Effect of LWR Coolant 

Environments on the 

Fatigue Life of 

Reactor Materials

Draft Report for Comment

Office of Nuclear Regulatory Research

NUREG/CR-6909, Rev. 1

ANL-12/60
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Effect of LWR Coolant 

Environments on the 

Fatigue Life of Reactor 

Materials

Draft Report for Comment

Manuscript Completed: March 2014

Date Published: March 2014

Prepared by: 

Omesh Chopra1 and Gary L. Stevens2

1

Argonne National Laboratory

9700 South Cass Avenue

Argonne, IL 60439

2

U.S. Nuclear Regulatory Commission

G. Stevens, NRC Project Manager

NRC Job Codes V6069 & V6269

Office of Nuclear Regulatory Research

NUREG/CR-6909, Rev. 1

ANL-12/60
COMMENTS ON DRAFT REPORT

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iii

Abstract

The ASME Boiler and Pressure Vessel Code provides rules for the design of Class 1 

components of nuclear power plants. Figures I–9.1 through I–9.6 of Appendix I to Section III of 

the Code specify fatigue design curves for applicable structural materials. However, the effects 

of light water reactor (LWR) coolant environments are not explicitly addressed by the Code 

design curves. The existing fatigue strain–vs.–life (ε–N) data illustrate potentially significant 

effects of LWR coolant environments on the fatigue resistance of pressure vessel and piping 

steels. Under certain environmental and loading conditions, fatigue lives in water relative to 

those in air can be a factor of approximately 12 lower for austenitic stainless steels, 

approximately 3 lower for Ni-Cr-Fe alloys, and approximately 17 lower for carbon and low-alloy 

steels. In 2007, the original version of NUREG/CR-6909, which is the technical basis document 

for NRC Regulatory Guide 1.207, summarized the work performed at Argonne National 

Laboratory on the fatigue of piping and pressure vessel steels in LWR environments. In that 

document, the existing fatigue ε–N data were evaluated to identify the various material, 

environmental, and loading parameters that influence fatigue crack initiation, and to establish 

the effects of key parameters on the fatigue lives of these steels. The report presented fatigue 

life models for estimating fatigue lives as a function of material, loading, and environmental 

conditions, and described the environmental fatigue correction factor, Fen, for incorporating the 

effects of LWR environments into ASME Section III fatigue evaluations. The report also 

presented a critical review of the ASME Code Section III fatigue adjustment factors of 2 on 

stress (or strain) and 20 on life and assessed the possible conservatism in the choice of these 

adjustment factors. 

This report provides updates and improvements to the environmental fatigue correction factor 

approach based on an extensive update to the fatigue ε–N data from testing and results 

available over the past decade since this report was first published. The updated expressions 

also address concerns from interested stakeholders related to: (a) the constants in the Fen

expressions that result in Fen values of approximately 2 even when the strain rate is very high or 

the temperature is very low, (b) the temperature dependence of Fen for carbon and low-alloy 

steels, and (c) the dependence of Fen on water chemistry for austenitic SSs. The Fen

methodology was validated by comparing the results of five different experimental data sets 

obtained from fatigue tests that simulate actual plant conditions with estimates of fatigue usage 

adjusted for environmental effects using the updated Fen expressions. The potential effects of 

dynamic strain aging on cyclic deformation and environmental effects are also discussed.

v

FOREWORD

This report summarizes, reviews, and quantifies the effects of the light-water reactor (LWR) 

environments on the fatigue lives of reactor materials, including carbon steels, low-alloy steels, 

nickel-chromium-iron (Ni-Cr-Fe) alloys, and austenitic stainless steels. The primary purpose of 

this report is to provide the background and technical bases to support Regulatory Guide 1.207, 

“Guidelines for Evaluating Fatigue Analyses Incorporating the Life Reduction of Metal 

Components Due to the Effects of the Light-Water Reactor Environment for New Reactors.”

The initial revision of this report included a review of the fatigue ε-N data available at that time 

for carbon steels, low-alloy steels, Ni-Cr-Fe alloys, and austenitic stainless steels to define the 

potential effects of key material, loading, and environmental parameters on the fatigue lives of 

the steels. By drawing upon a larger database than was used in earlier published reports, the 

U.S. Nuclear Regulatory Commission (NRC) updated the Argonne National Laboratory (ANL) 

fatigue life models used to estimate the fatigue curves as a function of those parameters, and 

presented a procedure for incorporating environmental effects into fatigue evaluations. In this 

revision, additional fatigue ε-N data available since the original publication of this report, most 

particularly from Japan, was incorporated into the database and the fatigue life models were 

updated. In addition, feedback from interested stakeholders obtained since the original 

publication of this report were evaluated and incorporated, where appropriate.

The database described in this report reinforces the position espoused by the NRC that the 

previously published guideline for incorporating the LWR environmental effects in fatigue life 

evaluations should be revised. Toward that end, this report maintains the previously 

established methods for establishing reference air fatigue curves, and defines updated 

environmental correction factors for use in evaluating the fatigue lives of reactor components 

exposed to LWR coolants and operational experience.

The data described in this updated review were used to verify the previously developed fatigue 

design curves in air that are consistent with the available fatigue data. The published data 

indicate that the existing ASME Code Section III curves are appropriate for austenitic stainless 

steels (e.g., Types 304, 316, and 316NG), and are conservative for carbon and low-alloy steels. 

Regulatory Guide 1.207 endorses the fatigue design curves presented herein for incorporation 

in fatigue analyses for new and operating reactors.

Brian W. Sheron, Director

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

vii

CONTENTS

Abstract .............................................................................................................................iii

Foreword ............................................................................................................................. v

Contents ............................................................................................................................vii

Figures ...........................................................................................................................xiii

Tables ...........................................................................................................................xxi

Executive Summary .............................................................................................................. xxiii

Abbreviations ....................................................................................................................... xxvii

Acknowledgments................................................................................................................. xxxi

1. Introduction........................................................................................................... 1

1.1 Definition of Fatigue Life ....................................................................................... 1

1.2 Air Fatigue Design Curves in Section III of the ASME Code ................................. 3

1.3 Subfactors Included in ASME Section III Air Fatigue Design Curves .................... 5

1.3.1 Effects of Reactor Coolant Environment on Fatigue Lives ....................... 6

1.3.2 Effects of Neutron Irradiation ................................................................... 9

1.4 Modeling of Environmental Effects...................................................................... 13

2. Mechanism of Fatigue......................................................................................... 17

2.1 Formation of an Engineering Crack in Air ........................................................... 17

2.2 Fatigue Cracking in LWR Environments ............................................................. 21

2.2.1 Carbon and Low-Alloy Steels................................................................. 21

2.2.1.1 Effects of Surface Micropits ..................................................... 21

2.2.1.2 Mechanisms of Corrosion Fatigue............................................ 22

2.2.1.3 Effects of Dynamic Strain Aging (DSA) .................................... 26

2.2.1.4 Crack Growth Rates in Smooth Fatigue Specimens................. 28

2.2.2 Austenitic Stainless Steels..................................................................... 29

2.2.2.1 Effects of Surface Micropits ..................................................... 31

2.2.2.2 Mechanisms of Corrosion Fatigue............................................ 31

2.2.2.3 Effects of Dynamic Strain Aging (DSA) .................................... 34

2.2.2.4 Crack Growth Rates in Smooth Fatigue Specimens................. 34
viii

3. Fatigue Strain vs. Life (ε–N) Behavior in Air........................................................ 39

3.1 Carbon and Low-Alloy Steels and Weld Metals .................................................. 39

3.1.1 Experimental Data ................................................................................. 39

3.1.2 Temperature.......................................................................................... 42

3.1.3 Strain Rate............................................................................................. 42

3.1.4 Sulfide Morphology ................................................................................ 43

3.1.5 Cyclic Strain Hardening Behavior .......................................................... 43

3.1.6 Fatigue Life Model ................................................................................. 44

3.1.7 Heat-to-Heat Variability.......................................................................... 47

3.1.8 Fatigue ε-N Behavior of Weld Metals ..................................................... 50

3.1.9 Surface Finish........................................................................................ 50

3.1.10 Extension of the Best-Fit Mean Curve from 106 to 1011 Cycles ............ 51

3.1.11 Fatigue Design Curves .......................................................................... 53

3.2 Wrought and Cast Austenitic Stainless Steels and Weld Metals ......................... 56

3.2.1 Experimental Data ................................................................................. 56

3.2.2 Specimen Geometry and Type of Loading............................................. 60

3.2.3 Strain Rate............................................................................................. 61

3.2.4 Temperature.......................................................................................... 61

3.2.5 Cyclic Strain Hardening Behavior .......................................................... 62

3.2.6 Fatigue Life Model ................................................................................. 63

3.2.7 Heat-to-Heat Variability.......................................................................... 65

3.2.8 Fatigue ε-N Behavior of Cast Austenitic Stainless Steels....................... 66

3.2.9 Fatigue ε-N Behavior of Weld Metals ..................................................... 67

3.2.10 Surface Finish........................................................................................ 68

3.2.11 Fatigue Design Curve ............................................................................ 69

3.3 Ni-Cr-Fe Alloys and Weld Metals ........................................................................ 71

3.3.1 Experimental Data ................................................................................. 72
ix

3.3.2 Fatigue Life Model ................................................................................. 74

4. Fatigue ε–N Behavior in LWR Environments....................................................... 77

4.1 Carbon and Low-Alloy Steels.............................................................................. 77

4.1.1 Experimental Data ................................................................................. 79

4.1.2 Strain Rate............................................................................................. 82

4.1.3 Strain Amplitude .................................................................................... 84

4.1.4 Temperature.......................................................................................... 88

4.1.5 Dissolved Oxygen.................................................................................. 91

4.1.6 Water Conductivity................................................................................. 92

4.1.7 Sulfur Content in Steel........................................................................... 92

4.1.8 Hold Periods .......................................................................................... 93

4.1.9 Flow Rate .............................................................................................. 96

4.1.10 Fatigue Life Model ................................................................................. 97

4.1.11 Environmental Fatigue Correction Factor............................................... 98

4.1.12 Surface Finish...................................................................................... 104

4.1.13 Heat-to-Heat Variability........................................................................ 106

4.1.14 Modified Rate Approach ...................................................................... 107

4.2 Wrought and Cast Austenitic Stainless Steels .................................................. 110

4.2.1 Experimental Data ............................................................................... 111

4.2.2 Strain Rate........................................................................................... 115

4.2.3 Strain Amplitude .................................................................................. 116

4.2.4 Temperature........................................................................................ 118

4.2.5 Dissolved Oxygen................................................................................ 119

4.2.6 Water Conductivity............................................................................... 120

4.2.7 Material Heat Treatment ...................................................................... 121

4.2.8 Cast Austenitic Stainless Steels........................................................... 121

4.2.9 Stainless Steel Weld Metals................................................................. 124
x

4.2.10 Hold Periods ........................................................................................ 125

4.2.11 Flow Rate ............................................................................................ 126

4.2.12 Fatigue Life Model ............................................................................... 127

4.2.13 Environmental Correction Factor ......................................................... 128

4.2.14 Surface Finish...................................................................................... 135

4.2.15 Heat-to-Heat Variability........................................................................ 136

4.3 Ni-Cr-Fe Alloys ................................................................................................. 138

4.3.1 Experimental Data ............................................................................... 138

4.3.2 Effects of Key Parameters ................................................................... 140

4.3.3 Environmental Correction Factor ......................................................... 141

5 Adjustment Factors in ASME Code Fatigue Design Curves .............................. 147

5.1 Material Variability and Data Scatter................................................................. 149

5.2 Size and Geometry........................................................................................... 150

5.3 Surface Finish................................................................................................... 151

5.4 Loading Sequence............................................................................................ 151

5.5 Air Fatigue Design Curve Adjustment Factors Summarized.............................. 152

6. Validation of Fen Expressions........................................................................... 157

6.1 Spectrum Straining ........................................................................................... 158

6.2 Complex Loading – Safety Injection Transient.................................................. 162

6.3 U-Bend Tests in Inert and PWR Water Environments....................................... 166

6.4 Simulation of Actual Plant Conditions ............................................................... 170

7. Summary .......................................................................................................... 173

8. References ....................................................................................................... 177

APPENDIX A: Incorporating Environmental Effects into Fatigue Evaluations ........................A-1

A1 Scope ................................................................................................................A-1

A2 Environmental Correction Factor (Fen)..............................................................A-1

A3 Fatigue Evaluation Procedure............................................................................A-3

APPENDIX B: MATERIAL INFORMATION...........................................................................B-1
xi

B1 Carbon and Low-Alloy Steels Included in the Fatigue Database........................B-1

B2 Wrought and Cast Austenitic Stainless Steels and Welds..................................B-4

B3 Ni-Cr-Fe Alloys and Welds.................................................................................B-7

APPENDIX C: SAMPLE PROBLEM..................................................................................... C-1

C1 Background ...................................................................................................... C-1

C2 Problem Description ......................................................................................... C-1

C3 Evaluation......................................................................................................... C-8

C4 Results ............................................................................................................C-11

C5 References ......................................................................................................C-73

xiii

FIGURES

Figure 1. Fatigue ε-N data for low-alloy steels and austenitic stainless steels in water 

compared to ASME Air Design Curve; RT = room temperature. ........................... 6

Figure 2. The effects of neutron irradiation on fatigue lives of Type 347 SSs at room 

temperature: (a) the fatigue ε–N behavior, and (b) variations in plastic strain 

amplitude as a function of fatigue cycles (Ref. 109)............................................ 10

Figure 3. Strain amplitude vs. fatigue life data in 325°C air or simulated PWR primary 

water environments for CW Type 316 SS irradiated to (a) less than 1022, 

(b) 2-6x1025, and (c) greater than 3x1026 n/m2 (E > 1.0 MeV) (Ref. 110)............. 12

Figure 4. Strain amplitude vs. fatigue life data in 325°C air and simulated PWR 

primary water environments for Type 304 SS irradiated to 5x1025–1026 n/m2

(E > 0.1 MeV) (Ref. 110).................................................................................... 12

Figure 5. Two stages of fatigue crack growth in smooth test specimens. ........................... 17

Figure 6. Schematic illustration of the plastic blunting process of fatigue crack growth 

in Stage II: (a) zero load; (b) small tensile load; (c) maximum tensile load, 

widening of slip bands; (d) crack closure, and formation of “ears” at crack tip; 

(e) maximum compressive load; (f) small tensile load in the subsequent 

cycle. .................................................................................................................. 18

Figure 7. Crack depth plotted as a function of fractional life for carbon and low–alloy 

steels tested in air (Refs. 11,165-167). ............................................................... 19

Figure 8. Schematic illustration of (a) growth of short cracks in smooth specimens as 

a function of fatigue life fraction, and (b) crack velocity as a function of crack 

depth. ................................................................................................................. 20

Figure 9. Fatigue life of carbon and low-alloy steel specimens in high-DO water at 

288°C compared with the fatigue life of specimens preoxidized in high-DO 

water and tested in either air or low-DO water at 288°C (Refs. 40,41,176). ........ 22

Figure 10. Schematic illustration of slip oxidation/dissolution process.................................. 23

Figure 11. Schematic illustration of hydrogen-induced cracking of low-alloy steel................ 25

Figure 12. Fatigue cracks on gauge surfaces of A106-Gr. B carbon steel tested in 

(a) air and (b) high-DO water at 288°C (Ref. 10)................................................. 26

Figure 13. Fatigue cracks along longitudinal sections of A106-Gr. B carbon steel tested 

in (a) air and (b) high-DO water at 288°C (Ref. 10)............................................. 26

Figure 14. (a) Fatigue crack initiation and (b) crack growth in DSA susceptible low-alloy 

steel exposed to high-temperature water environment (Ref. 147)....................... 27

Figure 15. Depth of largest crack plotted as a function of (a) fatigue cycles and 

(b) fraction of fatigue life for A533–Gr B low–alloy steel in air and water 

environments (Ref. 11). ...................................................................................... 28

Figure 16. (a) Morphology and length of surface crack after various numbers of cycles 

for A533-Gr. B steel in air at room temperature, and (b) fracture surface and 

probable crack front for surface cracks shown in (a) (Ref. 11). ........................... 28

Figure 17. Crack growth rates plotted as a function of crack depth for A533–Gr B low–

alloy steel tested in air and water environments (Ref. 11)................................... 29
xiv

Figure 18. Photomicrographs of oxide films that formed on Type 316NG stainless steel 

in (a) simulated PWR water and (b) high–DO water (Ref. 13)............................. 30

Figure 19. Schematic of the corrosion oxide film formed on austenitic stainless steels in 

LWR environments. ............................................................................................ 30

Figure 20. Effects of environment on formation of fatigue cracks in Type 316NG SS in 

air and low–DO water at 288°C. Preoxidized specimens were exposed for 

10 days at 288°C in water that contained either less than 5 ppb DO and 

approximately 23 cm3

/kg dissolved H2 or approximately 500 ppb DO and no 

dissolved H2 (Ref. 13). ....................................................................................... 31

Figure 21. Photomicrographs of the fatigue crack morphology of Type 304 SS in (a) air, 

(b) high-DO BWR water, and (c) low-DO PWR water at 289°C (Ref. 47)............ 32

Figure 22. Photomicrographs showing sites of fatigue crack initiation on fracture 

surfaces of Type 304 SS tested at 289°C in (a) air, (b) high-DO BWR water, 

and (c) low-DO PWR water (Ref. 47).................................................................. 33

Figure 23. Photomicrographs showing fatigue striations on fracture surfaces of Type 

304 SS tested at 289°C in (a) air, (b) high-DO BWR water, and (c) low-DO 

PWR water (Ref. 47)........................................................................................... 33

Figure 24. Depth of largest crack plotted as a function of fatigue cycles for austenitic 

stainless steels in air and water (Refs. 13,207)................................................... 35

Figure 25. Crack growth rates plotted as a function of crack length for austenitic 

stainless steels in (a) water and (b) air environments (Refs. 13,44,207). ............ 35

Figure 26. Crack growth rate data for Type 304 SS in high temperature water 

determined from (a) fracture mechanics CT specimens and (b) smooth 

cylindrical fatigue specimens (Ref. 208).............................................................. 36

Figure 27. Fatigue strain vs. life data for carbon and low–alloy steels in air at room 

temperature (JNUFAD database and Refs. 10,18,19,48).................................... 41

Figure 28. The change in fatigue lives of carbon and low-alloy steels in air as a function 

of temperature. ................................................................................................... 42

Figure 29. Effect of strain rate and temperature on cyclic stress of carbon and low–alloy 

steels.................................................................................................................. 44

Figure 30. Schematic diagram of the best-fit of the experimental data by minimizing the 

distance between the data point and the S-N curve............................................ 45

Figure 31. Experimental and predicted fatigue lives of (a, b) carbon steels and (c, 

d) low-alloy steels in air....................................................................................... 46

Figure 32. Estimated cumulative distribution of constant A in the ANL models for fatigue 

life data in the original revision of NUREG/CR-6909 (a, c) and this report (b, 

d); (a, b) for heats of carbon steels and (c, d) low–alloy steels in air. .................. 48

Figure 33. Fatigue ε–N behavior for carbon and low-alloy steel weld metals in air at 

room temperature and 289°C (Ref. 136)............................................................. 50

Figure 34. Effect of surface finish on the fatigue life of A106–Gr B carbon steel in air at 

289°C (Ref. 46)................................................................................................... 51

Figure 35. Fatigue design curves based on the ANL model for (a) carbon steels and 

(b) low-alloy steels in air. .................................................................................... 54
xv

Figure 36. Fatigue design curve for carbon steels in air. The curve developed from the 

ANL model is based on factors of 12 on life and 2 on stress............................... 55

Figure 37. Fatigue design curve for low-alloy steels in air. The curve developed from 

the ANL model is based on factors of 12 on life and 2 on stress......................... 55

Figure 38. Fatigue ε-N behavior for Types 304, 304L, 316, and 316NG SS austenitic 

stainless steels in air at various temperatures up to 400°C (Refs. 13,42-47, 

61,136). .............................................................................................................. 58

Figure 39. Influence of specimen geometry on fatigue lives of Types 304 and 316 

stainless steels (JNUFAD data). ......................................................................... 60

Figure 40. Influence of bending loading on fatigue lives of Types 304 and 316 stainless 

steels (JNUFAD data)......................................................................................... 60

Figure 41. Influence of temperature on fatigue lives of austenitic stainless steels in air 

(Ref. 61-63). ....................................................................................................... 61

Figure 42. Effects of strain amplitude, temperature, and strain rate on cyclic strain–

hardening behavior of Types 304 and 316NG SSs in air at 288°C and room 

temperature. ....................................................................................................... 62

Figure 43. Cyclic stress-strain curves for Types 316, 304 and 316NG SSs in air at room 

temperature and 288°C. ..................................................................................... 63

Figure 44. Experimental and predicted fatigue lives (using the ANL model) for austenitic 

SSs in air. ........................................................................................................... 64

Figure 45. Estimated cumulative distribution of constant A in the ANL model for fatigue 

lives for heats of austenitic SSs in air included in (a) the initial revision of 

NUREG/CR-6909 and (b) those included in this report. ...................................... 65

Figure 46. Fatigue ε–N behavior for several heats of CF-8M cast austenitic SSs in air at 

various temperatures.......................................................................................... 67

Figure 47. Fatigue ε–N behavior for austenitic SS weld metals in air at room 

temperature. ....................................................................................................... 68

Figure 48. Effects of surface roughness on fatigue lives of (a) Type 316NG and 

(b) Type 304 SSs in air (Ref. 46). ....................................................................... 68

Figure 49. Fatigue design curves for austenitic SSs in air.................................................... 70

Figure 50. Fatigue ε–N behavior for Alloys 600, 690 and 800 in air at temperatures 

between room temperature and 315°C (Refs. JNUFAD data, 61,66–75). ........... 73

Figure 51. Fatigue ε–N behavior for Alloys 62, 82, 132, 152, and 182 welds in air at 

various temperatures (Refs. JNUFAD data,61,66–75). ....................................... 73

Figure 52. Fatigue ε–N behavior for Inconel 718 in air at room temperature and 427°C 

(Refs. 61,72,73,136,210). ................................................................................... 73

Figure 53. Fatigue ε–N behavior for carbon and low-alloy steels in air at room 

temperature and high-purity water at temperatures below 150°C (Ref. 137)....... 79

Figure 54. Strain amplitude vs. fatigue life data for (a) A533–Gr B and (b) A106–Gr B 

steels in air and high–dissolved–oxygen water at 288°C (Ref. 10)...................... 81

Figure 55. Dependence of fatigue lives of carbon and low–alloy steels on strain rate 

(Refs. 10,23)....................................................................................................... 83
xvi

Figure 56. Fatigue life of A533–Gr. B low-alloy steel as a function of strain rate in high 

purity water with 0.1 or 2.0 ppm dissolved oxygen (Refs. 141,143)..................... 84

Figure 57. Fatigue strain-life behavior of A533–Gr. B and A508-Gr. 3 low-alloy steels at 

288°C in air and high-purity water with 0.1 ppm dissolved oxygen (Ref. 151). .... 84

Figure 58. Fatigue life of A106–Gr B carbon steel at 288°C and 0.75% strain range in 

air and water environments under different loading waveforms (Ref. 10)............ 85

Figure 59. Fatigue lives of carbon and low–alloy steels tested with loading waveforms 

where slow strain rate was applied during a fraction of the tensile loading 

cycle (Refs. 10,24).............................................................................................. 86

Figure 60. Experimental values of fatigue life and those predicted from the modified 

rate approach (a) without and (b) with consideration of a threshold strain 

(Ref. 136). .......................................................................................................... 87

Figure 61. Change in fatigue life of A333–Gr. 6 carbon steel and A508-Gr. 3 low-alloy 

steel with temperature and DO (Ref. 136)........................................................... 89

Figure 62. Waveforms for changes in temperatures and strains during exploratory 

fatigue tests (Ref. 21). ........................................................................................ 90

Figure 63. Fatigue lives of A333–Gr. 6 carbon steel tube specimens under varying 

temperature conditions, as indicated by horizontal bars (Ref. 21)....................... 90

Figure 64. Dependence on DO of the fatigue lives of carbon and low alloy steels in 

high-purity water (Ref. 18, 19, 22)....................................................................... 91

Figure 65. Effect of strain rate on fatigue life of low–alloy steels with different sulfur 

contents (Refs. 10, 136)...................................................................................... 92

Figure 66. Effect of strain rate on the fatigue lives of A333–Gr. 6 carbon steels with 

different sulfur contents (Ref. 10)....................................................................... 93

Figure 67. Fatigue lives of A106–Gr B steel in air and water environments at 288°C, 

0.78% strain range, and hold periods at peak tensile strain (Ref. 10). 

Hysteresis loops are for tests in air. .................................................................... 94

Figure 68. Effect of hold periods on the fatigue lives of A333–Gr. 6 carbon steel at 

289°C in water with 1 ppm DO (Ref. 24)............................................................. 95

Figure 69. Effects of water flow rate on fatigue lives of A333–Gr. 6 and A508-Gr. 1 

carbon steels and A533-Gr. B low-alloy steel at 289°C and 0.3 or 0.6% 

strain amplitudes and various strain rates (Ref. 25,26). ...................................... 96

Figure 70. Effect of flow rate on low–cycle fatigue of carbon steel tube bends in high–

purity water at 240°C (Ref. 55). RT = room temperature.................................... 97

Figure 71. Experimental fatigue lives of carbon steels in LWR environments vs. fatigue 

lives predicted from the (a) new expression, (b) JNES expression, and 

(c) the previous NUREG/CR-6909 expression.................................................... 99

Figure 72. Experimental fatigue lives of low-alloy steels in LWR environments vs. 

fatigue lives predicted from the (a) new expression, (b) JNES expression, 

and (c) the previous NUREG/CR-6909 expression. .......................................... 100

Figure 73. Comparison of the fatigue lives of carbon and low-alloy steels predicted from 

the new Fen expression and the JNES Fen expression.................................... 101
xvii

Figure 74. Residuals for predicted fatigue lives of carbon steels as a function of 

(a) Material ID, (b) water dissolved oxygen content, (c) strain rate, 

(d) temperature, (e) steel sulfur content, and (f) strain amplitude...................... 102

Figure 75. Residuals for predicted fatigue lives of low-alloy steels as a function of 

(a) Material ID, (b) water dissolved oxygen content, (c) strain rate, 

(d) temperature, (e) steel sulfur content, and (f) strain amplitude...................... 103

Figure 76. Residuals for predicted fatigue lives in air of carbon and low-alloy steels as a 

function of Material ID....................................................................................... 104

Figure 77. Effect of surface finish on the fatigue lives of (a) A106–Gr B carbon steel 

and (b) A533 low–alloy steel in air and high–purity water at 289°C (Ref. 46). ... 105

Figure 78. Relationship between surface finish and fatigue life reduction fraction for 

A533-Gr. B low-alloy steel in water at 288°C (Ref. 144).................................... 105

Figure 79. Estimated cumulative distribution of parameter A in the ANL model for 

fatigue lives for heats of carbon and low–alloy steels in LWR environments..... 107

Figure 80. Application of the modified rate approach to determine the environmental 

fatigue correction factor Fen during the increasing strain portion of a 

transient............................................................................................................ 108

Figure 81. Example showing Fen values computed using average temperatures 

compared to the Fen computed using an integrated (modified rate) approach. .. 109

Figure 82. Strain amplitude vs. fatigue life data for (a) Type 304 and (b) Type 316NG 

SSs in water at 288°C (JNUFAD and Refs. 13,45)............................................ 113

Figure 83. Fatigue stress - life data from load-controlled tests on Type 304L SSs, with 

and without mean stress, in air and PWR water (Ref. 60)................................. 114

Figure 84. Fatigue strain - life data from load-controlled tests on Type 304L SSs, with 

and without mean stress, in air (a, c) and PWR water (b, d) (Refs. 58,60). ....... 115

Figure 85. Dependence of fatigue lives of austenitic stainless steels on strain rate in 

low–DO water (Refs. 13,45,47,60).................................................................... 116

Figure 86. Dependence of fatigue lives of Types (a) 304 and (b) 316NG SSs on strain 

rate in high– and low–DO water at 288°C (Ref. 13,45,47)................................. 116

Figure 87. Results of strain rate change tests on Type 316 SSs in low–DO water at 

325°C. Low strain rate was applied during only a fraction of the tensile 

loading cycle. Fatigue life is plotted as a function of fraction of strain at high 

strain rate (Refs. 30,35). ................................................................................... 117

Figure 88. Change in fatigue lives of austenitic stainless steels in low–DO water with 

temperature (Refs. 13,29–31,34,45–47). .......................................................... 118

Figure 89. Fatigue lives of Type 316 SSs under constant and varying test temperatures 

(Ref. 29,30)....................................................................................................... 119

Figure 90. Effects of water conductivity and soaking period on fatigue lives of Type 304 

SSs in high–DO water (Ref. 13,45)................................................................... 120

Figure 91. The effects of material heat treatment on fatigue lives of Type 304 SSs in 

air, BWR and PWR environments at 289°C, approximately 0.38% strain 

amplitude, sawtooth waveform loading, and 0.004%/s tensile strain rate 

(Ref. 47). .......................................................................................................... 121
xviii

Figure 92. Fatigue lives of cast austenitic SSs in high-purity water at 289°C and 0.3% 

and 0.6% strain amplitude plotted as a function of DO content (Ref. 136). ....... 122

Figure 93. Strain amplitude vs. fatigue life data for cast austenitic SSs at 325°C and 

various strain rates in water with 0.005 ppm DO content (Ref. 29,34)............... 122

Figure 94. Dependence of fatigue lives of CF–8M cast SSs on strain rate in low–DO 

water at various strain amplitudes (Refs. 136,43,45). ....................................... 123

Figure 95. Change in fatigue lives of cast austenitic SSs in low–DO water with 

temperature (Ref. 136). .................................................................................... 124

Figure 96. Strain amplitude vs. fatigue lives for Types 308 and 316TP SS weld metals 

at 325°C and various strain rates in water with 0.005 ppm DO content 

(Ref. 136). ........................................................................................................ 124

Figure 97. Change in fatigue lives of SS weld metals in LWR environments with strain 

rate and temperature (Ref. 136)........................................................................ 125

Figure 98. Fatigue lives of Type 304 SSs tested in high–DO water at 260–288°C with 

trapezoidal or triangular waveform loadings (Refs. 14,31). ............................... 125

Figure 99. Effect of hold periods on the fatigue lives of Types 316NG and 316 SSs in 

LWR environments at various strain rates (Ref. 136)........................................ 126

Figure 100. Effects of water flow rate on the fatigue lives of Types 304, 304L, 316NG 

and CF-8M cast SSs in high-purity water at 289°C (Ref. 136). ......................... 127

Figure 101. Effects of water flow rates on the fatigue lives of Type 304 and 316 

austenitic SSs in PWR primary water at 325°C (Ref. 136). .............................. 127

Figure 102. Experimental fatigue lives of wrought and cast austenitic SSs in LWR 

environments vs. fatigue lives predicted from (a) the updated ANL 

expression, (b) the JNES expression, (c) the previous NUREG/CR-6909 

expression, and (d) fatigue lives of SS weld metals predicted from the 

updated ANL expression................................................................................... 130

Figure 103. Fatigue lives of wrought and cast austenitic SSs in LWR environments 

estimated from the new Fen expressions vs. those estimated from the JNES 

expression. ....................................................................................................... 131

Figure 104. Experimental fatigue lives of Types 304L and 316N austenitic SSs in LWR 

environments vs. fatigue lives predicted from (a) the updated ANL 

expression and (b) the JNES expression. ......................................................... 132

Figure 105. Experimental fatigue lives of wrought and cast austenitic SSs in water 

containing greater than 0.1 ppm DO vs. fatigue lives predicted from (a) the 

updated ANL expression and (b) the JNES expression..................................... 132

Figure 106. Residuals for predicted fatigue lives of wrought and cast austenitic SSs as a 

function of (a) ANL Material ID, (b) water DO content, (c) strain rate, 

(d) temperature, and (e) strain amplitude.......................................................... 134

Figure 107. Residuals for predicted fatigue lives of wrought and cast austenitic SSs in air 

as a function of ANL Material ID. ...................................................................... 135

Figure 108. Effect of surface finish on fatigue life of (a) Type 316NG and (b) Type 304 

stainless steels in air and high–purity water at 289°C. ...................................... 136
xix

Figure 109. Effects of surface finish on the fatigue lives of Type 304L SSs in air and 

PWR primary water environments at 300°C (Refs. 155,157). ........................... 136

Figure 110. Estimated cumulative distribution of constant A in the ANL model for fatigue 

lives of heats of austenitic SSs in LWR environments....................................... 137

Figure 111. Fatigue ε–N behavior for Alloy 600 and its weld alloys in simulated BWR 

water at approximately 289°C (Refs. 136, 39)................................................... 139

Figure 112. Fatigue ε–N behavior for Alloys 600 and 690 and associated weld metals in 

simulated PWR water at 325°C (Refs. 136, 75). ............................................... 139

Figure 113. Dependence of fatigue lives of Alloys 690 and 600 and associated weld 

metals on strain rate in PWR and BWR environments (Refs. 39, 75, 136)........ 140

Figure 114. Dependence of fatigue lives of Alloy 600 on temperature in a PWR 

environment (Refs. 39, 75, 136)........................................................................ 141

Figure 115. Experimental fatigue lives vs. fatigue lives predicted from the updated Fen

expression for Ni-Cr-Fe alloys and weld metals in simulated (a) BWR and 

(b) PWR environments. .................................................................................... 142

