1.10E+05 3.35E+05 1.59E+05 -7.80E+04 2.37E+05 26
0.011 0.00176 0.00462 0.0016 0.00025 0.000675 1.77E+05 2.77E+04 1.49E+051 1.25E+05 1.96E+04 1.05E+051 843
ma 25 .0095 9.40E-05 0.004703 0.00136 1.34E-05 0.0006733 1.49E+05 1478 1.48E+051 1.06E+05 1045 1.05E+051 1016
Ymax= 5 .0076 0 0.0038 0.00 1 0 0.0005 1.10E+051 0 1.10OE+05 7.84E+04 0 7.84E+04 1 3410
.0034 -0.0033 0.00335 0.00049 -0.00048 0.000485 5.40E+04 -5.30E+04 1.07E+05 3.80E+04 -3.70E+04 7.50E+041 7101
.0069 1.76E-04 0.003362 9.90E-04 2.50E-05 0.0004825 1.09E+05 2771 1.06E+05 7.70E+04 1959 7.50E+041 7356
0.014 0.007 0.0035 0.002 0.001 0.0005 2.25E+05 1.10E+05 1.15E+051 1.60E+05 7.80E+04 8.20E+041 7904
<213> 0.018 0 0.009 0.002 0 0.001 1.60E+05 0 1.60E+051 1.30E+05 0 1.30E+051 79
0.012 1.90E-04 0.005905 0.0013 2.10E-05 0.0006395 1.06E+05 1732 1.04E+05 8.60E+04 1400 8.46E+041 4175
Imx 29 .0088 0 0.0044 0.00098 0 0.00049 8.00E+04 0 8.00E+041 6.50E+04 0 6.50E+041 34676
ma 0088 0 0.0044 0.00098 0 0.00049 8.00E+04 0 8.00E+041 6.50E+04 0 6.50E+041 114789
<011> 0.015 6.50E-04 0.007175 0.0039 1.68E-04 0.001866 1.23E+05 5333 1.18E+051 1.73E+05 7538 1.65E+051 2672
Zmax = 15 0.015 0 0.0075 0.0039 0 0.00195 1.23E+05 0 1.23E+051 1.70E+05 0 1.70E+051 7532
ma 15 0.011 3.10E-04 0.005345 0.0029 8.00E-05 0.00141 9.30E+04 2532 9.05E+041 1.31E+05 3581 1.27E+051 30220
The following defini ions apply
ymax = Max shear strain of 30 slip systems for max specimen test strain value
ymix, = Max shear strain of 30 slip systems for min specimen test strain value
Imax = Max shear stress of 30 slip systems for max specimen test strain value
zms, = Max shear stress of 30 slip systems for min specimen test strain value









PWA1493 Data at Room Temperature (750F) in High Pressure Hydrogen

Turbine blades in the Space Shuttle Main Engine (SSME) Alternate High Pressure

Fuel Turbopump (AHPFTP) are made of PWAl493 single crystal material [3, 8, 21].

The blades are subjected to high-pressure hydrogen. From a fatigue crack nucleation

perspective, the effects of high-pressure hydrogen are most detrimental at room

temperature and are less pronounced at higher temperatures [5, 22].

The interaction between the effects of environment, temperature and stress intensity

determines which point-source defect species carbidess, eutectics, and micropores)

initiates a crystallographic or noncrystallographic fatigue crack [7] in PWAl480/1493.

At room temperature (260C), in high-pressure hydrogen, the eutectic y/7' initiates fatigue

cracks by an interlaminar (between yand y') failure mechanism, resulting in

noncrystallographic fracture [5, 22]. In room temperature air, carbides typically initiate

crystallographic fracture. Fatigue cracks frequently nucleate at microporosities when

tested in air at moderate temperature (above 4270C).

Figure 4-7 shows the strain amplitude vs. cycles to failure LCF data for PWAl493

at room temperature (260C, 750F) in 5000 psi hydrogen, for three different specimen

orientations. Testing was performed under strain control. The data in Fig. 4-7 shows a

fairly wide scatter. Table 4-3 shows the LCF data and other fatigue damage parameters

evaluated on the slip planes. Figure 4-8 shows a plot of [Azmax] vs. cycles to failure with

the power law curve fit showing a poor correlation. The presence of high-pressure

hydrogen at room temperature activates the eutectic and causes noncrystallographic

fracture, as explained earlier. This type of noncrystallographic fracture is not captured

well by an analysis of shear stresses on slip planes. A failure parameter that can model
























<001>

m 011>

..L mi A <111


the interlaminar failure mechanism between the y and y' structures would likely provide


better results.


v.o








S0.2


- .


.


0 20000 40000


60000

Cycles to


80000 100000 120000 140000
Failure


Figure 4-7. LCF data for PWAl493 at room temperature in 5000 psi high pressure
hydrogen: strain amplitude vs. cycles to failure.
































5 C


Power Law Curve Fit (R2 = 0.246): AT = 238,349 N-o.1oos


1.80E+05


1.60E+05


1.40E+05


1.20E+05


1.00E+05


8.00E+04


6.00E+04


4.00E+04


2.00E+04


0.00E+00


0 20000 40000 60000 80000 100000 120000 140000

Cycles to Failure


Figure 4-8. Shear stress amplitude (Almax) vs. cycles to failure for PWAl493 at room
temperature in 5000 psi hydrogen.


* <001>
II<011>
A <111>
-Pow er Law Fit














Table 4-3. PWAl493 LCF high pressure hydrogen (5000 psi) data at ambient temperature.
Max Min
Specimen Strain Strain Strain Ratio Strain A~max Cycles
Orientation R = mi/Smax Range A~max Em zmax to
Emax Emin (pS;> (pSi) Failure
0.005 -0.005 -1 0.01 0.01310 0.001 84,853 180,000 693
0.005 -0.005 -1 0.01 0.01310 0.001 84,853 180,000 1093
0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 2929
<001> 0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 3340
Imax = 21 0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 13964
0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 18324
0.003 -0.003 -1 0.006 0.00786 0.006 50,912 108,000 29551
0.003 -0.003 -1 0.006 0.00786 0.006 50,912 108,000 56172
0.005 -0.005 -1 0.01 0.008034 0.005514 115,010 216,820 826
0.005 -0.005 -1 0.01 0.008034 0.005514 115,010 216,820 930
0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 2897
<011> 0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 3256
zma = 227 0.004 -0.004 -1 0.0081 0.0064271 0.0044161 92,005 173,460 4234
0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 13388
0.003 -0.003 -1 0.006 0.004820 0.00339 69,004 130,090 10946
0.003 -0.003 -1 0.006 0.004820 0.00339 69,004 130,090 14465
0.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 496
0.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 985
0.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 5863
<111>0.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 7410
2s 003 -.03- .0 0064 .059 1580 26,7 09
2mx 0.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 14173

0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 44440
0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 53189
0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 124485











PWA1493 Data at 14000F and 16000F in High Pressure Hydrogen

At higher temperatures hydrogen does not activate the eutectic failure mechanism,


and under these conditions n Tmax is a good failure parameter for modeling LCF data.


Figures 4-9 and 4-10 show the strain amplitude vs. cycles to failure for PWAl493 in

high-pressure hydrogen (5000 psi) at 14000F and 16000F, respectively. There are only

three data points at 14000F and four at 16000F because of the difficulty and expense in


performing fatigue tests under these conditions. These tests were conducted at the NASA


MSFC. Figures 4-11 and 4-12 show the plots of [Armax] vs. cycles to failure for 14000F


and 16000F temperatures, respectively. The power law curve fits are seen to have a good

correlation because the resulting fractures are crystallographic in nature at these high


temperatures. Tables 4-4 and 4-5 show the LCF data and the fatigue parameters.


1.6

1.4

1.2


0 <001>
a i <011>
E. 0.8

*40.6

0.4

0.2



0 500 1000 1500 2000 2500 3000 3500 4000

Cycles to Failure


Figure 4-9. LCF data for PWAl493 at 14000F in 5000 psi high pressure hydrogen:
strain amplitude vs. cycles to failure.























I


4 <001>
g<011 >


200


400


600


800


1000


1200


Cycles to Failure



Figure 4-10. LCF data for PWAl493 at 16000F in 5000 psi high pressure hydrogen:
strain amplitude vs. cycles to failure.










Power Law Curve Fit (R^`2= 0.661): AT = 223,516N-0.102
<001>
a<011>
m Pow er Law Fit


1.60E+05


1.40E+05







8.00E+04


6.00E+04


I 4.00E+04


2.00E+04


0.00E+00~
0 500 1000 1500 2000 2500 3000 3500 4000
Cycles to Failure


Figure 4-11. Shear stress amplitude (Almax) vs. cycles to failure for PWAl493 at 14000F
in 5000 psi hydrogen.















Power Law Curve Fit (R^'2 = 0.9365): AT = 381,241 N-0.2034

<001>

\ ig <011>
-Power Law Fit


160E+05



140E05



120E+05



100E+05





6 800E+04









200E+04



0 00E+00


0 200 400 600 800 1000 1200

Cycles to Failure



Figure 4-12. Shear stress amplitude (Almax) vs. cycles to failure for PWAl493 at 16000F
in 5000 psi hydrogen.













