analysis of low cycle fatigue properties of single crystal...
Post on 06-Feb-2018
219 Views
Preview:
TRANSCRIPT
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.
iv
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.
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 Used in Isotropic Metals.......................................................9 Application of Failure Criteria to Uniaxial LCF Test Data........................................10
4 LCF TEST DATA ANALYSIS..................................................................................18
PWA1493 Data at 1200°F in Air................................................................................18 PWA1493 Data at Room Temperature (75°F) in High Pressure Hydrogen...............28 PWA1493 Data at 1400°F and 1600°F in High Pressure Hydrogen..........................32 SC 7-14-6 LCF Data at 1800°F in Air........................................................................36
5 CONCLUSION...........................................................................................................40
REFERENCES ..................................................................................................................41
BIOGRAPHICAL SKETCH .............................................................................................43
vi
LIST OF TABLES
Table page 3-1 Direction cosines of material (x, y, z) and specimen (x’, y’, z’) coordinate
systems. ....................................................................................................................11
3-2 Direction cosines for example..................................................................................15
4-1 Strain controlled LCF test data for PWA1493 at 1200°F 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 PWA1493 LCF high pressure hydrogen (5000 psi) data at ambient temperature. ..31
4-4 PWA1493 LCF data measured in high pressure hydrogen (5000 psi) at 1400°F. ...36
4-5 PWA1493 LCF data measured in high pressure hydrogen (5000 psi) at 1600°F. ...36
4-6 LCF data for single crystal Ni-base superalloy SC 7-14-6 at 1800°F in air. ...........39
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 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 (PWA1493 at 1200°F). ............20
4-2 [γmax + εn ] vs. N .......................................................................................................21
4-3 ⎥⎦
⎤⎢⎣
⎡ +∆
+∆
Enon σεγ
22 vs. N...................................................................................22
4.4 ⎥⎥⎦
⎤
⎢⎢⎣
⎡+
∆ )1(2
max
y
nkσ
σγ vs. N.....................................................................................23
4-5 ⎥⎦⎤
⎢⎣⎡∆
)(2
max1 σε
vs. N ............................................................................................24
4-6 Shear stress amplitude [∆τmax ] vs. N .......................................................................25
4-7 LCF data for PWA1493 at room temperature in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure......................................................29
4-8 Shear stress amplitude (∆τmax) vs. cycles to failure for PWA1493 at room temperature in 5000 psi hydrogen. ...........................................................................30
4-9 LCF data for PWA1493 at 1400°F in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure..................................................................................32
4-10 LCF data for PWA1493 at 1600°F in 5000 psi high pressure hydrogen: strain amplitude vs. cycles to failure..................................................................................33
viii
4-11 Shear stress amplitude (∆τmax) vs. cycles to failure for PWA1493 at 1400°F in 5000 psi hydrogen. ...................................................................................................34
4-12 Shear stress amplitude (∆τmax) vs. cycles to failure for PWA1493 at 1600°F in 5000 psi hydrogen. ...................................................................................................35
4-13 LCF data for SC 7-14-6 at 1800°F in air: strain amplitude vs. cycles to failure.....37
4-14 Shear stress amplitude (∆τmax) vs. cycles to failure for SC 7-14-6 at 1800°F in air..............................................................................................................................38
ix
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
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.
1
CHAPTER 1 INTRODUCTION
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
2
single crystal structure design and to lay a foundation for a mechanistic based life
prediction system is critical [5].
The objective 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 PWA1493/1480 at 1200°F in air; for PWA1493/1480 at 75°F,
1400°F, and 1600°F in high pressure hydrogen; and for SC 7-14-6 (Ni-6.8 Al-13.8 Mo-6)
at 1800°F 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.
3
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 γ’ precipitates in a γ matrix.
The γ’ 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,
γ, 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. 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 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
4
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 (SSME)
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]:
E-1 = S11 – [2(S11 – S12) – S44][cos2 φ(sin2 φ - sin2 θ cos2 φ cos2 θ)] (2.1)
where θ is the angle between the growth direction and <001> and φ 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 exhibits 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 the highest modulus and the modulus of the
<110> orientation is intermediate to that of the <001> and <111> directions.