Figure 116. Experimental fatigue lives vs. fatigue lives predicted from the Fen

expression in the original revision of NUREG/CR-6909 for Ni-Cr-Fe alloys 

and weld metals in simulated (a) BWR and (b) PWR environments.................. 143

Figure 117. Experimental fatigue lives vs. fatigue lives predicted from the JNES Fen

expression for Ni-Cr-Fe alloys and associated weld metals in simulated 

(a) BWR and (b) PWR environments. ............................................................... 143

Figure 118. Residuals for predicted fatigue lives of Ni-Cr-Fe alloys and associated weld 

metals as a function of (a) material ID, (b) water DO content, (c) strain rate, 

(d) temperature, and (e) strain amplitude.......................................................... 145

Figure 119. Residuals for predicted fatigue lives of Ni-Cr-Fe alloys and associated weld 

metals in air as a function of ANL Material ID. .................................................. 146

Figure 120. Fatigue data for (a) carbon and low–alloy steel and (b) Type 304 stainless 

steel components (Refs. 237,238). ................................................................... 148

Figure 121. Estimated cumulative distribution of parameter A in the ANL models that 

represent the fatigue lives of test specimens and actual components in air. ..... 155

Figure 122. Schematic of the repeated sequence of randomized block of 50 strain cycles 

(Ref. 158). ........................................................................................................ 159

Figure 123. Fatigue strain-life data for Type 316NG SS in PWR water at 320°C and for 

Ti-stabilized 316 SS in VVER water at 293°C (Refs. 158,159).......................... 161

Figure 124. Experimental and estimated fatigue lives for Type 316NG and Ti-stabilized 

316 SS tested with constant and spectrum strain loading (Refs. 158,159)........ 162

Figure 125. Typical strain cycle of cold and hot thermal shocks corresponding to a PWR 

safety injection transient (Ref. 155)................................................................... 163

Figure 126. Fatigue strain-life data for Type 304L SS in air and PWR environments at 

300°C (Refs. 155-157)...................................................................................... 164
xx

Figure 127. The experimental and estimated fatigue lives for Type 304L SS tested at 

300°C in air and a PWR environment using triangular and complex loading 

that simulated a PWR safety injection transient (Refs. 155-157)....................... 165

Figure 128. U-bend test specimen and nomenclature (Ref. 97). .......................................... 166

Figure 129. Overview of the extent and location of fatigue cracking in U-bend tests at 

strain amplitude of 0.6% (Ref. 97)..................................................................... 168

Figure 130. Overview of the extent and location of fatigue cracking in U-bend tests at 

strain amplitude of 0.4% (Ref. 97)..................................................................... 169

Figure 131. The experimental and predicted fatigue lives for Type 304L SS U-bend 

specimens at 240°C in inert and PWR environments (Refs. 97-99). ................. 170

Figure 132. Loading waveforms for Fatigue Test Nos. 1 and 7 (Ref. 154). .......................... 171

Figure 133. The experimental and predicted fatigue lives of Type 316 SS tested in PWR 

primary water using two blocks of fatigue cycles of different strain 

amplitudes and varying temperature and strain rate (Ref. 154)......................... 172

Figure A.1. Fatigue design curves for carbon steels in air. The curve developed from 

the ANL model is based on factors of 12 on life and 2 on stress........................A-4

Figure A.2. Fatigue design curves for low-alloy steels in air. The curve developed from 

the ANL model is based on factors of 12 on life and 2 on stress........................A-4

Figure A.3 Fatigue design curve for austenitic stainless steels in air. The curve 

developed from the ANL model is based on factors of 12 on life and 2 on 

stress.................................................................................................................A-5

Figure C.1. Sample Problem Geometry............................................................................... C-2

Figure C.2. Sample Problem Transient Time Histories ........................................................ C-4

Figure C.3. Sample Problem Transient Membrane Plus Bending Stress Histories for 

SCL 2 ............................................................................................................... C-5

Figure C.4. Sample Problem Transient Total Stress Histories for SCL 2 ............................. C-6

Figure C.5. Sample Problem Combined Transient Stress History for SCL 2........................ C-7

Figure C.6. Principal Stress Intensity Histories and Peaks and Valleys Used in 

Limiting CUF Calculation for Sample Problem for SCL 2 .................................C-13
xxi

TABLES

Table 1. Sources of the fatigue ε–N data on carbon and low-alloy steels in air 

environment........................................................................................................ 40

Table 2. Values of constant A in the ANL fatigue life model for carbon steels in air 

and the factors on life as a function of confidence level and percentage of 

population bounded. ........................................................................................... 49

Table 3. Values of constant A in the ANL fatigue life model for low–alloy steels in air 

and the factors on life as a function of confidence level and percentage of 

population bounded. ........................................................................................... 50

Table 4. Fatigue design curves for carbon and low-alloy steels including proposed 

updated extension to 1011 cycles....................................................................... 54

Table 5. Fatigue design curves for carbon and low-alloy steels and the extension to 

1011 cycles proposed in the initial revision to NUREG/CR-6909. ....................... 55

Table 6. Sources of the fatigue ε–N data on wrought and cast austenitic stainless 

steels in an air environment................................................................................ 56

Table 7. Values of constant A in the ANL fatigue life model for austenitic SSs and the 

factors on fatigue lives for austenitic SSs in air as a function of confidence 

level and percentage of population bounded....................................................... 66

Table 8. The ASME Code fatigue design curves for austenitic SSs in air. ........................ 69

Table 9. Sources of the fatigue ε–N data on Ni-Cr-Fe alloys and their weld metals in 

an air environment.............................................................................................. 71

Table 10. Sources of the fatigue ε–N data for carbon and low-alloy steels in LWR 

environments...................................................................................................... 80

Table 11. Sources of the fatigue ε–N data for cast and austenitic stainless steels in 

LWR environments. .......................................................................................... 112

Table 12. Sources of the fatigue ε–N data for Ni-Cr-Fe alloys and their weld metals in 

LWR environments. .......................................................................................... 138

Table 13. Statistical information for the constant A used to evaluate material variability 

and data scatter................................................................................................ 150

Table 14. Factors on life applied to the mean fatigue ε–N air curve to account for the 

effects of various material, loading, and environmental parameters.................. 153

Table 15. Factor applied to the mean values of fatigue life to bound 95% of the data 

population......................................................................................................... 154

Table 16. Chemical composition and tensile strength of test materials for the constant 

and spectrum strain amplitude fatigue tests...................................................... 158

Table 17. Environmental conditions for the constant and spectrum strain amplitude 

fatigue tests. ..................................................................................................... 159

Table 18. The conditions and results of fatigue tests on austenitic SSs obtained under 

constant and spectrum strain amplitude loading. .............................................. 160

Table 19. Chemical composition and tensile strength of Type 304L SS............................ 163
xxii

Table 20. Environmental conditions for fatigue tests in simulated PWR environment. ...... 163

Table 21. The conditions and results of fatigue tests on Type 304L austenitic SS at 

300°C in air and PWR environments using a triangular or complex strain 

cycle. ................................................................................................................ 165

Table 22. Summary of the key conditions and results of the U-bend tests at 240°C. ........ 168

Table 23. Chemical composition and tensile strength of Type 316 SS material. ............... 170

Table 24. Test matrix for the two blocks fatigue damage tests.......................................... 172

Table 25. Results of the two blocks fatigue damage tests................................................. 172

Table A.1. Fatigue design curves for carbon and low-alloy steels in air...............................A-5

Table A.2. Fatigue design curves for austenitic stainless steels in air. ................................A-5

Table C.1. Sample Problem Transient Definitions .............................................................. C-3

Table C.2. Limiting CUF Results for Sample Problem for SCL 2 .......................................C-12

Table C.3. CUFen Results Based for Sample Problem for SCL 2 (Average Strain Rate 

Approach)........................................................................................................C-14

Table C.4. CUFen Results Based for Sample Problem for SCL 2 (Modified Strain Rate 

Approach)........................................................................................................C-15

Table C.5. Principal Stress Intensity Histories Used in Limiting CUF Calculation for 

Sample Problem for SCL 2 ..............................................................................C-16
xxiii

EXECUTIVE SUMMARY

Cyclic loadings on a reactor pressure boundary component occur because of changes in 

mechanical and thermal loadings as the system goes from one load set (e.g., pressure, 

temperature, moment, and force loading) to another. The American Society of Mechanical 

Engineers (ASME) Boiler and Pressure Vessel Code Section III, Subsection NB contains rules 

for the design of Class 1 components of nuclear power plants and recognizes fatigue as a 

possible mode of failure in pressure vessel steels and piping materials. ASME Code Section III

fatigue analysis procedures consider all fatigue cycles based on the anticipated number of 

thermal and pressure transients, and for each load-cycle or load set pair, an individual fatigue 

usage factor is determined by the ratio of the number of cycles anticipated during the design 

lifetime of the component, as specified by the Owner, to the number of allowable cycles. 

Figures I–9.1 through I–9.6 of Mandatory Appendix I to Section III of the ASME Code specify 

fatigue design curves that define the allowable number of cycles as a function of applied stress 

amplitude. Those fatigue design curves have evolved significantly since the initial publication of 

Section III in 1963. However, Paragraph NB-3121 of the 2011 Addenda to Section III of the 

Code continues to state that the effects of coolant environments on the fatigue resistance of 

materials were not addressed in the fatigue design curves. Therefore, the effects of water 

environments on the fatigue resistance of materials used in operating pressurized water reactor 

(PWR) and boiling water reactor (BWR) plants, whose components were designed in 

accordance with the ASME Code Section III, may not adequately address long-term 

environmental effects on fatigue based on the data available at the time the fatigue design 

curves were derived. 

The current Section III design fatigue curves in air contained in Section III of the ASME Code 

were based primarily on strain–controlled fatigue tests of small polished specimens at room 

temperature in laboratory air environments. Best–fit curves to the experimental test data were 

first adjusted to account for the effects of mean stress and then lowered by a factor of 2 on 

stress and 20 on cycles (whichever was more conservative) to obtain the design fatigue air 

curves. These factors were not intended as “safety margins,” but rather they were intended as 

“adjustment factors” that were applied to the experimental laboratory data to obtain estimates of 

the fatigue lives of actual reactor components. Recent fatigue–strain–vs.–life (ε–N) data 

obtained primarily in the U.S. and Japan demonstrate that light water reactor (LWR) 

environments have potentially significant effects on the fatigue resistance of materials. 

Specimen lives obtained from laboratory tests in simulated LWR environments were much 

shorter than those obtained from corresponding tests in an air environment. 

In the original version of NUREG/CR-6909, the existing fatigue ε–N data for carbon and low–

alloy steels, wrought and cast austenitic stainless steels (SSs), and nickel-chromium-iron (Ni-CrFe) alloys in air and LWR environments were evaluated to identify the various material, 

environmental, and loading parameters that influence fatigue crack initiation. The results of 

those evaluations were used to establish the effects of key parameters on the fatigue lives of 

steels. The fatigue lives of materials were decreased in LWR environments; the magnitude of 

the reduction depended on the temperature, strain rate, dissolved oxygen (DO) level in the 

water, and, for carbon and low–alloy steels, the sulfur (S) content of the steels. For all steels, 

environmental effects on fatigue lives were significant only when critical parameters 

(temperature, strain rate, DO level, and strain amplitude) met certain threshold values. 

Environmental effects were moderate, e.g., less than a factor of 2 decrease in fatigue lives, 

when any one of the threshold conditions was not satisfied. The threshold values of the critical 

parameters and the effects of other parameters (such as water conductivity, water flow rate, and 

material heat treatment) on the fatigue lives of the steels were also discussed. 
xxiv

In this report, the comprehensive review of the fatigue ε–N data for nuclear power plant piping 

and pressure vessel steels presented in the original version of NUREG/CR-6909 was 

reevaluated using a much larger database. The results were updated to include this 

reevaluation, as well as to address concerns from interested stakeholders regarding the Fen

methodology for incorporating environmental effects into ASME Code Section III fatigue 

cumulative usage factor (CUF) evaluations. The resulting effects of various material, loading, 

and environmental parameters on the fatigue lives of steels are summarized in this report. 

The results indicated that the ASME Code Section III mean air curve for low–alloy steels is in 

good agreement with the available experimental data, and the ASME Code Section III mean air 

curve for carbon steels is conservative. In addition, the best-fit mean air data used to develop 

the fatigue design air curve for austenitic SSs in ASME Code Section III editions prior to 2009b 

Addenda is not consistent with the experimental data at strain amplitudes less than 0.5%; 

fatigue lives predicted by the ASME Code Section III mean air curve were longer than those 

obtained from experiments. Therefore, in the initial version of NUREG/CR-6909, new fatigue 

design air curves were developed for carbon and low-alloy steels and austenitic SSs that were 

based on the ANL fatigue life models and were consistent with the fatigue ε–N data available at 

that time. The air design curves were extended up to 1011 cycles using available high-cycle 

fatigue data. In 2009, the ANL design air curve for austenitic SSs was adopted into Mandatory 

Appendix I of Section III of the ASME Code. The reevaluation of the fatigue ε–N behavior of 

austenitic SS materials using a much larger database indicated that the air fatigue design 

curves previously developed by ANL are consistent with the available fatigue data, and do not 

warrant any modifications. However, in the present report, the extension of the air fatigue 

design curves for carbon and low-alloy steels up to 1011 cycles was modified to be consistent 

with the extension of the current ASME Code Section III fatigue design curve beyond 

106 cycles. 

The reevaluation results also indicated that the fatigue data for Ni-Cr-Fe alloys were not 

consistent with the current ASME Code mean air curve for austenitic SSs. The rather limited 

fatigue ε–N data for Ni-Cr-Fe alloys, such as Alloys 600, 690, and 800 and their welds, were 

consistent with the best-fit mean air curve for austenitic SSs at fatigue lives less than 104 cycles, 

and showed longer fatigue lives than the predicted values for fatigue lives greater than 

104 cycles. However, a separate air fatigue design curve was not developed for Ni-Cr-Fe alloys, 

and the current ASME Code fatigue air design curve for austenitic SSs, which is based on the 

ANL model, was used to represent the fatigue ε–N behavior of Ni-Cr-Fe alloys and associated 

weld metals. The data also indicated that the fatigue resistance of Inconel 718 is superior to 

that of the other Ni-Cr-Fe alloys. The slope of the Inconel 718 fatigue ε–N curve is flatter and 

the fatigue limit is higher than those for austenitic SSs. 

The fatigue lives of carbon and low–alloy steels, austenitic SSs, and Ni-Cr-Fe alloys were 

decreased in LWR environments. The reduction depended on some key material, loading, and 

environmental parameters. The fatigue ε–N data were consistent with the much larger 

database on enhancement of crack growth rates in these materials in LWR environments. The 

key parameters that influenced fatigue lives in these environments, e.g., temperature, DO level 

in the water, strain rate, strain (or stress) amplitude, and, for carbon and low–alloy steels, S 

content of the steel, were identified. In addition, the functional form of the dependence of 

fatigue lives on these parameters and the range of the values of these parameters within which 

environmental effects were significant was defined. If these critical loading and environmental 

conditions exist during reactor operation, then environmental effects may be significant and 

should be included in any relevant ASME Code Section III fatigue evaluations. 
xxv

In the initial version of NUREG/CR-6909 (published in 2007), fatigue life models were 

developed to predict the fatigue lives of small smooth specimens of carbon and low–alloy steels, 

wrought and cast austenitic SSs, and Ni-Cr-Fe alloys as a function of material, loading, and 

environmental parameters using the existing fatigue ε–N database. The functional form and 

bounding values of these parameters were based on experimental observations and data 

trends. An approach was presented that incorporated the effects of LWR coolant environments 

into the ASME Code Section III fatigue evaluations based on the environmental fatigue 

correction factor, Fen. The fatigue usage for a specific stress cycle or load set pair derived using 

the ASME Code Section III fatigue design air curves was multiplied by the Fen to account for 

environmental effects. 

In the present report, the Fen expressions were updated using a much larger fatigue ε–N 

database, primarily derived from extensive additional data provided from Japan. The updated 

expressions also address comments provided by interested stakeholders related to: (a) the 

constants in the Fen expressions that results in a Fen value of approximately 2 even when the 

strain rate is very high or temperature is very low, (b) the temperature dependence of Fen for 

carbon and low-alloy steels, and (c) the dependence of Fen on water chemistry for austenitic 

SSs. 

This report also presents a brief description of the mechanisms for fatigue cracking in air and 

LWR coolant environments. Fatigue life is conventionally divided into two stages: initiation and 

propagation. In LWR environments, the initiation stage involves the growth of microstructurally 

small cracks characterized by decelerating crack growth. The propagation stage involves the 

growth of mechanically small cracks characterized by accelerating crack growth. The available 

fatigue ε–N data indicated that LWR environments affect both the initiation and propagation of 

fatigue cracks. Two mechanisms are described in this report that potentially enhance both 

fatigue crack initiation and fatigue crack growth rates in LWR environments - slip 

oxidation/dissolution and hydrogen-induced cracking. The potential effects of dynamic strain 

aging on cyclic deformation and environmental effects are also discussed.

This report also presents a critical review of the ASME Code Section III fatigue adjustment 

factors of 2 on stress and 20 on life and assesses the possible conservatism in the choice of 

adjustment factors. Although these factors were intended to be conservative, they were not 

considered safety margins in the work presented in this report. Instead, these factors cover the 

effects of variables that influence fatigue lives but were not investigated in the experiments that 

were used to obtain the air fatigue design curves. Data available in the literature were reviewed 

to evaluate the factors on cycles that are needed to account for such differences and 

uncertainties. Monte Carlo simulations were performed to determine the factor on cycles 

needed to obtain a fatigue design curve in air that provided a conservative estimate of the 

number of cycles required to initiate a fatigue crack in reactor components. The results 

presented in the initial version of NUREG/CR-6909 indicated that, for carbon and low–alloy 

steels and austenitic SSs, the current ASME Code Section III requirements for a factor of 20 on 

cycles to account for the effects of material variability and data scatter, as well as size, surface 

finish, and loading history, may be decreased by at least a factor of 1.7. Thus, to reduce 

conservatism, fatigue design curves were developed based on the ANL fatigue life models and 

those curve were then adjusted for mean stress effects and by a factor of 2 on stress and 12 on 

cycles. These adjustments were made to account for the effects of four parameters - material 

variability and data scatter, size, surface finish, and loading sequence. In this report, the range 

of the these four parameters were modified and Monte Carlo simulations were repeated to 

determine the factor on cycles needed to obtain fatigue design curves in air. The results 

indicated that for carbon and low-alloy steels and austenitic SSs, a factor of 2 on stress and 10 

on cycles are adequate to develop air fatigue design curves from the best-fit mean air curves. 
xxvi

However, until these results are further validated with applicable fatigue data ε–N data, the air 

fatigue design curves presented in this report are based on factors of 2 on stress and 12 on life. 

The Fen methodology was also validated by comparing the results of several experimental data 

sets obtained from fatigue tests that simulated actual plant conditions with estimated fatigue 

usage using the updated Fen expressions. The data sets represented fatigue tests with 

changing strain rate and/or temperature, complex loading that simulated a PWR safety injection 

transient, spectrum loading (i.e., random strain amplitudes), and pipe U-bend tests. In all cases, 

the results indicated that the predicted fatigue lives were in good agreement with the 

experimental values; the differences between the experimental and predicted fatigue lives were 

within a factor of two, which is within the experimental data scatter. The predicted fatigue lives 

for the tests with the complex strain loading cycle were lower than the experimental values by a 

factor of about 2. The reason for this deviation was not clear but may be unique to the specific 

test loading cycle. Nonetheless, although the predicted lives were all lower, the estimated 

values were within the range of data scatter.

Finally, the detailed procedure for incorporating environmental effects into ASME Code Section 

III fatigue evaluations is presented.

Revision 1 of this report represents a comprehensive and detailed expansion of the Revision 0 

manuscript that incorporates significant additional background, test data, and test data 

descriptions. In addition, the content layout of the report was revised for clarity. As a result, the 

revisions made to the Revision 0 manuscript are not specifically identified throughout the text of 

this revision.
xxvii

ABBREVIATIONS

ANL Argonne National Laboratory

ANN Artificial Neural Network

ASME American Society of Mechanical Engineers

ASTM American Society for Testing and Materials

ATR Advanced Test Reactor

BTP Branch Technical Position

BNCS Board on Nuclear Codes and Standards

BWR Boiling Water Reactor

CGR Crack Growth Rate

CLEE Cyclic Life Environmental Effects

CT Compact Tension

CUF Cumulative Usage Factor

CVCS Chemical and Volume Control System

CW Cold Worked

da/dN Fatigue Crack Growth Rate (expressed as the change in crack depth, 

da, divided by the number of applied cycles, dN)

DO Dissolved Oxygen

DSA Dynamic Strain Aging

E Energy

EAC Environmentally Assisted Cracking

EBR II Experimental Breeder Reactor II

ECP electrochemical Potential

EFD Environmental Fatigue Data

EFT Environmental Fatigue Testing

EPR Electrochemical Potentiodynamic Reactivation

EPRI Electric Power Research Institute

ETR Experimental Test Reactor

FAP Fatigue Action Plan

GE General Electric Company

GSI Generic Safety Issue

H Hydrogen

HAZ Heat Affected Zone

He Helium

HWC Hydrogen Water Chemistry

ID Internal Diameter

IG Intergranular
xxviii

ABBREVIATIONS (continued) 

IHI Ishikawajima-Harima Heavy Industries

INEL Idaho National Engineering Laboratory

JAPEIC Japan Power Engineering and Inspection Corporation

JNES Japan Nuclear Energy Safety Organization

JNUFAD Revised and Renamed Fatigue Database “FADAL” from Japan 

KWU Kraftwerk Union Laboratories

LEFM Linear Elastic Fracture Mechanics

LWR Light Water Reactor

MA Mill Annealed

MEA Materials Engineering Associates 

MHI Mitsubishi Heavy Industries

mm Millimeters

MnS Manganese Sulfide

MOU Memorandum of Understanding

MPa Megapascals

MPA Materialprufungsanstalt

MSC Microstructurally Small Crack

N Number of Cycles

Nair Number of Cycles in Air

Nwater Number of Cycles in LWR Environment

Ni-Cr-Fe Nickel-Chrome-Iron

NPS Nominal Pipe Size

NRC Nuclear Regulatory Commission

NWC Normal Water Chemistry

OD Outer Diameter

ORNL Oak Ridge National Laboratory

ppb Parts Per Billion

ppm Parts Per Million

PSB Persistent Slip Band

PVRC Pressure Vessel Research Council

PWR Pressurized Water Reactor 

RCS Reactor Coolant System

RG Regulatory Guide

RHR Residual Heat Removal

RMS Root Mean Square 

RT Room Temperature

S Sulfur
xxix

ABBREVIATIONS (concluded) 

SICC Strain Induced Corrosion Cracking

SS Stainless Steel

T Temperature

TENPES Thermal and Nuclear Power Engineering Society

TG Transgranular

TMI Three Mile Island

UTS Ultimate Tensile Strength

VTT Valtion Teknillinen Tutkimuskeskus (Finnish: Technical Research 

Center of Finland)

VVER Voda-Vodyanoi Energetichesky Reaktor (Russian pressurized water 

reactor)

WRC Welding Research Council

YS Yield Strength

xxxi

ACKNOWLEDGMENTS

The authors are indebted to the Japan Nuclear Energy Safety Organization (JNES) for sharing 

their enormous fatigue (ε–N) database for use in the evaluations documented in this report. The 

authors are also grateful to Bill Shack for his invaluable input and guidance in preparing this 

report. The authors acknowledge Yogen Garud for his contributions and helpful comments. 

This work was co-sponsored by the Office of Nuclear Regulatory Research, U.S. Nuclear 

Regulatory Commission; Project Manager: Gary L. Stevens and the Electric Power Research 

Institute (EPRI) as Cooperative Nuclear Safety Research under the Environmentally Assisted 

Fatigue Effects Addendum to the NRC/EPRI Memorandum of Understanding (MOU), under 

NRC Job Codes V6069 and V6269. 

1

1. INTRODUCTION

The structural integrity of a metal component may gradually degrade when it is subjected to 

cyclic loading, even at magnitudes less than the design static loads, due to a well-known 

degradation mechanism called fatigue. The mechanism of fatigue damage can occur in flawfree components by developing cracks during service. The American Society of Mechanical 

Engineers (ASME) Boiler and Pressure Vessel Code Section III, Subsection NB, which contains 

rules for the design of Class 1 components for nuclear power plants, recognizes fatigue as a 

possible mode of failure in pressure vessel steels and piping materials. Fatigue is a major 

consideration in the design of rotating machinery and aircraft, where the components are 

subjected to a very large number of cycles, i.e., high–cycle fatigue. In these situations, the 

primary concern is the endurance limit, which is the stress level below which an infinite number 

of cycles can be applied without fatigue failure. However, cyclic loadings on a reactor pressure 

boundary component occur because of changes in mechanical and thermal loadings as the 

system goes from one load state to another. The number of cycles applied during the design 

life of the component seldom exceeds 100,000 and is typically less than a few thousand (e.g., 

low–cycle fatigue). The main difference between high–cycle and low–cycle fatigue is that the 

former involves little or no plastic strain, whereas the latter involves strains in excess of the yield 

strain. Therefore, design curves for low–cycle fatigue are based on tests in which strain rather 

than stress is the controlled variable.

The ASME Code fatigue evaluation procedures are described in NB-3200, “Design by Analysis,” 

and NB-3600, “Piping Design.” The ASME Code fatigue analysis considers all transient loads 

based on the anticipated number of thermal and pressure transients, and for each load-cycle or 

load set pair, an individual fatigue usage factor is determined by the ratio of the number of 

cycles anticipated during the lifetime of the component to the allowable cycles. Figures I–9.1 

through I–9.6 of Mandatory Appendix I to Section III of the ASME Boiler and Pressure Vessel 

Code specify fatigue design curves for various materials that define the allowable number of 

cycles as a function of applied stress amplitude. The cumulative usage factor (CUF) is the sum 

of the individual usage factors for all load set pairs, and ASME Code Section III requires that at 

each location the CUF, calculated based on Miner’s rule, must not exceed unity for acceptable 

fatigue design. 

Although the ASME Code Section III rules apply to Class 1 components, those fatigue design 

rules are sometimes applied to other classes of components to provide a robust fatigue design 

in situations where known fatigue issues exist or fatigue duty is high [e.g., Class 2 pressurized 

water reactor (PWR) feedwater nozzles]. As such, the methods described in this report are 

intended to apply to all components exposed to an LWR environment that utilize the fatigue 

calculation procedures from ASME Code Section III.

Revision 1 of this report represents a comprehensive and detailed expansion of the Revision 0 

manuscript that incorporates significant additional background, test data, and test data 

descriptions. In addition, the content layout of the report was revised for clarity. As a result, the 

revisions made to the Revision 0 manuscript are not specifically identified throughout the text of 

this revision.

1.1 Definition of Fatigue Life

Before discussing the fatigue design curves used in the ASME Code Section III fatigue CUF 

analysis, it is important to first define “fatigue life” in terms of its use in this report. In the 

American Society for Testing and Materials (ASTM) Designation E 1823-09a1 “Standard 

Terminology Relating to Fatigue and Fracture Testing,” fatigue life is defined as “the number of 
2

cycles of a specified character that a given specimen sustains before failure of a specified 

nature occurs. Fatigue life, or the logarithm of fatigue life, is a dependent variable.” 

Accordingly, the ASME Code fatigue design curves [i.e., stress amplitude (Sa) vs. number of 

cycles (N) curves] are generally considered to represent allowable number of cycles to failure. 

However, note that ASTM E1823 states that fatigue life is “failure of a specified nature.” 

Furthermore, Section 8.9 of ASTM Standard E 606-042 “Standard Practice for Strain-Controlled 

Fatigue Testing,” states that the definition of failure may vary with the ultimate use of the fatigue 

life information, and provides the following acceptable alternatives for determination of failure:

(i) Separation: Total separation or fracture of the specimen into two parts at (1) some 

location within the uniform section of the uniform-gage specimen, or (2) the vicinity of the 

minimum diameter in the hourglass specimen.

(ii) Modulus Method: For any specified number of cycles, N, during a fatigue test, the 

modulus for unloading following a peak tensile stress is defined as ENT and the modulus 

for loading following a peak compressive stress is ENC. Failure is defined as the number 

of cycles where the ratio ENT/ENC reaches one-half the value for the first cycle (i.e., is 

reduced by 50%). However, if total separation occurs first, as in item (i) above, fatigue 

life is defined by the number of cycles to separation.

(iii) Microcracking: The existence of surface microcracks (e.g., as observed optically or by 

replicas) that are larger than some preselected size consistent with the test objective.

(iv) Force (Stress) Drop: Failure is defined as the ability of a test specimen to sustain a 

tensile force (or stress). Failure is often defined as the point at which the maximum 

force (stress) or elastic modulus (as measured when unloading from a peak tensile 

stress) decreases by approximately 50% because of the presence of cracks. The exact 

method and the percentage drop should be documented. 

In the fatigue ε–N data used to develop the original ASME Code best-fit or mean-data curves,

failure was primarily defined as total separation or fracture of the specimen into two parts. 

However, in the fatigue tests performed during the last four decades, failure was defined 

according to the force (stress) drop method. In most of these tests, fatigue life was defined in 

terms of the number of cycles for the tensile stress to decrease 25% from its peak or steady–

state value (i.e., 25% load drop). For the typical cylindrical specimens used in these studies, 

this corresponded to the number of cycles needed to produce approximately 3–mm–deep 

cracks in test specimens. Thus, the fatigue life of a material was described in terms of three 

parameters, viz., strain or stress, cycles, and crack depth. The best–fit curve to the existing 

fatigue ε–N data describes, for a given strain or stress amplitude, the number of cycles needed

to develop a 3–mm deep crack. Note that, for consistency, all data used in this report were 

adjusted to be on an equivalent 25% load drop basis as discussed at the beginning of 

Chapter 3.

Based on the foregoing and the results of the majority of the test data evaluated, fatigue life is 

described in this report as the number of cycles of a specified strain amplitude that a specimen 

can sustain before the formation of a 3-mm-deep crack (i.e., an “engineering crack”). This 

equates to a 25% load drop in test specimens, and is assumed to equate to crack initiation in an 

actual component. Using this definition, a calculated fatigue CUF less than unity provides 

reasonable assurance that a fatigue crack has not formed in a component, and indicates that 

the probability of forming a crack in the component is low.
3

1.2 Air Fatigue Design Curves in Section III of the ASME Code

The ASME Code fatigue design curves, as given in Mandatory Appendix I of Section III, are 

based on strain–controlled tests of small polished specimens at room temperature in air. The 

data are typically obtained from fatigue tests conducted in accordance with ASTM Designation 

E 606-04 “Standard Practice for Strain-Controlled Fatigue Testing.” This practice covers the 

determination of fatigue properties of nominally homogeneous materials by the use of uniform 

gage section specimens subjected to axial strain-controlled, fully reversed (strain ratio, R, equal 

to -1) cycling. The practice is also applicable to hourglass specimens. The practice may be 

adapted to guide more general testing where strain or temperature may be varied according to 

application specific histories. The presentation and analysis of data are performed in 

accordance with ASTM Standard E 468, “Standard Practice for Presentation of Constant 

Amplitude Fatigue Test Results for Metallic Materials”3 and ASTM Standard E 739, “Standard 

Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε–N) 

Fatigue Data.”4 The guidance in Metals Handbook, Volume 8, “Fatigue Data Analysis”5 can 

also be used. The definitions of terms related to fatigue testing are described in ASTM 

Standard E 1823, “Standard Terminology Relating to Fatigue and Fracture Testing.”6

The design curves were developed from the best–fit curves to the experimental fatigue–strain–

vs.–life (ε–N) data, which are expressed in terms of the Langer equation7 of the form 

, (1)

where εa is the applied strain amplitude, N is the fatigue life, and A1, A2, and n1 are coefficients 

of the model. Equation 1 may be written in terms of stress amplitude Sa instead of εa. The 

stress amplitude is the product of εa and elastic modulus E, i.e., Sa = E⋅εa (stress amplitude is 

one-half the applied stress range). The current ASME Code best–fit or mean curve described in 

the Section III criteria document8 for various steels is given by 

, (2)

where E is the elastic modulus (MPa), Nf is the number of cycles to failure, and Af and Bf are 

constants related to reduction in area in a tensile test (percent) and endurance limit of the 

material at 107 cycles (MPa), respectively.7 The current Code mean curves were obtained from 

Eq. 2 and Af and Bf values of 68.5% and 149.2 MPa, 61.4% and 265.4 MPa, and 72.6% and 

299.9 MPa, respectively, for carbon steels, low-alloy steels, and austenitic stainless steels 

(SSs).8 Thus, using an elastic modulus of 206,843 MPa for carbon and low-alloy steels and 

179,264 MPa for austenitic SSs, the mean curves are expressed for carbon steels, as 

Sa = 59,734 (Nf)-0.5 + 149.2, (3)

for low-alloy steel, as 

Sa = 49,222 (Nf)-0.5 + 265.4, (4)

and for austenitic SSs, as 

Sa = 58,020 (Nf)-0.5 + 299.9. (5)
4

The fatigue ε–N data are typically expressed by rewriting Eq. 1 as

ln(N) = A – B ln(εa – C), (6)

where A, B, and C are constants; C represents the fatigue limit of the material; and B is the 

slope of the log-log plot of fatigue ε–N data. The ASME Code mean–data curves (i.e., Eqs. 3-5) 

may be expressed in terms of Eq. 6 as follows. The fatigue life of carbon steels is given by

ln(N) = 6.726 – 2.0 ln(εa – 0.072), (7)

for low-alloy steels, by

ln(N) = 6.339 – 2.0 ln(εa – 0.128), (8)

and, for austenitic SSs, the fatigue life corresponding to the fatigue design curve originally 

published in Section III of the ASME Code prior to the 2009b Addenda is given by

ln(N) = 6.954 – 2.0 ln(εa – 0.167), (9)

and, as derived in Section 3.2.6, the fatigue life corresponding to the fatigue design curves in 

2009b Addenda and later editions of the ASME Code, by 

ln(N) = 6.891 – 1.920 ln(εa – 0.112), (10)

where strain amplitude εa is in percent. The ε-N curve for austenitic SSs is also used for nickelchromium-iron (Ni-Cr-Fe) alloys (e.g., Alloy 600). 