Max Min Strain Cycles
SpecimenStrain Armax Aomax
SpcienStrain Strain Ratio A~a smax to
Orientation Range (psi) (psi) alr
6max Emin Emin/Emx aiur
<001>
xs0.0075 -0.0075 -1 0.0151 0.0199 0.0151 104,420 221,520 3733
Zmax =Z
<011> 0.00735 -0.00735 -1 0.0147 0.01212 0.0081 141,190 266,190 152
zmax = 27 0.005 -0.005 -1 0.01 0.00824 0.00551 96,051 181,080 1023


Table 4-5. PWAl493 LCF data measured in high pressure hydrogen (5000 psi) at
16000F.
Max Min Strain Cycles
Specimen Strain Ar,, As,
Strain Strain Ratio A~max Asa mxmax to
Orientation Range (psi) (psi) alr
Emax Emin Emin/Emx aiur
<001> 0.0071 -0.0071 -1 0.0143 0.01899 0.0143 92,555 196,340 1002
zma = 215 0.010 -0.010 -1 0.020 0.02657 0.020 129,450 274,600 303
<011> 0.0077 -0.0077 -1 0.0155 0.01295 0.00865 142,100 267,910 104
zma = 227 0.005 -0.005 -1 0.0101 0.00843 0.00564 92,597 174,570 905

SC 7-14-6 LCF Data at 18000F in Air

Figure 4-13 shows the strain amplitude vs. cycles to failure LCF data for SC 7-14-6

at 18000F in air for 5 different specimen orientations: <001>, <113>, <011>, <112>, and


<1 11> [7]. A wide amount of scatter is seen in the plot. Figure 4-14 shows [A rmax] vs.


cycles to failure plot with an excellent correlation for a power law fit. Table 4-6 shows


Table 4-4. PWAl493
14000F.


LCF data measured in high pressure hydrogen (5000 psi) at


the LCF data and the fatigue parameters.










1.2
+ <001>
m<113>

1 A <011>
*<112>
g<111>
S0.8m*



S0.6 A E



R 0.4


0.2




0 50000 100000 150000

Cycles to Failure

Figure 4-13. LCF data for SC 7-14-6 at 18000F in air: strain amplitude vs. cycles to
failure .








38



Power Law Curve Fit (R^`2 = 0.7931): Az = 230,275 N-0.1675
<001>
<113>
A <011>
e <112>
S<111>
S Pow er Law Fit


8.00E+04



7.00E+04



6.00E+04



5.00E+04



4.00E+04



3.00E+04



2.00E+04



1.00E+04



0.00E+00


0 20000 40000 60000 80000 100000 120000 140000 160000

Cycles to Failure


Figure 4-14. Shear stress amplitude (Almax) vs. cycles to failure for SC 7-14-6 at 18000F
in air.











Table 4-6. LCF data for single crystal Ni-base superalloy SC 7-14-6 at 18000F in air.
Specimen Strain ArmaxAema
Oretain Range Amx Am (psi) (psi) Fa lure

0.01 1.3337E-02 1.0000E-02 5.9350E+04 1.2590E+05 3985
<001>0.01 1.3337E-02 1.0000E-02 5.9350E+04 1.2590E+05 2649
1s 0.008 1.0670E-02 8.0000E-03 4.7480E+04 1.0072E+05 12608
max 0.007 9.3359E-03 7.0000E-03 4.1545E+04 8.8130E+04 41616
0.006 8.0022E-03 6.0000E-03 3.5610E+04 7.5540E+04 133615
0.008 1.2041E-02 8.5518E-03 6.2118E+04 1.1859E+05 3506
0.008 1.2041E-02 8.5518E-03 6.2118E+04 1.1859E+05 1698
<113>0.007 1.0536E-02 7.4829E-03 5.4353E+04 1.0377E+05 4042
1s 0.006 9.0311E-03 6.4139E-03 4.6588E+04 8.8946E+04 16532
max 0.0055 8.2785E-03 5.8794E-03 4.2706E+04 8.1533E+04 17500
0.0055 8.2785E-03 5.8794E-03 4.2706E+04 8.1533E+04 17383
0.005 7.5259E-03 5.3449E-03 3.8823E+04 7.4121E+04 96847
0.006 5.1090E-03 3.4154E-03 5.1940E+04 9.7922E+04 2616
0.006 5.1090E-03 3.4154E-03 5.1940E+04 9.7922E+04 3062
0.005 4.2575E-03 2.8462E-03 4.3283E+04 8.1601E+04 9112
<011> 0.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 34063
7max= 27 0.004 3.4060E-03 12.2769E-03 3.4627E+04 6.5281E+041 54951
0.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 47292
0.0035 2.9802E-03 1.9923E-03 3.0298E+04 5.7121E+04 97593
0.003 2.5545E-03 1.7077E-03 2.5970E+04 4.8961E+04 100000
0.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 3271
0.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 5024
0.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 9112
<112> 0.0045 6.4451E-03 4.6249E-03 5.1940E+04 9.7922E+04 8298
zma = 229 0.004 5.7290E-03 4.1110E-03 4.6169E+04 8.7042E+04 9665
0.004 5.7290E-03 4.1110E-03 4.6169E+04 8.7042E+04 11812
0.0035 5.0129E-03 3.5971E-03 4.0398E+04 7.6161E+04 33882
0.003 4.2967E-03 3.0832E-03 3.4627E+04 6.5281E+04 100000
0.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 2886
<111>0.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 3075
25 0.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 4652
max 0.0035 4.1498E-03 5.6567E-04 5.8968E+04 1.2507E+05 8382
0.0028 3.3198E-03 4.5254E-04 4.7175E+04 1.0005E+05 55647

[13]















CHAPTER 5
CONCLUSION

The purpose of this study was to find a parameter that best fits the experimental

data for single crystal materials PWAl480/1493 and SC 7-14-6 at various temperatures,

environmental conditions, and specimen orientations. Several fatigue failure criteria,

based on the normal stresses, shear stresses, and strains on the 24 octahedral and six cube

slip systems for a FCC crystal, are evaluated for strain controlled uniaxial LCF data. The

maximum shear stress amplitude A kax on the 30 slip systems was found to be an


effective fatigue failure parameter, based on the curve fit between A zax and cycles to


failure. The parameter [A zax] did not characterize the room temperature LCF data in

high-pressure hydrogen well because of the eutectic failure mechanism activated by

hydrogen at room temperature. LCF data in high-pressure hydrogen at 14000F and

16000F was characterized well by the A zax failure parameter. Since deformation

mechanisms in single crystals are controlled by the propagation of dislocations driven by

shear, A Tmax might indeed be a good fatigue failure parameter to use. This parameter

must be verified further for a wider range of R-values and specimen orientations as well

as at different temperatures and environmental conditions.
















REFERENCES


1. S. E. Cunningham, D. P. DeLuca, and F. K. Haake, "Crack Growth and Life
Prediction in Single-Crystal Nickel Superalloys," Materials Directorate, Wright
Laboratory, FR22593, Vol. 1, February 1996.

2. B. J. Peters, C. M. Biondo, and D. P. DeLuca, "Investigation of Advanced
Processed Single-Crystal Turbine Blade Alloys," George C. Marshall Space Flight
Center, NASA, FR24007, December 1995.

3. J. Morose, E~ffect of Second azydd~~~~~dddd~~~~ Crystal Orientation on Fatigue Crack Gi 1,n thr in
Single CrystalNickel Turbine Blad'e Superalloys, M.S. Thesis, Mechanical
Engineering Department, University of Florida, Gainesville, May 1999.

4. B. A. Cowels, "High Cycle Fatigue in Aircraft Gas Turbines: An Industry
Perspective," hIternational Journal ofFracture, Vol. 80, pp. 147-163, 1996.

5. D. Deluca and C. Annis, "Fatigue in Single Crystal Nickel Superalloys," Office of
Naval Research, Department of the Navy, FR23 800, August 1995.

6. D. C. Stouffer and L. T. Dame, hIelastic Deformation of~etals: M~odels,
Mechanical Properties, and Metallurgy, John Wiley & Sons, New York, 1996.

7. M. Gell and D.N. Duhl, "The Development of Single Crystal Superalloy Turbine
Blades," Processing and' Properties ofAdvanced High-Temperature Materials,
Eds. S.M. Allen, R.M. Pelloux, and R. Widmer, ASM, Metals Park, Ohio, pp. 41,
1986.

8. N. K. Arakere and G. Swanson, "Effect of Crystal Orientation on Fatigue Failure of
Single Crystal Nickel Base Turbine Blade Superalloys," ASM~E Journal of
Engineering of Gas Turbines and Power, Vol. 24, Issue 1, pp. 161-176, January
2002.

9. M. McLean, "Mechanical Behavior: Superalloys," Directionally Solidiiead
Materials for High Temperature Service, The Metals Society, London, pp. 151,
1983.

10. B. H. Kear and B. J. Picarcey, "Tensile and Creep Properties of Single Crystals of
the Nickel-Base Superalloy Mar-M 200," Trans. AIM~E, 239, pp. 1209, 1967.










11. D.M. Shah and D.N. Duhl, "The Effect of Orientation, Temperature and Gamma-
Prime Size on the Yield Strength of a Single Crystal Nickel Base Superalloy,"
Superalloys 1984, Eds. M. Gell, C.S. Kortovich, R.H. Bricknell, W.B. Kent, and
J.F. Radavich, TMS-AIME, Warrendale, pp. 105, 1984.

12. N. K. Arakere and E. M.Orozco, "Analysis of Low Cycle Fatigue Data of Single
Crystal Nickel-Base Turbine Blade Superalloys," High Temperature Materials and
Processes, Vol. 20, No. 4, pp. 403-419, 2001.