5
Tensile Properties
The tensile properties of superalloys are primarily controlled by the composition
and the size of the γ’ precipitates [10, 11]. Single crystal superalloys with the <001>
orientation deform by octahedral slip on the close packed {111} planes and 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} cube planes which have a lower
critical resolved shear stress. Tensile failure typically occurs in planar bands due to
concentration of slip that is characteristic of γ’-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 900°C, 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 [11]. 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 γ’ precipitate size and morphology. In addition, the test
temperature has an effect on the orientation anisotropy and the dependence of creep
strength on γ’ precipitate size [13, 14].
6
At intermediate temperatures (750°C - 850°C), the creep behavior of Ni-base single
crystal superalloys is extremely sensitive to crystal orientation and γ’ precipitate size [16,
17]. For a γ’ size in the range of 0.35 to 0.5µm, the highest creep strength is observed in
samples oriented near <001>. Samples with orientations near the <111> - <110>
boundary exhibited extremely short creep lives.
7
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 γ’ 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 (26°C to 427°C, 79°F to 800°F) the principal
deformation mechanism is by (111)/<110> slip; and hence fractures produced at these
temperatures exhibit (111) facets. Above 427°C (800°F) thermally activated cube cross
slip is observed which is manifested by an increasing yield strength up to 871°C (1600°F)
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.
8
100
τ13
τ1
001
010
τ2
τ14 τ3
τ15
Plane 1 Primary: τ1, τ2, τ3 Secondary: τ13, τ14, τ15
100
001
010 τ16
τ4 τ5 τ17 τ6
τ18
Plane 2 Primary: τ4, τ5, τ6 Secondary: τ16, τ17, τ18
100
τ19
τ7
001
010
τ8 τ20
τ9
τ21
Plane 3 Primary: τ7, τ8, τ9 Secondary: τ19, τ20, τ21
τ12
τ11
τ24 τ10
τ22
100
001
010
τ23
Plane 4Primary: τ10, τ11, τ12 Secondary: τ22, τ23, τ24
Figure 3-1. Primary (close pack) and secondary (non-close pack) slip directions on the
octahedral planes for a FCC crystal [6].
100
τ26
001
010
τ25
Plane 1
100
τ28
001
010
τ27
Plane 2
100
001
010 Plane 3
τ30 τ29
Figure 3-2. Cube slip planes and slip directions for an FCC crystal [6].
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 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) γmax is the max shear strain on the critical plane,
εn the normal strain on the same plane, S is a constant, and N is the cycles to initiation.
)(max NfS n =+ εγ (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 (∆γ) is
modified by the normal strain amplitude (∆ε) and the mean stress normal to the
maximum shear strain amplitude (σno).
)(22
NfEnon =+
∆+
∆ σεγ (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.
10
)()1(2
maxNfk
y
n =+∆
σσγ
(3.3)
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.
)()(2
max1 Nf=∆
σε
(3.4)
Two other parameters were also investigated: the maximum shear stress amplitude,
∆τmax, and the maximum shear strain amplitude, ∆εmax 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.
11
x <100>
y <010>
z <001>
x’
y’
z’ 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 systems.
x y z x` α1 β1 γ1 y` α2 β2 γ2 z` α3 β3 γ3
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]
{ } [ ]{ } { } [ ]{ }εε εσσ QQ '' ′=′= ; (3.5)
{ } [ ] { } [ ] { } { } [ ] { } [ ] { }εεε ′=′′=′=′′= −−εεσσσ QQQQ 11 ; (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
x
and
γγγεεε
γγγεεε
τττσσσ
σ
τττσσσ
σ εε;, (3.7)
12
[ ]
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+++++++++
=
)()()()()()()()()(
222222222
122113312332332211
122113312332332211
122113312332332211
12312323
22
21
12312323
22
21
12312323
22
21
βαβαβαβαβαβαβαβαβααγαγαγαγαγαγαγαγαγγβγβγβγβγβγβγβγβγβ
γγγγγγγγγβββββββββααααααααα
Q (3.8)
and
[ ]
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+++++++++
=
)()()(222)()()(222)()()(222
122113312332332211
122113312332332211
122113312332332211
12312323
22
21
12312323
22
21
12312323
22
21
βαβαβαβαβαβαβαβαβααγαγαγαγαγαγαγαγαγγβγβγβγβγβγβγβγβγβ
γγγγγγγγγβββββββββααααααααα
εQ (3.9)
The transformation matrix [Q] is orthogonal and hence [Q]-1 = [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].