The best-fit or mean-data curves (e.g., Eqs. 7-10) provide an estimate of the fatigue life that 

would lead to failure in 50% of the population under a given loading. However, as discussed 

later in this report, the ASME Code fatigue design curves are now defined to estimate

acceptable fatigue life for at least 95% of the population under a given loading. 

Another term that is often used in ASME Section III fatigue evaluations is fatigue limit (or 

endurance limit), which is defined as1 “the limiting value of the median fatigue strength as the 

fatigue life, Nf, becomes very large.” However, certain materials (e.g., carbon and low-alloy 

steels and austenitic SSs) and environments preclude the attainment of a fatigue limit. 

Therefore, in the literature, fatigue limit is typically defined as a value of stress, SN, for failure at 

a specified number of cycles, N (e.g., at 106 or 1011 cycles). 

The above ε–N curves describe the formation of engineering fatigue cracks in small, smooth 

test specimens in an air environment. To use the small-specimen data for actual reactor 

components, the best-fit ε–N curves for specimen data must be adjusted to account for the 

effects of variables that are known to affect fatigue life but were not accounted for in the smallspecimen data. Such variables include mean stress, surface finish, size, and loading history. 

Furthermore, the best-fit curve represents the average behavior of the material. To obtain a 

curve that assures a low probability for formation of fatigue cracks, the small specimen curve 

must also be adjusted to account for data scatter and material variability. 

The procedure used to develop the ASME Code fatigue design curves from the best-fit (or 

mean–data) curves for small specimens is as follows. First, the best-fit curves are adjusted to 

account for the effects of mean stress. This is necessary to account for mean stress effects not 
5

considered during specimen testing, such as weld residual stress. Mean stress was accounted 

for using the modified Goodman relationship given by

for < , (11)

and 

for > , (12)

where is the adjusted value of stress amplitude, and and are yield and ultimate 

strengths of the material, respectively. Equations 11 and 12 assume the maximum possible 

mean stress and typically give a conservative adjustment for mean stress. The original ASME 

Code Section III fatigue design curves were obtained by reducing the fatigue life at each point 

on the adjusted best-fit curve by a factor of 2 on strain (or stress) or 20 on cycles, whichever 

was more conservative. 

As described in the Section III criteria document,8 the factors of 2 and 20 are not safety margins,

but rather adjustment factors that were applied to the small–specimen data to account for the 

effects of variables that are known to affect fatigue life but were not accounted for in the smallspecimen data. These factors include (a) data scatter and material variability, (b) the 

differences in surface condition and size between the test specimens and actual reactor 

components, and (c) random load cycles as compared to constant strain cycles used to obtain 

the fatigue ε-N data. 

1.3 Subfactors Included in ASME Section III Air Fatigue Design 

Curves

In comments about the initial scope and intent of the ASME Code Section III fatigue design 

procedures, Cooper9 states that the factor of 20 on life was regarded as the product of three 

subfactors: 

Scatter of data (minimum to mean) 2.0

Size effect 2.5

Surface finish, atmosphere, etc. 4.0

Although the ASME Code Section III criteria document8 states that these factors were intended 

to cover such effects as environment, Cooper9 further states that the term “atmosphere” was 

intended to reflect the effects of an industrial atmosphere in comparison with an air-conditioned 

laboratory, which are different than the effects of a specific coolant environment. In addition, 

surface finish represented surface roughness of industrial-grade component surface compared 

to that of a polished test specimen. Subsubarticle NB-2160 (or Subsubarticle NG-2160 for core 

support structures) of Section III of the ASME Code states, “It is the responsibility of the Owner 

to select material suitable for the conditions stated in the Design Specifications (NCA-3250), 

with specific attention being given to the effects of service conditions upon the properties of the 

material.” The minimum contents of the Design Specifications are specified in Paragraph NCA3252 of Section III of the ASME Code. Paragraph NCA-3252(a)(3) states that the Design 

Specifications shall include “the environmental conditions, including radiation.” The 

environmental conditions that are likely to influence the properties of materials used in nuclear 
6

power plant structures and components include temperature, reactor coolant environment, and

neutron irradiation. 

Furthermore, Paragraph NB–3121 of Section III of the ASME Code (or Paragraph NG-3121 for 

core support structures) states, “It should be noted that the tests on which the fatigue design 

curves (Figs. I-9.0) are based did not include tests in the presence of corrosive environments 

which might accelerate fatigue failure.” Paragraph B-2131 in Nonmandatory Appendix B to 

Section III, “Owner’s Design Specifications,” states that the Owner's Design Specification should 

provide information about, “any reduction to design stress intensity values, allowable stress, or 

fatigue design curves that is necessitated by environmental conditions.” 

1.3.1 Effects of Reactor Coolant Environment on Fatigue Lives

Existing fatigue ε–N data (Fig. 1) illustrate potentially significant effects of light water reactor 

(LWR) coolant environments on the fatigue resistance of carbon and low–alloy steels, wrought 

and cast austenitic SSs, and Ni-Cr-Fe alloys.10-75 Small-scale laboratory fatigue test data 

indicate that under certain reactor operating conditions, fatigue lives of carbon and low–alloy 

steels can be a factor of 17 lower in the coolant environment than in air. Therefore, the factors 

in the ASME Code may be less conservative than originally intended.

The fatigue ε–N data are consistent with the much larger database on enhancement of crack 

growth rates (CGRs) in these materials in simulated LWR environments. The key parameters 

that influence fatigue life in these environments are temperature, the dissolved–oxygen (DO) 

level in the water, strain rate, strain (or stress) amplitude, and, for carbon and low–alloy steels, 

the sulfur content of the steel. The range of the values for these parameters within which 

environmental effects are significant has also been defined. If these critical loading and 

environmental conditions exist during reactor operation, then environmental effects may be 

significant and should be included in any associated ASME Code fatigue evaluations. 

Experience with nuclear power plants worldwide indicates that the critical range of loading and 

environmental conditions that leads to environmental effects on formation of fatigue cracks can 

and do occur during plant operation.56,76-92 It therefore is important that component design 

include consideration of environmental effects to prevent premature fatigue failures.

Experience with operating nuclear power plants worldwide reveals that many failures of reactor 

components were attributed to fatigue; examples include piping, nozzles, valves, and pumps.76-

83 In most cases, these failures were associated with thermal loading due to thermal 

Figure 1. Fatigue ε-N data for low-alloy steels and austenitic stainless steels in water 

compared to ASME Air Design Curve; RT = room temperature. 

101 102 103 104 105 106

0.1

1.0

10.0

Austenitic 

Stainless Steels

Fatigue Life (Cycles)

ASME Code

Mean Curve

RT Air

ASME Code 

Design Curve

Temp. (°C)

DO (ppm)

Rate (%/s) 

250–325

≈0.005

≤0.01

: 100–200

: ≈0.005

: 0.001-0.4

260–325

≥0.2

≥0.1

Strain Amplitude, εa (%)
7

stratification and striping, or mechanical loading due to vibratory loading. In piping components, 

several failures were associated with thermal loading due to thermal stratification and striping. 

Thermal stratification was typically caused by the injection of low–flow, relatively cold feedwater 

during plant startup, hot standby, and variations below 20% of full power, whereas thermal

striping was caused by rapid, localized fluctuations of the interface between hot and cold 

feedwater. 

Thermal loading due to flow stratification or striping was not typically included in the original 

design basis analyses for most U.S. nuclear power plants. Regulatory evaluation indicated that 

high-cycle thermal–stratification loading can occur in PWR surge lines as a result of in-surge 

and out-surge during heatup/cooldown transients.93 During heatup or cooldown, when, the 

pressurizer water is heated to approximately 227°C (440°F), the hotter water can flow at a very 

low rate from the pressurizer through the surge line to the hot–leg piping over the cooler water 

layer in the piping. The thermal gradients between the upper and lower parts of the pipe can be 

as high as 149°C (300°F). As a result, all U.S. PWRs performed revised fatigue analyses to 

address thermal stratification effects in surge lines. Furthermore, the effect of these loadings 

may also be aggravated by corrosion effects due to a high–temperature aqueous environment. 

The increased fatigue duty caused by such thermal loading increases the importance of 

evaluating environmental effects. 

The mechanism of cracking in feedwater nozzles and piping was attributed to corrosion fatigue 

or strain–induced corrosion cracking (SICC).84-86 Case histories and identification of conditions 

that lead to SICC of low–alloy steels in LWR systems were summarized by Hickling and Blind. 

A review of significant occurrences of corrosion fatigue damage and failures in various nuclear 

power plant systems was presented in an Electric Power Research Institute (EPRI) report.56 An 

assessment of the U.S. experience related to PWR primary system leaks observed during the 

period 1985 through 1996 was presented by Shah et al.88 

Hirschberg et al. summarized the operating experience regarding thermal fatigue of non–

isolable piping connected to PWR reactor coolant system (RCS).87 Significant cracking 

occurred in non-isolable sections of the safety injection system and residual heat removal 

(RHR) system piping connected to the PWR coolant system.89,90 At Farley, cracking occurred 

in the heat affected zone (HAZ) of the weld between the first elbow and the horizontal pipe, 

≈0.9 m (36 in.) from the RCS cold–leg nozzle. At Tihange, the crack was located in the base 

metal of an elbow, ≈0.6 m (24 in.) from the RCS hot–leg nozzle. At the Genkai plant, cracking 

occurred in the RHR suction line at the weld between the first elbow downstream of the hot–leg 

nozzle and the horizontal pipe section. Cracking due to thermal fatigue also occurred in the 

safety injection system at Dampierre 1 and 2 plants, and in the chemical and volume control 

system (CVCS) in Obrigheim plant. In all cases, thermal cycling was caused by interaction of 

hot RCS fluid from turbulent penetration at the top of the pipe, and cold valve leakage fluid that 

stratified at the bottom of the pipe. At Genkai, the valve internals alternately shrunk and 

expanded causing periodic leakage of hot fluid through the stem packing and leak-off line into 

the elbow. 

Thermal stratification, however, can occur even in the absence of valve leakage. The results of 

fatigue monitoring indicate that many PWR plants measured thermal–stratification cycling in the 

RHR suction line because of turbulence penetration of the hot leg fluid extending into the 

horizontal pipe section, which then stratified due to normal convection.87 For thermal 

stratification, the length of the vertical pipe section of the RHR suction line must be short 

enough for the hot fluid to reach the horizontal pipe section, and the length of the horizontal pipe 

section must be long enough to cause sufficient heat losses for stratification to develop. A 
8

typical temperature gradient of 49°C (120°F) was observed for typical cases of stratification, and 

temperature gradients as high as 177°C (350°F) were measured in some plants. 

Non-isolable leaks due to thermal–stratification cycling also occurred in reactor coolant loop 

drain lines, excess letdown lines, and makeup/high pressure injection lines at the Three Mile 

Island (TMI), Loviisa 2, Mihama, and Oconee plants.87,88 A leak in the cold–leg drain line 

[1.5 in. or 2 in. National Pipe Size (NPS)] occurred in the weld between the first elbow 

downstream of the loop nozzle and the horizontal pipe section at TMI, and in the elbow extrados 

at Oconee. In both cases, thermal stratification was caused by turbulence penetration of the 

RCS fluid periodically extending into the horizontal section and, because the pipe was not 

insulated, it stratified due to heat loss. The same mechanism caused a leak in the 2 in. NPS 

excess letdown line at Mihama. Whereas the Mihama line was insulated, stratification still 

occurred because the length of the horizontal section to the isolation valve was very long, 

resulting in significant heat loss. 

Thermal fatigue caused leaks in a connecting pipe and shell of the regenerative heat exchanger 

in the CVCS at Tsuruga 2,91,92 and in a 250–mm pipe section of the heat exchanger bypass on 

the RHR system at Civaux 1.76 Thermal–hydraulic mock–up tests indicate that at Tsuruga,

superposition of low–frequency temperature gradients due to changes in the flow pattern and 

high frequency temperature fluctuations due to mixing of the bypass flow and main flow caused 

thermal fatigue.91,92 

Cracking also occurred in austenitic SS channel heads in an experimental test loop used for 

stress corrosion cracking studies in a simulated PWR environment.94 Cracks were observed in 

a region that was subjected to temperature fluctuations between 170 and 190°C at a frequency 

of 0.05 Hz. The cracks initiated on the inner surface; the cracking morphology was essentially 

transgranular with fatigue–like striations visible in some regions of the fracture surface. Thermal 

fatigue, with possible effects of the PWR coolant environment, was concluded to be the root 

cause of these failures.94 

Such cracking in non-isolable pipe sections due to thermal cycling was generally termed as 

high–cycle fatigue, i.e., it occurs at stress levels that correspond to allowable fatigue cycles of 

105 or higher. The current understanding of turbulent penetration is not sufficient to accurately 

predict the frequency of thermal cycling associated with that phenomenon. Environmental 

effects on fatigue crack initiation may be significant in low–DO water at stress levels above the 

threshold value and at strain rates less than 0.4 %/s. 

Lenz et al.85 showed that in feedwater lines, the strain rates are 10–3–10–5%/s due to thermal 

stratification and 10–1%/s due to thermal shock. They also reported that thermal stratification is 

the primary cause of crack initiation due to SICC. Stephan and Masson95 subjected a full–scale 

mock–up of the steam generator feedwater system to various regimes of stratification. After 

4000 cycles of applied loading, destructive examination performed between two locations where 

stable states of stratification occurred revealed small cracks, 1.4–2.0 mm deep, in the weld 

region. The fatigue usage factors calculated with elastic and cyclic elastic–plastic computations 

gave values of 1.3–1.9. Because the average DO level in the water was approximately 5 ppb, 

which corresponds to the maximum admissible value under normal operating conditions (power 

greater than 25% nominal power) in French PWRs, environmental effects on life were expected 

to be minimal and environmental correction factors were not applied in the computations of the 

fatigue usage factor. 

Full–scale mock-up tests to generate thermal stratification in a pipe in a laboratory confirmed 

the applicability of laboratory data to component behavior.96 The material, loading, and 
9

environmental conditions were simulated on a 1:1 scale using only thermo-hydraulic effects. 

Under the conditions of strain rate and strain range typical of thermal stratification in these 

piping systems, the coolant environment has a significant effect on fatigue crack initiation.12,29,30

Finally, a study conducted on SS pipe bend specimens in simulated PWR primary water at 

240°C concluded that reactor coolant environment has a significant effect on the fatigue life of 

SSs.97-99 Relative to fatigue lives in an inert environment, lives in a PWR environment at strain 

amplitudes of 0.4% and 0.6% were decreased by factors of 2.9 and 1.4 at strain rates of 

0.0005 %/s and 0.01 %/s, respectively. These values show very good agreement with the 

values predicted from the Argonne National Laboratory (ANL) models presented later in this 

report for incorporating environmental effects into the ASME Code Section III fatigue 

evaluations.

1.3.2 Effects of Neutron Irradiation 

The potential effects of neutron irradiation on the fatigue life of reactor structural materials such 

as low-alloy pressure vessel steel, austenitic stainless steels, and Ni-Cr-Fe alloys and their weld 

metals are not fully characterized. Irradiation effects were not included in the ASME Code 

Section III fatigue evaluations performed for reactor core support structures and reactor internal 

components. The majority of the existing data on the effects of neutron irradiation resulted from 

fatigue crack growth tests on austenitic SSs that were irradiated in fast reactors [primarily 

Experimental Breeder Reactor II (EBR-II)] at test temperatures of 427 (800°F) and 593°C 

(1100°F).100-104 The CGR test results indicated that for Type 304 and 316 SS irradiated at 405-

410°C (760-770°F) to 1.2x1022 n/cm2 (E>0.1 MeV) fluence, the fatigue CGRs at 427°C (800°F) 

were up to a factor of 2 higher than those for unirradiated material at low values of stress 

intensity factor range (∆K) [less than 40 ksi in.1/2 (43.9 MPa m1/2)], but were lower for higher ∆K 

values. These observations were reversed at 593°C (1100°F). Crack growth rates were 

comparable or lower at higher values of ∆K. A similar behavior was observed for Type 316 weld

metal. Tests on Type 304 and 316 SS irradiated in a thermal reactor [Advanced Test Reactor 

(ATR)] at 288°C (550°F) to 1.8x1021 n/cm2 (E>0.1 MeV) and tested at 427°C (800°F) showed 

superior resistance to crack growth; CGRs were 25 to 50% lower than those for unirradiated 

material.105 Based on these studies EPRI concluded,106 “The work of several researchers 

suggest that neutron irradiation does not result in a further reduction in fatigue properties and in 

some cases suggest an improvement.” 

Other limited fatigue ε–N data on materials irradiated under LWR conditions and tested at LWR 

operating temperatures also showed significant differences in the microstructure and 

microchemistry of LWR irradiated materials, and materials irradiated in fast neutron test 

reactors. Specifically, cavities and helium (He) bubbles were observed in austenitic SSs 

irradiated at a temperature of 320°C (608°F) to high neutron fluence levels in PWRs. Such 

microstructures could lead to embrittlement of the material.107 Therefore, fatigue data on LWR 

irradiated materials should be developed to further quantify the effects of neutron irradiation on 

fatigue lives. 

Fatigue ε–N data on irradiated Type 308 SS weld metals showed moderate decreases in fatigue 

lives in the low-cycle regime and superior fatigue lives in the high-cycle regime.108 Similar

effects from neutron irradiation were also observed on the room-temperature fatigue ε–N 

behavior of Type 347 SSs irradiated in the Engineering Test Reactor (ETR) at 60°C (140°F) to 

total integrated fast flux (>1 MeV) exposures of 5.5x1025, 1.1x1026, and 1.6x1026 n/m2, as 

shown in Fig. 2a.109 Neutron irradiation decreased the room-temperature fatigue lives of Type 

347 SSs at high strain amplitudes (above 0.35%) and had beneficial effects on fatigue lives at 

low strain amplitudes (below 0.25%). The decreases in fatigue lives increased with increased 
10

total neutron doses. The reductions in fatigue lives were likely related to the irradiation-induced 

decreases in ductility of the materials. 

The fatigue test results also indicated significant differences in the cyclic hardening behavior of 

the irradiated materials relative to unirradiated materials. Typically, at room temperature, 

austenitic SSs exhibited strain softening after the initial cyclic hardening during the first ten

cycles. For the irradiated Type 347 SSs, although total strain was held constant, the plastic 

strain varied significantly during the fatigue tests, as shown in Fig. 2b. The plastic strains were 

insignificant initially and increased gradually during the fatigue tests due to strain softening until 

a later stage where plastic strains started to decrease due to secondary strain hardening and 

formation of fatigue cracks in the specimens. The extent of strain softening increased with 

increased neutron doses (Fig. 2b). The rapid increases in plastic strains near the end of the 

tests were associated with specimen fracture. In contrast, the unirradiated Type 347 SSs 

exhibited slight strain hardening and plastic strain decreased at a very low rate; later, the 

materials also showed faster decreases in plastic strains because of secondary strain hardening 

and formation of fatigue cracks. Thus, the impact of irradiation on fatigue life is not readily 

apparent from these data because of several competing factors.

The fatigue ε–N data on cold-worked (CW) Type 316 SS tube materials and solution-annealed 

Type 304 bar materials removed from an operating PWR are shown in Figs. 3 and 4, 

respectively.110 The data were obtained in simulated PWR water at 325°C (617°F) on CW 

Type 316 SS tube specimens with a 6.48 mm outer diameter and a 0.71 mm wall thickness. 

The tube specimens were irradiated to fluence values of less than 1022, 2 - 6x1025, and greater 

than 3x1026 n/m2 (E>0.1MeV), while the 5.08-mm diameter cylindrical specimens of Type 304 

SS were irradiated to fluence levels ranging from 5x1025 to 1026 n/m2 (E>0.1MeV). However, 

the baseline fatigue data for the unirradiated materials for the same heats of SSs were not 

available. To determine the possible effects of specimen configuration (i.e., solid cylindrical vs. 

thin-walled tube specimens), fatigue tests using the two specimen geometries were conducted 

on another heat of CW Type 316 SS in air at 325°C. The results indicated that the fatigue 

strengths of the solid specimens were 1.4 times those of the cylindrical tube specimens. The 

ASME Code Section III best-fit mean air curves for austenitic SSs are shown in the plots in 

Figs. 3 and 4 for comparison. Based on these test results, the authors concluded, “The fatigue 

life of irradiated SS was longer than that of unirradiated SS in the range of this research, that is, 

(a) (b)

Figure 2. The effects of neutron irradiation on fatigue lives of Type 347 SSs at room 

temperature: (a) the fatigue ε–N behavior, and (b) variations in plastic strain 

amplitude as a function of fatigue cycles (Ref. 109).

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100 101 102 103 104

Plastic Strain Amplitude, εp (%)

Fatigue Cycles

Type 347 SS

Unirradiated

5.5 x 1025 n/m2

1.1 x 1026 n/m2

1.6 x 1026 n/m2
11

strain amplitude was less than 0.6%. This increase in fatigue strength was considered due to 

an increase of tensile strength after irradiation.” 

In the absence of sufficient baseline fatigue data on unirradiated materials, the above 

conclusion that the fatigue lives of irradiated materials are longer than those of unirradiated 

materials is not fully justified. For example, the fatigue lives of irradiated Type 304 SSs in air 

are close to the ASME Code Section III best-fit mean curves. However, the effects of neutron 

irradiation are not available because there is insufficient fatigue ε–N data in air on unirradiated 

materials for these heats of Type 304 SSs. The fatigue data for irradiated CW Type 316 SSs 

were obtained on thin-walled tube specimens, and were not consistent with the ASME Code 

Section III mean air curve for austenitic SSs because the majority of the data were obtained 

from solid cylindrical specimens. The experimental ε–N behavior showed a lower ε–N slope 

than that for the ASME Code Section III mean curve (Fig. 3). Even after adjusting by a factor of 

1.4 on strain to account for the effect of specimen geometry, the fatigue lives in air at 0.3% 

strain amplitude fall to the right of the ASME Code Section III mean curve, whereas, the fatigue 

lives at 0.6% strain amplitude are significantly to the left. The primary reason for this 

inconsistency is likely caused by inadequate specimen size (tube specimens with 0.71-mm thick 

wall) for fatigue tests performed at high strain amplitudes. However, the fatigue data in Figs. 3

and 4 show that fatigue lives of austenitic SSs were decreased in a PWR primary water 

environment. Except for the data on CW Type 316 SSs irradiated to a fluence greater than 

3x1026 n/m2, the data for irradiated materials and the data for irradiated Type 304 SSs show 

lower fatigue lives in PWR primary water environment compared to those in air. The effects of 

the environment increase with decreasing strain rates.

The limited available data are inconclusive with regard to the impact of irradiation on the fatigue 

lives of materials exposed to LWR environments. Although some small-scale laboratory fatigue 

ε–N test data indicate that neutron irradiation decreases the fatigue lives of austenitic SSs, 

particularly at high strain amplitudes, it is not possible to quantify the impact of irradiation on the 

prediction of fatigue lives based on the limited data currently available. Additional fatigue data 

on reactor structural materials irradiated under LWR operating conditions are needed to 

determine whether there are measurable effects of neutron irradiation on the fatigue lives of 

these materials and, if so, to better define how those impacts may be quantified. In the absence 

of such data, the methods described in this report are considered appropriate for application to

materials exposed to significant levels of irradiation, such as SS reactor internals components, 

when mandated by regulation or required by the current licensing basis.
12

Figure 4.

Strain amplitude vs. fatigue life data 

in 325°C air and simulated PWR 

primary water environments for Type 

304 SS irradiated to 5x1025–1026 n/m2

(E > 0.1 MeV) (Ref. 110).

(a) (b)

Figure 3.

Strain amplitude vs. fatigue life data in 

325°C air or simulated PWR primary 

water environments for CW Type 316 

SS irradiated to (a) less than 1022, 

(b) 2-6x1025, and (c) greater than 

3x1026 n/m2 (E > 1.0 MeV) (Ref. 110).

(c)
13

1.4 Modeling of Environmental Effects 

In 1991, the U.S. Nuclear Regulatory Commission (NRC) issued a draft Branch Technical 

Position (BTP) for fatigue evaluation of nuclear plant components for license renewal. The BTP 

raised a concern about the adequacy of the ASME Code in addressing environmental effects on 

fatigue resistance of materials for operating PWRs and boiling water reactors (BWRs), whose 

primary–coolant pressure boundary components were constructed as specified in Section III of 

the ASME Code. In 1993, the Commission directed the NRC staff to treat fatigue as a potential 

safety issue within the existing regulatory process for operating reactors. The staff developed a 

Fatigue Action Plan (FAP) to resolve three principal issues: (a) adequacy of fatigue resistance 

of older vintage plants designed to the United States of America Standard B31.1 Code that did 

not require an explicit fatigue analysis of components, (b) effect of LWR environments on the 

fatigue resistance of primary pressure boundary materials, and (c) appropriate corrective action 

required when ASME Code fatigue allowable limits are exceeded, i.e., when the CUF is greater 

than unity. 

The Idaho National Engineering Laboratory (INEL) assessed the significance of ANL-developed 

interim fatigue design curves, by performing fatigue evaluations of a sample of components in 

the reactor coolant pressure boundary.111 In all, six locations were evaluated from facilities 

designed by each of the four U.S. nuclear steam supply system vendors. Selected components 

from older vintage plants designed according to the B31.1 Code were also included in the 

evaluation. Conservatism in the original fatigue evaluations, e.g., actual loading cycles instead 

of assumed cycles, was removed, and fatigue usage was evaluated with a fatigue design curve 

that considered the effects of the coolant environment. The results indicated that most of the 

locations had a CUF of less than the ASME Code limit of 1.0 for 40 years. The risk to reactor–

coolant pressure boundary components from failure due to fatigue was assessed under Generic 

Safety Issue (GSI) 78, “Monitoring of Fatigue Transient Limits for the Reactor Coolant System,” 

and GSI-166, “Adequacy of Fatigue Life of Metal Components.”112 Based on these studies, it 

was concluded113 that no immediate action was necessary to address the three fatigue issues 

identified in the FAP. A risk study indicated that fatigue failure of piping was not a significant 

contributor to core damage frequency. Based on the risk assessment, a backfit to incorporate 

environmental effects into the fatigue analyses of operating plants was not justified.114 

However, because the NRC studies were less certain that the conservatism in the original 

fatigue calculations could be used to account for an additional 20–years of operation, the NRC 

staff recommended that environmental effects be considered by evaluating the sample locations 

in the INEL study (NUREG/CR-6260)111 for plants pursuing license renewal. These 

recommendations were documented in GSI-190, “Fatigue Evaluation of Metal Components for 

60-year Plant Life.”112 Based on probabilistic analyses and sensitivity studies, interactions with 

the industry, and various programs available to licensees to manage the effects of aging, it was 

concluded that no generic regulatory action was required. For some components, although 

cumulative probabilities of crack initiation and through-wall cracks approached 1.0 for the 

renewal period, the maximum failure rate was generally low, in the range of 10–2 through-wall 

cracks per year. 

In addition, the predicted failure rates were generally associated with high CUF locations and 

components with thin walls; in most cases, any leakage that might result from these throughwall cracks was estimated to be small and not likely to lead to core damage. However, the 

calculations that supported the resolution of this issue indicated the potential for an increase in 

the frequency of pipe leaks as plants continue to operate. Thus, the NRC staff recommended 

that aging–management programs for license renewal should address component fatigue, 

including the effects of the reactor coolant environment. It should, however, be noted that when 
14

the INEL study was performed, it was not known that the effects of high-temperature reactor 

coolant environment on fatigue cracking of austenitic SSs are greater in low-DO environments 

than in high-DO environments. Thus, the six sample locations evaluated in the INEL study may 

not necessarily be the bounding locations for some plants, and additional plant-specific 

component locations than those considered in NUREG/CR-6260 should be included in the 

fatigue CUF evaluations, including the effects of environment.

In 1991, the ASME Board on Nuclear Codes and Standards (BNCS) requested the Pressure 

Vessel Research Council (PVRC) to examine the existing worldwide ε–N data and develop 

recommendations for the ASME. The PVRC compiled and evaluated fatigue ε–N data related 

to the effects of LWR coolant environments on the fatigue life of pressure boundary materials; 

the results were summarized by Van Der Sluys and Yukawa.115,116 The staff agreed with the 

concept of using an environmental correction factor (Fen) approach to obtain fatigue usage 

reflecting environmental effects for ASME Code Section III fatigue evaluations. This information 

was forwarded to the appropriate ASME Code committee.117

An analysis of the existing fatigue ε–N data and the procedures for incorporating environmental 

effects into ASME Code Section III fatigue evaluations was presented in several review 

articles115,116,118–126 and ANL reports.10,12,13,45–47 The fatigue ε-N data in air and LWR 

environments were also examined from the standpoint of fracture mechanics and CGR data.127

,128 Further details are presented in the next section of this report. The key material, loading, 

and environmental parameters that influence the fatigue lives of carbon, low–alloy, and 

austenitic stainless steels were identified, and the range of these key parameters where 

environmental effects are significant, was defined. Two approaches were proposed for 

incorporating the environmental effects into ASME Section III fatigue evaluations for primary 

pressure boundary components in operating nuclear power plants: (a) develop new fatigue 

design curves for LWR applications, or (b) use an environmental fatigue correction factor to 

account for the effects of the coolant environment. 

In the first approach, following the same procedures used to develop the fatigue design curves 

in ASME Code Section III, environmentally adjusted fatigue design curves were developed from 

fits to experimental data obtained in LWR environments. Interim fatigue design curves that 

address environmental effects on the fatigue life of carbon, low–alloy, and austenitic stainless 

steels were first proposed by Majumdar et al.129 However, as mentioned above, the “interim” 

fatigue design curve for austenitic SSs was based on little or no data in low-DO environments. 

As a result, at the time of the development of the interim design curves, it was not known that 

the effects of high-temperature reactor coolant environment on fatigue lives are greater in lowDO environments than in high-DO environments. Fatigue design curves based on a more 

rigorous statistical analysis of experimental data were developed by Keisler et al.130 These 

design curves were subsequently revised based on updated ANL models.10,12,45,46 However, in 

LWR environments, the fatigue life of carbon and low–alloy steels, Ni-Cr-Fe alloys, and 

austenitic SSs depends on several loading and environmental parameters. Therefore, such an 

approach requires development of several design curves to cover all possible environmental 

conditions encountered during plant operation. Depending on the number of such design 

curves for the desired loading and environmental conditions, development of additional curves 

may be a significant undertaking.

The second approach, proposed by Higuchi and Iida in 1991,19 considers the effects of reactor 

coolant environments on fatigue life in terms of an environmental fatigue correction factor, Fen, 

that is defined as the ratio of fatigue life in air at room temperature to that in water under reactor 

operating conditions. To incorporate environmental effects into fatigue evaluations, this 

approach required that the fatigue usage factor for a specific stress cycle or load set pair, based 
15

on the ASME Code Section III design fatigue curves, be multiplied by the environmental fatigue 

correction factor. Specific expressions for Fen, based on the ANL fatigue life models, were 

developed.10,45 Such an approach is relatively simple for application to previously-developed 

fatigue analyses and is recommended in this report. A similar methodology was also developed 

in Japan by the Environmental Fatigue Data (EFD) Committee of the Thermal and Nuclear 

Power Engineering Society (TENPES) under the Project on Environmental Fatigue Testing 

(EFT). The EFT was also supported by the Japan Power Engineering and Inspection 

Corporation (JAPEIC) and the Japan Nuclear Energy Safety (JNES) Organization, and some 

utilities.131-135 Updated technical results were published in a JNES report,136 JNES-SS-1005 

“Environmental Fatigue Evaluation Method for Nuclear Power Plants.” All of that data were 

considered in the results documented in this report.

In 2007, the original version of NUREG/CR-6909,137 which is the technical basis document for 

NRC Regulatory Guide (RG) 1.207, Revision 0, “Guidelines for Evaluating Fatigue Analyses 

Incorporating the Life Reduction of Metal Components Due to the Effects of the Light Water 

Reactor Environment for New Reactors,” presented an overview of the existing fatigue ε–N data 

for carbon and low–alloy steels, Ni-Cr-Fe alloys, and wrought and cast austenitic SSs in air and 

LWR environments. The existing fatigue ε–N data were evaluated to (a) identify the various 

material, environmental, and loading parameters that influence fatigue cracking, and 

(b) establish the effects of key parameters on the fatigue lives of these steels. Fatigue life 

models, presented in earlier reports for estimating fatigue life as a function of material, loading, 

and environmental conditions were updated using the fatigue ε–N database available at that 

time. The report also described the Fen approach for incorporating effects of LWR environments 

into ASME Section III fatigue evaluations, and presented a critical review of the ASME Code 

fatigue adjustment factors of 2 on stress (or strain) and 20 on life to assess the possible 

conservatism in the choice of adjustment factors. The Fen methodology was identified as 

applicable to all reactor coolant pressure boundary components exposed to reactor water that 

require an ASME Section III fatigue CUF calculation.