13. R. P. Dalal, C. R. Thomas, and L. E. Dardi, "The Effect of Crystallographic
Orientation on the Physical and Mechanical Properties of an Investment Cast
Single Crystal Nickel-Base Superalloy," Superalloys, Eds. M. Gell, C.S. Kortovich,
R.H. Bricknell, W.B. Kent, and J.F. Radavich, TMS-AIME, Warrendale, pp. 185-
197, 1984.

14. J. J. Jackson, M. J. Donachie, R. J. Hendricks, and M. Gell, "The Effect of Volume
Percent of Fine y' on Creep in DS Mar-M 200 + Hf," Met. Trans. A, 8A, pp. 1615,
1977.

15. F. A. Kandil, M. W. Brown, and K. J. Miller, Biaxial Low Cycle Fatigue of 316
Stainless Steel at Elevated Temperatures, Metals Society, London, pp. 203-210,
1982.

16. D. F. Socie, P. Kurath, and J. Koch, "A Multiaxial Fatigue Damage Parameter,"
presented at the Second International Symposium on Multiaxial Fatigue, Sheffield,
U.K., 1985.

17. A. Fatemi, and D. Socie, "A Critical Plane Approach to Multiaxial Fatigue Damage
Including Out-of-Phase Loading," Fatigue Fracture in Engineering Ma'~terials, Vol.
11, No. 3, pp. 149-165, 1988.

18. K. N Smith, P. Watson, and T. M. Topper, "A Stress-Strain Function for the
Fatigue of Metals," Journal of2aterials, Vol. 5, No. 4, pp. 767-778, 1970.

19. J. A. Banantine and D. F. Socie, "Observations of Cracking Behavior in Tension
and Torsion Low Cycle Fatigue," presented at ASTM Symposium on low cycle
fatigue Directions for the Future, Philadelphia, 1985.

20. S. G. Lekhnitskii, Theory ofla~sticity ofan Anisotropic Elastic Body, Holden-Day
Inc. Publisher, San Francisco, 1963.

21. Pratt and Whitney Corporation, "SSME Alternate Turbopump Development
Program HPFTP Critical Design Review," P&W FR24581-1, NASA Contract
NAS8-36801, December 23, 1996.

22. D. P. Deluca and B. A. Cowles, "Fatigue and Fracture of Single Crystal Nickel in
High Pressure Hydrogen", Hydrogen E~ffects on Material Behavior, Eds. N. R.
Moody and A. W. Thomson, TMS, Warrendale, 1989.
















BIOGRAPHICAL SKETCH

Evelyn Orozco-Smith was born in Hialeah, Florida, in 1974. She attended the

University of Florida in Gainesville, Florida, where she received a Bachelor of Science in

aerospace engineering in 1997. She worked for Pratt & Whitney in the structures group

creating and analyzing finite element models of the Space Shuttle Main Engine (SSME)

High Pressure Fuel Turbo Pump, which at the time were under final approval review for

production. In 1999 she enrolled at the University of Florida to pursue a Master of

Science from the Mechanical Engineering Department under the direction of Dr. Nagaraj

K. Arakere on a project funded by NASA. She now works at Kennedy Space Center as a

systems engineer processing the Main Propulsion System and the SSME for the Space

Shuttle Program.




Full Text

PAGE 1

ANALYSIS OF LOW CYCLE FATIGUE PROPERTIES OF SINGLE CRYSTAL NICKEL-BASE TURBINE BLADE SUPERALLOYS By EVELYN M. OROZCO-SMITH A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Evelyn M. Orozco-Smith

PAGE 3

To my loving parents, Alvaro E. and Elizabet h Orozco, for always believing in me and to my husband, Andrew P. Smith, for always being there for me.

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iv ACKNOWLEDGMENTS The author is thankful for the guidan ce given by Dr. Nagaraj Arakere and Dr. Gregory Swanson at the NASA Ma rshall Space Flight Center. The author also gratefully acknowledges the NASA Graduate Student Research Fellowship for its financial and technical support.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT....................................................................................................................... ix CHAPTER 1 INTRODUCTION........................................................................................................1 2 MATERIAL SUMMARY............................................................................................3 Elastic Modulus............................................................................................................4 Tensile Properties.........................................................................................................5 Creep Properties............................................................................................................5 3 FAILURE CRITERIA..................................................................................................7 Fatigue Failure Theories Us ed in Isotropic Metals.......................................................9 Application of Failure Criteria to Uniaxial LCF Test Data........................................10 4 LCF TEST DATA ANALYSIS..................................................................................18 PWA1493 Data at 1200F in Air................................................................................18 PWA1493 Data at Room Temperature ( 75F) in High Pressure Hydrogen...............28 PWA1493 Data at 1400F and 1600F in High Pressure Hydrogen..........................32 SC 7-14-6 LCF Data at 1800F in Air........................................................................36 5 CONCLUSION...........................................................................................................40 REFERENCES..................................................................................................................41 BIOGRAPHICAL SKETCH.............................................................................................43

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vi LIST OF TABLES Table page 3-1 Direction cosines of material (x, y, z) and specimen (xÂ’, yÂ’, zÂ’) coordinate systems.....................................................................................................................11 3-2 Direction cosines for example..................................................................................15 4-1 Strain controlled LCF test data for PWA1493 at 1200F for four specimen orientations...............................................................................................................26 4-2 Maximum values of shear stress and sh ear strain on the slip systems and normal stress and strain values on the same planes..............................................................27 4-3 PWA1493 LCF high pressure hydrogen (5000 psi) data at ambient temperature...31 4-4 PWA1493 LCF data measured in high pr essure hydrogen (5000 psi) at 1400F....36 4-5 PWA1493 LCF data measured in high pr essure hydrogen (5000 psi) at 1600F....36 4-6 LCF data for single crystal Ni-base superalloy SC 7-14-6 at 1800F in air............39

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vii LIST OF FIGURES Figure page 3-1 Primary (close pack) and secondary (non-close pack) slip directions on the octahedral planes for a FCC crystal [6]......................................................................8 3-2 Cube slip planes and slip di rections for an FCC crystal [6].......................................8 3-3 Material (x, y, z) and specimen (xÂ’, yÂ’, zÂ’) coordinate systems...............................11 4-1 Strain range vs. cycles to failure for LCF test data (PWA1493 at 1200F).............20 4-2 [max + n ] vs. N.......................................................................................................21 4-3 Eno n 2 2 vs. N...................................................................................22 4.4 ) 1 ( 2max y nk vs. N.....................................................................................23 4-5 ) ( 2max 1 vs. N............................................................................................24 4-6 Shear stress amplitude [ max ] vs. N.......................................................................25 4-7 LCF data for PWA1493 at room temp erature in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure......................................................29 4-8 Shear stress amplitude ( max) vs. cycles to failure for PWA1493 at room temperature in 5000 psi hydrogen............................................................................30 4-9 LCF data for PWA1493 at 1400F in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure..................................................................................32 4-10 LCF data for PWA1493 at 1600F in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure..................................................................................33

PAGE 8

viii 4-11 Shear stress amplitude ( max) vs. cycles to failure for PWA1493 at 1400F in 5000 psi hydrogen....................................................................................................34 4-12 Shear stress amplitude ( max) vs. cycles to failure for PWA1493 at 1600F in 5000 psi hydrogen....................................................................................................35 4-13 LCF data for SC 7-14-6 at 1800F in air: strain amplitude vs. cycles to failure.....37 4-14 Shear stress amplitude ( max) vs. cycles to failure for SC 7-14-6 at 1800F in air............................................................................................................................ ..38

PAGE 9

ix Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ANALYSIS OF LOW CYCLE FATIGUE PROPERTIES OF SINGLE CRYSTAL NICKEL-BASE TURBINE BLADE SUPERALLOYS By Evelyn M. Orozco-Smith August 2006 Chair: N. K. Arakere Major Department: Mechanic al and Aerospace Engineering The superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities of single-crystal Ni-base superalloys PWA 1480/1493 and PWA 1484 over polycrystalline alloys make them excellent c hoices for aerospace structures. Both alloys are used in the NASA SSME Alternate Tu rbopump design, a liquid hydrogen fueled rocket engine. The failure modes of single crystal turbine blades are complicated and difficult to predict due to mate rial orthotropy and variations in crystal orie ntations. The objective of this thesis is to perform a detaile d analysis of experimentally determined low cycle fatigue (LCF) data for a single crystal ma terial with different specimen orientations in order to determine the most effective parameter in predicting fatigue failure. This study will help in developing a methodical a pproach to designing damage tolerant Nibase single crystal superalloy blades (as well as other components made of this material) with increased fatigue and temperature capab ility and lay a foundation for a mechanistic based life prediction system.