{ } [ ]{ }σε ija= (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 Eyy, shear modulus, Gyz, and Poisson
ratio, νyx and νxy. Therefore, Equation (3.10) reduces to Equation (3.11).
13
[ ]
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
44
44
44
111212
121112
121211
000000000000000000000000
aa
aaaaaaaaaa
ija (3.11)
where the elastic constants are
yy
xy
xx
yx
yzxx EEa
Ga
Ea
νν−=−=== 124411 ,1,1 (3.12)
The elastic constants in the generalized Hooke’s law of an anisotropic body, [aij], 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’ij] in the
(x’, y’, z’) coordinate system that relates {ε’} and {σ’} is given by the transformation
Equation (3.13) [20].
[ ] [ ] [ ][ ]
)6......,,2,1,(
6
1
6
1
=
==′ ∑∑= =
ji
QQam n
njmimnT QaQa ijij (3.13)
Shear stresses in the 30 slip systems, shown in Figures 3-1 and 3-2, are denoted by τ1,
τ2… τ30. The shear stresses on the 24 octahedral slip systems are shown in Equation
(3.14) [6].
14
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−−−−−−−−
−−−−−−
−−−−−−−−
−−−−−−−−−−−
−−−−−−
−−−
=
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−−−−−
−−−−−−
−−−−−
−−−−−−−−−−
−−−−
=
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
yz
zx
xy
zz
yy
xx
yz
zx
xy
zz
yy
xx
σσσσσσ
ττττττττττττ
σσσσσσ
ττττττττττττ
112211121121
211112121121211112
112211211112112211121121
112211211112
121121
231,
110011101101
011110101101
011110110011
011110110011101101110011
011110101101
61
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
(3.14)
The shear stresses on the six cube slip systems are shown in Equation (3.15) [6].
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−
−
−
=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
yz
zx
xy
zz
yy
xx
σσσσσσ
ττττττ
110000110000101000
101000011000011000
21
30
29
28
27
26
25
(3.15)
Engineering shear strains on the 30 slip systems are calculated using similar kinematic
relations.
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, Gyz = 1.57E-7 psi, and νyx = 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.
15
Table 3-2. Direction cosines for example. x y z
x` α1=0.57735 β1=0.57735 γ1=0.57735 y` α2=-0.70710 β2=0.0 γ2=0.70710 z` α3=0.40824 β3=-0.81649 γ3=0.40824
The stress-strain relationship in the specimen coordinate system is given by Equation
(3.16)
{ } [ ]{ }σε ′′=′ ija (3.16)
The [a’ij] matrix is calculated using Equation (3.13) and is shown as Equation (3.17).
(All of the elements in [a’ij] have units of psi-1.)
[ ]
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=′
7-E425.108-E574.5000
07-E425.108--2.787E8-E787.20
8-E574.507-E031.1000
08--2.787E08-E537.38--1.618E9-6.326E-
08-E787.208--1.618E8-3.537E9-6.326E-
0009--6.326E9-6.326E-8-2.552E
ija (3.17)
The uniaxial stress, σx’, is the only nonzero stress in the specimen coordinate system and
is show in Equation (3.18).
psiEEa
xx 5776.4
8552.201219.0
11
=−
=′′
=′ε
σ (3.18)
Use of Equation (3.10) yields the result for {ε’} shown in Equation (3.19).
{ } [ ]
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
′=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
′′′′′′
=′
3-6.435E3-4.815E3-1.785E
3-6.805E-4-9.059E-
0.01212E
xy
zx
yz
z
y
x
00000
5776.4
ija
γγγεεε
ε (3.19)
16
The stresses and strains in the material coordinate system can be calculated using
Equation (3.6) as shown in Equation (3.20).
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
5+1.592E5+1.592E5+1.592E5+1.592E5+1.592E5+1.592E
3-5.070E3-5.070E3-5.070E3-2.049E3-2.049E3-2.049E
xy
zx
yz
z
y
x
xy
zx
yz
z
y
x
τττσσσ
γγγεεε
, (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).
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
0
0
0
0
0
0
0
00
5+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
ττττττ
ττττττττττττ
ττττττττττττ
(3.21)
The engineering shear strains on the 30 slip planes are shown in Equation (3.22).