This report presents a revision to the original version of NUREG/CR-6909 in its entirety. The 

Fen expressions were updated using a much larger fatigue ε–N database. The additional data 

include the JNES data summarized in JNES-SS-1005 on carbon and low-alloy steels, wrought 

and cast austenitic SSs, and Ni-Cr-Fe alloys, and their associated weld metals, tested in air and 

LWR environments,136 and fatigue ε–N test results from the open literature on several heats of 

carbon and low-alloy steels tested in BWR environments.138-146 we have not used any bending 

tests in our environmental effects analysis. Most of the data evaluated for this report were 

obtained from completely reversed, axial, strain-controlled tests on small laboratory specimens. 

The results from a small number of bending tests were also considered for austenitic stainless 

steels in air (see Table 6 in Section 3.2.1), Ni-Cr-Fe alloy steels in air (see Table 9 in 

Section 3.3), and carbon and low-alloy steels in water (see Table 10 in Section 4.1.1). These 

data were included to improve the best fit evaluation of the fatigue life data. Section 3.2.2 

includes figures that support the use of these bending test data for austenitic stainless steels, 

which show that the bending test data points fall evenly on both side of the best fit curve of all 

the data. Only a small number of high-cycle fatigue tests conducted in load control were 

considered.

The updated environmental fatigue expressions in this report also address comments from 

interested stakeholders related to: (a) the constants in the Fen expressions that results in a Fen

value of approximately 2 even when the strain rate is very high or temperature is very low, 

(b) the temperature dependence of Fen for carbon and low-alloy steels, and (c) the dependence 

of Fen on water chemistry for austenitic SSs. Finally, the updated methodology described in this 

report applies to any component exposed to the LWR environment that requires an ASME CUF 
16

calculation as part of its design, or if required by the safety basis for the component, or if 

required by the plant current licensing basis, unless otherwise justified.

In addition, the appropriateness of a strain threshold and the possible effects of hold periods 

were also evaluated. The potential effects of dynamic strain aging (DSA) on cyclic deformation 

and environmental effects are discussed.147-153 The Fen methodology proposed in this report 

was validated by comparing the results of five different experimental data sets obtained from 

fatigue tests that simulate actual plant conditions with estimates of fatigue usage adjusted for 

environmental effects using the updated Fen expressions. The five data sets represent fatigue 

tests with (a) changing strain rate and/or temperature,154 (b) complex loading (actual PWR 

transient),155-157 (c) spectrum loading (random strain amplitudes),158,159 (d) thermal fatigue of a 

stepped pipe,160 and (e) pipe U-bend tests.98,99 Appendix C of this report presents a sample 

application of the Fen methodology that is intended to address by example some of the practical 

issues identified by interested stakeholders associated with the Fen calculations.161
17

2. MECHANISM OF FATIGUE

2.1 Formation of an Engineering Crack in Air

Deformation and microstructural changes in the surface grains of metals are responsible for 

fatigue cracking. During cyclic straining, the irreversibility of dislocation glide leads to the 

development of surface roughness. Strain localization in persistent slip bands (PSBs) results in 

the formation of extrusions and intrusions. With continued cycling, microcracks ultimately form 

in PSBs or at the edges of slip–band extrusions. At high strain amplitudes, microcracks form in 

notches that develop at grain, twin, or phase boundaries (e.g., ferrite/pearlite) or by cracking of 

second–phase particles (e.g., sulfide or oxide inclusions). 

Once a microcrack forms, it continues to grow along its primary slip plane or a PSB as a Mode II 

(shear) crack in Stage I growth (where the orientation of the crack is usually at 45° to the stress 

axis). At low strain amplitudes, a Stage I crack may extend across several grain diameters 

before the increasing stress intensity of the crack promotes slip on planes other than the 

primary slip plane. A dislocation cell structure normally forms at the crack tip. Because slip is 

no longer confined to planes at 45° to the stress axis, the crack begins to propagate as a Mode I 

(tensile) crack, normal to the stress axis in Stage II growth. At high strain amplitudes, the stress 

intensity is quite large and the crack propagates entirely by the Stage II process. Stage II crack 

propagation continues until the crack reaches an engineering size. The two stages of fatigue 

crack growth in smooth specimens are shown in Fig. 5. 

Figure 5. Two stages of fatigue crack growth in smooth test specimens.

In air or mildly corrosive environments, Stage II cracking is characterized by fatigue striations. 

The process of Stage II fatigue crack growth and formation of fatigue striations162 is illustrated in 

Fig. 6. As tensile load is applied, slip bands form at the double notch or “ears” of the crack tip 

(Fig. 6b). The slip bands widen with further straining, causing blunting of the crack tip (Fig. 6c). 

Crack surfaces close during compressive loading and slip is reversed, producing ears at the 

edges of the blunt crack tip (Figs. 6d and 6e). The ears are observed as fatigue striations on 

the fracture surface. However, there is not necessarily a 1:1 correlation between striation 

spacing and fatigue cycles. At high strain amplitudes, several striations may be created during 

one cycle, whereas at low strain amplitudes, one striation may represent several cycles.
18

(a) (d)

(b) (e)

(c) (f)

Figure 6. Schematic illustration of the plastic blunting process of fatigue crack 

growth in Stage II: (a) zero load; (b) small tensile load; (c) maximum tensile 

load, widening of slip bands; (d) crack closure, and formation of “ears” at 

crack tip; (e) maximum compressive load; (f) small tensile load in the 

subsequent cycle.

Thus, the formation of surface cracks and their growth as shear and tensile cracks (Stages I and 

II growth) to an “engineering” size (e.g., a 3–mm–deep) crack constitute the fatigue life of a 

material, which is represented by the fatigue ε–N curves. Fatigue life is conventionally divided 

into two stages: initiation, expressed as the number of cycles required to form microcracks on 

the surface; and propagation, expressed as the number of cycles required to propagate the 

surface cracks to an engineering size. Thus, the definition of a CUF value of unity, as described 

in Section 1.1, conventionally includes both initiation and some amount of propagation.

An alternative approach considers fatigue life of engineering structures and components to be 

entirely composed of the growth of short fatigue cracks, i.e., cracks less than “engineering ” 

size.163,164 For polycrystalline materials, the time for the formation of surface cracks is 

negligible. During cyclic loading, surface cracks, 5 μm or longer, form early in life at surface 

irregularities either already in existence or produced by slip bands, grain boundaries, second–

phase particles, etc. (Fig. 7).11,165-167 Thus, fatigue life may be considered to constitute 

propagation of cracks from 10 to 3000 μm long, and fatigue damage in a material may be 

considered as the current size of the fatigue crack.164 However, the growth rates of short 

cracks cannot be predicted accurately from fracture mechanics methodology based on the

range of stress intensity factor (∆K) alone. Under the same ∆K loading, short fatigue cracks 

(i.e., cracks having lengths comparable to the unit size of the microstructure) grow at a faster 

rate than longer fatigue cracks.168 In addition, shorter cracks can grow at ∆K values below 

those predicted from linear elastic fracture mechanics (LEFM). The differences between the 
19

growth rates of short and long cracks are attributed to interactions with microstructural features, 

contributions of crack closure with increasing crack length, effects of mixed mode crack 

propagation, and an inadequate characterization of the crack tip stress/strain fields associated 

with short cracks.

Figure 7. Crack depth plotted as a function of fractional life for carbon and low–alloy 

steels tested in air (Refs. 11,165-167).

A schematic illustration of the two stages of fatigue crack growth including (a) initiation, and 

(b) propagation, is shown in Fig. 8. The initiation stage involves growth of “microstructurally 

small cracks” (MSCs), characterized by decelerating crack growth (Region AB in Fig. 8a). The 

propagation stage involves growth of “mechanically small cracks,” characterized by accelerating 

crack growth (Region BC in Fig. 8a). The MSCs correspond to Stage-I cracks and grow along 

slip planes as shear cracks in the early stage of growth. The growth of the MSCs is very 

sensitive to microstructure.11,166-171 For MSCs, microstructural effects are strong because of 

Stage I growth, i.e., crystallographic growth. The growth rates are markedly decreased by grain 

boundaries, triple points, and phase boundaries. In ferritic-pearlitic steels, fatigue cracks initiate 

and propagate preferentially in the ferrite phase that forms as long allotriomorphs at prior 

austenite phase boundaries.166,170,171 The ferrite/pearlite phase boundaries act as strong 

barriers to crack propagation, and growth rates decrease significantly when small cracks grow 

into the pearlite from the ferrite.166 Limited data suggest that microstructural effects are more 

pronounced at negative stress ratios; the compressive component of the applied load plays an 

important role in the formation of Stage I facets and formation of cracks.169 
20

(a) (b)

Figure 8. Schematic illustration of (a) growth of short cracks in smooth specimens 

as a function of fatigue life fraction, and (b) crack velocity as a function of 

crack depth. 

Fatigue cracks greater than a critical size, show little or no influence of microstructure and are 

considered mechanically small cracks.169 Mechanically small cracks correspond to Stage II 

(tensile) cracks, which are characterized by striated crack growth, with the fracture surface 

normal to the direction of maximum principal stress. The growth of mechanically small cracks is

characterized in terms of the J-integral range, ∆J, and CGR data in air and LWR environments. 

The CGRs estimated from smooth specimen ε-N data show good agreement with CGRs 

obtained on fracture mechanics compact tension (CT) specimens in air and water 

environments.13 

Various criteria, summarized in Section 5.4.1 of Ref. 12, are used to define the crack depth for 

transition from microstructurally to mechanically small cracks. The transition crack depth is a 

function of applied stress (σ) and the microstructure of the material. For completely reversed 

fatigue straining, the transition from a MSC to a mechanically small crack for several materials is

estimated to be approximately 8 times the unit size of the microstructure;169 actual values may 

range from 150 to 250 μm. 

At low stress levels (∆σ1) (Fig. 8a), the transition from MSC growth to accelerating crack growth 

does not occur. This circumstance represents the fatigue limit for a smooth specimen. 

Although cracks can form below the fatigue limit, they grow to engineering size only at stresses 

greater than the fatigue limit. The fatigue limit for a material is applicable only for constant 

loading conditions. Under variable loading conditions, MSCs can grow at high stresses (∆σ3) 

(Fig. 8b) to depths larger than the transition crack depth, and then continue to grow at stress 

levels below the fatigue limit (∆σ1).

As discussed in Section 1.1, fatigue life is described in this report as the number of cycles of a 

specified strain amplitude that a specimen can sustain before the formation of a 3-mm-deep 

crack (i.e., an “engineering crack”). This is assumed throughout this report to equate to crack 

initiation in an actual component. Using this definition, a calculated fatigue CUF less than unity 

provides reasonable assurance that a fatigue crack has not formed in a component, and 

indicates that the probability of forming a crack in the component is low.
21

2.2 Fatigue Cracking in LWR Environments

The available small-scale laboratory fatigue test data indicate a significant decrease in fatigue 

life of reactor structural materials in LWR environments. The extent of environmental effects 

depends on the applied strain, temperature, strain rate, DO in the water, and for carbon and 

low-alloy steels, the sulfur content in the steel. Although the structure and cyclic hardening 

behavior of carbon and low–alloy steels are distinctly different, there is little or no difference in 

susceptibility to environmental degradation of fatigue life of these steels. Reduction in fatigue 

life in LWR coolant environments may arise from easy formation of surface microcracks 

consisting of the growth of MSCs (i.e., the initiation stage) and/or an increase in growth of 

mechanically small cracks (i.e., propagation stage). The formation and growth characteristics of 

fatigue cracks are discussed in detail for carbon and low-alloy steels and wrought and cast 

austenitic SSs in the following sections. Similar information for Ni-Cr-Fe alloys is very limited.

2.2.1 Carbon and Low-Alloy Steels 

Carbon and low–alloy steels tested in air show slight discoloration, while those tested in water 

develop a gray/black corrosion scale and are covered with magnetite (Fe3O4) at all DO levels. 

Hematite (α–Fe2O3) forms on these materials at DO levels above 200 parts per billion 

(ppb).20,22,172 The amount of hematite increases with increasing DO levels in the water.20 

Studies on the pitting behavior of carbon and low-alloy steels173,174 in high–purity water indicate 

that pitting corrosion does not occur in these steels at reactor operating temperatures in low–DO 

PWR environments [typically less than 0.01 parts per million (ppm) DO], and at temperatures 

above 200°C in water that contains 0.1–0.2 ppm DO, which represents normal BWR water 

chemistry. However, even under these conditions, micropits form in both types of steels due to 

dissolution of manganese sulfide (MnS) inclusions18 or by anodic reaction in the S contaminated 

matrix175 close to sulfide inclusions. These micropits and cavities can act as stress raisers and 

provide preferred sites for the formation of fatigue cracks.

2.2.1.1 Effects of Surface Micropits

The strain rate effects in water are such that fatigue life decreases with decreasing strain rate. 

These effects are often explained by a higher density of micropits at lower strain rates. Some 

investigators argue that the longer test durations for slow strain rate tests result in a higher 

density of micropits and, therefore, shorter periods for the formation of surface microcracks.18 

However, if the presence of micropits was responsible for the reduction in fatigue lives of carbon 

and low–alloy steels in LWR environments, then specimens pre-exposed to high–DO water 

followed by testing in air should also show a decrease in fatigue life.

Figure 9 shows a comparison of the fatigue lives of carbon and low-alloy steels tested in highDO water at 288°C with the fatigue lives of carbon and low-alloy steels preoxidized at 288°C for 

30–100 hours in water with 0.6–0.8 ppm DO and then tested in either air or low–DO water with 

less than 0.01 ppm DO.40,41,176 The fatigue lives of the preoxidized specimens were identical to 

those of the unoxidized specimens; life was expected to decrease if surface micropits facilitate 

the formation of fatigue cracks. Only a moderate decrease in life was observed for both 

preoxidized and unoxidized specimens tested in low–DO water. Furthermore, if micropits were 

responsible for the decrease in fatigue lives in LWR environments, then the fatigue limit of these 

steels should be lower in water than in air.
22

Figure 9. Fatigue life of carbon and low-alloy steel specimens in high-DO water at 

288°C compared with the fatigue life of specimens preoxidized in high-DO 

water and tested in either air or low-DO water at 288°C (Refs. 40,41,176). 

The extent of fatigue cracking, as measured by the number of cracks with depths greater than 

10 μm, along longitudinal sections of carbon and low-alloy steel specimens as a function of 

strain range in air, simulated PWR, and high–DO water was also investigated.176 The results 

indicated that, with the exception of low-alloy steel tested in simulated PWR water, the water 

environment had no effect on the frequency (number per unit gauge length) of cracks. For 

similar loading conditions, the number of cracks in the specimens tested in air and high–DO 

water was identical, although fatigue lives were lower by a factor of approximately 8 in water. If 

the reduction in life was caused by enhanced crack nucleation, the specimens tested in high–

DO water should have shown a higher number of cracks. Detailed metallographic evaluations 

of the fatigue test specimens176 also indicated that, irrespective of environment, cracks in 

carbon and low–alloy steels nucleated along slip bands, carbide particles, or at the 

ferrite/pearlite phase boundaries.11,176 

2.2.1.2 Mechanisms of Corrosion Fatigue

The environmental enhancement of fatigue crack growth in pressure vessel steels in high–

temperature oxygenated water and the effects of sulfur content, loading rate, and flow velocities 

are well documented.177-189 Dissolution of MnS inclusions changes the water chemistry near 

the crack tip, making it more aggressive. This results in enhanced crack growth rates because 

either (a) the dissolved sulfides decrease the repassivation rate, which increases the amount of 

metal dissolution for a given oxide rupture rate;189 or (b) the dissolved sulfide poisons the 

recombination of hydrogen (H) atoms liberated by corrosion, which enhances H uptake by the 

steel at the crack tip.

The enhanced CGRs in LWR environments are attributed to either slip oxidation/dissolution189-

193 or hydrogen–induced cracking mechanisms.194-196 For the slip oxidation/dissolution 

mechanism, a critical concentration of sulfide (S2–) or hydrosulfide (HS–) ions, which are 

produced by the dissolution of sulfide inclusions in the steel, is required at the crack tip for 

environmental effects to occur. The crack tip is supplied with S2– and HS– ions as the 

advancing crack intersects the sulfide inclusions, and the inclusions dissolve in the high–

temperature water environment. Sulfide ions are removed from the crack tip by one or more of 

the following processes: (a) diffusion due to a concentration gradient, (b) ion transport due to an 

electrochemical potential (ECP) gradient, (c) pumping action due to cyclic loading on the crack, 

and/or (d) fluid flow induced within the crack due to the flow of coolant outside the crack. The 
23

morphology, size, and distribution of sulfide inclusions and the probability of advancing the 

crack to intercept the sulfide inclusions are important parameters affecting growth rates of 

carbon and low-alloy steels in LWR environments.183,185-188 

The requirements for a slip dissolution model are that a protective oxide film is 

thermodynamically stable to ensure that a crack will propagate with a high aspect ratio without 

degrading into a blunt pit, and that a strain increment occurs to rupture that film and thereby 

expose the underlying matrix to the environment, Fig. 10. Once the passive oxide film is 

ruptured, crack extension is controlled by dissolution of freshly exposed surfaces and by the 

oxidation characteristics. The effect of the environment increases with decreasing strain rate. 

The mechanism assumes that environmental effects do not occur during the compressive load 

cycle because during that period water does not have access to the crack tip. Ford, Andresen, 

et al.191,192 proposed that the average environmentally assisted crack growth rate, 

(centimeters/second), is related to the crack tip strain rate, , by the relationship 

, (13)

where the constants A and n depend on the material and environmental conditions at the crack 

tip. There is a lower limit of crack propagation rate associated either with blunting when the 

crack tip cannot keep up with the general corrosion rate of the crack sides, or with the fact that a 

critical level of sulfide ions cannot be maintained at the crack tip. For example, the latter 

condition may occur when the crack growth rate falls below a critical value such that a high 

concentration of sulfide ions cannot be maintained at the crack tip. The critical crack growth 

rate at which this transition occurs depends on the DO level, flow rate, and S content of the 

steel. 

Figure 10.

Schematic illustration of slip 

oxidation/dissolution process.

The average critical velocity, (millimeters/second), for initiation or cessation of 

environmentally assisted cracking (EAC), was shown to depend on the balance between sulfide 

supply rate and mass transport away from the crack tip.178,182 Initiation of EAC requires a 

critical concentration of sulfide ions at the crack tip, which is supplied with sulfide ions as the 

advancing crack intersects the sulfide inclusions, and the inclusions dissolve in the hightemperature water. Crack growth studies in high-temperature, low-DO environment (i.e., less 

than 0.05 ppm DO) indicate that is given by 

, (14)
24

where a is the crack depth (mm). Thus, for a 2.54 mm crack depth, a minimum average crack 

velocity of 5 x 10–7 millimeters/second is required to produce the sulfide ion concentration for 

environmental effects on crack growth to be pronounced.182 In addition, the critical velocity 

must be maintained for a minimum crack extension of 0.33 mm to achieve the concentration of 

sulfide ions needed for initiating environmental enhancement of growth rates.178 Equation 14

indicates that the minimum crack velocity to initiate environmental effects increases with 

decreasing crack depth. For crack depths between 0.01 and 3 mm, crack velocities in the range 

of 1.27 x 10–4 to 4.23 x 10–7 millimeters/second are required to cause s measurable reduction in 

fatigue lives of carbon and low-alloy steels in low–DO water. For smooth cylindrical fatigue 

specimens, these growth rates are not achieved under the loading conditions typically used for 

fatigue ε–N data, which suggests that environmental effects on fatigue lives in low–DO 

environments are not significant. This behavior is consistent with the existing fatigue ε –N data; 

for most compositions of carbon and low-alloy steels, only moderate reductions in fatigue life 

(less than a factor of 2) are observed in 288°C water containing less than 0.01 ppm DO, which 

is within the data scatter. 

In addition, consistent with the slip dissolution mechanism assumption mentioned previously, it 

is assumed that environmental enhancement of crack propagation does not occur during the 

compressive load cycle because, during that period, the water does not have access to the 

crack tip due to crack closure. The total crack advance during a fatigue cycle is given by the 

summation of crack advance in air due to mechanical factors, and crack advance during the 

tensile load cycle (i.e., increasing strain) from a slip–dissolution mechanism, once the tensile 

strain increment exceeds the fracture strain of the oxide.

Hydrogen-induced cracking (Fig. 11) of carbon and low-alloy steels is caused by hydrogen 

produced by the oxidation reaction at the crack tip that is partly absorbed into the metal; it

interacts with MnS inclusions and leads to the formation of cleavage cracks at the inclusion 

matrix interface. Crack extension occurs by linkage of the cleavage cracks. Other hydrogeninduced fracture processes may also enhance growth rates in LWR environments. According to 

the decohesion mechanism, significant accumulation of hydrogen at or near the crack tip 

decreases the cohesive interatomic strength of the lattice.197 Hydrogen–induced bond rupture 

ahead of the crack tip links up with the main crack resulting in discontinuous, but enhanced 

crack growth. Furthermore, adsorbed hydrogen lowers the surface energy of the metal, thus 

facilitating crack growth at a lower fracture stress level. In addition, hydrogen can cause 

localized crack tip plasticity by reducing the stress required for dislocation motion.198 Note that 

the hydrogen produced at the crack tip by this mechanism is not related to the hydrogen content 

of the bulk fluid; as a result, hydrogen content of the bulk fluid is not a parameter in the Fen

expressions.

Both the slip-oxidation/dissolution and hydrogen-induced cracking mechanisms are dependent 

on oxide rupture rates, passivation rates, and liquid diffusion rates. Therefore, it is difficult to 

differentiate between the two mechanisms or to establish their relative contribution to crack 

growth rates in LWR environments. However, fatigue crack morphologies in test specimens 

indicate that both the slip-oxidation/dissolution and hydrogen-induced cracking mechanisms are 

important for environmental effects of the fatigue lives of carbon and low-alloy steels in LWR 

environments. A change in fracture appearance from ductile striations in air to brittle facets or 

cleavage–like fracture in LWR environments lends the greatest support for hydrogen–induced 

cracking.142,143,187,195,196 
25

Figure 11.

Schematic illustration of 

hydrogen-induced cracking 

of low-alloy steel.

The fatigue crack morphologies of carbon and low-alloy steels in a BWR environment also show 

a strong dependence and change with strain rate. At high strain rates, surface crack 

morphology is predominantly a zigzag pattern and inclined to the loading axis, whereas entirely 

straight crack morphology normal to the loading axis is observed at slow strain rates.10,139,143 

The surface crack morphology in A106-Gr. B carbon steel tested in air and high-DO water at 

288°C is shown in Fig. 12. In addition, high strain rates lead to a rough fracture surface with the

typical fan-like or quasi-cleavage cracking pattern, and slow strain rates result in a flat, 

nondescript fracture surface.139,142 The propagation of fatigue cracks in A106-Gr. B carbon 

steel is shown in Fig. 13. In air, fatigue cracks grow along relatively soft ferrite regions and 

avoid the hard pearlite regions. In contrast, in a high-DO BWR environment, fatigue cracks 

appear to grow straight, normal to the stress axis, and through both the soft ferrite and the hard 

pearlite regions. Such crack growth characteristics are consistent with the slipoxidation/dissolution mechanism and crack extension by anodic dissolution of the matrix in a 

corrosive environment.

Wu and Katada142 attributed the change in crack morphology to a change in the corrosion 

fatigue mechanism from hydrogen-induced cracking to a slip-oxidation/dissolution mechanism

with decreasing strain rate. The authors reasoned that, during cyclic loading in high 

temperature water, plastic deformation induces slip bands at the crack tip along the maximum 

shear or preferred slip directions. The extrusion of slip bands may rupture the protective oxide 

film at the crack tip. The slip bands are the favored path for hydrogen transportation and the 

interfaces between the matrix and inclusions or precipitations in the region of maximum 

hydrostatic tension are the preferred traps for hydrogen. Thus, hydrogen tends to accumulate 

at these sites and embrittle them. As a result, at high strain rates, fatigue cracking preferentially 

occurs along the slip bands or preferred slip directions as well as the matrix/inclusions 

interfaces, which results in macroscopically tortuous fatigue cracks and a rough fracture 

surface. However, at low strain rates, fatigue crack growth in high-temperature water is 

controlled by the film-rupture/oxidation-dissolution mechanism, which results in macroscopically 

straight fatigue cracks and a relatively flat, featureless fracture surface.
26

2.2.1.3 Effects of Dynamic Strain Aging (DSA)

Several studies showed that DSA may play a significant role in the cyclic deformation process of 

carbon and low-alloy steels in LWR environments.147-151 DSA occurs in alloys containing 

solutes that segregate strongly to dislocations resulting in strong interactions between the solute 

and the stress-strain field of the dislocations, which leads to dislocation pinning, Fig. 14. In 

carbon and low-alloy steels, DSA occurs due to interstitial elements such as nitrogen and 

carbon. DSA is sufficiently rapid to occur during fatigue straining and produces a variety of 

inhomogeneous deformations such as serrated yielding, jerky or serrated flow, etc. These 

effects depend on temperature and strain rate.

(a) (b)

Figure 12. Fatigue cracks on gauge surfaces of A106-Gr. B carbon steel tested in 

(a) air and (b) high-DO water at 288°C (Ref. 10).

(a) (b)

Figure 13. Fatigue cracks along longitudinal sections of A106-Gr. B carbon steel 

tested in (a) air and (b) high-DO water at 288°C (Ref. 10).
27

Figure 14. (a) Fatigue crack initiation and (b) crack growth in DSA susceptible lowalloy steel exposed to high-temperature water environment (Ref. 147). 

Under certain combinations of temperature and strain rate conditions, DSA may significantly 

affect the EAC behavior of carbon and low-alloy steels by increasing the yield and tensile 

strength, the strain hardening exponent, the creep rate, and the crack-tip strain and strain 

rate.149 DSA also results in planar deformation, an increase in dislocation density and 

inhomogeneous localization of deformation. These factors favor brittle crack extension and 

rupture of the protective oxide film, thereby enhancing crack advance by either anodic 

dissolution or hydrogen embrittlement processes. In high-temperature water, the synergistic 

interactions between EAC and DSA during fatigue straining may be rationalized as follows:149

- Hydrogen vacancies produced by the corrosion reaction at the crack tip enter the steel 

and hydrogen diffuses to strong trapping sites inside the crack-tip maximum hydrostatic 

stress region (e.g., MnS inclusions) ahead of the crack tip.

- These sites act as initiation sites for local quasi-cleavage cracking, as well as void 

formation, and these microcracks link with the main crack.

- In addition, at a given macroscopic strain due to external loads, the microscopic strain in 

steels that are susceptible to DSA is higher because of strain localization to small areas, 

which leads to higher rates and larger steps of oxide film rupture. As a result, the slip 

oxidation/dissolution process enhances fatigue crack initiation or fatigue crack growth 

rates.

- Such interactions, however, occur only under certain conditions of temperature, strain 

rate, and DO level in the environment.

In carbon and low-alloys steels, the interaction of nitrogen and dislocations during plastic 

deformation reduces plasticity, which causes strain localization in the material.147 Small areas 

can deform plastically adjacent to areas that might be blocked by nitrogen/dislocation 

interactions. For a given macroscopic strain, the microscopic strain is higher due to strain 

localization in steels that are susceptible to DSA. Thus, because of strain localization, stress 

concentrations at active slip planes lead to higher rates and larger steps of oxide rupture and,

simultaneously, to a decreased repassivation rate.147,148 Consequently, both crack initiation 

and growth rates may be enhanced in carbon and low-alloy steels.
28

2.2.1.4 Crack Growth Rates in Smooth Fatigue Specimens

Studies on the formation and growth characteristics of short cracks in smooth fatigue specimens 

in LWR environments indicated that the decrease in fatigue life in LWR environments is caused 

primarily by the effects of the environment on the growth of MSCs (i.e., cracks less than 200 μm 

deep) and, to a lesser extent, on the growth of mechanically small cracks.10,11 Measured crack 

lengths as a function of fatigue cycles and fraction of fatigue life for smooth cylindrical 

specimens of A533-Gr B low-alloy steel in air, simulated PWR environment, and high-DO water 

are shown in Fig. 15. An example of the growth of a surface crack in A533-Gr. B steel tested in 

air at room temperature, and the fracture surface and probable crack front for the crack, are

shown in Fig. 16. The results indicate that, for this example, three cracks merged to form the 

final fracture surface. The primary crack initiated near an inclusion and reached a surface 

length of approximately 100 μm after 3,062 cycles (i.e., approximately 50% of the fatigue life). 

Two secondary cracks merged with the primary crack after approximately 5,700 and 6,000 

cycles. Crack depth was determined by dividing the surface crack length by pi (π). 

Figure 15. Depth of largest crack plotted as a function of (a) fatigue cycles and 

(b) fraction of fatigue life for A533–Gr B low–alloy steel in air and water 

environments (Ref. 11). 

(a) (b)

Figure 16. (a) Morphology and length of surface crack after various numbers of cycles 

for A533-Gr. B steel in air at room temperature, and (b) fracture surface and 

probable crack front for surface cracks shown in (a) (Ref. 11). 
29

The crack growth rates corresponding to the data shown in Fig. 15 are plotted as a function of 

crack depth in Fig. 17. The results indicate that, in LWR environments, the period spent in the 

growth of MSCs is decreased. At approximately 0.8% strain range, only 30-50 cycles are 

needed to form a 100-μm crack in high-DO water, whereas approximately 450 cycles are 

required to form a 100-μm crack in a low-DO PWR environment and more than 3,000 cycles in 

air. These values correspond to average growth rates of approximately 2.5, 0.22, and 

0.033 μm/cycle in high-DO water, low-DO PWR environment, and air, respectively. The results 

also indicate that, relative to air, CGRs in high-DO water are nearly two orders of magnitude 

higher during the initial stages of fatigue life (i.e., for crack sizes less than 100 μm), and are one 

order of magnitude higher for crack sizes greater than 100 μm.

Figure 17.

Crack growth rates plotted as a 

function of crack depth for A533–

Gr B low–alloy steel tested in air 

and water environments (Ref. 11).

The surface crack and fracture surface morphologies of the test specimens indicate that, in 

high-temperature, high–DO water with slow strain rates, the surface cracks appear to grow 

entirely in Stage II growth as Mode I tensile cracks normal to the stress axis (Figs. 12 and 13). 

In air and low–DO PWR environments, both Stage I and Stage II growths are observed. 

Surface cracks grow initially as Mode II (shear) cracks along planes 45° to the stress axis and, 

when the stress intensities are large enough to promote slip on axes other than the primary slip 

axis, they grow as Mode I (tensile) cracks normal to the stress axis. Also, for A106-Gr. B 

carbon steel, Stage I crack growth in air and low–DO water occurs entirely along the soft ferrite 

grains, whereas in high–DO water, cracks propagate across both ferrite and pearlite regions. 

These results are consistent with the slip-oxidation/dissolution mechanism in high-DO water.

2.2.2 Austenitic Stainless Steels

Austenitic SSs exposed to LWR environments develop an oxide film that consists of two layers: 

a fine–grained, tightly–adherent, chromium–rich inner layer, and a crystalline, nickel–rich outer 

layer composed of large and intermediate–sized particles. Photomicrographs of the gauge 

surface of Type 316NG specimens tested in simulated PWR water and high–DO water are 

shown in Fig. 18. The inner layer forms by solid–state growth, whereas the crystalline outer 

layer forms by precipitation or deposition from the solution. A schematic representation of the 

surface oxide film is shown in Fig. 19.
30

(a) (b)

Figure 18. Photomicrographs of oxide films that formed on Type 316NG stainless 

steel in (a) simulated PWR water and (b) high–DO water (Ref. 13). 

Figure 19. Schematic of the corrosion oxide film formed on austenitic 

stainless steels in LWR environments. 

Several studies characterized the oxide films that form on austenitic SSs in LWR 

environments.199-205 The inner layer consists of chromium–rich spinel (NixCryFe3-x-yO4) with a

nonstoichiometric composition; the actual composition of spinels varies with environmental 

conditions. Da Cunha Belo, et al.203 determined that the inner layer that formed on Type 316L 

SS in a PWR environment at 350°C consisted of mixed chromium oxides (Cr2O3 + FeCr2O4) 

and Fe3O4. Nakayama and Oshida205 characterized the oxide film on SSs exposed to high–DO 

(8 ppm) water at 300°C as chiefly composed of NiO·(Cr,Fe)2O3 and/or NiFe2O4, which may be 

formed by a solid reaction between NiO and (Cr,Fe)2O3 or α–Fe2O3. Kim199,200 identified the 

FeCr2O4 spinel chromite (or FexCr3–xO4), along with NiFe2O4, in the inner layer formed on 

Types 304 and 316 SSs exposed at 288°C under BWR normal water chemistry (NWC) or BWR 

hydrogen water chemistry (HWC) conditions. Kim also noted that the inner oxide layer formed 

in a NWC BWR environment contained a lower concentration of chromium than that formed in a 

HWC low–DO environment. Such differences were attributed to chromium oxidation in high–DO 

water.