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1 CHAPTER 1 INTRODUCTION In the aerospace industry turbine engine co mponents, such as vanes and blades, are exposed to severe environments consisting of high operating temperatures, corrosive environments, high mean stresses, and hi gh cyclic stresses while maintaining long component lifetimes. The consequence of stru ctural failure is expensive and hazardous. Because directionally solidifie d (DS) columnar-grained a nd single crystal superalloys have the highest elevated-temperature capabil ities of any superalloys, they are widely used for these structures. Understanding how single crystal materials behave and predicting how they fatigue and crack is importa nt because of their widespread use in the commercial, military, and space propulsion industries [1, 2]. Single crystal materials are used extensivel y in applications where the prediction of fatigue life is crucial and their anisotropic nature hampers this pr ediction. Single-crystal materials are different from polycrystalline allo ys in that they have highly orthotropic properties, making the orientation of the crys tal lattice relative to the part geometry a main factor in the analysis. In turbine bl ades the low modulus orientation is solidified parallel to the material growth direction to acquire better thermal fatigue and creeprupture resistance [3, 4]. There are computer codes that can calculate stress intensity factors for a given stress field and fatigue lif e for isotropic materials; however, assessing a reasonable fatigue life for orthotropic mate rials requires that material testing data be altered to the isotropic conditi ons. The ability to apply da mage tolerant concepts to

PAGE 11

2 single crystal structure desi gn and to lay a foundation for a mechanistic based life prediction system is critical [5]. The objective of this thesis is to presen t a detailed analysis of experimentally determined low cycle fatigue (LCF) propert ies for different specimen orientations. Because mechanical and fatigue properties of single crystal materials are highly dependent on crystal orientation [2, 6-12] LCF properties for different specimen orientations are analyzed in this paper. Fa tigue failure parameters are investigated for LCF data of single crystal mate rial based on the shear stresses normal stresses, and strain amplitudes on the 30 possible slip systems for a face-centered cubic (FCC) crystal. The LCF data is analyzed for PWA1493/1480 at 1200F in air; for PWA1493/1480 at 75F, 1400F, and 1600F in high pressure hydrogen; and for SC 7-14-6 (Ni-6.8 Al-13.8 Mo-6) at 1800F in air [2, 8]. Ultimately, a fatigue life equation is developed based on a powerlaw curve fit of the failure parameter to the LCF test data.

PAGE 12

3 CHAPTER 2 MATERIAL SUMMARY Single crystal nickel-base superalloys provide superior creep, st ress rupture, melt resistance and thermomechanical fatigue capabilities over their polycrystalline counterparts [3, 5-6]. Nickel based si ngle-crystal superall oys are precipitation strengthened, cast monograin superalloys based on the Ni-Cr-Al system. The microstructure consists of approximately 60% by volume of Â’ precipitates in a matrix. The Â’ precipitate, is based on the intermetallic compound Ni3Al, is the strengthening phase in nickel-base superalloys, and is a face centered cubic (FCC) structure. The base, is comprised of nickel with cobalt, chromi um, tungsten and tantalum in solution [5]. Single crystal superalloys have highly or thotropic material properties that vary significantly with direction relative to the cr ystal lattice [5, 13]. Currently the most widely used single crysta l turbine blade superalloys are PWA 1480/1493, PWA 1484, CMSX-4 and Rene N-4. These alloys play an important role in commercial, military and space propulsion systems. PWA1493, which is identical to PWA1480 except with tighter chemical constituent control, is currently being used in the NASA SSME alternate turbopump, a liquid hydrogen fu eled rocket engine. Single-crystal materials differ significantly from polycrystalli ne alloys in that they have highly orthotropic propertie s, making the position of the crys tal lattice relative to the part geometry a significant factor in the ove rall analysis. Directional solidification is used to produce a single cr ystal turbine blade with the <001> low modulus orientation parallel to the growth direction, which im parts good thermal fatigue and creep-rupture

PAGE 13

4 resistance [3, 5-6]. The secondary direction no rmal to the growth di rection is random if a grain selector is used to form the single crysta l. If seeds are used to generate the single crystal both the primary and s econdary directions can be selected. However, in most turbine blade castings, grain selectors are used to produce the desired <001> growth direction. In this case, the secondary orient ations of the single crystal components are determined but not controlled. Initially, co ntrol of the secondary orientation was not considered necessary [7]. However, recent reviews of space shuttle main engine (SSME) turbine blade lifetime data has indicated th at secondary orientation has a significant impact on high cycle fatigue resistance [3,8]. The mechanical and fatigue pr operties of single crystals is a strong function of the test specimen crystal orientati on [2, 3, 5-8, 13]. Some of the properties and the effect of orientation on those properties which are used for design pur poses, are discussed below. Elastic Modulus For single crystal superalloys, the elastic or Young’s modulus (E) can be expressed as a function of orientation over the standard stereographic triangle by Equation (2.1) [9]: E-1 = S11 – [2(S11 – S12) – S44][cos2 (sin2 sin2 cos2 cos2 )] (2.1) where is the angle between the growth direction and <001> and is the angle between the <001> <110> boundary of the triangle. The terms S11, S12 and S44 are the elastic compliances. Since the <001> orientation exhi bits the lowest room temperature modulus, any deviation of the crystal from the <001> orientation results in an increase in the modulus. The <111> orientation exhibits th e highest modulus and the modulus of the <110> orientation is intermediate to th at of the <001> and <111> directions.

PAGE 14

5 Tensile Properties The tensile properties of superalloys ar e primarily controlled by the composition and the size of the Â’ precipitates [10, 11]. Single cr ystal superalloys with the <001> orientation deform by octahedral slip on the close packed {111} planes and exhibit yield strengths similar to those of the conv entionally cast, equiaxed, polycrystalline superalloys. Lower yield strengths and greater ductilities are reported for samples with <110> orientations. The <111> oriented samp les exhibit the highest strengths but have the lowest ductilities at all test temperatures. Single crystals with high modulus orientations (i.e., <110> and <111>) can exhibit lower strengths as a result of their deforming on {100} cube planes which have a lower critical resolved shear stress. Tensile failu re typically occurs in planar bands due to concentration of slip that is characteristic of Â’-strengthened alloys. The planar, inhomogeneous nature of slip results in con centrated strains and ultimately slip plane failure with the formation of macroscopic crystallographic facets on the fracture surface of tensile samples that appear brit tle. At test temp eratures above 900 C, deformation becomes more homogeneous and the facets become less pronounced. In addition to being a function of orientation, the yield strengt h of single crystals is also a function of the type of loading [11]. The tensile and the compressive yield st resses are not equal. Creep Properties In general, the creep properties of singl e crystal alloys are anisotropic, depending on both orientation and Â’ precipitate size and morphol ogy. In addition, the test temperature has an effect on the orientat ion anisotropy and the dependence of creep strength on Â’ precipitate size [13, 14].

PAGE 15

6 At intermediate temperatures (750 C 850 C), the creep behavior of Ni-base single crystal superalloys is extremely sensitive to crystal orientation and Â’ precipitate size [16, 17]. For a Â’ size in the range of 0.35 to 0.5 m, the highest creep st rength is observed in samples oriented near <001>. Samples w ith orientations near the <111> <110> boundary exhibited extremely short creep lives.

PAGE 16

7 CHAPTER 3 FAILURE CRITERIA This chapter depicts the development of the formulas that gov ern single crystal fatigue theory by using failure parame ters of polycrystalline materials. The development requires an understanding of the behavior of the single crystal material. Slip in metal crystals often occurs on planes of high atomic density in closely packed directions. The four octahedral pl anes corresponding to the high-density planes in the FCC crystal are shown in Fig. 3-1 [6]. Each octahedral plane has six slip directions associated with it. Three of these are termed easy-slip or primary sl ip directions and the other three are secondary slip directions. Thus there are 12 primary and 12 secondary slip directions associated with the four octahedral planes [6 ]. In addition, there are six possible slip directions in the three cube planes, as s hown in Fig. 3-2. Deformation mechanisms operative in high ’ fraction nickel-base superalloys such as PWA 1480/1493 and SC –7-14-6 with FCC crystal struct ure are divided into three temperature regions [5]. In the low temperature regime (26C to 427C, 79F to 800F) the principal deformation mechanism is by (111)/<110> slip ; and hence fractures produced at these temperatures exhibit (111) facets. Above 427C (800F) thermally activated cube cross slip is observed which is manifested by an increasing yield stre ngth up to 871C (1600F) and a proportionate increase in ( 111) dislocations that have cr oss slipped to (001) planes. Thus nickel-based FCC single crystal supera lloys slip primarily on the octahedral and cube planes in specif ic slip directions.

PAGE 17

8 100 13 1 001 010 2 14 3 15 Plane 1 Primary: 1, 2, 3 Secondary: 13, 14, 15 100 001 010 16 4 5 17 6 18 Plane 2 Primary: 4, 5, 6 Secondary: 16, 17, 18 100 19 7 001 010 8 20 9 21 Plane 3 Primary: 7, 8, 9 Secondary: 19, 20, 21 12 11 24 10 22 100 001 010 23 Plane 4 Primary: 10, 11, 12 Secondary: 22, 23, 24 Figure 3-1. Primary (close pack) and seconda ry (non-close pack) sl ip directions on the octahedral planes for a FCC crystal [6]. 100 26 001 010 25 Plane 1 100 28 001 010 27 Plane 2 100 001 010 Plane 3 30 29 Figure 3-2. Cube slip planes and slip directions for an FCC crystal [6].