17
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
=
⎪⎪⎪⎪⎪⎪⎪⎪
⎭
⎪⎪⎪⎪⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
00.01400.01400.014
,
3-9.561E-3-4.780E3-4.780E3-4.780E3-9.561E-
3-4.780E3-4.780E3-4.780E3-9.561E-
000
,
08.28E03-8.28E03-8.28E03-
08.28E03-8.28E03-8.28E03-
0000
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
γγγγγγ
γγγγγγγγγγγγ
γγγγγγγγγγγγ
(3.22)
The normal stresses and strains on the principal and secondary octahedral planes are
shown in Equation (3.23).
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
−−−−−−
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
3331.13331.13331.1
012.0
,
4307.54307.54307.55776.4
4
3
2
1
4
3
2
1
EEE
EEEE
n
n
n
n
n
n
n
n
εεεε
σσσσ
(3.23)
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.
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 ∆τmax, and ∆εmax to measured fatigue data for
PWA1493 and SC 7-14-6 specimens. Initially, all of the theories are applied to strain-
controlled LCF data for PWA1493 in air at 1200°F. 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 PWA1493 specimens in air at room
temperature, for PWA1493 specimens in high-pressure hydrogen (5000 psi) at 1400°F
and 1600°F,and for SC 7-14-6 specimens in air at 1800°F [13].
PWA1493 Data at 1200°F in Air
Strain controlled LCF tests conducted at 1200°F in air for PWA1480/1493 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.
19
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 (τ14, γ14 and τ15,
γ15 respectively). For the <111> and <213> configurations maximum shear stress and
strain occur on the cube slip system (τ25, γ25 and τ29, γ29 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 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 [∆τmax] shown in Fig. 4-6. The parameter ∆τmax is appealing to use for its
simplicity; its power law curve fit is shown in Equation (4.1).
∆τmax = 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 ∆τmax might indeed be a good fatigue failure parameter
to use.
20
Power Law Curve Fit (R2 = 0.469): ∆ε = 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
1 10 100 1000 10000 100000 1000000Cycles to Failure
<001>
<111>
<213>
<011>
Figure 4-1. Strain range vs. cycles to failure for LCF test data (PWA1493 at 1200°F).
21
Power Law Curve Fit (R2 = 0.130): [γmax + εn ] = 0.0249 N-0.773
0
0.005
0.01
0.015
0.02
0.025
1 10 100 1000 10000 100000 1000000Cycles to Failure
<001>
<111>
<213>
<011>
Figure 4-2. [γmax + εn ] vs. N
22
Power Law Curve Fit (R2 = 0.391): ⎥⎦
⎤⎢⎣
⎡ +∆
+∆
Enon σεγ
22= 0.0206 N-0.101
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
1 10 100 1000 10000 100000 1000000Cycles to Failure
<001>
<111>
<213>
<011>
Figure 4-3. ⎥⎦
⎤⎢⎣
⎡ +∆
+∆
Enon σεγ
22 vs. N
23
Power Law Curve Fit (R2 = 0.383): ⎥⎥⎦
⎤
⎢⎢⎣
⎡+
∆ )1(2
max
y
nkσ
σγ = 0.0342 N-0.143
0
0.005
0.01
0.015
0.02
0.025
1 10 100 1000 10000 100000 1000000Cycles to Failure
<001>
<111>
<213>
<011>
Figure 4.4. ⎥⎥⎦
⎤
⎢⎢⎣
⎡+
∆ )1(2
max
y
nkσ
σγ vs. N
24
Power Law Curve Fit (R2 = 0.189): ⎥⎦⎤
⎢⎣⎡∆
)(2
max1 σε
= 334.6 N-0.209
0
50
100
150
200
250
300
350
1 10 100 1000 10000 100000 1000000Cycles to Failure
<001>
<111>
<213>
<011>
Figure 4-5. ⎥⎦⎤
⎢⎣⎡∆
)(2
max1 σε
vs. N
25
0
50000
100000
150000
200000
250000
300000
350000
1 10 100 1000 10000 100000 1000000Cycles to Failure
<001>
<111>
<213>
<011>
Power Law Curve Fit (R2 = 0.674): ∆τ = 397,758 N-0.1598
Figure 4-6. Shear stress amplitude [∆τmax ] vs. N
26
Table 4-1. Strain controlled LCF test data for PWA1493 at 1200°F for four specimen orientations.