The structure and composition of the crystalline outer layer vary with the water chemistry. In 

BWR environments, the large particles in the outer layer are primarily composed of γ–Fe2O3

hematite in NWC, and Fe3O4 magnetite in HWC.199,200 The intermediate particles in the outer 

layer are composed of α–Fe2O3 in NWC and Fe3O4 in HWC. The structure of the outer layer 

varies when the water chemistry is cycled between NWC and HWC. In PWR environments, the 

large particles were identified as Ni0.75Fe2.25O4 spinel and the intermediate particles as 

Ni0.75Fe2.25O4 + Fe3O4.203 The possible effects of minor differences in the surface oxide film on 

fatigue crack initiation are discussed in the next section.
31

2.2.2.1 Effects of Surface Micropits

The characteristics of the surface oxide films that form on austenitic SSs in LWR coolant 

environments influence the mechanism and kinetics of corrosion processes and thereby 

influence the initiation stage, i.e., the growth of MSCs. As discussed earlier, the reduction of 

fatigue lives in high–temperature water may be due to the presence of surface micropits. To 

investigate the effect of surface micropits, fatigue tests were conducted on Type 316NG (Heat 

P91576) specimens that were pre-exposed to either low–DO or high–DO water and then tested 

in air or water environments.13 The results of these tests, as well as data obtained earlier on 

this heat and Heat D432804 of Type 316NG SS in air and low–DO water at 288°C, are plotted 

in Fig. 20. The fatigue lives of specimens preoxidized in high–DO water and then tested in low–

DO water were identical to those of specimens tested without preoxidation. Also, fatigue lives of 

specimens preoxidized at 288°C in low–DO water and then tested in air were identical to those 

of unoxidized specimens (Fig. 20). If micropits were responsible for the reduction in life, the 

pre-exposed specimens should have shown a decrease in life. Furthermore, the fatigue limit of 

these steels should have also been lower in water than in air, but the data indicated this limit 

was the same in both water and air environments. These results indicate that surface micropits 

or minor differences in the composition or structure of the surface oxide film had little or no 

effect on the formation of fatigue cracks. 

Figure 20.

Effects of environment on 

formation of fatigue cracks in 

Type 316NG SS in air and low–

DO water at 288°C. Preoxidized 

specimens were exposed for 10 

days at 288°C in water that 

contained either less than 

5 ppb DO and approximately 

23 cm3

/kg dissolved H2 or 

approximately 500 ppb DO and 

no dissolved H2 (Ref. 13).

2.2.2.2 Mechanisms of Corrosion Fatigue

Both the slip oxidation/dissolution and the hydrogen–induced cracking mechanisms depend on 

the rates of oxide rupture, passivation, and liquid diffusion. Therefore, it is difficult to 

differentiate between the two processes or to establish their relative contribution to fatigue 

cracking in LWR environments. However, for austenitic SSs, lower fatigue lives in low–DO 

water versus high–DO water are difficult to reconcile in terms of the slip oxidation/dissolution 

mechanism, which assumes that crack growth rates increase with increasing DO in the water. 

Metallographic examination of fatigue test specimens suggested that hydrogen–induced 

cracking may have played an important role in environmentally assisted reduction in fatigue 

lives of austenitic SSs.47 For example, hydrogen can cause localized crack tip plasticity by 

reducing the stress required for dislocation motion, which leads to higher rates and larger steps 

of oxide film rupture. Thus, fatigue lives may be decreased, not because of increased growth 

rates, but because of increased film rupture frequency. 
32

A detailed metallographic evaluation of austenitic SS fatigue test specimens was performed to 

characterize the crack and fracture morphology of the various heats under various heat 

treatment conditions.47 Photomicrographs of the crack morphology of Type 304 SS specimens 

under all test and environmental conditions are presented in Fig. 21. In all cases, the tensile 

axis was vertical (parallel to the plane of each photomicrograph). For austenitic SSs, the fatigue 

crack surface morphology was similar to that observed for carbon and low-alloy steels. In an air 

environment, fatigue cracks were more likely to be oblique, approaching 45° with respect to the 

tensile axis. By contrast, the cracks that formed in either BWR or PWR environments tended to 

be perpendicular to the tensile axis.

(a) (b) (c)

Figure 21. Photomicrographs of the fatigue crack morphology of Type 304 SS in (a) air, 

(b) high-DO BWR water, and (c) low-DO PWR water at 289°C (Ref. 47). 

Photomicrographs of the crack morphology of Type 304 SS under all test and environmental 

conditions are presented in Fig. 22. In air, the fracture mode for crack initiation (i.e., crack 

depths up to 200 μm) and crack propagation (i.e., crack depths greater than 200 μm) was 

transgranular (TG), most likely along crystallographic planes, leaving behind relatively smooth 

surfaces. With an increasing degree of sensitization, cleavage–like, or stepped, TG fracture 

and ridge structures were observed on the smooth surfaces. In simulated NWC BWR 

environments, the initial crack appeared intergranular (IG) under all heat treatment conditions, 

implying a weakening of the grain boundaries. The extent of IG fracture increased with the 

degree of sensitization. Nevertheless, for crack depths beyond 200 μm, the initial IG mode 

transformed into a TG mode with cleavage–like features. In simulated PWR environments, 

however, fatigue cracks initiated and propagated in a TG mode irrespective of the degree of 

sensitization. Prominent features of the fracture surfaces included highly angular, cleavage–like 

fracture facets that exhibited well–defined “river” patterns.47 Intergranular facets were rarely 

observed, but when they were found, it was mostly in the more heavily sensitized alloys. 

In addition, fatigue striations normal to the crack advance direction were clearly visible beyond 

approximately 200-μm-crack depths on the fracture surfaces of all materials under all 

environmental conditions. An example of the fatigue striations observed in Type 304 SS in 

different environments is shown in Fig. 23. Striations were found on both the TG and IG facets 

of the samples tested under BWR NWC conditions, or co-existing with the “river” patterns 

specific to the samples tested in the PWR environments. However, the striations on specimens 

tested in PWR water were quite faint compared to those tested in NWC BWR water. 

Furthermore, examination of the specimens after chemical cleaning suggested that some 

striations were produced by rupture of the surface oxide film rather than the formation of double 

notches or “ears” at the crack tip. 
33

(a) (b)

Figure 22.

Photomicrographs showing sites of 

fatigue crack initiation on fracture 

surfaces of Type 304 SS tested at 

289°C in (a) air, (b) high-DO BWR 

water, and (c) low-DO PWR water

(Ref. 47).

(c)

(a) (b)

Figure 23.

Photomicrographs showing fatigue 

striations on fracture surfaces of 

Type 304 SS tested at 289°C in (a) air, 

(b) high-DO BWR water, and (c) lowDO PWR water (Ref. 47).

(c)
34

The characterization of surface cracks and fracture morphology in austenitic SSs suggests that, 

in LWR environments, although film rupture was apparent, the formation and growth of fatigue 

cracks were primarily caused by hydrogen-induced cracking.

2.2.2.3 Effects of Dynamic Strain Aging (DSA)

DSA was observed in austenitic SSs in air at strain rates below 0.3 %/s and temperatures in the 

range of 300-600°C; the peak effects occurred at 500-600°C.206 The fatigue life of a heat of 

Type 316LN SS at low strain rates was greater at 600°C than at 500°C. Typically at 

temperatures above 400°C, the fatigue life of austenitic SSs decreased with an increase in 

temperature or a decrease in strain rate.57 DSA increased the dislocation density at slow strain 

rates, which enhanced the degree of inhomogeneity of deformation during fatigue loading. 

DSA was also observed in Type 304L SS under LWR operating conditions. At 0.4 %/s strain 

rate, the fatigue life and fatigue limit in air were higher at 300°C than at 150°C (due to 

secondary strain hardening at 300°C).58 A similar behavior was observed for this heat of SS in 

PWR water. At 0.4 %/s, fatigue life decreased in PWR water relative to that in air at 150°C, but 

not at 300°C. This difference was identified as secondary hardening at 300°C, which was not 

observed at 150°C. The secondary hardening at 300°C may be due to DSA, although the 

temperature was relatively low.

2.2.2.4 Crack Growth Rates in Smooth Fatigue Specimens

Studies on the formation and growth characteristics of short cracks in smooth fatigue specimens 

of austenitic SSs in LWR environments indicated that, although the growth rates of mechanically 

small cracks were greater in water than in air, the decrease in fatigue lives was caused 

predominantly by the effects of the environment on the growth of MSCs.44 The growth of the 

largest crack in austenitic SSs with respect to fatigue cycles, in air and water environments, is 

shown in Fig. 24. In the figure, the crack length for the test in air at 288°C and 0.75% strain 

range was measured only near the end of the test. The data obtained by Orbtlik, et al.207 for 

Type 316L SS in air at 25°C and approximately 0.2% strain range were used to estimate the 

crack growth in air at 0.75% strain range. Similar studies on carbon and low-alloy steels

indicate11,165-167 that the fatigue crack size at various life fractions was independent of strain 

range, strain rate, and temperature; consequently, the depth of the largest crack at various life 

fractions was approximately the same at strain ranges of 0.75% and 0.2%. The curve for the 

test in air at 0.75% (shown as a dashed line in Fig. 24) was calculated from the best-fit equation 

of the experimental data for Type 316L SS at 0.2% strain range; the estimated crack lengths at 

0.75% strain range show very good agreement with the measured values. The results showed

that, at the same number of cycles, the crack length was longer in low–DO (PWR) water than in 

air, e.g., after 1,500 cycles, the crack length in air, high-DO (BWR)water, and PWR water was 

approximately 40, 300, and 1,100 μm, respectively. The growth of cracks during the initiation 

stage, i.e., growth of MSCs, was enhanced in water; the fatigue cycles needed to form a 

500-μm crack were a factor of approximately 12 lower in low–DO water than in air. Figure 24

shows that the number of cycles required to produce a 500–μm crack is 800, 3,000, and 9,000 

in low–DO (PWR) water, high-DO (BWR) water, and air environments, respectively; thus, the 

number of cycles was more than a factor of 10 lower in low–DO water than in air. 

The CGRs during the propagation stage, i.e., growth of mechanically small cracks, in air and 

water environments are plotted as a function of crack length in Fig. 25; they were calculated 

from the best fit of the data in Fig. 24. The CGRs in high–DO water for the specimen with a 

24–hour soak period (closed diamonds in Fig. 25) were determined from measurements of 

fatigue striations. The CGRs were a factor of 2–6 higher in water than in air. Growth rates in 
35

PWR water or high–DO water with a 24–hour soak period were higher than those in high–DO 

water with a 120–hour soak period. At a crack length of approximately 1,000 μm, the CGRs in 

air, high–DO water, and low–DO water were 0.30, 0.64, and 1.05 μm/cycle, respectively. For 

the 0.75% strain range and 0.004%/s strain rate, these values corresponded to growth rates of 

approximately 1.6 x 10–9, 3.4 x 10–9, and 5.6 x 10–9 meters/second in air, high–DO water, and 

low–DO water, respectively. Thus, growth rates were a factor of 3.5 greater in low–DO water 

than in air.

Figure 24.

Depth of largest crack plotted as a 

function of fatigue cycles for 

austenitic stainless steels in air and 

water (Refs. 13,207).

(a) (b)

Figure 25. Crack growth rates plotted as a function of crack length for 

austenitic stainless steels in (a) water and (b) air environments 

(Refs. 13,44,207).

The existing fatigue crack growth (da/dN) data obtained from fracture–mechanics tests on CT

specimens of wrought and cast SSs in LWR environments were compiled by Shack and 

Kassner.208 The results indicated significant enhancement of CGRs in high–DO water; at CGRs 

of less than 10–10 meters/second in air, the rates in BWR NWC conditions exceeded the air 

curve in Section III of the ASME Code by a factor of approximately 20–30. The experimental 

CGRs for sensitized Type 304 SS in high–DO water and those predicted in air for the same 

mechanical loading conditions are plotted in Fig. 26a. The fatigue CGRs in air, 

(meters/second), were determined from a correlation at 288°C given by 
36

= 3.43 x 10-12 S(R) ∆K3.3/TR, (15)

where the function S(R) is expressed as

S(R) = 1.0 R ≤ 0

S(R) = 1.0 + 1.8R 0 < R ≤ 0.79

S(R) = –43.35 + 57.97R, 0.79 < R < 1.0, (16)

and TR is the rise time (seconds) of the loading waveform, R is the load ratio (Kmin/Kmax), and 

∆K is Kmax – Kmin. The fatigue CGR in water [ (meters/second)] with 0.2 ppm DO (i.e., BWR 

NWC) is expressed in terms of the fatigue CGR in air ( ) by the relationship 

= + 4.5 x 10-5 ( )0.5. (17)

(a) (b)

Figure 26. Crack growth rate data for Type 304 SS in high temperature water 

determined from (a) fracture mechanics CT specimens and (b) smooth 

cylindrical fatigue specimens (Ref. 208).

The CGR data from fracture–mechanics tests in low–DO PWR environments are sparse, 

particularly at rates that are less than 10–9 meters/second. At high CGRs, the observed 

enhancement in both low– and high–DO environments was relatively small, and the magnitude 

of the enhancement under the same loading conditions was comparable in the two 

environments. Until further data become available at low CGRs in simulated PWR water, Shack 

and Kassner208 recommended that the environmental enhancement represented by Eq. 17 for 

0.2 ppm DO water should also be considered for PWR environments. 

The CGRs determined from fatigue ε–N tests on smooth, cylindrical specimens in high–DO and 

low–DO (PWR) water environments at 289°C, are plotted in Fig. 26b. The rates in high–DO and 

low–DO (PWR) water represent the measured values shown as open diamonds and circles, 

respectively, from Fig. 25a. The CGRs in air for the same loading conditions (i.e., the same 

crack length) were determined from the estimated rates in air, shown by the solid line in Fig. 25

a. The results from fatigue ε–N tests showed good agreement with the data obtained from the 
37

fracture–mechanics tests. The CGRs in high–DO water were consistent with the trend 

predicted from Eq. 17. The rates in low–DO water were slightly higher. 

The large reductions in fatigue life of austenitic SSs in PWR environments cannot be explained 

entirely on the basis of enhanced CGRs during the propagation stage, i.e., growth of 

mechanically small cracks. For example, the CGRs in low–DO water are a factor of 1.6 greater 

than those in high–DO water, but fatigue lives are approximately a factor of 4 lower in low–DO 

water than in high–DO water. As indicated by the results shown in Fig. 25a, the decrease in 

fatigue lives of austenitic SSs in PWR environments was caused predominantly by the effects of 

environment on the growth of MSCs.

It should also be noted that, if enhanced CGRs alone were responsible for the environmentally 

assisted decrease in fatigue lives of materials in LWR environments, environmental effects on 

the fatigue lives of Alloy 600 and austenitic SSs in LWR environments should be comparable. 

In air, the fatigue ε–N behavior of Alloy 600 is comparable to that of austenitic SSs.61 Fatigue 

CGR data indicate that the enhancement of CGRs of Alloy 600 and austenitic SSs in LWR 

environments is also comparable.209 However, the fatigue ε–N behaviors of Alloy 600 and 

austenitic SSs in water differ significantly; only moderate effects of environment are observed 

for Alloy 600 base material and welds both in low–DO and high–DO water. For example, the 

fatigue life of Alloy 600 weld metal in water with less than 0.005 ppm DO at 325°C and 0.6% 

strain amplitude decreased by a factor of approximately 2.5 when the strain rate was decreased 

from 0.4 to 0.001 %/s. Under similar environmental and loading conditions, the fatigue lives of 

austenitic SSs were decreased by a factor of approximately ten.

39

3. FATIGUE STRAIN VS. LIFE (ε–N) BEHAVIOR IN AIR

During 1990s, the existing fatigue ε–N data developed at various establishments and research 

laboratories worldwide were compiled by the PVRC Working Group on ε–N Curve and Data 

Analysis. The database used in the ANL studies, and presented in the initial revision to

NUREG/CR-6909, was an extended version of the PVRC database. The reanalysis of the 

fatigue ε–N data presented in this report is based on a much larger fatigue ε–N database. The 

additional data include the JNES data summarized in JNES-SS-1005 on carbon and low-alloy 

steels, wrought and cast austenitic SSs, Ni-Cr-Fe alloys, and their associated weld metals 

tested in air and LWR environments,136 and fatigue ε–N test results from the open literature on 

several heats of carbon and low-alloy steels tested in BWR environments.138-146 Nearly 60% of 

the data in the more recent JNES database were included the old JNUFAD210 database. The 

JNUFAD database formed a portion of the PVRC database, which was used in the original 

revision to NUREG/CR-6909 report. 

Unless otherwise mentioned, the fatigue database was obtained from smooth cylindrical gauge 

specimens that were tested under strain control with fully reversed loading, i.e., strain ratio, R, 

of –1. Tests on notched specimens or at R values other than –1 were excluded from the fatigue 

ε–N data analysis performed for this report. For the previous fatigue testing performed at ANL, 

the estimated uncertainty in the strain measurements was about 4% of the reported values. For 

the data obtained in other laboratories, the uncertainty in the reported values of strain is 

unknown, but was assumed to be small enough such that the results were not significantly 

impacted.

In nearly all tests, fatigue life was defined as the number of cycles necessary for the tensile 

stress to drop 25% from its peak or steady–state value, N25. As discussed in Section 1.1, for 

the specimen sizes used in these studies, e.g., 5.1–9.5 mm (0.2–0.375 in.) diameter cylindrical 

specimens, failure corresponds to an approximately 3–mm–deep crack. Some of the earlier 

tests in air were carried out to complete failure of the specimens, and in some other tests,

fatigue lives were defined as the number of cycles for peak tensile stresses to decrease by 10 

or 50%. Fatigue lives defined by a criterion other than a 25% load drop were therefore 

converted to consistent N25 values according to the following formula: 

N25 = NX/(0.947 + 0.00212X), (18)

where X is the failure criterion (e.g., 10, 50 or 100% decrease in peak tensile stress).10 The 

estimated uncertainty in fatigue life determined by this procedure is about 2%, which is within 

the strain measurement uncertainty.

The 25% load drop criterion was not used for the tests that were performed using tube 

specimens. For tube specimens, fatigue lives were represented by the number of cycles to 

develop a leak because, with the exception of a few specimens, all tube specimens had 3-mm 

wall thicknesses.

3.1 Carbon and Low-Alloy Steels and Weld Metals

3.1.1 Experimental Data

The primary sources of fatigue ε–N data for carbon and low–alloy steels are the tests performed 

by General Electric Co. (GE) in a test loop at the Dresden 1 reactor;14,15 work sponsored by 

EPRI at GE;16,17 the work of Terrell at Materials Engineering Associates (MEA);48–50 the work at 
40

ANL on fatigue of pressure vessel and piping steels;10–13,40–47 the large JNES database136

“Environmental Fatigue Evaluation Method for Nuclear Power Plants,” studies at IshikawajimaHarima Heavy Industries (IHI), Hitachi, and Mitsubishi Heavy Industries (MHI) in Japan;18–36 and 

the studies at Kraftwerk Union Laboratories (KWU) and Materialprufungsanstalt (MPA) in 

Germany.55,56 From these sources, the total database for fatigue tests in air is composed of 

684 tests; 254 tests on carbon steels and 430 tests on low-alloy steels. Carbon steels include 

19 heats of A106–Grades B and C, A333–Grade 6, A508–Grade 1, and A333–Grade 6 weld 

metals. Low–alloy steels include 22 heats of A302–Grade B, A508–Grade 2 and 3, and A533–

Grade B steel. A summary of the sources included in the updated database used for the 

present analyses, as categorized by material type and test environment, is presented in Table 1. 

Other material information such as chemical composition, heat treatment, and room 

temperature tensile properties of the various types and heats of materials is given in 

Appendix B. 

Table 1. Sources of the fatigue ε–N data on carbon and low-alloy steels in air 

environment.

ANL 

Mat. 

ID

Material

Specification

Sulfur 

Content 

(wt.%)

Test 

Temperature 

(°C)

Number 

of Data

Points

Source Applicable 

Reference

Carbon Steels

1 A106-Gr.B 0.015 25, 288 3, 17 ANL 10

3 A106-Gr.B 0.020 25, 288 13, 12 MEA 48-50

4 A106-Gr.C (STS480) 0.006 25 5 JNES (Kanasaki) 136

- A106-Gr.C (STS480) 0.003 25 2 JNES (Kanasaki) 136

6 A106-Gr.B (STS49) 0.007 25 9 JNES (Higuchi) 136

9 A333-Gr.6 (STS42) 0.015 25, 250, 290 13, 7, 3 JNES (Higuchi) 136

10 A333-Gr.6 (STS42) 0.014 25 7a JNES (Higuchi) 136

11 A333-Gr.6 0.006 288 1 JNES (Higuchi) 136

12 A333-Gr.6 (STS410) 0.012 25, 100, 200, 

288

5, 4, 4, 2 JNES (Nakao), ANL 136, 10

13 A333-Gr.6 0.030 25, 288 7, 6 GE 14-17

14 A333-Gr.6 (STS410) 0.008 25, 289 24, 10 JNES (Hirano) 136

15 A333-Gr.6 (STS410) 0.016 25, 289 12, 5 JNES (Hirano) 136

18 A508-Gr.1 (SFVC2B) 0.004 25, 289 6, 5 JNES (Hirano) 136

19 A508-Gr.1b 0.008 25 14 JNES (PLEX) 136

24 CS - 25, 170 10, 28 MPA 55,56

Carbon Steel Weld Metals

- A336-Gr.6 (STS410) 0.001 25, 288 6, 4 JNES (Hirano) 136

- A336-Gr.6 (STS410) 0.010 25, 289 5, 5 JNES (Hirano) 136

Low-alloy Steels

1 A302-Gr.B 0.027 288 7 ANL 10

2 A508-Gr.2 0.003 25 9 JNES (Nakao/Higuchi) 136

6 A508-Gr. 3 (SFVV3) 0.003 25, 288 6, 14 JNES (Nagata) 136

7 A508-Gr. 3 (SFVV3) 0.002 25, 288 7, 8 JNES (Narumoto) 136

8 A508-Gr. 3 (SFVV3) 0.003 25 8 JNES (Narumoto) 136

9 A508-Gr. 3 (SFVV3) 0.005 25, 200 31, 2 JNES (Ikemoto, 

Iwadate, Kou, Nihei, 

Fukakura)

136

10 A508-Gr. 3 (SFVV3) 0.003 150, 200, 290 18, 15, 

13

JNES (Kou, Fukakura, 

Iida)

136

11 A508-Gr. 3 (SFVV3) 0.003 25, 200, 290 11, 17, JNES (Nihei, Kou, 136
41

ANL 

Mat. 

ID

Material

Specification

Sulfur 

Content 

(wt.%)

Test 

Temperature 

(°C)

Number 

of Data

Points

Source Applicable 

Reference

24 Fukakura, Iwadate,)

12 A508-Gr. 3 (SFVV3) 0.003 25 10 JNES (Higuchi, Endou) 136

13 A508-Gr. 3 (SFVV3) 0.008 25 8b JNES (Kanasaki) 136

14 A508-Gr. 3 0.002 288 14 Wu & Katada 141

16 A533-Gr. B 0.012 25, 288 6, 16 ANL 10,11,12

17 A533-Gr. B (SQV2A) 0.007 25, 288 14, 14 JNES (Nagata), 

Wu & Katada

136,141

18 A533-Gr. B (SQV2A) 0.001 25, 350 34, 10 JNES (Kazuo Toyam) 136

19 A533-Gr. B (SQV2A) 0.003 25, 300 6, 6 JNES (Narumoto) 136

20 A533-Gr. B (SQV2A) 0.002 25, 286 9, 8 JNES (Narumoto) 136

21 A533-Gr. B (SQV2A) 0.010 25 18c JNES (Iida) 136

22 A533-Gr. B (SQV2A) 0.008 25, 150, 200, 

250, 289

19,

b 1, 1, 

1, 4

JNES (Hirano) 136

23 A533-Gr. B 0.013 288 7 Wu & Katada 143

28 A533-Gr. B 0.014 270 2 MPA 55,56

29 LAS - 25, 170 16, 16 MPA 55,56

31 17MnMoV64 0.018 200 3 S/KWU 55,56 a Six tests performed under load control were excluded. b Includes test results for thermally aged materials. c Tests performed using a sine waveform, and data include results for thermally aged materials. 

In air, the fatigue lives of both carbon and low–alloy steels depend on steel type, temperature, 

and for some compositions, applied strain rate and sulfide morphology. Fatigue ε–N data from 

various investigations on carbon and low–alloy steels are shown in Fig. 27. The best-fit air 

curves based on the ANL models (Eqs. 24 and 25 from Section 3.1.6) and the ASME Section III 

mean–data air curves at room temperature (Eqs. 7 and 8 from Section 1.2) are also included in 

the plots in this figure. The results indicate that, although significant scatter is apparent due to 

material variability, the fatigue lives of these steels are comparable at less than 5 x 105 cycles, 

and those of low–alloy steels are greater than carbon steels for greater than 5 x 105 cycles. In 

addition, the fatigue life at 106 cycles of low–alloy steels is higher than that of carbon steels.

Figure 27. Fatigue strain vs. life data for carbon and low–alloy steels in air at room 

temperature (JNUFAD database and Refs. 10,18,19,48).
42

The results also indicate that the existing fatigue ε–N data for low–alloy steels are in good 

agreement with the ASME mean data curve. The existing data for carbon steels are consistent 

with the ASME mean data curve for fatigue lives below 5 x 105 cycles, and are above the ASME 

mean data curve at longer lives. Thus, for carbon steels above 5 x 105 cycles, the ASME mean 

data curve is conservative with respect to the existing fatigue ε–N data. 

• The ASME Code mean data air curves for carbon and low-alloy steels (Eqs. 7 and 8) are 

either consistent with the existing fatigue ε–N data or are somewhat conservative under 

some conditions.

3.1.2 Temperature

In air, the fatigue lives of both carbon and low–alloy steels decrease with increasing 

temperature; however, the effect is relatively small (less than a factor of 1.5). The existing 

fatigue ε–N data in air at 25–290°C are shown in Fig. 28. As discussed in Section 3.1.1 for 

each grade of steel, the data represent several heats of material. The solid lines in the plots

represent the temperature dependence defined by Eq. 22 in Section 3.1.6. The results indicate 

a factor of approximately 1.5 decrease in fatigue lives of both carbon and low–alloy steels as the 

temperature is increased from room temperature to 300°C. 

• Variations in the fatigue lives in air due to the effects of temperature for carbon and low-alloy 

steels were accounted for in the subfactor for “data scatter and material variability.”

Figure 28. The change in fatigue lives of carbon and low-alloy steels in air as a 

function of temperature. 

3.1.3 Strain Rate

The effect of strain rate on the fatigue lives of carbon and low-alloy steels in air appears to 

depend on the material composition. The existing data indicate that in the temperature range of 

dynamic strain aging (200–370°C), some heats of carbon and low–alloy steels were sensitive to 

strain rate; with decreasing strain rate, the fatigue lives in air were either unaffected,10

decreased for some heats,211 or increased for others.212 The carbon and nitrogen contents in 

the steel are considered to have an important influence on strain rate effects. Inhomogeneous 

plastic deformation can result in localized plastic strains. This localization retards blunting of 

propagating cracks that is usually expected when plastic deformation occurs and can result in 

higher crack growth rates.211 The increases in fatigue lives were attributed to retardation of 
43

CGRs due to crack branching and suppression of the plastic zone.212 Furthermore, as 

discussed earlier, the formation of cracks may be enhanced in the presence of DSA. 

• Variations in fatigue lives in air due to the effects of strain rate for carbon and low-alloy steels 

were accounted for in the subfactor for “data scatter and material variability.” 

3.1.4 Sulfide Morphology

Some high–sulfur steels exhibit very poor fatigue properties in certain orientations because of 

structural factors such as the distribution and morphology of sulfides in the steel. For example, 

fatigue tests on a high–sulfur heat of A302–Gr. B steel in three orientations* in air at 288°C 

indicated that the fatigue life and fatigue limit in the radial (T2) orientation are lower than those 

in the rolling (R) and transverse (T1) orientations.10 At low strain rates, fatigue lives in the T2 

orientation were nearly one order of magnitude lower than in the R orientation. In the 

orientation with poor fatigue resistance, crack propagation occurred preferentially along the 

sulfide stringers and is facilitated by sulfide cracking. 

• Variations in fatigue lives in air due to differences in sulfide morphology for carbon and lowalloy steels were accounted for in the subfactor for “data scatter and material variability.” 

3.1.5 Cyclic Strain Hardening Behavior

The cyclic stress–strain response of carbon and low–alloy steels varies with steel type, 

temperature, and strain rate. In general, these steels show initial cyclic hardening, followed by 

cyclic softening or a saturation stage at all strain rates. Carbon steels, with a pearlite and ferrite 

structure and low yield stress, exhibit significant initial hardening. Low–alloy steels, with a 

tempered bainite and ferrite structure and a relatively high yield stress, show little or no initial 

hardening and may exhibit cyclic softening with continued cycling. For both steels, the 

maximum stress increases as applied strain increases and generally decreases as temperature 

increases. However, at 200–370°C, these steels exhibited DSA, which resulted in enhanced

cyclic hardening, a secondary hardening stage, and negative strain rate sensitivity.211,212 The 

temperature range and extent of DSA varied with composition and structure. 

The effects of strain rate and temperature on the cyclic stress response of A106–Gr B carbon 

steel and A533–Gr B low-alloy steel are shown in Fig. 29. For both steels, cyclic stresses were 

higher at 288°C than at room temperature. At 288°C, all steels exhibited greater cyclic and 

secondary hardening because of DSA. The extent of hardening increased as the applied strain 

rate decreased. 

• Cyclic strain hardening behavior influenced the fatigue limits of materials; variations in fatigue 

lives in air due to the effects of strain hardening for carbon and low-alloy steels were 

accounted for in the subfactor for “data scatter and material variability.” 

 *The three orientations were represented by the direction that was perpendicular to the fracture plane. Both transverse (T1) and radial (T2) 

directions were perpendicular to the rolling direction, but the fracture plane was across the thickness of the plate in the transverse orientation and 

parallel to the plate surface in the radial orientation.
44

3.1.6 Fatigue Life Model

ASTM Standard E 739, “Standard Practice for Statistical Analysis of Linear or Linearized 

Stress–Life (S–N) and Strain–Life (ε–N) Fatigue Data,”4 treats fatigue life, N (or the logarithm of 

the fatigue life), as the dependent variable, and the controlled variables, e.g., stress or strain, as 

the independent variable. The coefficients of a “linear” model are commonly established 

through least–squares curve–fitting of the data using fatigue life as the dependent variable. An 

optimization program sets the coefficients to minimize the sum of the square of the residual 

errors, which are the differences between the predicted and actual values of N or ln(N). 

However, such an approach may not adequately determine the optimum coefficients for a

nonlinear expression such as the Langer curve (Eq. 6), which includes a constant term, C,

related to the fatigue limit. The model does not address the fact that at low strain amplitudes, 

most of the error in life is due to uncertainty associated with either measurement of stress or 

strain or variation in threshold strain caused by material variability. A predictive model based on 

a least–squares fit on N or ln(N) is biased for low strain amplitude (εa); also, data obtained at 

strain amplitudes less than the constant C in Eq. 6 cannot be included in the analysis. On the 

other hand, a least–squares fit on εa does not work well for higher strain amplitudes. The two 

kinds of models are transformations of each other, although the precise values of the 

coefficients differ.

In the statistical model presented in Refs. 130 and 10, the two approaches were combined by 

minimizing the sum of the squared Cartesian distances from the data points to the predicted 

curve (Fig. 30). For low εa, this is very close to optimizing the sum of squared errors in 

predicted εa; at high εa, this is very close to optimizing the sum of squared errors in predicted 

life; and at medium εa, this model combines both factors. Therefore, the use of this model 

addresses the weaknesses identified previously for the model based on residual errors alone. 

To perform this alternate optimization, it was necessary to normalize the x and y axes by 

assigning relative weights that are used in combining the error in life and strain amplitude 

because the x and y–axes are not in comparable units. In this analysis, errors in strain 

amplitude (%) were weighted 20 times as heavily as errors in ln(N). A value of 20 was selected 

for two related reasons. First, this factor led to approximately equal weighting of low and high 

strain amplitude data in the least–squared error computation of model coefficients. Second, 

when the factor was applied to the model to generate probability curves, it yielded a standard 

deviation on strain amplitude comparable to that obtained from the best fit of the high cycle 

fatigue data to Eq. 1.130 Because there was judgment applied in the selection of this value, a 

sensitivity analysis was performed that demonstrated that the coefficients of the model do not

Figure 29. Effect of strain rate and temperature on cyclic stress of carbon and low–

alloy steels.
45

Figure 30.

Schematic diagram of the best-fit of 

the experimental data by minimizing 

the distance between the data point 

and the S-N curve.

change significantly for weight factors between 10 and 25. The normal distance from the best-fit 

curve was estimated as

, (19)

where and represent predicted values, and k = 20. Although R–squared is only applicable 

for linear regression, an approximate value for combined R–squared was derived for illustrative 

purposes. The combined R–squared was defined as

, (20)

where (21)

and and represent the 25th percentile of x and y, respectively. The 25th percentile is 

selected instead of the mean because the mean values are exaggerated due to the nonlinearity 

of the equations, and because higher values are less influential to the model. The value from 

Eq. 20 is not a true R-squared value, but often falls between the x–based R–squared and the y–

based R–squared values; therefore, it is considered to be a better qualitative measure of the 

model’s predictive accuracy because it is not distorted in the way x–based R–squared and y–

based R–squared measures would be.

