analysis of low cycle fatigue properties of single crystal...

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


100

τ19

τ7

001

010

τ8 τ20

τ9

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


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



(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


<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


<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


<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


<001>

<111>

<213>

<011>

Figure 4-5. ⎥⎦⎤

⎢⎣⎡∆

)(2

max1 σε

vs. N

25

0

50000

100000

150000

200000

250000

300000

350000


<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.


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.


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


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.


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.


Max Strain

εmax

Min Strain

εmin

Strain Ratio

εmin/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


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.



∆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

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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.

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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.

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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.

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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.

analysis of low cycle fatigue properties of single crystal...

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