Specimen Orientation
Max Test Strain
Min Test Strain
R Ratio
Strain Range
Cycles to
Failure <001> .01509 .00014 0.01 .01495 1326 <001> .0174 .0027 0.16 0.0147 1593 <001> .0112 .0002 0.02 0.011 4414 <001> .01202 .00008 0.01 0.0119 5673 <001> .00891 .00018 0.02 .00873 29516 <111> .01219 -0.006 -0.49 .01819 26 <111> .0096 .0015 0.16 0.0081 843 <111> .00809 .00008 0.01 .00801 1016 <111> .006 0.0 0.0 0.006 3410 <111> .00291 -0.00284 -0.98 .00575 7101 <111> .00591 .00015 0.03 .00576 7356 <111> .01205 0.00625 0.52 0.0058 7904 <213> .01212 0.0 0.0 .01212 79 <213> .00795 .00013 0.02 .00782 4175 <213> .00601 .00005 0.01 .00596 34676 <213> .006 0.0 0.0 0.006 114789 <011> .0092 .0004 0.04 0.0088 2672 <011> .00896 .00013 0.01 .00883 7532 <011> .00695 .00019 0.03 .00676 30220
27
Table 4-2. Maximum values of shear stress and shear strain on the slip systems and normal stress and strain values on the same planes.
Specimen Orientation
γmax γmin ∆γ/2 εmax εmin ∆ε/2 τmax
psi τmin
psi ∆τ psi
σmax
psi σmin
psi ∆σ 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 τmax = τ14 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
γmax = γ14 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
τmax = τ25 .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
γmax = γ25 .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
τmax = τ29 .0088 0 0.0044 0.00098 0 0.00049 8.00E+04 0 8.00E+04 6.50E+04 0 6.50E+04 34676
γmax = γ29 .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 τmax = τ15 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
γmax = γ15 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 γmax = Max shear strain of 30 slip systems for max specimen test strain value γmin = Max shear strain of 30 slip systems for min specimen test strain value τmax = Max shear stress of 30 slip systems for max specimen test strain value τmin = Max shear stress of 30 slip systems for min specimen test strain value
28
PWA1493 Data at Room Temperature (75°F) in High Pressure Hydrogen
Turbine blades in the Space Shuttle Main Engine (SSME) Alternate High Pressure
Fuel Turbopump (AHPFTP) are made of PWA1493 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 (carbides, eutectics, and micropores)
initiates a crystallographic or noncrystallographic fatigue crack [7] in PWA1480/1493.
At room temperature (26°C), in high-pressure hydrogen, the eutectic γ/γ’ initiates fatigue
cracks by an interlaminar (between γ and γ’) 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 427°C).
Figure 4-7 shows the strain amplitude vs. cycles to failure LCF data for PWA1493
at room temperature (26°C, 75°F) 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 [∆τmax] 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
29
the interlaminar failure mechanism between the γ and γ’ structures would likely provide
better results.
0
0.2
0.4
0.6
0.8
1
1.2
0 20000 40000 60000 80000 100000 120000 140000
Cycles to Failure
Stra
in A
mpl
itude
(%)
<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.
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
0 20000 40000 60000 80000 100000 120000 140000
Cycles to Failure
Max
She
ar S
tres
s A
mpl
itude
<001>
<011>
<111>
Pow er Law Fit
Power Law Curve Fit (R2 = 0.246): ∆τ = 238,349 N-0.1095
Figure 4-8. Shear stress amplitude (∆τmax) vs. cycles to failure for PWA1493 at room
temperature in 5000 psi hydrogen.
31
Table 4-3. PWA1493 LCF high pressure hydrogen (5000 psi) data at ambient temperature.