Fatigue life models presented in the original version of NUREG/CR-6909 for estimating the 

fatigue lives in air of carbon and low-alloy steels in air were developed at ANL as best fits of a 

Langer curve to an updated version of the PVRC database.10,46 From those best fits, the 

fatigue lives, N, of carbon steels was represented by

ln(N) = 6.614 – 0.00124 T – 1.975 ln(εa – 0.113), (22)

and that of low–alloy steels by 

ln(N) = 6.480 – 0.00124 T – 1.808 ln(εa – 0.151), (23)
46

where εa is applied strain amplitude (%), and T is the test temperature (°C). Thus, in roomtemperature (25°C) air, the fatigue lives of carbon steels was expressed as 

ln(N) = 6.583 – 1.975 ln(εa – 0.113), (24)

and that of low–alloy steels, by

ln(N) = 6.449 – 1.808 ln(εa – 0.151). (25)

(a) (b)

(c) (d)

Figure 31. Experimental and predicted fatigue lives of (a, b) carbon steels and 

(c, d) low-alloy steels in air.

Note that Eqs. 24 and 25 were based on incorporation of additional fatigue data and the 

analysis presented in Section 4.1.7 of Ref. 137; the values of the constant A in the equations 

were updated from the values reported in NUREG/CR-658310 and NUREG/CR-6815.46 The 

heat-to-heat variability of these equations is discussed further in Section 3.1.7 of this report. 

Relative to the models presented in NUREG/CR-6583, the fatigue lives predicted by the models 

in the original revision to NUREG/CR-6909 were approximately 2% higher for carbon steel and 

approximately 16% lower for low–alloy steels. The predicted fatigue lives showed good 
47

agreement with the experimental values; the experimental and predicted values were within a 

factor of 3. The experimental and predicted fatigue lives of carbon and low-alloy steel data 

using the expressions defined by Eqs. 24 and 25 are shown in Fig. 31. As discussed in Section 

3.1.7, the greater–than–observed fatigue lives for A106–Gr B steel at room temperature and for 

A216-Gr. WCC at 325°C appear to be due to heat–to–heat variability and not temperature 

effects. 

• The fatigue life models for carbon and low-alloy steels represent mean values of fatigue lives 

in air for specimens tested under fully reversed strain-controlled loading. The effects of 

parameters (such as mean stress, surface finish, size and geometry, and loading history) 

known to influence fatigue lives were accounted for in the several subfactors that were 

applied to the mean data air curve to obtain the fatigue design air curve. 

3.1.7 Heat-to-Heat Variability

Several factors, such as small differences in material composition and structure, can change the 

tensile and fatigue properties of materials. The effect of interstitial element content on DSA and 

the effect of sulfide morphology on fatigue lives are discussed in Sections 3.1.5 and 3.1.4, 

respectively. The effect of tensile strength on fatigue lives was included in the expression for 

the ASME mean data air curve described in the Section III criteria document, i.e., constant Af in 

Eq. 2. In addition, the material fatigue limit was correlated with tensile strength, e.g., the fatigue 

limit increases with increasing tensile yield stress.213

The effects of material variability and data scatter must be included in the data evaluation to 

ensure that the resulting design curves not only describe the available test data adequately, but 

also adequately describe the fatigue lives of the much larger number of heats of material that 

are found in the field compared to the limited number of heats used for testing. The effects of 

material variability and data scatter are often evaluated by comparing the experimental data to a

specific model for fatigue crack initiation, e.g., the best fit (in some sense) to the data. The 

adequacy of the evaluation depends on the sample of data used in the analysis. For example, if 

most of the data were obtained from a heat of material that has poor resistance to fatigue 

damage or under loading conditions that show significant environmental effects, the results may 

be conservative for most of the materials or service conditions of interest. Conversely, if most 

data are from a heat of material with a high resistance to fatigue damage, the results may be 

nonconservative for many heats in service.

Another method to assess the effect of material variability and data scatter is to consider the 

best–fit curves determined from tests on individual heats of materials or loading conditions as 

samples of a much larger population of heats of materials and service conditions of interest. To 

do this, the fatigue behavior of each of the heats or loading conditions was characterized by the 

value of the constant A in Eq. 6. The values of A for the various data sets were rank-ordered, 

and median ranks were used to estimate the cumulative distribution of A for the

population.214,215 The distributions were fit to lognormal curves. No rigorous statistical 

evaluation was performed for these curves, but the fits appeared reasonable and described the 

observed variability adequately. The data were normalized to room-temperature values using 

Eqs. 22 and 23 (Section 3.1.6). The median value of the constant A, reported in the original 

revision of NUREG/CR-6909, was 6.583 and 6.449, respectively, for the fatigue lives of carbon 

steels and low-alloy steels in room-temperature air. The estimated cumulative distributions of 

constant A in the ANL model for fatigue lives for heats of carbon and low-allow steels included 

in the original revision of NUREG/CR-6909 and those included in this report are shown in 

Fig. 32. 
48

(a) (b)

(c) (d)

Figure 32. Estimated cumulative distribution of constant A in the ANL models for 

fatigue life data in the original revision of NUREG/CR-6909 (a, c) and this 

report (b, d); (a, b) for heats of carbon steels and (c, d) low–alloy steels in air. 

The results indicate that the ANL fatigue models presented in the original revision of 

NUREG/CR-6909 for predicting fatigue lives of carbon and low alloy steels in air remain valid. 

In spite of a significant increase in the number of data points, the median value of the constant 

A in Eq. 6 did not change significantly for carbon steels (changed from 6.583 to 6.593) or for 

low-alloy steels (changed from 6.449 to 6.513). Note that the two heats of A106–Gr B carbon 

steel were in the 10th to 25th percentile of the data, i.e., the fatigue lives of these heats were 

much lower than the average value for carbon steels. Also, the average value of the constant A 

for the A216-Gr. WCC steel at 325°C (after adjusting for temperature effects) was 4.899, which 
49

is significantly lower than the median value of 6.583 for carbon steels. Therefore, it was not 

included in the reanalysis of the updated fatigue ε–N database, and the value of the constant A 

for A216-Gr. WCC is not shown in Fig. 32.

As discussed in the original revision of NUREG/CR-6909, the A values that describe the 5th 

percentile of these distributions give fatigue ε–N curves that are expected to bound the fatigue 

lives of 95% of the heats of the materials tested. The cumulative distributions of A values in 

Fig. 32 contain two potential sources of error. The means and standard deviations of the 

populations must be estimated from the means and standard deviations of the samples,216 and 

confidence bounds must be obtained on the population means and standard deviations in terms 

of the sample means and standard deviations. Secondly, even these conditions did not fully 

address the uncertainties in the distributions because of the large uncertainties in the sample 

values themselves, i.e., the “horizontal” uncertainty in the actual value of A for a heat of 

material, as indicated by the error bars in Fig. 32. Therefore, a Monte Carlo analysis was 

performed to address both sources of uncertainty. The results for the median values and 

standard deviations of the constant A from the Monte Carlo analysis did not differ significantly 

from those determined directly from the experimental values. 

The results for carbon and low-alloy steels are summarized in Tables 2 and 3, respectively, in 

terms of values for the constant A that provide bounds for the portion of the population and the 

confidence that is desired in the estimates of the bounds. In air, the 5th percentile value of 

constant A at a 95% confidence level was 5.559 for carbon steels and 5.689 for low-alloy steels. 

From Fig. 32. Since the reanalysis did not change the constants significantly, the median 

values of the constant A for carbon and low-alloy steels were not changed in this report. Thus, 

constant A for the sample remains 6.583 for carbon steels and 6.449 for low-alloy steels, and 

the 95/95 values of the factor to account for material variability and data scatter are 2.8 and 2.1 

on life for carbon and low-alloy steels, respectively. These factors provide 95% confidence that 

the resultant lives are greater than those observed for 95% of the materials of interest.

• The mean data air curves for carbon and low-alloy steels used to develop the fatigue design 

air curves represented the average fatigue behavior; heat-to-heat variability was included in 

the subfactor that was applied to the mean data air curve to obtain the fatigue design air 

curve to account for “data scatter and material variability.” 

Table 2. Values of constant A in the ANL fatigue life model for carbon steels in 

air and the factors on life as a function of confidence level and 

percentage of population bounded. 

Confidence Percentage of Population Bounded (Percentile Distribution of A)

Level 95 (5) 90 (10) 75 (25) 67 (33) 50 (50)

Values of Constant A

50 5.798 5.971 6.261 6.373 6.583

75 5.700 5.883 6.183 6.295 6.500

95 5.559 5.756 6.069 6.183 6.381

Factors on Life

50 2.2 1.8 1.4 1.2 1.0

75 2.4 2.0 1.5 1.3 1.1

95 2.8 2.3 1.7 1.5 1.2
50

Table 3. Values of constant A in the ANL fatigue life model for low–alloy steels in 

air and the factors on life as a function of confidence level and 

percentage of population bounded.

Confidence Percentage of Population Bounded (Percentile Distribution of A)

Level 95 (5) 90 (10) 75 (25) 67 (33) 50 (50)

Values of Constant A

50 5.832 5.968 6.196 6.284 6.449

75 5.774 5.916 6.150 6.239 6.403

95 5.689 5.840 6.085 6.175 6.337

Factors on Life

50 1.9 1.6 1.3 1.2 1.0

75 2.0 1.7 1.3 1.2 1.0

95 2.1 1.8 1.4 1.3 1.1

3.1.8 Fatigue ε-N Behavior of Weld Metals

Available fatigue ε–N data for carbon and low-alloy steel weld metals in air at room temperature 

and 289°C are plotted in Fig. 33. The results indicated that, in air, the fatigue lives of carbon 

and low-alloy steel weld metals were slightly lower than the mean ε–N behavior of non-welded 

carbon or low-alloy steel test specimens. Except for one data set for CM US-56B/MF-27 weld 

metal for which fatigue lives were a factor 2 lower than the mean data curves, the fatigue lives 

of the other data sets were marginally lower. The results also indicated that the fatigue lives at 

289°C were slightly lower than at room temperature. Despite these observations, the available 

fatigue ε–N data for carbon and low-alloy steel weld metals were insufficient to accurately 

establish their fatigue behavior relative to the mean data air curve for carbon steels or low-alloy 

steels, respectively.

Figure 33.

Fatigue ε–N behavior for carbon 

and low-alloy steel weld metals in 

air at room temperature and 289°C

(Ref. 136).

• Until additional fatigue ε–N data for carbon and low-alloy steel weld metals are available, the 

fatigue mean air curves for carbon steel or low-alloy steels may also be used for weld metals. 

3.1.9 Surface Finish

The effect of surface finish was considered to account for the difference in fatigue lives 

expected in an actual component with an industrial–grade surface finish compared to the 

smooth polished surface of test specimens. Fatigue lives are sensitive to surface finish; cracks 

can initiate at surface irregularities that are normal to the axis of applied stress. The height, 
51

spacing, shape, and distribution of surface irregularities are important for crack initiation. The 

most common measure of roughness is average surface roughness, Ra, which is a measure of 

the height of the irregularities. Investigations of the effects of surface roughness on the low–

cycle fatigue of Type 304 SS in air at 593°C indicated that fatigue lives decreased as surface 

roughness increased.217,218 The effect of roughness on crack initiation, Ni

(R), is given by

Ni

(R) = 1012 Rq

–0.21, (26)

where the root–mean–square (RMS) value of surface roughness, Rq, is in μm. Typical values of 

Ra for surfaces finished by different metalworking processes in the automotive industry219

indicated that a value of Ra of 3 μm (or an Rq of 4 μm) represented the maximum surface 

roughness for drawing/extrusion, grinding, honing, and polishing processes, and a mean value 

for the roughness range for milling or turning processes. For carbon or low–alloy steels, an Rq

of 4 μm in Eq. 26 would decrease fatigue life by a factor of 3.7 (the Rq of a smooth polished 

specimen is approximately 0.0075 μm).217 

A fatigue test was conducted on a A106–Gr B carbon steel specimen that was intentionally 

roughened in a lathe, under controlled conditions, with 50-grit sandpaper to produce 

circumferential scratches with an average roughness of 1.2 μm and an Rq of 1.6 μm 

(approximately 62 micro in.).46 The results for smooth and roughened specimens are shown in 

Fig. 34. In air, the fatigue life of a roughened A106–Gr B specimen was a factor of 

approximately 3 lower than that of smooth specimens. Another study of the effect of surface 

finish on the fatigue lives of carbon steels in room–temperature air showed a factor of 2 

decrease in life when Ra was increased from 0.3 to 5.3 μm.220 These results are consistent with 

Eq. 26. Thus, a factor of 2 to 3 on cycles is necessary to account for surface finish effects on 

the fatigue lives of carbon and low-alloy steels. 

Figure 34.

Effect of surface finish on the 

fatigue life of A106–Gr B carbon 

steel in air at 289°C (Ref. 46).

• The effect of surface finish was included as part of the “surface finish and environment” 

subfactor that was applied to the mean data air curves to obtain the fatigue design air curves 

for carbon and low-alloy steels. 

3.1.10 Extension of the Best-Fit Mean Curve from 106 to 1011 Cycles

The experimental fatigue ε–N air curves that were used to develop the 2011 ASME Code 

Section III fatigue design air curve for carbon and low-alloy steels were based on low-cycle 

fatigue data (less than 2 x 105 cycles). The design air curves proposed in this report were 
52

developed from a larger database that included fatigue lives up to 108 cycles. Both the ASME 

mean air curves and the ANL models in this report used the modified Langer equation to 

express the best-fit mean air curves; they are not recommended for estimating fatigue lives 

beyond the range of the experimental data, i.e., in the high–cycle fatigue regime. 

An extension of the current high-cycle fatigue design curves in Section III and Section VIII, 

Division 2 of the ASME Code for carbon and low-alloy steels from 106 to 1011 cycles was 

proposed by W. J. O’Donnell to the ASME Section III Subgroup on Fatigue Strength.* In the 

high-cycle regime at temperatures not exceeding 371°C (700°F), the stress amplitude vs. life 

relationship is expressed as

Sa = Eεa = C1N–0.05, (27)

where εa is applied strain amplitude, E is the elastic modulus, N is the fatigue life, and C1 is a 

constant. A fatigue life exponent of -0.05 was selected based on the fatigue stress range vs. 

fatigue life data on plain plates, notched plates, and typical welded structures given in Welding 

Research Council (WRC) Bulletin 398.221 Because the data were obtained from load-controlled 

tests with an R ratio of zero, they take into account the effect of maximum mean stresses and

may over-estimate the effect of mean stress under strain-controlled loading conditions. In 

addition, the fatigue data presented in WRC Bulletin 398 extend only up to 5 x 106 cycles; 

extrapolation of the results to 1011 cycles using a fatigue life exponent of -0.05 may yield overly 

conservative estimates of fatigue life. Finally, ASME received feedback from the evaluation of 

plant trouble reports, laboratory tests of socket welded joints, and plant operating experience 

that supported their use of Eq. 27.

Manjoine and Johnson213 developed fatigue design curves up to 1011 cycles for carbon steels 

and austenitic SSs from inelastic and elastic strain relationships, which were correlated with 

ultimate tensile strength. The log–log plots of the elastic strain amplitudes vs. fatigue life data 

were represented by a bilinear curve. In the high–cycle regime, the elastic–strain–vs.–life curve 

had a small negative slope instead of a fatigue limit.213 For carbon steel data at room 

temperature and 371°C (700°F) and fatigue lives extending up to 4 x 107 cycles, Manjoine and 

Johnson obtained an exponent of -0.01. The fatigue ε-N data used in this report at room 

temperature and with fatigue lives up to 108 cycles yielded a fatigue life exponent of 

approximately -0.007 for both carbon and low-alloy steels. Because the data are limited, the 

more conservative exponent value (i.e., -0.01) obtained by Manjoine and Johnson213 was used 

in the initial edition of NUREG/CR-6909 report. In the high–cycle regime, the applied stress 

amplitude was expressed by the relationship

Sa = Eεa = C2N–0.01. (28)

In the initial edition of the NUREG/CR-6909, Eq. 28 was used to extend the best-fit mean air 

curves beyond 106 cycles (in the high–cycle regime); thus, the mean stress-life curves exhibited

a small negative slope instead of the fatigue limit predicted by the modified Langer equation. 

The selection of a smaller value for the fatigue life exponent to extend the best-fit curve was 

based on evaluation of thermal fatigue data, which are bounded by Eq. 28. However, the highcycle thermal fatigue data are limited, and the data do not consider mechanical fatigue (i.e., 

vibration). 

 *W. J. O’Donnell, “Proposed Extension of ASME Code Fatigue Design Curves for Carbon and Low-Alloy Steels from 106 to 1011 Cycles for 

Temperatures not Exceeding 700°F,” presented to ASME Subgroup on Fatigue Strength, December 4, 1996.
53

As discussed earlier in this report, the classical fatigue limit for ferrous alloys is a consequence 

of performing fatigue tests at constant cyclic stress or strain range and determining the 

threshold range below which cracks cannot propagate beyond microstructural barriers and

fatigue failures do not occur. Miller and O’Donnell222 discussed the causes that lead to 

elimination of the fatigue limit, including the introduction of transitory cyclic processes or timedependent mechanisms that permit a previously nonpropagating crack to grow across 

microstructural barriers. The authors argued that the most probable significant condition for 

engineering plants designed to last beyond 106 cycles is the introduction of very low cyclic 

stress vibrations at high mean stress levels, with or without other mechanisms such as 

corrosion or time-dependent mechanisms. Therefore, in this report, to better accommodate the 

vibration data (e.g., Ref. 221), the extension of the fatigue stress or strain-life curves beyond

106 cycles is based on the more conservative Eq. 27 rather than Eq. 28, i.e., an exponent 

of -0.05 is used. The value of constant C1 was determined from the value of strain amplitude at 

which the slope of the curve expressed by Eq. 27 is the same as that of the fatigue ε-N curve 

expressed by Eq. 24 for carbon steels or Eq. 25 for low-alloy steels. 

• The fatigue design air curves for carbon and low-alloy steels were extended beyond 

106 cycles using Eq. 27, which is consistent with the methodology used to develop the fatigue 

design air curve for carbon and low-alloy steels in the 2011 Addenda of ASME Code Section 

III.

3.1.11 Fatigue Design Curves

Although the two equations for the ASME Code mean air curves for carbon and low–alloy steels 

(i.e., Eqs. 7 and 8) are significantly different (because the mean stress correction is much larger 

for the low-alloy steels), the differences between the curves are much smaller when mean 

stress corrections are considered. Thus, ASME Code, Section III provides one common fatigue 

design air curve for both carbon and low-alloy steels. The ASME Code fatigue design air curves 

for carbon and low-alloy steels were obtained from the best-fit curves in air (i.e., Eqs. 7 and 8, 

respectively) by first correcting for mean stress effects by using the modified Goodman 

relationship, followed by reducing the mean-stress adjusted curves by factors of 2 on stress or 

20 on cycles, whichever was more conservative. The discussions presented in Section 7.5 of 

the original edition of NUREG/CR-6909 indicated that the current ASME Code requirement of a 

factor of 20 on cycles, to account for the effects of material variability and data scatter, 

specimen size, surface finish, and loading history, was conservative by at least a factor of 1.7

for these steels. To reduce this conservatism, separate fatigue design air curves based on the 

ANL models for carbon and low-alloy steels were developed using factors of 12 on life and 2 on 

stress. The fatigue design air curves developed following this approach for carbon and lowalloy steels are shown in Fig. 35. The difference between the design air curves based on the 

ANL models and the ASME Code design air curve is due to the difference in the factor on life 

used to obtain these curves i.e., 20 for the ASME Code curve and 12 for the ANL curves. In 

addition, for the carbon steel design air curve, the conservatism in the high-cycle regime was 

corrected in the ANL models.

The ASME Code fatigue design air curve for carbon and low–alloy steels with ultimate tensile 

strength (UTS) less than 552 MPa (80 ksi) included an extension of the design curve to 

1011 cycles, which was proposed by W. J. O’Donnell and was based on Eq. 27 in this report. In 

the initial edition of NUREG/CR-6909, the fatigue design air curves developed based on the 

ANL fatigue ε-N models were extended in the high–cycle regime beyond 106 cycles using 

Eq. 28 instead of Eq. 27. However, as discussed in Section 3.1.10, and to better accommodate 

the field vibration data, the extension of the fatigue design curves beyond 106 cycles is based 

on Eq. 27. The values of stress amplitude (Sa) vs. cycles for the ASME Code Section III fatigue 
54

design air curve with O’Donnell’s extension, and the design curve based on Eq. 27 and the ANL 

fatigue life models from Eq. 24 for carbon steels and Eq. 25 for low-alloy steels, are listed in 

Table 4. The corresponding fatigue design air curves are shown in Figs. 36 and 37, 

respectively, for carbon and low-alloy steels. The values of stress amplitude vs. cycles 

presented in the initial edition of NUREG/CR-6909 for the fatigue design air curves based on the 

ANL fatigue ε-N models and Eq. 28 are presented in Table 5 for comparison.

• Separate fatigue design air curves were developed for carbon and low-alloy steels. These 

curves were developed from the ANL models using factors of 12 on life and 2 on stress. The 

results indicated that the ASME Code Section III fatigue design air curve for carbon and lowalloy steels for ultimate tensile strengths less than 552 MPa (80 ksi) was conservative with 

respect to the existing fatigue ε–N data, particularly for carbon steels. In this report, the 

extension of the fatigue design air curves beyond 106 cycles was based on Eq. 27 instead of 

Eq. 28 used in the initial revision to NUREG/CR-6909.

Table 4. Fatigue design curves for carbon and low-alloy steels including proposed 

updated extension to 1011 cycles. 

Stress Amplitude (MPa/ksi) Stress Amplitude (MPa/ksi)

Cycles

ASME 

Code Curve

Eqs. 24 & 27

Carbon Steel

Eqs. 25 & 27

Low-Alloy 

Steel

Cycles

ASME 

Code Curve

Eqs. 24 & 27

Carbon Steel

Eqs. 25 & 27

Low-Alloy 

Steel

1 E+01 3999 (580) 5355 (777) 5467 (793) 2 E+05 114 (16.5) 176 (25.5) 141 (20.5)

2 E+01 2827 (410) 3830 (556) 3880 (563) 5 E+05 93.1 (13.5) 154 (22.3) 116 (16.8)

5 E+01 1896 (275) 2510 (364) 2438 (354) 1 E+06 86.2 (12.5) 142 (20.6) 106 (15.4)

1 E+02 1413 (205) 1820 (264) 1760 (255) 2 E+06 130 (18.9) 98 (14.2)

2 E+02 1069 (155) 1355 (197) 1300 (189) 5 E+06 120 (17.4) 94 (13.6)

5 E+02 724 (105) 935 (136) 900 (131) 1 E+07 76.8 (11.1) 115 (16.7) 91 (13.2)

1 E+03 572 (83) 733 (106) 720 (104) 2 E+07 110 (16.0) 88 (12.7)

2 E+03 441 (64) 584 (84.7) 576 (83.5) 5 E+07 105 (15.2) 84 (12.2)

5 E+03 331 (48) 451 (65.4) 432 (62.7) 1 E+08 68.5 (9.9) 101 (14.7) 81 (11.8)

1 E+04 262 (38) 373 (54.1) 342 (49.6) 1 E+09 61.1 (8.8) 90 (13.1) 72.3 (10.5)

2 E+04 214 (31) 305 (44.2) 276 (40.0) 1 E+010 54.4 (7.9) 81 (11.7) 64.4 (9.3)

5 E+04 159 (23) 238 (34.5) 210 (30.5) 1 E+011 48.5 (7.0) 72 (10.4) 57.4 (8.3)

1 E+05 138 (20.0) 201 (29.2) 172 (24.9)

(a) (b)

Figure 35. Fatigue design curves based on the ANL model for (a) carbon steels and 

(b) low-alloy steels in air. 
55

 

Figure 36.

Fatigue design curve for 

carbon steels in air. The 

curve developed from the 

ANL model is based on 

factors of 12 on life and 2 on 

stress.

 

Figure 37.

Fatigue design curve for 

low-alloy steels in air. The 

curve developed from the 

ANL model is based on 

factors of 12 on life and 2 

on stress. 

Table 5. Fatigue design curves for carbon and low-alloy steels and the extension to 

1011 cycles proposed in the initial revision to NUREG/CR-6909. 

Stress Amplitude (MPa/ksi) Stress Amplitude (MPa/ksi)

Cycles

ASME 

Code Curve

Eqs. 24 & 28

Carbon Steel

Eqs. 25 & 28

Low-Alloy 

Steel

Cycles

ASME 

Code Curve

Eqs. 24 & 28

Carbon Steel

Eqs. 25 & 28

Low-Alloy 

Steel

1 E+01 3999 (580) 5355 (777) 5467 (793) 2 E+05 114 (16.5) 176 (25.5) 141 (20.5)

2 E+01 2827 (410) 3830 (556) 3880 (563) 5 E+05 93 (13.5) 154 (22.3) 116 (16.8)

5 E+01 1896 (275) 2510 (364) 2438 (354) 1 E+06 86 (12.5) 142 (20.6) 106 (15.4)

1 E+02 1413 (205) 1820 (264) 1760 (255) 2 E+06 130 (18.9) 98 (14.2)

2 E+02 1069 (155) 1355 (197) 1300 (189) 5 E+06 120 (17.4) 94 (13.6)

5 E+02 724 (105) 935 (136) 900 (131) 1 E+07 76.5 (11.1) 115 (16.7) 91 (13.2)

1 E+03 572 (83) 733 (106) 720 (104) 2 E+07 110 (16.0) 90 (13.1)

2 E+03 441 (64) 584 (84.7) 576 (83.5) 5 E+07 107 (15.5) 88 (12.8)

5 E+03 331 (48) 451 (65.4) 432 (62.7) 1 E+08 68.3 (9.9) 105 (15.2) 87 (12.6)

1 E+04 262 (38) 373 (54.1) 342 (49.6) 1 E+09 60.7 (8.8) 102 (14.8) 83 (12.0)

2 E+04 214 (31) 305 (44.2) 276 (40.0) 1 E+010 54.5 (7.9) 97 (14.1) 80 (11.6)

5 E+04 159 (23) 238 (34.5) 210 (30.5) 1 E+011 48.3 (7.0) 94 (13.6) 77 (11.2)

1 E+05 138 (20.0) 201 (29.2) 172 (24.9)
56

3.2 Wrought and Cast Austenitic Stainless Steels and Weld Metals

3.2.1 Experimental Data

The relevant fatigue ε–N data used to evaluate wrought and cast austenitic SSs in air include

the large JNES database;136 data developed at ANL45 and GE;14,15 results of Keller,63 and the 

data64,65,70,73 compiled by Jaske and O'Donnell61 for developing fatigue design criteria for 

pressure vessel alloys. The database is composed of 770 tests from which 622 data points 

were obtained; 332 tests (267 data points) on Type 304 SS, 315 tests (244 data points) on 

Type 316 SS, 96 tests (77 data points) on SS weld metals (34 tests (23 data points) on Type 

304 SS and 62 tests (54 data points) on Type 316 SS weld metals), and 37 tests (34 data 

points) for CF-8M grade of cast austenitic SSs. Both low-carbon and high-carbon grades of 

Types 304 and 316 SS are included in the database. Out of these, 432 data points were 

obtained at room temperature, 7 data points were obtained at 100-200°C, and 183 data points 

were obtained at 250–325°C. Another 70 data points obtained at temperatures of 400°C and 

above were not included in the present reanalysis to verify the fatigue ε–N expression for 

austenitic SSs in air because they were outside of the temperature range experienced in LWRs. 

As discussed in Section 3.2.4, the fatigue ε–N data for austenitic SSs shows some temperature 

dependence above 460°C. A summary of the points included in the updated database used for 

the present analyses, as categorized by material type and test environment, is presented in

Table 6. Other material information such as chemical composition, heat treatment, and room 

temperature tensile properties of the various types and heats of materials is given in 

Appendix B.

Table 6. Sources of the fatigue ε–N data on wrought and cast austenitic stainless steels 

in an air environment.

ANL 

Mat. 

ID

Material 

Heat 

Designationa

Carbon 

Content 

(wt.%)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

Type 304 Stainless Steels

1 304-1 0.050 288 10 JNES (Tokimasa) 136

2 304-30, 31 0.050 25 10, 4 JNES (Yamanaka), 136

3 304-3H 0.060 25 8 JNES (Enomoto), 136

4 304-4B 0.050 25 10 JNES (Kitigawa) 136

5 304-5B 0.060 25 3 JNES (Sakamoto) 136

6 304-6B 0.060 25 11 JNES (Tsunenari) 136

7 304-7B 0.059 25 10 JNES (Kasahara) 136

8 304-8B 0.060 25 6 JNES (Ichihara) 136

10 304-10, 10H 0.060 25, 300, 100 2, 7, 2 JNES (Usami) 136

11 304-11H 0.070 25 7 JNES (Yamanaka) 136

12 304-12 - 25 11 JNES (Nishijima) 136

13 304-13 0.026 21 10 Jaske & O’Donnell 64

14 304-14 0.026 21 9 Jaske & O’Donnell 64

15 304-15 - 21 6 Jaske & O’Donnell 63

16 304-16 0.060 21 8 Jaske & O’Donnell 70

17 304-17 - 21 6 Jaske & O’Donnell 65

18 304-18 0.020 27 8 Jaske & O’Donnell 73

20 304-G 0.060 25, 260 9, 9b GE 14,15

21 304-A2 0.060 288 4 ANL 45

22 304-21, 21T 0.060 25, 325 2, 7 JNES (Kanasaki, 

Tsutsumi) 136
57

ANL 

Mat. 

ID

Material 

Heat 

Designationa

Carbon 

Content 

(wt.%)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

23 304-32 0.070 300 3 JNES (Endo) 136

24 304-35 0.070 25, 289 8,

c 5 JNES (Hirano) 136

26 304HP-1 0.050 25 6 JNES (Nishijima) 136

27 304HP-2 0.060 25 17,

c 14c,d JNES (Nishijima) 136

28 304L-E 0.039 150,300 5, 11 Solomon 58-60

29 304L-1 0.017 25 5 JNES (Hirano) 136

30 304L-G 0.022 260 7 GE 14,15

31 304L 0.013 25 9 JNES (Suzuki) 136

Type 316 Stainless Steels

32 316-1H 0.055 25, 290 7, 8 JNUFAD (Tokimasa) 210

33 316-2 0.050 25 6 JNES (Kaneo) 136

34 316-3H 0.040 25 6 JNES (Ikemoto) 136

35 316-4 0.060 21 4 Jaske & O’Donnell 63

38 316-7 - 21 8 Jaske & O’Donnell 61

39 316-8 - 22 3 Jaske & O’Donnell 61

40 316-9 - 21 5 Jaske & O’Donnell 61

41 316-10 - 21 4 Jaske & O’Donnell 61

42 316-12T, 25T 0.060 325, 25 7, 5 JNES (Kanasaki, 

Tsutsumi) 136

45 316-25, -25, -27T 0.040, 

0.060 25, 325, 25 4, 6, 6 JNES (EFT, PLEX) 136

46 316-26T 0.057 25 10e JNES (EFT) 136

47 316-1H, 316L-1H 0.055, 

0.015 25, 290 7, 7 JNES (Tokimasa) 136

48 316N-1 0.010 25, 288 25b, 18b JNES (Yamauchi, 

Matsuno, Tokimasa) 136

50 316N-3H 0.012 25, 290 7, 7 JNES (Tokimasa) 136

51 316N-6 0.007 25 12 JNES (Higuchi) 136

52 316N-7 0.008 25, 290 25, 14

JNES (Utsunomiya, 

Nagata, Higuchi, 

Kanasaka, Ogawa)

136

53 316N-8 0.011 25, 289 5, 8 JNES (Hirano) 136

54 316N-A 0.013 22, 288, 320 12, 6, 3 ANL 45

Stainless Steel Weld Metals

55 304HP-WM-1 0.058 25 7d, 10 JNES (Nishijima) 136

56 304-WM-2 0.034 25 6 JNES (Kanasaki) 136

57 316-WM 0.020 25 6f JNES (EFT) 136

58 316N-WM-1 0.018 25, 290 13, 11 JNES (Ogawa, Nagata) 136

59 316N-WM-2 0.017 25, 289 10, 7 JNES (Hirano) 136

60 316N-WM-3 0.002 25 7 JNES (Kanasaki) 136

Cast Austenitic Stainless Steels

61 CF–8M-1 0.053 325 12 JNES (Tsutsumi) 136

62 CF–8M-2 0.050 25 10 JNES (Hirano) 136

63 CF–8M-3 0.050 25 6 JNES (Kanasaki) 136

68 CF–8M-8 0.064 288 5b ANL 45

69 CF–8M-9 0.065 288 1b ANL 45 a The last letter at the end of the material heat designation refers to the following: H = hourglass specimens, T = tube specimens, 

and B = bending tests. b Includes thermally aged specimens. c Half the tests performed on hourglass specimens. d Tests performed in axial load-control using a sinusoidal waveform. e Five tests each performed on solid cylindrical specimens and tube specimens. 

f Tests performed on tube specimens.
58

The fatigue ε–N data for Types 304, 304L, 316, and 316NG SSs in air at temperatures between 

room temperature and 400°C are shown in Fig. 38. The best–fit air curve based on the updated 

ANL fatigue life model (Eq. 29 in Section 3.2.6) and the mean-data air curve from ASME Code 

Section III prior to the 2009b Addenda are included in the plots in this figure. The results 

indicate that the fatigue lives of Types 304, 304L, and 316 SS are comparable and show 

excellent agreement with the ANL model with respect to the mean data air curve. The fatigue 

lives of Type 316NG are slightly higher than those for Types 304, 304L, and 316 SS at high 

strain amplitudes. However, all of the data are evenly distributed within the scatter band along 

the ANL mean air curve for austenitic SSs. Some of the tests on Type 316 SS in room–

temperature air were conducted in load–control mode at stress levels in the range of 190–

230 MPa. The data are shown as triangles in Fig. 38, with strain amplitudes of 0.1–0.12% and 

fatigue lives in the range of 7 x 104 to 3 x 107 cycles. For these tests, the strain amplitude was 

calculated only as elastic strain rather than also including the portion of the strain from plastic 

loading. When plastic strain was considered, based on cyclic stress–vs.–strain correlations for 

Type 316 SS,45 actual strain amplitudes for these tests ranged from 0.23 to 0.32%. Therefore, 

these results were excluded from the analysis of the fatigue ε–N data to develop the model for 

estimating the fatigue lives of these steels in air so as not to interject an inconsistent bias in the 

evaluation. 