PAGE 18

9 Fatigue Failure Theories Used in Isotropic Metals Four fatigue failure theories used for polycrystalline material subjected to multiaxial states of fatigue stress were considered towards identifying fatigue failure criteria for single crystal mate rial. Since turbine blades are subjected to large mean stresses from the centrifugal stress field, any fa tigue failure criteria chosen must have the ability to account for hi gh mean stress effects. Kandil et al. [15] presented a shear a nd normal strain based model, shown in Equation (3.1), based on the critical plane ap proach which postulates that cracks nucleate and grow on certain planes and that the normal st rains to those planes assist in the fatigue crack growth process. In Equation (3.1) max is the max shear strain on the critical plane, n the normal strain on the same plane, S is a constant, and N is the cycles to initiation. ) (maxN f Sn (3.1) Socie et al. [16] presented a modified ve rsion of this theory, shown in Equation (3.2), to include mean stress effects. He re the maximum shear strain amplitude ( ) is modified by the normal strain amplitude ( ) and the mean stress normal to the maximum shear strain amplitude (no). ) ( 2 2 N f E no n (3.2) Fatemi and Socie [17] have presented an alternate shear based model for multiaxial mean-stress loading that exhibits substantia l out-of-phase hardening, shown in Equation (3.3). This model indicates th at no shear direction crack growth occurs if there is no shear alternation.

PAGE 19

10 ) ( ) 1 ( 2maxN f ky n (3.3) Smith et al. [18] proposed a uniaxial para meter to account for mean stress effects which was modified for multiaxial loading, shown in Equation (3.4), by Banantine and Socie [19]. Here the maximum principal st rain amplitude is modified by the maximum stress in the direction of maxi mum principal strain amplitude that occurs over one cycle. ) ( ) ( 2max 1N f (3.4) Two other parameters were also investig ated: the maximum shear stress amplitude, max, and the maximum shear strain amplitude, max on the 30 slip systems. These parameters seemed like good candidates since de formation mechanisms in single crystals are controlled by the propagation of dislocation driven by shear. Application of Failure Criteria to Uniaxial LCF Test Data The polycrystalline failure parameters descri bed by Equations (3.1) through (3.4) will be applied for single crystal uniaxial strain contro lled LCF test data. Transformation of the stress and strain tensors between the material and specimen coordinate systems (Fig. 3-3) is necessary for implementing the failure theories outlined. The direction cosines between the (x, y, z) and (xÂ’, yÂ’, zÂ’) c oordinate axes are given in Table 3-1.

PAGE 20

11 x <100> y <010> z <001> xÂ’ yÂ’ zÂ’ Figure 3-3. Material (x, y, z) and specimen (xÂ’, yÂ’, zÂ’) coordinate systems. Table 3-1. Direction cosines of material (x, y, z) and specim en (xÂ’, yÂ’, zÂ’) coordinate systems. x y z x` 1 1 1 y` 2 2 2 z` 3 3 3 The components of stresses and strains in th e (xÂ’, yÂ’, zÂ’) system in terms of the (x, y, z) system is given by Equa tions (3.5) and (3.6) [20] Q Q' ; (3.5) Q Q Q Q1 1; (3.6) where xy zx yz z y x xy zx yz z y x xy zx yz z y x xy zx yz z y xand ; (3.7)

PAGE 21

12 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 2 2 2 2 2 2 2 21 2 2 1 1 3 3 1 2 3 3 2 3 3 2 2 1 1 1 2 2 1 1 3 3 1 2 3 3 2 3 3 2 2 1 1 1 2 2 1 1 3 3 1 2 3 3 2 3 3 2 2 1 1 1 2 3 1 2 3 2 3 2 2 2 1 1 2 3 1 2 3 2 3 2 2 2 1 1 2 3 1 2 3 2 3 2 2 2 1 Q (3.8) and ) ( ) ( ) ( 2 2 2 ) ( ) ( ) ( 2 2 2 ) ( ) ( ) ( 2 2 21 2 2 1 1 3 3 1 2 3 3 2 3 3 2 2 1 1 1 2 2 1 1 3 3 1 2 3 3 2 3 3 2 2 1 1 1 2 2 1 1 3 3 1 2 3 3 2 3 3 2 2 1 1 1 2 3 1 2 3 2 3 2 2 2 1 1 2 3 1 2 3 2 3 2 2 2 1 1 2 3 1 2 3 2 3 2 2 2 1 Q (3.9) The transformation matrix [Q] is orthogonal and hence [Q]-1 = [Q]T = [Q Â’]. The generalized HookeÂ’s law for a homogeneous anisotropic body in Cartesian coordinates (x, y, z) is given by Equation (3.10) [20]. ija (3.10) where [aij] is the matrix of 36 elastic coefficien ts, of which only 21 are independent, since [aij] =[aji]. The elastic properties of FCC crystals exhibit cubic symmetry, also described as cubic syngony. Material s with cubic symmetry have three independent elastic constants derived from the elastic modulus, Exx and Eyy, shear modulus, Gyz, and Poisson ratio, yx and xy. Therefore, Equation (3.10) reduces to Equation (3.11).

PAGE 22

13 44 44 44 11 12 12 12 11 12 12 12 110 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a a a a a a a a a a a aija (3.11) where the elastic constants are yy xy xx yx yz xxE E a G a E a 12 44 11, 1 1 (3.12) The elastic constants in th e generalized HookeÂ’s law of an anisotropic body, [aij], vary with the direction of the coor dinate axes. In the case of an isotropic body the constants are invariant in any orthogonal coordinate system. The elastic constant matrix [aÂ’ij] in the (xÂ’, yÂ’, zÂ’) coordinate system that relates {Â’} and {Â’} is given by the transformation Equation (3.13) [20]. ) 6 ......, 2 1 (6 1 6 1 j i Q Q amn nj mi mn TQ a Q aij ij (3.13) Shear stresses in the 30 slip systems, s hown in Figures 3-1 and 3-2, are denoted by 1, 2Â… 30. The shear stresses on the 24 octahedral slip systems are shown in Equation (3.14) [6].

PAGE 23

14 yz zx xy zz yy xx yz zx xy zz yy xx 1 1 2 2 1 1 1 2 1 1 2 1 2 1 1 1 1 2 1 2 1 1 2 1 2 1 1 1 1 2 1 1 2 2 1 1 2 1 1 1 1 2 1 1 2 2 1 1 1 2 1 1 2 1 1 1 2 2 1 1 2 1 1 1 1 2 1 2 1 1 2 1 2 3 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 01 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 6 124 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1(3.14) The shear stresses on the six cube slip sy stems are shown in Equation (3.15) [6]. yz zx xy zz yy xx 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 2 130 29 28 27 26 25 (3.15) Engineering shear strains on the 30 slip syst ems are calculated using similar kinematic relations. As an example a uniaxial test specimen is loaded in the [111] direction (chosen as the xÂ’ axis in Fig. 3-3) unde r strain control. The applied strain for the specimen is 1.219 %. The material properties are Exx = 1.54E-7 psi, Gyz = 1.57E-7 psi, and yx = 0.4009. The problem is to calculate the stresses and st rains in the material coordinate system and the shear stresses on the 30 slip systems. The xÂ’ axis is aligned along the [111] direc tion and the yÂ’ axis is chosen to lie in the xz plane. This yields the di rection cosines shown in Table 3-2.

PAGE 24

15 Table 3-2. Direction cosines for example. x y z x` 1=0.57735 1=0.57735 1=0.57735 y` 2=-0.70710 2=0.0 2=0.70710 z` 3=0.40824 3=-0.81649 3=0.40824 The stress-strain relationship in the specime n coordinate system is given by Equation (3.16) ija (3.16) The [aÂ’ij] matrix is calculated using Equation (3 .13) and is shown as Equation (3.17). (All of the elements in [aÂ’ij] have units of psi-1.) 7 E 425 1 0 8 E 574 5 0 0 0 0 7 E 425 1 0 8 -2.787E 8 E 787 2 0 8 E 574 5 0 7 E 031 1 0 0 0 0 8 -2.787E 0 8 E 537 3 8 -1.618E 9 6.326E 0 8 E 787 2 0 8 -1.618E 8 3.537E 9 6.326E 0 0 0 9 -6.326E 9 6.326E 8 2.552Eija(3.17) The uniaxial stress, xÂ’, is the only nonzero stress in th e specimen coordinate system and is show in Equation (3.18). psi E E ax x5 776 4 8 552 2 01219 011 (3.18) Use of Equation (3.10) yields the result for {Â’} shown in Equation (3.19). 3 6.435E 3 4.815E 3 1.785E 3 6.805E 4 9.059E 0.01212 Exy zx yz z y x0 0 0 0 0 5 776 4ija (3.19)

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16 The stresses and strains in the material coordinate system can be calculated using Equation (3.6) as shown in Equation (3.20). 5 + 1.592E 5 + 1.592E 5 + 1.592E 5 + 1.592E 5 + 1.592E5 + 1.592E 3 5.070E 3 5.070E 3 5.070E 3 2.049E 3 2.049E 3 2.049Exy zx yz z y x xy zx yz z y x (3.20) The shear stresses on the 30 slip planes are cal culated using Equations (3.14) and (3.15) as shown in Equation (3.21). 0 0 0 0 0 0 0 0 05 + 2.252E 5 + 2.252E 5 + 2.252E 5 + 1.501E 4 + 7.505E 4 + 7.505E 4 + 7.505E 5 + 1.501E 4 + 7.505E 4 + 7.505E 5 + 1.501E 0 0 5 + 1.3E 5 + 1.3E 5 + 1.3E 4 + 1.3E 5 + 1.3E 5 + 1.3E -30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1, 0 (3.21) The engineering shear strains on the 30 slip planes are shown in Equation (3.22).