Specimen Orientation
Max Strain
εmax
Min Strain
εmin
Strain Ratio R = εmin/εmax
Strain Range ∆γmax ∆εmax ∆τmax
(psi)
∆σmax
(psi)
Cycles to
Failure
0.005 -0.005 -1 0.01 0.01310 0.001 84,853 180,000 6930.005 -0.005 -1 0.01 0.01310 0.001 84,853 180,000 10930.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 29290.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 33400.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 139640.004 -0.004 -1 0.008 0.01048 0.008 67,882 144,000 183240.003 -0.003 -1 0.006 0.00786 0.006 50,912 108,000 29551
<001> τmax = τ15
0.003 -0.003 -1 0.006 0.00786 0.006 50,912 108,000 561720.005 -0.005 -1 0.01 0.008034 0.005514 115,010 216,820 8260.005 -0.005 -1 0.01 0.008034 0.005514 115,010 216,820 9300.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 28970.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 32560.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 42340.004 -0.004 -1 0.008 0.006427 0.004416 92,005 173,460 133880.003 -0.003 -1 0.006 0.004820 0.00339 69,004 130,090 10946
<011> τmax = τ27
0.003 -0.003 -1 0.006 0.004820 0.00339 69,004 130,090 144650.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 4960.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 9850.004 -0.004 -1 0.008 0.00927 0.007998 167,830 355,950 58630.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 74100.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 100970.003 -0.003 -1 0.006 0.006943 0.00599 125,870 266,970 141730.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 444400.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 53189
<111> τmax = τ25
0.002 -0.002 -1 0.004 0.004628 0.00399 83,914 177,980 124485
32
PWA1493 Data at 1400°F and 1600°F in High Pressure Hydrogen
At higher temperatures hydrogen does not activate the eutectic failure mechanism,
and under these conditions ∆τmax is a good failure parameter for modeling LCF data.
Figures 4-9 and 4-10 show the strain amplitude vs. cycles to failure for PWA1493 in
high-pressure hydrogen (5000 psi) at 1400°F and 1600°F, respectively. There are only
three data points at 1400°F and four at 1600°F 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 [∆τmax] vs. cycles to failure for 1400°F
and 1600°F 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.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 500 1000 1500 2000 2500 3000 3500 4000
Cycles to Failure
Stra
in A
mpl
itude
(%)
<001>
<011>
Figure 4-9. LCF data for PWA1493 at 1400°F in 5000 psi high pressure hydrogen:
strain amplitude vs. cycles to failure.
33
0
0.5
1
1.5
2
2.5
0 200 400 600 800 1000 1200
Cycles to Failure
Stra
in A
mpl
itude
(%)
<001>
<011>
Figure 4-10. LCF data for PWA1493 at 1600°F in 5000 psi high pressure hydrogen:
strain amplitude vs. cycles to failure.
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
0 500 1000 1500 2000 2500 3000 3500 4000
Cycles to Failure
Max
She
ar S
tress
Am
plitu
de
<001>
<011>
Pow er Law Fit
Power Law Curve Fit (R^2 = 0.661): ∆τ = 223,516 N-0.1023
Figure 4-11. Shear stress amplitude (∆τmax) vs. cycles to failure for PWA1493 at 1400°F
in 5000 psi hydrogen.
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
0 200 400 600 800 1000 1200
Cycles to Failure
Max
She
ar S
tres
s A
mpl
itude
<001>
<011>
Pow er Law Fit
Power Law Curve Fit (R^2 = 0.9365): ∆τ = 381,241 N-0.2034
Figure 4-12. Shear stress amplitude (∆τmax) vs. cycles to failure for PWA1493 at 1600°F
in 5000 psi hydrogen.
36
Table 4-4. PWA1493 LCF data measured in high pressure hydrogen (5000 psi) at 1400°F.
Specimen Orientation
Max Strain
εmax
Min Strain
εmin
Strain Ratio
εmin/εmax
Strain Range ∆γmax ∆εmax
∆τmax (psi)
∆σmax (psi)
Cycles to
Failure<001>
τmax = τ15 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> τmax = τ27 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
1600°F.
Specimen Orientation
Max Strain
εmax
Min Strain
εmin
Strain Ratio
εmin/εmax
Strain Range ∆γmax ∆εmax
∆τmax (psi)
∆σmax (psi)
Cycles to
Failure0.0071 -0.0071 -1 0.0143 0.01899 0.0143 92,555 196,340 1002<001>
τmax = τ15 0.010 -0.010 -1 0.020 0.02657 0.020 129,450 274,600 3030.0077 -0.0077 -1 0.0155 0.01295 0.00865 142,100 267,910 104<011>
τmax = τ27 0.005 -0.005 -1 0.0101 0.00843 0.00564 92,597 174,570 905
SC 7-14-6 LCF Data at 1800°F in Air
Figure 4-13 shows the strain amplitude vs. cycles to failure LCF data for SC 7-14-6
at 1800°F in air for 5 different specimen orientations: <001>, <113>, <011>, <112>, and
<111> [7]. A wide amount of scatter is seen in the plot. Figure 4-14 shows [∆τmax] vs.
cycles to failure plot with an excellent correlation for a power law fit. Table 4-6 shows
the LCF data and the fatigue parameters.