Figure 38. Fatigue ε-N behavior for Types 304, 304L, 316, and 316NG SS austenitic 

stainless steels in air at various temperatures up to 400°C (Refs. 13,42-47,

61,136).
59

The results in Fig. 38 indicated that the mean-data air curve in Section III of the ASME Code 

prior to the 2009b Addenda was not consistent with the existing fatigue ε–N data for austenitic 

SSs. At strain amplitudes less than 0.3% [stress amplitudes less than 585 MPa (84.9 ksi)], the 

ASME Code mean air curve predicted significantly longer fatigue lives than those observed 

experimentally for several heats of austenitic SSs with compositions and tensile strengths within 

the ASME specifications. The difference between the ASME Code Section III mean air curve 

and the best–fit of the available experimental data was caused by differences in the tensile 

strengths of the steels. The ASME Code Section III mean air curve represents SSs with 

relatively high tensile strengths; the fatigue ε–N data obtained during the last 30 years were 

obtained on SSs with lower tensile strengths. Furthermore, for the mean air curve from 

Section III of the ASME Code prior to the 2009b Addenda, the 106-cycles fatigue limit (i.e., the 

stress amplitude at a fatigue life of 106 cycles) was 389 MPa, which is greater than the 

monotonic yield strength of austenitic SSs most commonly used (approximately 303 MPa). 

Consequently, the fatigue design air curve for austenitic SSs in Section III of the ASME Code 

did not include a mean stress correction for fatigue lives below 106 cycles. Studies by Wire et 

al.223 and Solomon, et al.,58 on the effects of residual stress on fatigue lives demonstrated that 

mean stress decreased the 106-cycles fatigue limits of materials; the extent of these effects 

depended on the cyclic hardening behavior of the materials and the resultant decreases in 

strain amplitudes developed during load-controlled cycling. Strain hardening is more 

pronounced at high temperatures (e.g., 288-320°C) or at high mean stress values (e.g., greater 

than 70 MPa); therefore, as observed by Wire et al. and Solomon et al., fatigue lives for loadcontrolled tests with mean stress were actually increased at high temperatures or large values 

of mean stress. In both studies, under load controlled conditions, mean stress effects were 

observed at low temperatures (150°C) or at relatively low mean stress values (less than 

70 MPa).

Wire et al.223 performed fatigue tests on two heats of Types 304 SS to establish the effects of 

mean stress under both strain controlled and load controlled conditions. The strain-controlled 

tests indicated “an apparent reduction of up to 26% in strain-amplitude occurred in the low and 

intermediate cycle regime (<106 cycles) for a mean stress of 138 MPa.” However, the results 

were affected by both mean stress and cold work. Although the composition and vendorsupplied tensile strengths for the two heats of Type 304 SS were within ASME Code 

specifications, the measured mechanical properties showed much larger variations than 

indicated by the vendor properties. Wire et al. stated, “at 288°C, yield strength varied from 152-

338 MPa. These wide variations are attributed to variations in [cold] working from the surface to 

the center of the thick cylindrical forgings.” After separating the individual effects of mean stress 

and cold work, the Wire et al. results indicated a 12% decrease in strain amplitude for a mean 

stress of 138 MPa. These results were consistent with the predictions based on conventional 

mean stress models such as the Goodman correlation. 

The current ASME Code Section III fatigue design air curve (i.e., 2009b Addenda or later 

editions of the ASME Code) is based on the ANL model presented in Eq. 29. This curve is 

consistent with the extensive fatigue ε–N data analyzed in this report. Additional details of the 

analysis are presented in Section 3.2.6.

• The ASME Code Section III fatigue design air curve is now based on the ANL model and is 

consistent with the existing fatigue ε–N data for austenitic SSs.
60

3.2.2 Specimen Geometry and Type of Loading

The influence of specimen geometry (hourglass vs. gauge length specimens) on the fatigue 

lives of Types 304 and 316 SS is shown in Fig. 39. At temperatures up to 300°C, specimen 

geometry had little or no effect on the fatigue lives of austenitic SSs; the fatigue lives of 

hourglass specimens were comparable to those of gauge specimens.

Figure 39. Influence of specimen geometry on fatigue lives of Types 304 and 316 

stainless steels (JNUFAD data).

Figure 40 shows the results of strain-controlled bending fatigue tests tested on rectangular bar 

specimens of Type 304 SS in room-temperature air. Although all of the fatigue tests were 

performed at high strain amplitudes (i.e., producing fatigue lives less than 104 cycles), the 

bending-test data were evenly distributed along the ANL mean data air curve for austenitic SSs.

• Fatigue ε–N data obtained on hourglass specimens, straight gauge specimens, or bending 

test specimens may be used to develop the fatigue design air curves.

Figure 40.

Influence of bending loading on 

fatigue lives of Types 304 and 316 

stainless steels (JNUFAD data).
61

3.2.3 Strain Rate

A statistical analysis of the fatigue ε–N data presented in Ref. 45 indicated that the fatigue lives 

of austenitic SSs in an air environment decreased with decreasing strain rate at temperatures 

between 400 and 430°C. However, studies at EdF in France indicated that variations in strain 

rate in the range of 0.4–0.008%/s had no effect on the fatigue lives of SSs at temperatures up to

400°C.57 Thus, for the fatigue data analysis presented in this report, strain rate effects on 

fatigue lives in air were considered insignificant.

• Effects of strain rate on the fatigue lives of austenitic SSs in air were considered insignificant. 

3.2.4 Temperature

The fatigue lives of austenitic SSs in air at temperatures between room temperature and 400°C 

are plotted in Fig. 38. The results indicated that the fatigue lives of Types 304, 304L, 316, and 

316NG SS did not show any dependence on temperature from room temperature up to 400°C. 

These results are consistent with the observation of Amzallag et al. (Ref. 57). 

Additional fatigue data at temperatures between 427 and 456°C are plotted in Fig. 41.61-63 The 

results indicated that the fatigue ε–N data at temperatures between 400 and 460°C were evenly 

distributed along the ANL best-fit air curve. Furthermore, for austenitic SSs, DSA is typically 

observed at temperatures of 500-600°C.206 Therefore, based on these results, the fatigue ε–N

data for austenitic SSs in air was represented by a single curve for temperatures from room 

temperature up to 450°C.

Figure 41.

Influence of temperature on fatigue 

lives of austenitic stainless steels in 

air (Ref. 61-63).

 

However, studies at GE by Solomon et al. indicate that temperature influenced the fatigue limit 

of austenitic SSs because of differences in the secondary hardening behavior of the material.60 

Secondary hardening is the transformation of retained austenite to martensite causing an 

increase in hardness. This frequently occurs in high alloy steels due to precipitation of carbides 

during the tempering process. For a heat of Type 304L SS, the fatigue limit was higher at 

300°C than at 150°C because of significant secondary hardening at 300°C. 

• Temperature had no significant effect on the fatigue lives of austenitic SSs in air at 

temperatures from room temperature up to 450°C. Variations in fatigue lives due to the 

effects of secondary hardening behavior were accounted for in the factor applied on stress 

that was applied to obtain the design air curve from the mean data air curve.
62

3.2.5 Cyclic Strain Hardening Behavior

Under cyclic loading, austenitic SSs exhibited rapid hardening during the first 50–100 cycles; as 

shown in Fig. 42, the extent of hardening increased with increasing strain amplitude and 

decreasing temperature and strain rate.45 The initial hardening was followed by a softening and 

saturation stage at high temperatures and by continuous softening at room temperature. 

The cyclic stress–vs.–strain curves for Types 316, 304, and 316NG SS at room temperature 

and 288°C are shown in Fig. 43; cyclic stress corresponds to the value at half-life at a strain rate 

of 0.4%/s. For the various steels, cyclic stresses increased in magnitude in the following order: 

Types 316NG, 304, and 316.45

• Cyclic strain hardening behavior influenced the fatigue lives of SS materials; variations in 

fatigue lives due to such effects were accounted for in the factor of 2 on stress that was 

applied to obtain the design air curve from the mean data air curve.

Figure 42.

Effects of strain amplitude, 

temperature, and strain rate on cyclic 

strain–hardening behavior of Types 

304 and 316NG SSs in air at 288°C and 

room temperature.
63

Figure 43.

Cyclic stress-strain curves for Types 

316, 304 and 316NG SSs in air at room 

temperature and 288°C.

3.2.6 Fatigue Life Model

In the initial revision of NUREG/CR-6909,137 an updated version of the PVRC database was 

used to develop the best-fit mean air curve for austenitic SSs. The sources were listed in 

Table 1 of the report. The data were obtained on smooth specimens tested under straincontrolled conditions with fully reversed loading (i.e., R = -1) in compliance with consensus 

standard approaches used for the development of such data. The database consisted of 520 

tests on Types 304, 316, 304L, 316L and 316NG SSs; approximately 220 of the tests were for 

Type 304 SS; 150 tests were for Type 316 SS; and 150 tests were for Types 316NG, 304L, and 

316L SSs. The austenitic SSs used in these studies complied with the compositional and 

strength requirements of ASME Code specifications. The best-fit methodology described in 

Section 3.1.6 for carbon and low-alloy steels was also used for the analysis of the fatigue ε-N 

data for austenitic SSs. 

Several different best-fit mean ε-N curves for austenitic SSs were previously proposed in the 

literature. Examples include Jaske and O’Donnell,61 Diercks,224 Chopra,45 Tsutsumi et al.,34

and Solomon and Amzallag.225 These curves differ by up to 50%, particularly in the 104 to 107

cycles regime. The constant C in Eq. 6 (related to the fatigue limit of the material) varied from a

value of 0.110 proposed by Tsutsumi and 0.112 by Jaske and O’Donnell to a value of 0.167 

proposed in the original ASME Code Section III mean air curve. The differences primarily 
64

occurred because different databases were used in developing these models for the mean ε-N 

curves. The analyses by Jaske and O’Donnell and by Diercks were based on Jaske and 

O’Donnell’s data.

Tsutsumi et al. used the JNUFAD data, which are included in the JNES database.136 In the 

initial revision of NUREG/CR-6909, the updated PVRC data were analyzed to develop the ANL 

model for austenitic SSs; the updated PVRC data included the JNUFAD database. In addition, 

unlike the earlier ANL reports that proposed separate expressions for high-carbon and lowcarbon grades of SSs, a single expression was developed for the fatigue ε–N behavior of 

austenitic SSs. The model assumed that fatigue lives in air were independent of temperature 

and strain rate. Consistent with the models proposed by Tsutsumi34 and by Jaske and 

O’Donnell,61 the value of the constant C in the modified Langer equation (Eq. 6) was lower than 

that in earlier reports (i.e., 0.112 instead of 0.126). The proposed curve yielded an R2 value of 

0.851 when compared with the updated PVRC data; the R2 values for the mean curves derived 

by Tsutsumi et al., Jaske and O’Donnell, and the ASME Code were 0.839, 0.826, and 0.568, 

respectively.

In air at temperatures up to 400°C, the fatigue lives for Types 304, 304L, 316, 316L, and 316NG 

SSs were represented by the expression: 

ln(N) = 6.891 – 1.920 ln(εa – 0.112) (29)

where εa is applied strain amplitude (%). The experimental values of fatigue lives and those 

predicted by Eq. 29 for austenitic SSs in air are plotted in Fig. 44. The predicted lives showed 

good agreement with the experimental values; for most tests, the differences between the 

experimental and predicted values were within a factor of 3. For some tests, the observed 

fatigue lives at low strain amplitudes (i.e., amplitudes that yielded fatigue lives greater than 

5x104 cycles) were significantly longer than the predicted values.

• The ANL fatigue life model for austenitic SSs represents mean values of fatigue lives in air. 

The effects of parameters (such as mean stress, surface finish, size and geometry, and 

loading history) known to influence fatigue lives were accounted for in the factors of 12 on life 

and 2 on stress that were applied to the mean data air curve to obtain the fatigue design air 

curve.

Figure 44. Experimental and predicted fatigue lives (using the ANL model) for 

austenitic SSs in air.
65

3.2.7 Heat-to-Heat Variability

The effects of material (heat-to-heat) variability and data scatter were included in the fatigue

model to ensure that the design curves describe the available test data adequately, and 

adequately describe the fatigue lives of the much larger number of heats of materials found in 

the field compared to the limited numbers of heats tested in the laboratory. As mentioned 

earlier for carbon and low-alloy steels, heat-to-heat variability and data scatter in the fatigue ε-N 

data for austenitic SSs were also evaluated by considering the best–fit curves determined from 

tests on individual heats of materials or loading conditions as samples of the much larger 

population of heats of materials and service conditions of interest. The fatigue lives of each of 

the heats or loading conditions were characterized by the value of the constant A in Eq. 6. The 

values of A for the various data sets were rank-ordered, and median ranks were used to 

estimate the cumulative distribution of A for the population. The distributions were fit to 

lognormal curves. The estimated cumulative distributions of constant A in the ANL model for 

fatigue lives of heats of wrought and cast austenitic SSs included in the initial revision of 

NUREG/CR-6909 and those included in this report are shown in Fig. 45. Note that the new 

updated database used in this report consisted of 622 data points; a significant increase (74%) 

compared to the 357 data points used in the initial revision of NUREG/CR-6909. The data were 

obtained on 5 types of austenitic SSs, 4 types of associated SS weld metals, and one type of 

cast austenitic SS. There are a total of 86 different heats of these materials.

(a) (b)

Figure 45. Estimated cumulative distribution of constant A in the ANL model for 

fatigue lives for heats of austenitic SSs in air included in (a) the initial 

revision of NUREG/CR-6909 and (b) those included in this report.

The results of the reanalysis indicated that the ANL fatigue model presented in the initial 

revision of NUREG/CR-6909 for predicting fatigue lives of austenitic SSs in air was adequate 

and remains representative of the updated (larger) database. Despite the significant increase in 

data, the reanalysis of the much larger updated database yielded an insignificant change in the 

median value of the constant A in Eq. 6. The constant A increased from 6.891 to 6.917. In 
66

addition, Fig. 45 indicates that the various heats of wrought austenitic SSs and the associated 

SS weld metals were evenly distributed about the median value of constant A. The few heats of 

CF–8M cast austenitic SS were in the 15th – 30th percentile of the data, i.e., the fatigue lives of 

the heats of CF–8M were lower than the average values for austenitic SSs. However, this does 

not necessarily indicate that cast CF–8M materials have marginally lower fatigue lives than the 

average wrought SS material. This behavior is representative for this specific sample. 

Additional fatigue ε–N data are needed on cast austenitic SSs to better establish the typical 

fatigue behavior of cast SS materials. 

The values of the constant A that describe the 5th percentile of the statistical distributions 

produced a fatigue ε–N curve that bounded the fatigue lives of 95% of the heats of austenitic 

SSs. A Monte Carlo analysis was performed to address the data uncertainties in the median 

value and standard deviation of the sample used for the analysis. For austenitic SSs, the 

values for A that provided bounds for the portion of the population and the confidence that was 

desired in the estimates of the bounds are summarized in Table 7. From Fig. 45, since the 

reanalysis did not change the constant A significantly, the median value of the constant A for 

austenitic SSs was not changed in this report. Thus, the median value of A for the sample 

remains 6.891. From Table 7, the 95/95 value of the factor to account for material variability 

and data scatter is 2.3 on life. This factor is needed to provide reasonable confidence that the 

resultant lives are greater than those observed for 95% of the SS materials of interest.

Table 7. Values of constant A in the ANL fatigue life model for austenitic SSs

and the factors on fatigue lives for austenitic SSs in air as a function of 

confidence level and percentage of population bounded. 

Confidence Percentage of Population Bounded (Percentile Distribution of A)

Level 95 (5) 90 (10) 75 (25) 67 (33) 50 (50)

Values of Constant A

50 6.205 6.356 6.609 6.707 6.891

75 6.152 6.309 6.569 6.668 6.851

95 6.075 6.241 6.510 6.611 6.793

Factors on Life

50 2.0 1.7 1.3 1.2 1.0

75 2.1 1.8 1.4 1.2 1.0

95 2.3 1.9 1.5 1.3 1.1

• The mean data air curve for austenitic SSs used to develop the fatigue design air curve 

represented the average fatigue behavior; heat-to-heat variability was included in the 

subfactor that was applied to the mean data air curve to obtain the fatigue design air curve to 

account for “data scatter and material variability.” 

3.2.8 Fatigue ε-N Behavior of Cast Austenitic Stainless Steels

Available fatigue ε–N data29,34,43,45 indicated that the fatigue lives of cast CF–8M SSs in air 

were similar to those of wrought austenitic SSs. The fatigue ε–N data for CF–8M cast austenitic 

SS in air, at temperatures between room temperature and 325°C, are plotted in Fig. 46. The 

results indicated that the fatigue lives of cast SSs were evenly distributed along the ANL best-fit 

curve for the mean data for wrought austenitic SSs. 
67

Figure 46.

Fatigue ε–N behavior for 

several heats of CF-8M cast 

austenitic SSs in air at various 

temperatures.

The effects of thermal aging at 250–400°C on the fracture toughness properties of cast 

austenitic SSs are well established. Fracture toughness decreased significantly after thermal 

aging because of the spinodal decomposition of the ferrite phase to form a Cr–rich α’ phase.229-

232 The cyclic–hardening behavior of cast austenitic SSs was also influenced by thermal 

aging.45 The spinodal decomposition of the ferrite phase during thermal aging at 400°C 

strengthened the ferrite phase and increased cyclic hardening. At 288°C, cyclic stresses of cast 

SSs aged for 10,000 h at 400°C were higher than for unaged material or wrought SSs. The 

existing data were too sparse to establish the effects of thermal aging on strain–rate effects on 

the fatigue lives of cast SSs in air. 

• The fatigue mean data air curve for wrought austenitic SSs may be used for cast austenitic 

SSs. 

3.2.9 Fatigue ε-N Behavior of Weld Metals

Available fatigue ε–N data for Types 304, 340HP (i.e., high purity), 316, and 316NG weld metals 

in air at room temperature are plotted in Fig. 47. The results indicated that the fatigue lives of 

SS weld metals were slightly lower than the mean ε–N air curve for austenitic SSs in the lowcycle fatigue regime (i.e., fatigue lives less than 104 cycles), and generally longer in the highcycle regime. However, the weld metal data were within the scatter band for the various grades 

and heats of austenitic SSs.

• The limited fatigue ε–N air data indicate that the mean data air curve for wrought austenitic 

SSs may be used for SS weld metals. 
68

Figure 47.

Fatigue ε–N behavior for 

austenitic SS weld metals 

in air at room temperature.

3.2.10 Surface Finish

Fatigue tests were conducted on Types 304 and 316NG SS specimens that were intentionally 

roughened in a lathe, under controlled conditions, with 50-grit sandpaper to produce 

circumferential scratches with an average surface roughness of 1.2 μm.46 The results are 

shown for Types 316NG and 304 SS in Figs. 48a and b, respectively. For both steels, the 

fatigue lives of the roughened specimens were a factor of approximately 3 lower than those of 

the smooth specimens.

• The effect of surface finish was included as part of the “surface finish and environment” 

subfactor that was applied to the mean data air curve to obtain the fatigue design air curve 

for austenitic SSs.”

(a) (b)

Figure 48. Effects of surface roughness on fatigue lives of (a) Type 316NG and 

(b) Type 304 SSs in air (Ref. 46). 
69

3.2.11 Fatigue Design Curve

As discussed in Section 3.2.1, the ASME Code mean–data that were used to develop the 

current ASME Code Section III fatigue design air curve were not consistent with the existing 

fatigue ε–N data. Therefore, a fatigue design air curve that was consistent with the existing 

database was derived from the ANL model (Eq. 29) by following the same procedure that was 

used to develop the ASME Code Section III fatigue design air curve. The discussions 

presented in Section 5.5 indicated that the current ASME Code Section III requirement for a 

factor of 20 on cycles to account for the effects of material variability and data scatter, specimen 

size, surface finish, and loading history was conservative by at least a factor of 1.7. Therefore, 

to reduce this conservatism, an fatigue design air curve based on the ANL model for austenitic 

SSs (Eq. 29) was developed by correcting for mean stress effects using the modified Goodman 

relationship and then lowering the mean–stress–adjusted curve by a factor of 2 on stress and

12 on cycles, whichever was more conservative. The resulting fatigue design air curve and the 

fatigue design air curve in ASME Code Section III prior to the 2009b Addenda were presented in 

the original revision of NUREG/CR-6909. The two fatigue design air curves were identical 

beyond 108 cycles. In 2009, the new fatigue design air curve based on the ANL model for 

austenitic SSs was adopted into Mandatory Appendix I of Section III of the ASME Code. Both 

of the ASME Code Section III air fatigue design air curves are shown in Fig. 49, and the values 

of stress amplitude vs. cycles for the current and the proposed design air curves are given in 

Table 8. In 2005, a new fatigue design air curve was also proposed for austenitic SSs and 

Alloy 600 and 800 materials by the ASME Section III Subgroup on Fatigue Strength.125

• A new fatigue design air curve for austenitic SSs that is consistent with the existing data was 

developed from the ANL model using factors of 12 on life and 2 on stress. This curve is the 

same as the ASME Code Section III fatigue design air curve implemented in 2009.

Table 8. The ASME Code fatigue design curves for austenitic SSs in air.

No. of Stress Amplitude MPa (ksi) No. of Stress Amplitude MPa (ksi)

Applied 

Cycles

ASME Code Design 

Curve

ASME Code Design 

Curve Prior to 2009

Applied 

Cycles

ASME Code Design 

Curve

ASME Code Design 

Curve Prior to 2009

1 E+01 6000 (870) 4881 (708) 2 E+05 168 (24.4) 248 (35.9)

2 E+01 4300 (624) 3530 (512) 5 E+05 142 (20.6) 214 (31.0)

5 E+01 2748 (399) 2379 (345) 1 E+06 126 (18.3) 195 (28.3)

1 E+02 1978 (287) 1800 (261) 2 E+06 113 (16.4) 157 (22.8)

2 E+02 1440 (209) 1386 (201) 5 E+06 102 (14.8) 127 (18.4)

5 E+02 974 (141) 1020 (148) 1 E+07 99 (14.4) 113 (16.4)

1 E+03 745 (108) 820 (119) 2 E+07 105 (15.2)

2 E+03 590 (85.6) 669 (97.0) 5 E+07 98.6 (14.3)

5 E+03 450 (65.3) 524 (76.0) 1 E+08 97.1 (14.1) 97.1 (14.1)

1 E+04 368 (53.4) 441 (64.0) 1 E+09 95.8 (13.9) 95.8 (13.9)

2 E+04 300 (43.5) 383 (55.5) 1 E+10 94.4 (13.7) 94.4 (13.7)

5 E+04 235 (34.1) 319 (46.3) 1 E+11 93.7 (13.6) 93.7 (13.6)

1 E+05 196 (28.4) 281 (40.8) 2 E+10
70

Figure 49. Fatigue design curves for austenitic SSs in air. 
71

3.3 Ni-Cr-Fe Alloys and Weld Metals

The relevant fatigue ε–N data for Ni-Cr-Fe alloys and their welds in air environments include the 

data compiled by Jaske and O'Donnell61 for developing fatigue design criteria for pressure 

vessel alloys; the JNES database from Japan, which included studies at MHI, IHI, and Hitachi;39

,136,210 studies at Bettis Atomic Power Laboratory,70 Knolls Atomic Power Laboratory,67,68

NASA;73 Battelle’s Columbus Laboratories69 and GE;14,71,72 work sponsored by EPRI at 

Westinghouse Electric Corporation;66 and the tests performed by Van Der Sluys et al.75 The 

database was composed of 588 tests from which 559 data points were obtained; 191 data 

points for 17 heats of Alloy 600, 17 data points for 3 heats of Alloy 690, 23 data points for 2 

heats of Alloy 800, 196 data points for 7 heats of Alloy 718; and 140 tests of Ni-Cr-Fe weld 

metals from which 132 data points were obtained for 1 heat of Alloy 690 weld metal, 5 heats of 

Alloy 82 weld metal, 4 heats of Alloy 182 weld metal, and 6 heats of other Ni-Cr-Fe weld metals. 

Out of these, 427 data points were obtained from tests conducted at room temperature, 40 data 

points were obtained from tests conducted at 260–316°C, and 92 data points were obtained 

from tests conducted at 427°C. A summary of the sources included in the updated database 

used for this report, as categorized by material type and test environment, is presented in 

Table 9. Other material information such as chemical composition, heat treatment, and room 

temperature tensile properties of these Ni-Cr-Fe alloys and associated weld metals is given in 

Appendix B.

Table 9. Sources of the fatigue ε–N data on Ni-Cr-Fe alloys and their weld metals in an 

air environment.

ANL 

Mat. 

ID

Material 

Heat 

Designationa

Yield 

Strength

(MPa)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

Alloy 600

1 Alloy 600-1 310 25 12 JNES (Higuchi) 136

2 Alloy 600-2 294 25 9 JNES (Nakao), 136

3 Alloy 600-3 - 25 6 JNES (Hirano), 136

4 Alloy 600-4 289 25 6 JNES (Hirano) 136

5 Alloy 600-5 264 25 11 JNES (Hirano) 136

6 Alloy 600-6 303 25 6 JNES (Kanasaki) 136

7 Alloy 600-7 253 24, 93, 204, 316 5, 5, 10, 7 KAPL (Dinerman) 67

8 Alloy 600-8 - 24 8a KAPL (Mowbray) 68

9 Alloy 600-9 - 24 10a KAPL (Mowbray) 68

10 Alloy 600-10 - 24 8a KAPL (Mowbray) 68

11 Alloy 600-11 - 24 13a KAPL (Mowbray) 68

12 Alloy 600-12 - 24 7a KAPL (Mowbray) 68

13 Alloy 600-13 - 24, 316 9, 9 EPRI (Jacko) 66

14 Alloy 600-14 - 21 19 Bettis (McGowan&Faber) 70

15 Alloy 600-15 386 260 6 GE (Hale) 14

16 Alloy 600-16 - 21 15 Jaske & O’Donnell 61

17 Alloy 600-17 - 24, 83 5, 5 Jaske & O’Donnell 61

Alloy 690

20 Alloy 690-1 280 25 6 JNES (Kanasaki) 136

21 Alloy 690-2 - 25 5 PVP (Higuchi) 39

22 Alloy 690-3 - 315 6 PVP (Van der Sluys) 75

Alloy 800

25 Alloy 800-1 - 21 7 BMI (Jaske et al.) 69

26 Alloy 800-2 - 427 6, 10 BMI (Jaske et al.), GE 

(Conway) 69,71

Alloy 718
72

ANL 

Mat. 

ID

Material 

Heat 

Designationa

Yield 

Strength

(MPa)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

30 Inconel 718-1 - 21 18 ASME Data File 210

31 Inconel 718-2 - 21 4 J. Miller (J of Mat.) 72

32 Inconel 718-3 - 24, 427 17, 31 ASME Data File 61

33 Inconel 718-4 - 24, 427 30, 10 ASME Data File 61

34 Inconel 718-5 - 21, 427 34, 4 ASME Data File 61

35 Inconel 718-6 - 27, 427 12, 8 ASME Data File, NASA 

(Natchigall) 61,73

36 Inconel 718-7 - 22, 427 5, 23 ASME Data File 61

Ni-Cr-Fe Alloy Weld Metals

38 Alloy 690 WM 431 25 6 JNES (Kanasaki) 136

39 Alloy 62 - 24 9a KAPL (Mowbray) 68

40 Alloy 82-1 - 24 8b KAPL (Mowbray) 68

41 Alloy 82-2 - 24 8a KAPL (Mowbray) 68

42 Alloy 82-3 - 24 17a KAPL (Mowbray) 68

43 NiCrFe WM-1 - 24 9 Higuchi, Iida SGFS 

1988

44 Arcaloy 8N12 - 24 6a KAPL (Mowbray) 68

45 NiCrFe WM-2 - 25 9, 5 JNUFAD (Higuchi, 

Nakao) 210

46 Alloy 82-4 322 260 7 KAPL (Mowbray) 68

47 Alloy 182-1 - 25 13 PVP (Higuchi) 39

48 Alloy 182-2 456 290 7 JNES (Higuchi) 136

49 Alloy 182-3 405 25 5 JNES (Nakao) 136

50 Alloy 182-4 409 25 6 JNES (Kanasaki) 136

51 Alloy 82-5 339 315 5 PVP (Van der Sluys) 75

52 Alloy 152 - 25 6 PVP (Higuchi) 39

53 Alloy 132 - 25 6 PVP (Higuchi) 39

a Tests performed under bending fatigue. b Six tests performed under bending fatigue and four under rotating bending.

3.3.1 Experimental Data

The fatigue ε–N data for Alloys 600, 690, and 800 in air at temperatures between room 

temperature and 427°C are shown in Fig. 50, and those for Alloys 62, 82, 132, 152, 182, and 

other Ni-Cr-Fe alloy weld metals in air at temperatures between room temperature and 315°C 

are shown in Fig. 51. The fatigue ε–N data for Inconel 718 in air at room temperature and 

427°C is shown in Fig. 52. Fatigue CUF evaluations for Ni-Cr-Fe alloy components were 

performed using the fatigue design air curve for austenitic SSs because there is not a separate 

curve for Ni-Cr-Fe materials in Section III of the ASME Code. Therefore, the best–fit air curve 

for austenitic SSs based on the ANL model (Eq. 29 in Section 3.2.6) is included in these three

figures. The results indicate that, although the data for Alloys 690 and 800 are limited, the 

fatigue lives of these alloys were comparable to those of Alloy 600 (Fig. 50). The fatigue ε–N 

data for Ni-Cr-Fe alloy weld metals indicated that the fatigue lives of the various weld metals 

were comparable, although the data for Alloy 82 at 260 to 315°C showed significant scatter
73

Figure 50. Fatigue ε–N behavior for Alloys 600, 690 and 800 in air at temperatures 

between room temperature and 315°C (Refs. JNUFAD data, 61,66–75).

Figure 51. Fatigue ε–N behavior for Alloys 62, 82, 132, 152, and 182 welds in air at 

various temperatures (Refs. JNUFAD data,61,66–75).

Figure 52.

Fatigue ε–N behavior for Inconel 

718 in air at room temperature 

and 427°C (Refs. 61,72,73,136

,210).
74

(Fig. 51). The fatigue lives of the Ni-Cr-Fe alloy weld metals were comparable to those of the 

wrought Alloys 600 and 690 in the low–cycle regime (i.e., less than 105 cycles) and were slightly

superior to the lives of wrought materials in the high–cycle regime. The results also indicated 

that the fatigue limit for the weld metals was higher than that for wrought materials. Overall, the 

available fatigue ε–N data indicated that the fatigue lives of Ni-Cr-Fe alloys was represented by 

the fatigue design air curve for austenitic SSs; however, fatigue evaluations for Ni-Cr-Fe weld 

metals were conservative under this assumption.

The fatigue ε–N data in Fig. 52 indicate that the fatigue lives of Inconel 718 were longer than 

those for austenitic SSs or other Ni-Cr-Fe alloys and their weld metals, particularly at strain 

amplitudes less than 0.5% (i.e., in the high-cycle regime). The fatigue limit for Inconel 718 was 

much higher than that of austenitic SSs. Therefore, fatigue analyses for Inconel 718 that used

the fatigue design air curve for austenitic SSs yielded conservative estimates of fatigue usage. 

To avoid this conservatism, a separate fatigue design air curve is appropriate for Inconel 718. 

Jaske and O’Donnell proposed the following expression for fatigue lives of Inconel 718 in air,

ln(N) = 6.859 – 2.0 ln(εa – 0.210). (30)

The Jaske and O’Donnell best-fit air curve for Inconel 718 is also shown in Fig. 52. 

The available fatigue ε–N data for Ni-Cr-Fe alloys also indicated that, unlike austenitic SSs that 

do not show temperature dependencies of fatigue lives under LWR operating conditions, the 

fatigue lives of Alloy 600 were generally longer at high temperatures compared to those at room 

temperature, particularly for Alloy 82 weld metal (Fig. 51a).66–68 A similar behavior was 

observed for Inconel 718 (Fig. 52). However, limited data for Alloy 690 (Fig. 50b) and Alloys 62, 

132, 182, and 690 weld metals (Fig. 51b), indicated little or no effects of temperature on their 

fatigue lives. The existing data were insufficient to adequately determine the effect of strain rate 

on the fatigue lives of Ni-Cr-Fe alloys. 

Overall, the results indicated that the best-fit mean air curve for austenitic SSs represented 

slightly conservative estimates of the fatigue lives for Ni-Cr-Fe alloys in the high-cycle regime 

(fatigue lives greater than 5 x 104 cycles), particularly for Ni-Cr-Fe alloy weld metals. However, 

the best-fit mean data curve for austenitic SSs yielded very conservative estimates of fatigue 

lives for Inconel 718 for fatigue lives greater than 104 cycles. To reduce this conservatism, the 

fatigue behavior of Inconel 718 should be represented by a separate fatigue ε–N curve.