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17 0 0.014 0 0.014 0 0.014 3 9.561E 3 4.780E 3 4.780E 3 4.780E 3 -9.561E 3 4.780E 3 4.780E 3 4.780E 3 9.561E 0 0 0 0 8.28E03 8.28E03 8.28E03 0 8.28E03 8.28E03 8.28E03 0 0 0 030 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 (3.22) The normal stresses and strains on the princi pal and secondary octahedral planes are shown in Equation (3.23). 3 331 1 3 331 1 3 331 1 012 0 4 307 5 4 307 5 4 307 5 5 776 44 3 2 1 4 3 2 1E E E E E E En n n n n n n n (3.23) The normal stresses and strains on the c ube slip planes are simply the normal stresses and strains in the ma terial coordinate system along (100), (010), and (001) axes. This procedure computes the normal stresses, shear stresses, and stra ins in the material coordinate system for uniaxial test specime ns loaded in strain control in different orientations.

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18 CHAPTER 4 LCF TEST DATA ANALYSIS This chapter illustrates the application of the four theories introduced in Equations (3.1) through (3.4) in Chapter 3 as well as max, and max to measured fatigue data for PWA1493 and SC 7-14-6 specimens. Initially, a ll of the theories ar e applied to straincontrolled LCF data for PWA1493 in air at 1200F The theories are then reduced to one that shows good correlation. This is then a pplied to various sets of measured straincontrolled LCF data to see how they comp are for PWA1493 specimens in air at room temperature, for PWA1493 specimens in high-pressure hydrogen (5000 psi) at 1400F and 1600F,and for SC 7-14-6 specimens in air at 1800F [13]. PWA1493 Data at 1200F in Air Strain controlled LCF tests conducted at 1200F in air for PWA1480/1493 uniaxial smooth specimens for four diffe rent orientations is shown in Table 4-1. The four specimen orientations are <001>, <111>, <213> and <011>. Figure 4-1 shows the plot of strain range vs. cycles to failure. A wi de scatter is observed in the data with poor correlation for a power law fit. The first step towards applying the failure criteria discussed earlier is to compute the shear st resses, normal stresses, and strains on all 30 slip systems for each data point for maximum and minimum test strain values, as outlined in the example problem. The maximum shear stress and strain for each data point for minimum and maximum test strain values is selected from the 30 values corresponding to the 30 slip systems. The maximum normal stress and strain value on the planes, where the shear stress is maximum, is also calculated. These values are tabulated in Table 4-2.

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19 Both the maximum shear stress and maximum shear strain occur on the same slip system for the four different configurations examin ed. For the <001> and <011> configurations the maximum shear stress and strain o ccur on the secondary slip system ( 14, 14 and 15, 15 respectively). For the <111> and <213> configurations maximum shear stress and strain occur on the cube slip system ( 25, 25 and 29, 29 respectively). Using Table 4-2 the composite failure parameters highlighted in Equations (1-4) can be calculated and plotted as a function of cycles to failure. Figures 4-2 through 4-5 show that the f our parameters based on polycrystalline fatigue failure parameters, Equations (3.1)-(3.4), do not correlate well with the test data. This may be due to the insensitivity of these pa rameters to the critical slip systems. The parameter that gives the best correlation is a power law fit to the maximum shear stress amplitude [max] shown in Fig. 4-6. The parameter max is appealing to use for its simplicity; its power law curve f it is shown in Equation (4.1). max = 397,758 N-0.1598 (4.1) Since the deformation mechanisms in single cr ystals are controlled by the propagation of dislocations driven by shear, the max might indeed be a good fatigue failure parameter to use.

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20 Power Law Curve Fit (R2 = 0.469 ): = 0.0238 N-0.124 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 1101001000100001000001000000 Cycles to Failure <001> <111> <213> <011> Figure 4-1. Strain range vs cycles to failure for LCF test data (PWA1493 at 1200F).

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21 Power Law Curve Fit (R2 = 0.130 ): [ max + n ] = 0.0249 N 0.773 0 0.005 0.01 0.015 0.02 0.025 1101001000100001000001000000 Cycles to Failure <001> <111> <213> <011> Figure 4-2. [max + n ] vs. N

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22 Power Law Curve Fit (R2 = 0.391 ): Eno n 2 2= 0.0206 N-0.101 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 1101001000100001000001000000 Cycles to Failure <001> <111> <213> <011> Figure 4-3. Eno n 2 2 vs. N

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23 Power Law Curve Fit (R2 = 0.383 ): ) 1 ( 2max y nk = 0.0342 N-0.143 0 0.005 0.01 0.015 0.02 0.025 1101001000100001000001000000 Cycles to Failure <001> <111> <213> <011> Figure 4.4. ) 1 ( 2max y nk vs. N

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24 Power Law Curve Fit (R2 = 0.189 ): ) ( 2max 1 = 334.6 N-0.209 0 50 100 150 200 250 300 350 1 10100100010000 1000001000000 Cycles to Failure <001> <111> <213> <011> Figure 4-5. ) ( 2max 1 vs. N

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25 0 50000 100000 150000 200000 250000 300000 350000 1101001000100001000001000000 Cycles to Failure <001> <111> <213> <011>Power Law Curve Fit (R2 = 0.674 ): = 397,758 N-0.1598 Figure 4-6. Shear stress amplitude [max ] vs. N

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26 Table 4-1. Strain contro lled LCF test data for PWA1493 at 1200F for four specimen orientations. Specimen Orientation Max Test Strain Min Test Strain R Ratio Strain Range Cycles to Failure <001> .01509.000140.01.014951326 <001> .0174.00270.160.01471593 <001> .0112.00020.020.0114414 <001> .01202.000080.010.01195673 <001> .00891.000180.02.0087329516 <111> .01219-0.006-0.49.0181926 <111> .0096.00150.160.0081843 <111> .00809.000080.01.008011016 <111> .0060.00.00.0063410 <111> .00291-0.00284-0.98.005757101 <111> .00591.000150.03.005767356 <111> .012050.006250.520.00587904 <213> .012120.00.0.0121279 <213> .00795.000130.02.007824175 <213> .00601.000050.01.0059634676 <213> .0060.00.00.006114789 <011> .0092.00040.040.00882672 <011> .00896.000130.01.008837532 <011> .00695.000190.03.0067630220

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27Table 4-2. Maximum values of shear stre ss and shear strain on the slip systems and normal stress and strain values on the same planes. Specimen Orientation max min max min max psi min psi psi max psi min psi psi Cycles to Failure <001> 0.02 0.000185 0.0099075 0.00097 9.25E-06 0.0004804 1.10E+05 1016 1.08E+05 7.75E+04 719 7.68E+04 1326 0.023 0.0036 0.0097 0.0015 1.78E-04 0.000661 1.26E+05 1. 96E+04 1.06E+05 8.93E+04 1.39E+04 7.54E+04 1593 max = 14 0.015 2.64E-04 0.007368 7.34E-04 1.32E-05 0.0003604 8.13E+04 1452 7.98E+04 5.75E+04 1027 5.65E+04 4414 max = 14 0.016 0 0.008 7.94E-04 0 0.000397 8.73E+04 0 8.73E+04 6.17E+04 0 6.17E+04 5673 0.012 0 0.006 5.89E-04 0 0.0002945 6.47E+04 0 6.47E+04 4.57E+04 0 4.57E+04 29516 <111> 0.014 -7.06E-03 0.01053 2.05E-03 -1.01E-03 0.00153 2.25E+ 05 -1.10E+05 3.35E+05 1.59E+05 -7.80E+04 2.37E+05 26 0.011 0.00176 0.00462 0.0016 0.00025 0.000675 1.77E+05 2.77E+04 1.49E+05 1.25E+05 1.96E+04 1.05E+05 843 max = 25 .0095 9.40E-05 0.004703 0.00136 1.34E-05 0.0006733 1.49E+05 1478 1.48E+05 1.06E+05 1045 1.05E+05 1016 max = 25 .0076 0 0.0038 0.001 0 0.0005 1.10E+05 0 1.10E+05 7.84E+04 0 7.84E+04 3410 .0034 -0.0033 0.00335 0.00049 -0.00048 0.000485 5.40E+04 -5 .30E+04 1.07E+05 3.80E+04 -3.70E+04 7.50E+04 7101 .0069 1.76E-04 0.003362 9.90E-04 2.50E-05 0.0004825 1.09E+05 2771 1.06E+05 7.70E+04 1959 7.50E+04 7356 0.014 0.007 0.0035 0.002 0.001 0.0005 2.25E+05 1.10E +05 1.15E+05 1.60E+05 7.80E+04 8.20E+04 7904 <213> 0.018 0 0.009 0.002 0 0.001 1.60E+05 0 1.60E+05 1.30E+05 0 1.30E+05 79 0.012 1.90E-04 0.005905 0.0013 2.10E-05 0.0006395 1.06E+05 1732 1.04E+05 8.60E+04 1400 8.46E+04 4175 max = 29 .0088 0 0.0044 0.00098 0 0.00049 8.00E+04 0 8.00E+04 6.50E+04 0 6.50E+04 34676 max = 29 .0088 0 0.0044 0.00098 0 0.00049 8.00E+04 0 8.00E+04 6.50E+04 0 6.50E+04 114789 <011> 0.015 6.50E-04 0.007175 0.0039 1.68E-04 0.001866 1.23E+05 5333 1.18E+05 1.73E+05 7538 1.65E+05 2672 max = 15 0.015 0 0.0075 0.0039 0 0.00195 1.23E+05 0 1.23E+05 1.70E+05 0 1.70E+05 7532 max = 15 0.011 3.10E-04 0.005345 0.0029 8.00E-05 0.00141 9.30E+04 2532 9.05E+04 1.31E+05 3581 1.27E+05 30220 The following definitions apply max = Max shear strain of 30 slip systems for max specimen test strain value min = Max shear strain of 30 slip systems for min specimen test strain value max = Max shear stress of 30 slip systems for max specimen test strain value min = Max shear stress of 30 slip systems for min specimen test strain value