37
0
0.2
0.4
0.6
0.8
1
1.2
0 50000 100000 150000
Cycles to Failure
Stra
in A
mpl
itude
(%)
<001><113><011><112><111>
Figure 4-13. LCF data for SC 7-14-6 at 1800°F in air: strain amplitude vs. cycles to
failure.
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
0 20000 40000 60000 80000 100000 120000 140000 160000
Cycles to Failure
Max
She
ar S
tress
Am
plitu
de
<001>
<113>
<011>
<112>
<111>
Pow er Law Fit
Power Law Curve Fit (R^2 = 0.7931): ∆τ = 230,275 N-0.1675
Figure 4-14. Shear stress amplitude (∆τmax) vs. cycles to failure for SC 7-14-6 at 1800°F
in air.
39
Table 4-6. LCF data for single crystal Ni-base superalloy SC 7-14-6 at 1800°F in air.
Specimen Orientation
Strain Range ∆γmax ∆εmax
∆τmax (psi)
∆σmax (psi)
Cycles to
Failure 0.01 1.3337E-02 1.0000E-02 5.9350E+04 1.2590E+05 39850.01 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 126080.007 9.3359E-03 7.0000E-03 4.1545E+04 8.8130E+04 41616
<001> τmax = τ15
0.006 8.0022E-03 6.0000E-03 3.5610E+04 7.5540E+04 1336150.008 1.2041E-02 8.5518E-03 6.2118E+04 1.1859E+05 35060.008 1.2041E-02 8.5518E-03 6.2118E+04 1.1859E+05 16980.007 1.0536E-02 7.4829E-03 5.4353E+04 1.0377E+05 40420.006 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 175000.0055 8.2785E-03 5.8794E-03 4.2706E+04 8.1533E+04 17383
<113> τmax = τ15
0.005 7.5259E-03 5.3449E-03 3.8823E+04 7.4121E+04 968470.006 5.1090E-03 3.4154E-03 5.1940E+04 9.7922E+04 26160.006 5.1090E-03 3.4154E-03 5.1940E+04 9.7922E+04 30620.005 4.2575E-03 2.8462E-03 4.3283E+04 8.1601E+04 91120.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 340630.004 3.4060E-03 2.2769E-03 3.4627E+04 6.5281E+04 549510.004 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> τmax = τ27
0.003 2.5545E-03 1.7077E-03 2.5970E+04 4.8961E+04 1000000.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 32710.005 7.1612E-03 5.1387E-03 5.7711E+04 1.0880E+05 50240.005 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 82980.004 5.7290E-03 4.1110E-03 4.6169E+04 8.7042E+04 96650.004 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> τmax = τ29
0.003 4.2967E-03 3.0832E-03 3.4627E+04 6.5281E+04 1000000.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 28860.004 4.7426E-03 6.4648E-04 6.7392E+04 1.4294E+05 30750.004 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> τmax = τ25
0.0028 3.3198E-03 4.5254E-04 4.7175E+04 1.0005E+05 55647 [13]
40
CHAPTER 5 CONCLUSION
The purpose of this study was to find a parameter that best fits the experimental
data for single crystal materials PWA1480/1493 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 ∆τmax on the 30 slip systems was found to be an
effective fatigue failure parameter, based on the curve fit between ∆τmax and cycles to
failure. The parameter [∆τmax] 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 1400°F and
1600°F was characterized well by the ∆τmax failure parameter. Since deformation
mechanisms in single crystals are controlled by the propagation of dislocations driven by
shear, ∆τmax 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.
41
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. 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 Single Crystal Nickel Superalloys,” 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 Development of Single Crystal Superalloy Turbine Blades,” Processing and Properties of Advanced 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 Behavior: 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.
42
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 γ’ 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 Materials, 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 of Materials, 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 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 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 Effects on Material Behavior, Eds. N. R. Moody and A. W. Thomson, TMS, Warrendale, 1989.
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 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.
top related