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28 PWA1493 Data at Room Temperature (75F) in High Pressure Hydrogen Turbine blades in the Space Shuttle Main Engine (SSME) Alternate High Pressure Fuel Turbopump (AHPFTP) are made of PWA1 493 single crystal material [3, 8, 21]. The blades are subjected to high-pressure hydrogen. From a fatigue crack nucleation perspective, the effects of high-pressure hydrogen are most detrimental at room temperature and are less pronounced at higher temperatures [5, 22]. The interaction between the effects of envi ronment, temperature and stress intensity determines which point-source defect specie s (carbides, eutectics, and micropores) initiates a crystallographic or noncrystallogr aphic fatigue crack [7] in PWA1480/1493. At room temperature (26C), in hi gh-pressure hydrogen, the eutectic /Â’ initiates fatigue cracks by an interlaminar (between and Â’) failure mechanism, resulting in noncrystallographic fracture [5, 22]. In room temperature air, carbide s typically initiate crystallographic fracture. Fatigue cracks fr equently nucleate at microporosities when tested in air at moderate temperature (above 427C). Figure 4-7 shows the strain amplitude vs. cycles to failure LCF data for PWA1493 at room temperature (26C, 75F) in 5000 ps i hydrogen, for three different specimen orientations. Testing was perf ormed under strain control. Th e data in Fig. 4-7 shows a fairly wide scatter. Table 4-3 shows the LC F data and other fatigue damage parameters evaluated on the slip planes. Figure 4-8 shows a plot of [max] vs. cycles to failure with the power law curve fit showing a poor corr elation. The presen ce of high-pressure hydrogen at room temperature activates th e eutectic and causes noncrystallographic fracture, as explained earlier. This type of noncrystallogr aphic fracture is not captured well by an analysis of shear st resses on slip planes. A failure parameter that can model

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29 the interlaminar failure mechanism between the and Â’ structures would likely provide better results. 0 0.2 0.4 0.6 0.8 1 1.2 020000400006000080000100000120000140000 Cycles to FailureStrain Amplitude (%) <001> <011> <111> Figure 4-7. LCF data for PWA1493 at room temperature in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure.

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30 0.00E+00 2.00E+04 4.00E+04 6.00E+04 8.00E+04 1.00E+05 1.20E+05 1.40E+05 1.60E+05 1.80E+05 020000400006000080000100000120000140000Cycles to FailureMax Shear Stress Amplitude <001> <011> <111> Power Law FitPower Law Curve Fit (R2= 0.246): = 238,349 N-0.1095 Figure 4-8. Shear stress amplitude ( max) vs. cycles to failure for PWA1493 at room temperature in 5000 psi hydrogen.

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31Table 4-3. PWA1493 LCF high pressure hydrogen (5000 psi) data at ambient temperature. Specimen Orientation Max Strain max Min Strain min Strain Ratio R = min/max Strain Range max max max (psi) max (psi) Cycles to Failure 0.005 -0.005 -1 0.01 0.01310 0.001 84,853 180,000 693 0.005 -0.005 -1 0.01 0.01310 0.001 84,853 180,000 1093 0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 2929 0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 3340 0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 13964 0.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 18324 0.003 -0.003 -1 0.006 0.00786 0.006 50,912 108,000 29551 <001> max = 15 0.003 -0.003 -1 0.006 0.00786 0.006 50,912 108,000 56172 0.005 -0.005 -1 0.01 0.008034 0.005514 115,010 216,820 826 0.005 -0.005 -1 0.01 0.008034 0.005514 115,010 216,820 930 0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 2897 0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 3256 0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 4234 0.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 13388 0.003 -0.003 -1 0.006 0.004820 0.00339 69,004 130,090 10946 <011> max = 27 0.003 -0.003 -1 0.006 0.004820 0.00339 69,004 130,090 14465 0.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 496 0.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 985 0.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 5863 0.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 7410 0.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 10097 0.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 14173 0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 44440 0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 53189 <111> max = 25 0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 124485

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32 PWA1493 Data at 1400F and 1600F in High Pressure Hydrogen At higher temperatures hydroge n does not activate the eutectic failure mechanism, and under these conditions max is a good failure parameter for modeling LCF data. Figures 4-9 and 4-10 show the strain amplit ude vs. cycles to failure for PWA1493 in high-pressure hydrogen (5000 ps i) at 1400F and 1600F, respectively. There are only three data points at 1400F and four at 1600F because of the difficulty and expense in performing fatigue tests under these conditions. These tests were conducted at the NASA MSFC. Figures 4-11 and 4-12 show the plots of [max] vs. cycles to failure for 1400F and 1600F temperatures, respectively. The power law curve fits are seen to have a good correlation because the resulting fractures ar e crystallographic in nature at these high temperatures. Tables 4-4 and 4-5 show the LCF data and the fatigue parameters. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 05001000150020002500300035004000 Cycles to FailureStrain Amplitude (%) <001> <011> Figure 4-9. LCF data for PWA1493 at 1400F in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure.

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33 0 0.5 1 1.5 2 2.5 020040060080010001200 Cycles to FailureStrain Amplitude (% ) <001> <011> Figure 4-10. LCF data for PWA1493 at 1600F in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure.

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34 0.00E+00 2.00E+04 4.00E+04 6.00E+04 8.00E+04 1.00E+05 1.20E+05 1.40E+05 1.60E+05 05001000150020002500300035004000Cycles to FailureMax Shear Stress Amplitude <001> <011> Power Law FitPower Law Curve Fit (R^2 = 0.661): = 223,516 N-0.1023 Figure 4-11. Shear stress amplitude ( max) vs. cycles to failure for PWA1493 at 1400F in 5000 psi hydrogen.

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35 0.00E+00 2.00E+04 4.00E+04 6.00E+04 8.00E+04 1.00E+05 1.20E+05 1.40E+05 1.60E+05 020040060080010001200Cycles to FailureMax Shear Stress Amplitude <001> <011> Power Law FitPower Law Curve Fit (R^2 = 0.9365): = 381,241 N-0.2034 Figure 4-12. Shear stress amplitude ( max) vs. cycles to failure for PWA1493 at 1600F in 5000 psi hydrogen.

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36 Table 4-4. PWA1493 LCF data measured in high pressure hydrogen (5000 psi) at 1400F. Specimen Orientation Max Strain max Min Strain min Strain Ratio min/ max Strain Range max max max (psi) max (psi) Cycles to Failure <001> max = 15 0.0075 -0.0075 -1 0.0151 0.0199 0.0151 104,420 221,520 3733 0.00735 -0.00735 -1 0.0147 0.01212 0.0081 141,190 266,190 152 <011> max = 27 0.005 -0.005 -1 0.01 0.00824 0.00551 96,051 181,080 1023 Table 4-5. PWA1493 LCF data measured in high pressure hydrogen (5000 psi) at 1600F. Specimen Orientation Max Strain max Min Strain min Strain Ratio min/ max Strain Range max max max (psi) max (psi) Cycles to Failure 0.0071 -0.0071 -1 0.0143 0.01899 0.0143 92,555 196,340 1002 <001> max = 15 0.010 -0.010 -1 0.020 0.02657 0.020 129,450 274,600 303 0.0077 -0.0077 -1 0.0155 0.01295 0.00865 142,100 267,910 104 <011> max = 27 0.005 -0.005 -1 0.0101 0.00843 0.00564 92,597 174,570 905 SC 7-14-6 LCF Data at 1800F in Air Figure 4-13 shows the strain amplitude vs. cy cles to failure LCF data for SC 7-14-6 at 1800F in air for 5 different specimen or ientations: <001>, <113>, <011>, <112>, and <111> [7]. A wide amount of scatter is seen in the plot. Figure 4-14 shows [max] vs. cycles to failure plot with an excellent correlation for a pow er law fit. Table 4-6 shows the LCF data and the fatigue parameters.

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37 0 0.2 0.4 0.6 0.8 1 1.2 050000100000150000 Cycles to FailureStrain Amplitude (%) <001> <113> <011> <112> <111> Figure 4-13. LCF data for SC 7-14-6 at 1800F in air: strain amplitude vs. cycles to failure.

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38 0.00E+00 1.00E+04 2.00E+04 3.00E+04 4.00E+04 5.00E+04 6.00E+04 7.00E+04 8.00E+04 020000400006000080000100000120000140000160000Cycles to FailureMax Shear Stress Amplitude <001> <113> <011> <112> <111> Power Law FitPower Law Curve Fit (R^2 = 0.7931): = 230,275 N-0.1675 Figure 4-14. Shear stress amplitude ( max) vs. cycles to failure for SC 7-14-6 at 1800F in air.

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39 Table 4-6. LCF data for single crystal Ni -base superalloy SC 7-14-6 at 1800F in air. Specimen Orientation Strain Range max max max (psi) max (psi) Cycles to Failure 0.01 1.3337E-02 1.0000E-02 5.9350E+04 1.2590E+05 3985 0.01 1.3337E-02 1.0000E-02 5.9350E+04 1.2590E+05 2649 0.008 1.0670E-02 8.0000E-03 4.7480E+04 1.0072E+05 12608 0.007 9.3359E-03 7.0000E-03 4.1545E+04 8.8130E+04 41616 <001> max = 15 0.006 8.0022E-03 6.0000E-03 3.5610E+04 7.5540E+04 133615 0.008 1.2041E-02 8.5518E-03 6.2118E+04 1.1859E+05 3506 0.008 1.2041E-02 8.5518E-03 6.2118E+04 1.1859E+05 1698 0.007 1.0536E-02 7.4829E-03 5.4353E+04 1.0377E+05 4042 0.006 9.0311E-03 6.4139E-03 4.6588E+04 8.8946E+04 16532 0.0055 8.2785E-03 5.8794E-03 4.2706E+04 8.1533E+04 17500 0.0055 8.2785E-03 5.8794E-03 4.2706E+04 8.1533E+04 17383 <113> max = 15 0.005 7.5259E-03 5.3449E-03 3.8823E+04 7.4121E+04 96847 0.006 5.1090E-03 3.4154E-03 5.1940E+04 9.7922E+04 2616 0.006 5.1090E-03 3.4154E-03 5.1940E+04 9.7922E+04 3062 0.005 4.2575E-03 2.8462E-03 4.3283E+04 8.1601E+04 9112 0.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 34063 0.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 54951 0.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 47292 0.0035 2.9802E-03 1.9923E-03 3.0298E+04 5.7121E+04 97593 <011> max = 27 0.003 2.5545E-03 1.7077E-03 2.5970E+04 4.8961E+04 100000 0.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 3271 0.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 5024 0.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 9112 0.0045 6.4451E-03 4.6249E-03 5.1940E+04 9.7922E+04 8298 0.004 5.7290E-03 4.1110E-03 4.6169E+04 8.7042E+04 9665 0.004 5.7290E-03 4.1110E-03 4.6169E+04 8.7042E+04 11812 0.0035 5.0129E-03 3.5971E-03 4.0398E+04 7.6161E+04 33882 <112> max = 29 0.003 4.2967E-03 3.0832E-03 3.4627E+04 6.5281E+04 100000 0.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 2886 0.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 3075 0.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 4652 0.0035 4.1498E-03 5.6567E-04 5.8968E+04 1.2507E+05 8382 <111> max = 25 0.0028 3.3198E-03 4.5254E-04 4.7175E+04 1.0005E+05 55647 [13]

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40 CHAPTER 5 CONCLUSION The purpose of this study was to find a para meter that best fits the experimental data for single crystal materials PWA1480/ 1493 and SC 7-14-6 at va rious temperatures, environmental conditions, and specimen orientat ions. Several fati gue failure criteria, based on the normal stresses, shear stresses, a nd strains on the 24 octahedral and six cube slip systems for a FCC crystal, are evaluated for strain controlled uniaxial LCF data. The maximum shear stress amplitude max on the 30 slip systems was found to be an effective fatigue failure parameter, based on the curve fit between max and cycles to failure. The parameter [max] did not characterize the room temperature LCF data in high-pressure hydrogen well because of the eutectic failure mechanism activated by hydrogen at room temperature. LCF data in high-pressure hydrogen at 1400F and 1600F was characterized well by the max failure parameter. Since deformation mechanisms in single crystals are controlled by the propagation of dislocations driven by shear, max might indeed be a good fatigue failure parameter to use. This parameter must be verified further for a wider range of R-values and specimen orientations as well as at different temperatures and environmental conditions.

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41 REFERENCES 1. S. E. Cunningham, D. P. DeLuca, and F. K. Haake, “Crack Growth and Life Prediction in Single-Crystal Nickel Supera lloys,” Materials Directorate, Wright Laboratory, FR22593, Vol. 1, February 1996. 2. B. J. Peters, C. M. Biondo, and D. P. DeLuca, “Investigation of Advanced Processed Single-Crystal Turbine Blade A lloys,” George C. Marshall Space Flight Center, NASA, FR24007, December 1995. 3. J. Moroso, Effect of Secondary Crystal Orientation on Fatigue Crack Growth in Single Crystal Nickel Turbine Blade Superalloys, M.S. Thesis, Mechanical Engineering Department, University of Florida, Gainesville, May 1999. 4. B. A. Cowels, “High Cycle Fatigue in Aircraft Gas Turbines: An Industry Perspective,” International Journal of Fracture, Vol. 80, pp. 147-163, 1996. 5. D. Deluca and C. Annis, “Fatigue in Singl e Crystal Nickel Supe ralloys,” Office of Naval Research, Department of the Navy, FR23800, August 1995. 6. D. C. Stouffer and L. T. Dame, Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy, John Wiley & Sons, New York, 1996. 7. M. Gell and D.N. Duhl, “The Developmen t of Single Crystal Superalloy Turbine Blades,” Processing and Properties of Adv anced High-Temperature Materials, Eds. S.M. Allen, R.M. Pelloux, and R. Widmer, ASM, Metals Park, Ohio, pp. 41, 1986. 8. N. K. Arakere and G. Swanson, “Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys,” ASME Journal of Engineering of Gas Turbines and Power, Vol. 24, Issue 1, pp. 161-176, January 2002. 9. M. McLean, “Mechanical Be havior: Superalloys,” Directionally Solidified Materials for High Temperature Service, The Metals Society, London, pp. 151, 1983. 10. B. H. Kear and B. J. Piearcey, “Tensile and Creep Properties of Single Crystals of the Nickel-Base Superalloy Mar-M 200,” Trans. AIME, 239, pp. 1209, 1967.

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42 11. D.M. Shah and D.N. Duhl, “The Effect of Orientation, Temperature and GammaPrime Size on the Yield Strength of a Si ngle Crystal Nickel Base Superalloy,” Superalloys 1984, Eds. M. Gell, C.S. Kortovich, R.H. Bricknell, W.B. Kent, and J.F. Radavich, TMS-AIME, Warrendale, pp. 105, 1984. 12. N. K. Arakere and E. M.Orozco, “Analysi s of Low Cycle Fatigue Data of Single Crystal Nickel-Base Turbine Blade Superalloys,” High Temperature Materials and Processes, Vol. 20, No. 4, pp. 403-419, 2001. 13. R. P. Dalal, C. R. Thomas, and L. E. Dardi, “The Effect of Crystallographic Orientation on the Physical and Mechanical Properties of an Investment Cast Single Crystal Nickel-Base Superalloy,” Superalloys, Eds. M. Gell, C.S. Kortovich, R.H. Bricknell, W.B. Kent, and J.F. Radavich, TMS-AIME, Warrendale, pp. 185197, 1984. 14. J. J. Jackson, M. J. Donachie, R. J. Hendricks, and M. Gell, “The Effect of Volume Percent of Fine ’ on Creep in DS Mar-M 200 + Hf,” Met. Trans. A, 8A, pp. 1615, 1977. 15. F. A. Kandil, M. W. Brown, and K. J. Miller, Biaxial Low Cycle Fatigue of 316 Stainless Steel at Elevated Temperatures, Metals Society, London, pp. 203-210, 1982. 16. D. F. Socie, P. Kurath, and J. Koch, “A Multiaxial Fatigue Damage Parameter,” presented at the Second International Sy mposium on Multiaxial Fatigue, Sheffield, U.K., 1985. 17. A. Fatemi, and D. Socie, “A Critical Plan e Approach to Multiaxial Fatigue Damage Including Out-of-Phase Loading,” Fatigue Fracture in Engineering Materials, Vol. 11, No. 3, pp. 149-165, 1988. 18. K. N Smith, P. Watson, and T. M. Toppe r, “A Stress-Strain Function for the Fatigue of Metals,” Journal of Materials, Vol. 5, No. 4, pp. 767-778, 1970. 19. J. A. Banantine and D. F. Socie, “Obser vations of Cracking Be havior in Tension and Torsion Low Cycle Fatigue,” presen ted at ASTM Symposium on low cycle fatigue – Directions for the Future, Philadelphia, 1985. 20. S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day Inc. Publisher, San Francisco, 1963. 21. Pratt and Whitney Corporation, “ SSME Alternate Turbopump Development Program HPFTP Critical Design Revi ew,” P&W FR24581-1, NASA Contract NAS8-36801, December 23, 1996. 22. D. P. Deluca and B. A. Cowles, “Fatigue a nd Fracture of Single Crystal Nickel in High Pressure Hydrogen”, Hydrogen Effects on Material Behavior, Eds. N. R. Moody and A. W. Thomson, TMS, Warrendale, 1989.

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43 BIOGRAPHICAL SKETCH Evelyn Orozco-Smith was born in Hialeah, Florida, in 1974. She attended the University of Florida in Gainesville, Florida, where she received a B achelor of Science in aerospace engineering in 1997. She worked fo r Pratt & Whitney in the structures group creating and analyzing finite element models of the Space Shuttle Main Engine (SSME) High Pressure Fuel Turbo Pump, which at th e time were under final approval review for production. In 1999 she enrolled at the Univ ersity of Florida to pursue a Master of Science from the Mechanical Engineering De partment under the direction of Dr. Nagaraj K. Arakere on a project funded by NASA. Sh e now works at Kennedy Space Center as a systems engineer processing the Main Propulsion System and the SSME for the Space Shuttle Program.