• For Ni-Cr-Fe alloys and their welds, the ANL fatigue life air model proposed in this report for 

austenitic SSs (Eq. 29) was either consistent or conservative with respect to the fatigue ε–N 

data.

3.3.2 Fatigue Life Model

For Ni-Cr-Fe alloys, fatigue evaluations are based on the fatigue design air curve for austenitic 

SSs because there is not a separate curve for Ni-Cr-Fe materials in Section III of the ASME 

Code. However, the rather limited fatigue ε–N data for Ni-Cr-Fe alloys (such as Alloys 600, 690, 

and 800 and their welds) were consistent with the best-fit mean air curve for austenitic SSs for 

fatigue lives less than 104 cycles. The data also showed longer fatigue lives than the estimated 

values for fatigue lives greater than 104 cycles. The data were comparable or slightly 

conservative with respect to the ANL model for austenitic SSs, e.g., Eq. 29. Estimates of the 

cumulative distribution of Constant A in the fatigue ε–N curve for the various heats of Alloys 

600, 690, and 800, and their associated weld metals, yielded a median value of 7.129. This 

value was slightly greater than the value of Constant A derived for austenitic SSs. In other 
75

words, the fatigue lives of these Ni-Cr-Fe alloys were approximately 25% greater than those for 

austenitic SSs. Based on these findings, the current ASME Code Section III fatigue design air 

curve for austenitic SSs, which is the same as the ANL model presented in Fig. 49 and Table 8,

adequately represented the fatigue ε–N behavior of Ni-Cr-Fe alloys and their welds. 

However, the fatigue design air curve for austenitic SSs yielded very conservative estimates of 

fatigue lives for Inconel 718. A detailed analysis of the cumulative distribution of Constant A for 

the various data sets available for Inconel 718 was not performed because the Constants B (the 

slope of the curve) and C (the constant associated with the fatigue limit) in the fatigue ε–N curve 

were significantly different than those for austenitic SSs. For Inconel 718, the slope of the 

fatigue ε–N curve was flatter and the fatigue limit (i.e., fatigue life at 106 cycles) was higher. 

• The ASME Code Section III fatigue design air curve for austenitic SSs, which is the same as 

the ANL air model for austenitic SSs, may also be used for Ni-Cr-Fe alloys and their welds. 

The current design fatigue air curve for austenitic SSs yielded conservative estimates of 

fatigue lives for Inconel 718.

77

4. FATIGUE ε–N BEHAVIOR IN LWR ENVIRONMENTS

An analysis of the existing fatigue ε–N data and the procedures for incorporating environmental 

effects into ASME Code fatigue evaluations was presented in several review articles118–126 and 

ANL topical reports.10,12,13,45–47 The key material, loading, and environmental parameters that 

influenced the fatigue lives of carbon and low–alloy steels and austenitic stainless steels were

identified, and the ranges of these key parameters where environmental effects were significant 

were defined. How various material, loading, and environmental parameters affected fatigue 

lives and how these effects are incorporated into the ASME Code fatigue evaluations are 

discussed in detail for carbon and low-alloy steels, wrought and cast SSs, and Ni-Cr-Fe alloys in 

the following three sections of this chapter.

4.1 Carbon and Low-Alloy Steels

Fatigue-life models for estimating the fatigue life of carbon and low–alloy steels in LWR 

environments presented in the initial revision of NUREG/CR-6909 were based on the updated 

PVRC database available at that time. The effects of key parameters, such as temperature, 

strain rate, DO content in water, and sulfur content in the steel, were included in the 

correlations. The functional forms for the effects of strain rate, temperature, DO level in water, 

and sulfur content in the steel, were based on the data trends. For both carbon and low-alloy 

steels, the model assumed threshold and saturation values of 1.0 and 0.001%/s, respectively, 

for strain rate; 0.001 and 0.015 wt.%, respectively, for sulfur; and 0.04 and 0.5 ppm, 

respectively, for DO. The model also considered a threshold value of 150°C for temperature

below which environmental effects were considered to be insignificant. The fatigue ε-N data in 

LWR environments were fitted to a modified version of Eq. 6 expressed as 

ln(N) = A – B ln(εa – C) – D S* T* O* *, (31)

where S*, T*, O*, and * are transformed sulfur content, temperature, DO level, and strain rate, 

respectively, defined in Eqs. 35-38, and D is a constant. The slope, B, of the fatigue ε-N 

behavior in LWR environments was considered to be the same as in air, and the constant C 

was also considered the same because, as discussed in Section 4.1.3, environmental effects on 

fatigue were not observed below a threshold strain level. The constants A and D were 

determined from the best-fit of the fatigue ε-N data in LWR environments. The constant A in the 

ANL models presented in the initial revision of NUREG/CR-6909 differed from the value 

reported earlier in NUREG/CR–6583 and NUREG/CR–6815. Relative to the earlier model, the 

fatigue lives predicted by the updated model in the initial revision of NUREG/CR-6909 were 

approximately 6% lower for carbon steels and approximately 2% higher for low–alloy steels. 

The effects of reactor coolant environments on fatigue lives were expressed in terms of an 

environmental fatigue correction factor, Fen, which was defined as the ratio of life in air at room 

temperature, NRTair, to that in water at the service temperature, Nwater. Values of Fen were 

obtained from the ANL fatigue life models, where 

ln(Fen) = ln(NRTair) – ln(Nwater). (32)

The environmental fatigue correction factor for carbon steels was given by

Fen = exp(0.632 – 0.101 S* T* O* *), (33)

and for low–alloy steels, by 
78

Fen = exp(0.702 – 0.101 S* T* O* *), (34)

where S*, T*, O*, and * are transformed sulfur content (S)†, temperature, DO level, and strain 

rate, respectively, defined as:

S* = 0.015 (DO > 1.0 ppm)

S* = 0.001 (DO ≤1.0 ppm and S ≤ 0.001 wt.%)

S* = S (DO ≤1.0 ppm and 0.001 < S ≤ 0.015 wt.%)

S* = 0.015 (DO ≤1.0 ppm and S > 0.015 wt.%) (35)

T* = 0 (T ≤ 150°C)

T* = T – 150 (150 < T ≤ 350°C) (36)

O* = 0 (DO ≤ 0.04 ppm)

O* = ln(DO/0.04) (0.04 ppm < DO ≤ 0.5 ppm)

O* = ln(12.5) (DO > 0.5 ppm) (37)

* = 0 ( > 1%/s) * = ln( ) (0.001 ≤ ≤ 1%/s) * = ln(0.001) ( < 0.001%/s). (38)

These models were recommended for predicting fatigue lives of less than or equal to 106 cycles. 

It was also noted that, as discussed in Section 4.2.7 of the initial revision of NUREG/CR-6909, 

because the effect of sulfur on the fatigue lives of carbon and low–alloy steels depended on the 

DO level in water, an environmental correction factor Fen determined from Eqs. 33–38 probably 

yielded nonconservative estimates of fatigue life for low–sulfur (less than 0.005 wt.%) steels in 

high–temperature water with greater than 1 ppm DO. However, this behavior is associated with 

laboratory test data and not likely to be applicable to LWR operating conditions. 

During the time since the publication of the initial revision of NUREG/CR-6909, the NRC 

received several comments from interested stakeholders on the fatigue life models proposed 

therein. These comments have focused on the constants (i.e., 0.632 and 0.702 in Eqs. 33 and 

34, respectively), which result in Fen values of approximately 2 even at temperatures below 

150°C or at very high strain rates. Although this behavior seems inconsistent with the 

mechanisms that were proposed for environmental fatigue effects (because the calculated CUF 

step increases at the time environmental effects are applied), the constants were appropriate 

based on analyses of the fatigue ε-N data and assumed constraints that were applied in the 

data reduction and analysis. The fatigue ε-N behavior for carbon and low-alloy steels in air at 

room temperature and high-purity water at temperatures below 150°C is shown in Fig. 53. 

These results indicated that in both low-DO PWR and NWC BWR environments, the fatigue 

lives of carbon and low-alloy steels were a factor of two lower, thereby indicating the need for 

the constant terms in Eqs. 33 and 34. Another comment received from interested stakeholders 

was in regards to the temperature range specified in Eq. 36. The maximum temperature limit 

was specified as 350°C even though there were sparse data on carbon and low-alloys steels at 

temperatures above 300°C.

In this report, the Fen expressions (i.e., Eqs. 33-38) for incorporating environmental effects on 

the fatigue lives of carbon and low-alloy steels were updated to address the stakeholders 

comments using a much larger database that is described in Section 4.1.1. In LWR 

environments, the fatigue lives of carbon and low-alloy steels remains dependent on strain rate, 

 † In the expressions for Fen, the letter S is used for the metal sulfur content in the transformed sulfur term S*. 
79

DO level, temperature, and sulfur content of the steel; the effects of these and other parameters 

on the fatigue lives of these materials are discussed in the following sections. 

4.1.1 Experimental Data

The primary sources of fatigue ε–N data for carbon and low–alloy steels in LWR environments

are the tests performed by GE in a test loop at the Dresden 1 reactor;14,15 the work of Terrell at 

MEA;48–50 the work at ANL on fatigue of pressure vessel and piping steels;10–13,40–47 the large 

JNES database136 that includes studies at IHI, Hitachi, and MHI in Japan,18–36 the work at KWU

and MPA in Germany;55,56 and some recent investigations by Wu and Katada.138-144 The 

database in LWR environments used in this report was composed of a total of 1,174 tests, 

which represented 638 tests on carbon steels and 536 tests on low-alloy steels. The carbon 

steel tests included 21 heats of A106–Grades B and C, A333–Grade 6, A508–Grade 1, A226 

Cl. 4, A516–G70, and A516–KC70 steels. The low–alloy steel tests included 20 heats of A302–

Grade B, A508–Grades 2 and 3, A533–Grade B, 15MnNi63, and 17MnMoV64 steels. A 

summary of the data sources for the updated database used in this report, as categorized by 

material type and test environment, is shown in Table 10. Other material information, such as 

chemical composition, heat treatment, and room temperature tensile properties, for the various 

types and heats of materials is given in Appendix B.

A sampling of fatigue ε–N data on carbon and low–alloy steels in air and high–DO water at 

288°C are shown in Fig. 54. The curves based on the ANL air models (Eqs. 24 and 25 in 

Section 3.1.6) are also included in the figures. The fatigue data in LWR environments indicated 

a significant decrease in fatigue lives for carbon and low–alloy steels when four key threshold 

conditions were satisfied simultaneously, viz., applied strain range, service temperature, and 

DO in the water were above a minimum threshold level, and the loading strain rate was below a 

threshold value. The sulfur content of the steel was also an important parameter for 

environmental effects on the fatigue lives for carbon and low-alloy steels. Although the 

microstructures and cyclic–hardening behavior of carbon and low–alloy steels were significantly 

different, environmental degradation of the fatigue lives for these steels was nearly identical. As 

shown in Fig. 53, for both steels, environmental effects on the fatigue lives were moderate (i.e., 

a factor of approximately 2 lower) if any one of the key threshold conditions was not satisfied.

Figure 53. Fatigue ε–N behavior for carbon and low-alloy steels in air at room 

temperature and high-purity water at temperatures below 150°C (Ref. 137).
80

Table 10. Sources of the fatigue ε–N data for carbon and low-alloy steels in LWR 

environments.

ANL

Mat. 

ID

Material

Specifications

Sulfur 

Content 

(wt.%)

Dissolved 

Oxygen 

(ppm)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

Carbon Steels

1 A106-Gr.Ba 0.015 0.001-8.0 288 35 ANL, JNES (Higuchi) 10-13, 136

2 A106-Gr.B 0.007 0.005 100, 290 8, 7 JNES (Kanasaki) 136

3 A106-Gr.B 0.020 0.01 288 18 MEA 48

4 A106-Gr.C 

(STS480)

0.006 0.005 100, 290 12, 9 JNES (Tsutsumi) 136

5 A106-Gr.C 

(STS480)

0.020 0.005 290 4 JNES (Tsutsumi) 136

7 A226-Cl.4

(SFVC2B)

0.004 0.05-8.0 289 15 JNES (Hirano) 136

8 A333-Gr.6

(STS42)

0.015 8.0 250 8 JNES (Ishihara) 136

9 A333-Gr.6 

(STS42)

0.015 0.01-8.0 100, 150, 200, 

250, 290

6, 12, 11, 

32, 13

JNES (Higuchi) 136

10 A333-Gr.6 

(STS42)

0.014 0.2 288 12 JNES (Higuchi, 

Emnomoto)

136

11 A333-Gr.6 

(STS410)

0.006 8.0 288 5 JNES (Higuchi) 136

12 A333-Gr.6 

(STS410)b

0.012 0.01-8.0 25, 50, 100, 

150, 200, 250, 

288/290

1, 3, 18, 19, 

22, 13, 62

JNES (Higuchi, 

Hirano, Kanasaki, 

Nakao), ANL

136, 10-13

14 A333-Gr.6 

(STS410)

0.008 0.01-8.0 50, 100, 150, 

200, 250, 

289/290

2, 1, 5, 5, 

5, 105

JNES (Abe, Higuchi, 

Kanasaki, Hirano) 

136

15 A333-Gr.6 

(STS410)

0.016 0.01-8.0 100, 200, 250,

289/290

7, 12, 4, 91 JNES (Hirano, 

Higuchi, Kanasaki)

136

16 A333-Gr.6 

(STS410)

0.026 0.05-8.0 289 12 JNES (Hirano) 136

17 A508-Gr.1 

(SFVV1)

0.008 8.0 300 14 JNES (Kitagawa) 136

21 A516-KC70 0.033 0.2 260 14c GE 14, 15

22 A516-G70

(SGV480)

0.002 8.0 290 3 JNES (Higuchi) 136

23 CS tube 0.025 0.01-8.0 240 13 S/KWU 55,56

Low-Alloy Steels

1 A302-Gr.B 0.027 0.001-0.9 288 9 ANL 10-13

2 A508-Gr.2 0.003 0.2 288 21d JNES (Nakao, 

Higuchi)

136

4 A508-Gr.2e 0.008 0.05-8.0 200, 250, 289 6, 9, 39 JNES (Hirano) 136

5 A508-Gr.2e 0.008 0.005 100, 150, 200, 

250, 290

10, 2, 10, 

2, 13

JNES (Nomura) 136

6 A508-Gr. 3 

(SFVV3)

0.003 0.1 288 9 JNES (Nagata) 136

12 A508-Gr. 3 

(SFVV3)

0.003 0.05-8.0 50, 100, 150, 

200, 250, 283/

2, 12, 29, 

27, 8, 

JNES (Endou, Kasai, 

Higuchi)

136
81

ANL

Mat. 

ID

Material

Specifications

Sulfur 

Content 

(wt.%)

Dissolved 

Oxygen 

(ppm)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

288/290 60

14 A508-Gr. 3 0.002 0.1 288 16 Wu & Katada 141, 143

15 A508-Gr. 3 0.018 0.5 285 3 MPA 55,56

16 A533-Gr. B 0.012 0.001-0.9 288 30 ANL 10-13

17 A533-Gr. B 

(SQV2A)

0.007 0.1, 

(0.01-4.0)

288, 

(20, 100, 

147/150, 200, 

250, 288)

8, 

(1, 4, 2, 2, 

1, 23)

JNES (Nagata), 

Wu & Katada

136,

(141, 143)

21 A533- Gr. B 

(SQV2A)

0.010 0.2-8.0 288/290 53e JNES (Nakao, 

Higuchi)

136

23 A533-Gr. B 0.013 0.1 288 27 Wu & Katada 139, 142, 

143

24 A533-Gr. B 0.025 0.1 288 6 Wu & Katada 143

25 A533-Gr. B 0.038 0.1, 2.0 200, 288 6, 13 Wu & Katada 139

26 A533- Gr. B 

(SQV2A)

0.021 0.05-1.0 200, 289 5, 29 JNES (Higuchi) 136

27 A533-Gr. B

Cl. 2

<0.001 1.0 289 3 JNES (Hirano) 136

28 A533-Gr. B 0.003, 

0.005, 

0.014

2.0 285 3, 2, 5 MPA 55,56

30 15MnNi63 0.003 0.4, 8.0 240 1, 4 MPA 55,56

31 17MnMoV64 0.018 0.45 210 21 S/KWU 55,56 a This material was tested at ANL and IHI (Higuchi). b This material was also tested at ANL. c Tests performed on rectangular bars under bending fatigue. d Four tests performed under load control using sine waveform. e Data include results for thermally aged materials. 

(a) (b)

Figure 54. Strain amplitude vs. fatigue life data for (a) A533–Gr B and (b) A106–Gr B 

steels in air and high–dissolved–oxygen water at 288°C (Ref. 10).
82

The existing fatigue data indicated that slow strain rates applied during tensile–loading cycles 

were primarily responsible for environmentally assisted reduction in the fatigue lives of these 

steels.10 The mechanism of environmentally assisted reduction in the fatigue lives of carbon 

and low-alloy steels was termed SICC.78,85,86 Slow strain rates applied during both the tensile–

load and compressive–load portions of load cycles (i.e., slow/slow strain rate test) did not further 

decrease the fatigue lives, e.g., refer to the solid diamond and solid square symbols in Fig. 54b 

for A106–Gr B carbon steel. Limited data from fast/slow tests indicated that slow strain rates 

during compressive load cycles also decreased fatigue lives. However, the decrease in life was 

relatively small; for fast/slow strain rate tests, the major contribution of environment occurred 

during slow compressive loading near peak tensile loads. For example, the fatigue lives of 

A533–Gr B low-alloy steels at 288°C, 0.7 ppm DO, and approximately 0.5% strain range 

decreased by factors of 5, 8, and 35 for the fast/fast, fast/slow, and slow/fast tests, respectively, 

i.e., refer to the solid circle, diamond, and inverted triangle symbols in Fig. 54a. Similar results 

were observed for A333–Gr. 6 carbon steel;23 relative to the fast/fast test, the fatigue lives for 

the slow/fast and fast/slow tests at 288°C, 8 ppm DO, and 0.6% strain amplitude decreased the 

fatigue lives by factors of 7.4 and 3.4, respectively. 

Environmental effects on the fatigue lives of carbon and low-alloy steels were consistent with 

the slip oxidation/dissolution mechanism for crack propagation, particularly at slow strain 

rates.189,190 A critical concentration of sulfide (S2-

) or hydrosulfide (HS-) ions, which is produced 

by the dissolution of sulfide inclusions in the steel, is required at the crack tip for environmental 

effects to occur. For this mechanism, a model for the initiation or cessation of EAC of these 

steels in low-DO PWR environments was also proposed.182 Initiation of EAC requires a critical 

concentration of sulfide ions at the crack tip, which is supplied with the sulfide ions as the 

advancing crack intersects the sulfide inclusions, and the inclusions dissolve in the hightemperature water. Thus, environmental fatigue is controlled by the synergistic effects of sulfur

content, environmental conditions, and flow rate. The EAC initiation/cessation model was used 

to determine the minimum crack extension and CGRs that are required to maintain the critical 

sulfide ion concentration at the crack tip and sustained environmental enhancement of growth 

rates. 

• LWR environments have significant effects on the fatigue lives of carbon and low-alloy steels; 

such effects were not considered in the original ASME Code fatigue design curves. 

Environmental effects for carbon and low-alloy steels may be incorporated into ASME Code 

fatigue evaluations using the Fen expression given in Eq. 41 (Section 4.1.11).

4.1.2 Strain Rate

The effects of strain rate on the fatigue lives of carbon and low-alloy steels in LWR 

environments were determined to be significant when other key threshold conditions, e.g., strain 

amplitude, temperature, and DO content, were satisfied. When any one of the threshold 

conditions was not satisfied, e.g., if low–DO PWR environments or temperatures less than 

150°C were not present, the effects of strain rate were consistent with those observed in air. 

When all threshold conditions were satisfied, the fatigue lives of carbon and low-alloy steels 

decreased logarithmically with decreasing strain rate. The fatigue lives of A106–Gr B and 

A333–Gr. 6 carbon steels and A533–Gr B low–alloy steel10,23 are plotted as a function of strain 

rate in Fig. 55. The lines in this figure represent the predicted fatigue lives determined from the 

updated Fen expressions presented later in Section 4.1.10 (for water for the two DO values 

identified on each plot) and either Eqs. 24 or 25 (for air). Only a moderate decrease in fatigue 

lives was observed in simulated (low–DO) PWR water, e.g., at DO levels of less than or equal to 

0.04 ppm. For the heats of A106–Gr. B and A333-Gr. 6 carbon steel and A533–Gr. B low–alloy 
83

steel, the effects of strain rate on fatigue lives saturated between values of 0.004 and 

0.0004 %/s strain rate. Although the data for A333–Gr. 6 carbon steel at 250°C and 8 ppm DO 

did not indicate saturation for strain rates up to 0.0001%/s, the results were comparable to those 

for the other two steels. The Fen expressions proposed by JNES for incorporating 

environmental effects on the fatigue lives of carbon and low-alloy steels recommended a 

saturation strain rate of 0.0004 %/s for DO levels up to 0.7 ppm and 0.0001 %/s above 0.7 ppm. 

Based on the data shown in Fig. 55, the saturation strain rate in the ANL model was also 

changed to 0.0004 %/s for all DO levels.

(a) (b)

Figure 55.

Dependence of fatigue lives of 

carbon and low–alloy steels on 

strain rate (Refs. 10,23).

(c)

For carbon and low-alloy steels, the potential effects of DSA are also likely to affect fatigue lives. 

The strain-rate dependence of fatigue life of A533-B low-carbon steel at 288°C and 200°C in 

high-purity water with 0.1 and 2.0 ppm DO is shown in Fig. 56. The lines represent the 

predicted fatigue lives based on the revised Fen expressions given in Eq. 41. The results 

indicated that the predicted fatigue lives at 0.001 %/s strain rate were greater than the 

experimental values, particularly at 200°C (i.e., the ANL models yielded nonconservative 

estimates for these environmental and loading conditions). This behavior was attributed to 

DSA. However, the difference between the estimated and experimental values was a factor of 

2, which is within the range of data scatter for the fatigue ε-N data for carbon and low-alloy 

steels in LWR environments. Therefore, no additional adjustments were made to accommodate 

DSA effects in the revised ANL model for carbon and low-alloy steels.
84

The methodology for calculating Fen under conditions where temperature and strain rate are 

changing (i.e., actual load transients) is discussed in Section 4.1.14, and guidance is provided 

for defining the strain rate for a specific load cycle or load set pair. 

• The effect of strain rate on the fatigue lives of carbon and low-alloy steels in LWR 

environments were explicitly considered in the Fen expression given in Eq. 41 

(Section 4.1.11); the saturation strain rate limit was changed from the value of 0.001 %/s, 

specified in the original revision of NUREG/CR-6909, to 0.0004 %/s to more appropriately 

reflect the data in the updated database. 

Figure 56. Fatigue life of A533–Gr. B low-alloy steel as a function of strain rate in high 

purity water with 0.1 or 2.0 ppm dissolved oxygen (Refs. 141,143).

4.1.3 Strain Amplitude

The fatigue lives of carbon and low-alloy steels in LWR environments were observed to be 

lower than those in air. However, limited data indicated that at strain amplitudes below 0.3%, 

the fatigue lives of A533-B and A508-3 low-alloy steels were greater than those in air (Fig. 57). 

The reasons for this behavior were not clear. However, under the environmental and loading 

conditions that resulted in such behavior, estimates of fatigue lives of low-alloy steels were

Figure 57. Fatigue strain-life behavior of A533–Gr. B and A508-Gr. 3 low-alloy steels at 

288°C in air and high-purity water with 0.1 ppm dissolved oxygen (Ref. 151).
85

conservative. Therefore, in this report, this behavior was not explicitly addressed in the Fen

methodology for estimating environmental effects on fatigue lives. 

The available small-scale laboratory fatigue test data indicated that a minimum threshold strain 

range was required to cause an environmentally assisted decrease in fatigue lives, i.e., LWR 

coolant environments had no effect on the fatigue lives of these steels at strain ranges below 

the threshold value. The fatigue lives of A533–Gr B and A106–Gr B steels in high–DO water at 

288°C and various strain rates10 are shown in Fig. 54. Fatigue tests at low strain amplitudes 

were rather limited. Because environmental effects on fatigue lives increased with decreasing 

strain rates, fatigue tests at low strain amplitudes and strain rates that would result in significant 

environmental effects are restrictively time consuming. For the limited data that were available, 

the threshold strain amplitude (one-half the threshold strain) was slightly above the fatigue limits 

for these steels.

Exploratory fatigue tests with changing strain rate were conducted to determine the threshold 

strain ranges beyond which environmental effects were significant. The tests were performed 

with waveforms in which slow strain rates were applied during a portion of the tensile loading 

cycles.10,24 The results for A106–Gr B steel tested in air and low– and high–DO environments 

at 288°C and approximately 0.75% strain range are summarized in Fig. 58. The loading 

waveforms implemented in the tests consisted of segments of loading and unloading at fast and

A Air: 3,253; 3,753

 PWR: 2,230; 1,525

 Hi DO: 2,077; 1,756

B 

Air: 3,721; 3,424; 6,275

PWR: 2,141

Hi DO: 303; 469

C Air: 4,122

 PWR: –

 Hi DO: 888

D Air: 5,139

 PWR: –

 Hi DO: 615; 553

E Air: 5,261

 PWR: –

 Hi DO: 545

F Air: 3,893

 PWR: –

 Hi DO: 340

G 

 Air: 4,087

 PWR: –

 Hi DO: 1,649; 2,080

H 

 Air: –

 PWR: –

 Hi DO: 1,935

I 

 Air: 4,356

 PWR: –

 Hi DO: 615

Figure 58. Fatigue life of A106–Gr B carbon steel at 288°C and 0.75% strain range in 

air and water environments under different loading waveforms (Ref. 10). 
86

slow strain rates. The variation in fatigue lives of two heats of carbon steel and one heat of low–

alloy steel10,24 is plotted as a function of the fraction of the loading strain at slow strain rate in 

Fig. 59. Open symbols indicate tests where the slow strain rate loading occurred near the 

maximum tensile strain, and closed symbols indicate tests where the slow strain rate loading 

occurred near the maximum compressive strain. If the relative damage was the same at all 

strain levels, fatigue lives should have decreased linearly from A to C along the chain–dot lines 

in Fig. 59. Instead, the results indicated that, during a strain cycle, the relative damage due to 

slow strain rate occurred only after the strain level exceeded a threshold value. The threshold 

strain range for these steels was in the range of 0.32–0.36%. 

(a) (b)

Figure 59.

Fatigue lives of carbon and low–alloy 

steels tested with loading waveforms 

where slow strain rate was applied 

during a fraction of the tensile loading 

cycle (Refs. 10,24).

(c)

Loading histories with slow strain rate applied near the maximum tensile strain (i.e., waveforms 

C, D, E, or F in Fig. 58) showed continuous decreases in fatigue lives (lines AB in Fig. 59), 

followed by saturation when a portion of the slow strain rate occurred at strain levels below the 

threshold value (lines BC in Fig. 59). In contrast, loading histories with slow strain rates applied 

near the maximum compressive strain (i.e., waveforms A, G, H, or I in Fig. 58) did not produce 

any fatigue damage (line AD in Fig. 59a) until the fraction of the strain was sufficiently large 

such that the slow strain rates occurred at strain levels greater than the threshold value. 
87

However, tests with such loading histories often showed lower fatigue lives than the predicted 

values, e.g., the solid inverted triangle or solid diamond symbols in Fig. 59a. The fatigue ε-N 

data presented in Fig. 54 indicated that the threshold strain was between 0.25 and 0.40 %. As 

discussed in Section 4.2.2, similar tests on austenitic SSs in PWR environments also showed 

the existence of a strain threshold below which the material was insensitive to environmental 

effects.35 The threshold strain range, ∆εth, was independent of material type (weld metal or 

base metal) and temperature in the range of 250–325°C, but it tended to decrease as the strain 

range was decreased. For austenitic SSs, the threshold strain was expressed in terms of the 

applied strain range, ∆ε (Eq. 56). At a low strain amplitude (e.g., 0.3%), the proposed 

expression yielded a strain threshold of approximately 0.28%. Since the contribution of strain 

threshold was more significant at low strain amplitudes, a value of 0.28% was proposed in the 

initial revision of NUREG/CR-6909. After applying a factor of 2 on strain to account for the 

uncertainties associated with material variability and experimental scatter, a threshold “strain 

amplitude” of 0.07% [or a stress amplitude of 145 MPa (21 ksi)] was specified in the initial 

revision of NUREG/CR-6909 for use when performing ASME Code fatigue CUF evaluations for 

both carbon and low-alloy steels. The modified rate approach, described in Section 4.1.14, was

used to predict the results from tests on A106-B and A333-6 carbon steels and A533-B low-alloy 

steel, conducted with changing strain rate in high-DO water (0.8-8.0 ppm DO) at 289°C.136

The experimental values of fatigue lives and those predicted from the modified rate approach, 

with and without the consideration of a threshold strain, are shown in Fig. 60. Most of the 

scatter in the data was due to heat-to-heat variations. The results indicated that estimates of 

fatigue lives based on the modified rate approach, without the consideration of a strain 

threshold, were in good agreement with the experimental values for A106-B and A333-6 carbon 

steels (Fig. 60a). However, the data for A533-B low-alloy steel (shown as circular symbols in 

Fig. 60) show an unusual behavior. First, the material showed a very strong dependence of 

environmental effects on applied strain amplitude. For example, for the tests with no strain-rate 

change (shown by closed symbols), the fatigue lives at 0.6% strain amplitude (i.e., fatigue lives 

in the range of 100 to 800 cycles) showed excellent agreement with the experimental values.

 

(a) (b)

Figure 60. Experimental values of fatigue life and those predicted from the modified 

rate approach (a) without and (b) with consideration of a threshold strain 

(Ref. 136). 

102

103

104

102 103 104

A106-B

A333-6

A533-B

Predicted Life (Cycles)

Experimental Life (Cycles)

Modified Rate Approach 

with strain threshold

Carbon & Low-Alloy Steels

Open Symbols: Rate change

Closed Symbols: No change

Factor 

of 3
88

However, the predicted fatigue lives at 0.4% strain amplitude (i.e., fatigue lives in the range of

250 to 1,500 cycles) were a factor of 2 higher; and, at 0.3% strain amplitude (i.e., fatigue lives in 

the range of 350 to 3,300 cycles) the predicted fatigue lives were more than a factor of 3 higher. 

In addition, nearly all fatigue tests where slow strain rates were applied near the compressivestrain peak, particularly the tests at 0.4% or 0.3% strain amplitudes, exhibited unusually low 

fatigue lives. The reasons for such a dependence of environmental effects on applied strain 

amplitude are not understood. 

The results shown in Fig. 60b included a threshold strain of 0.28%. It was assumed that, during 

a strain cycle beginning from the peak compressive strain, environmental effects on fatigue lives

occurred only when the strain exceeded the strain threshold (the Fen was determined in 

accordance with the modified rate approach defined by Eq. 50). Once again, the results for 

A106-B and A333-6 carbon steel either showed little or no changes in the resulting fatigue lives, 

or they showed better agreement with the experimental values, but the data for A533-B lowalloy steel, particularly for tests with slow strain rate imposed at the peak compressive strain, 

exhibited an unusual behavior. These results indicated that the modified rate approach, without 

consideration of a strain threshold, yielded the best estimates of fatigue lives of carbon and lowalloy steels in LWR environments.

• The procedure for calculating Fen in LWR coolant environments is defined in Eq. 41

(Section 4.1.11) and Eqs. 49 or 50 (Section 4.1.14), where the equations may consider a 

threshold strain below which environment has no effect on fatigue lives (i.e., Fen = 1). 

However, while using the modified rate approach to determine Fen for a stress cycle or load 

set pair (Eq. 50 in Section 4.1.14), inclusion of a threshold strain may yield nonconservative 

estimates for fatigue lives.

4.1.4 Temperature

The change in fatigue lives of two heats of A333–Gr. 6 carbon steel18,19,22 as a function of test 

temperature at different levels of DO and strain rates is shown in Fig. 61. The sulfur content of 

the two heats of A333-Gr. 6 carbon steel was 0.015% and 0.012 wt. %. For all these tests, the 

strain amplitude was 0.6%, which is above the threshold strain limit for environmental effects. 

In air, both heats had a fatigue life of 2,993 cycles. The results indicated a threshold 

temperature of 150°C, above which the environment decreased the fatigue life if the DO content 

in the water was also above the critical level of 0.05 ppm. An artificial neural network (ANN) 

was used to find patterns and identify the threshold temperature below which environmental 

effects were moderate.226 The main benefits of the ANN approach were that estimates of lives 

were based purely on the data and not on preconceptions, and by learning trends; the network 

interpolated effects where data were not present. The factors that affected fatigue lives had 

synergistic effects on one another. The neural network detected and utilized these effects in its 

predictions. The training of the neural network was all based on the same data set, but the 

order in which the data were presented to the ANN for training was varied, and the initial ANN 

weights were randomized to guard against overtraining and to ensure that the network did not 

arrive at a solution that was a local minimum. The results indicated that at high strain rates 

(0.4%/s), fatigue lives were relatively insensitive to temperature. At low strain rates (0.004%/s), 

fatigue lives decreased with an increase in temperature beyond a threshold value of 

approximately 150°C.226 The precision of the data indicated that this trend was present in the 

data used to train the ANN. Only a moderate decrease in fatigue lives was observed in water at 

temperatures below the threshold value of 150°C or at DO levels less than or equal to 0.05 

ppm. Under these conditions, fatigue lives in water were a factor of approximately 2 lower than 

in air; Fig. 61 shows an average life of approximately 2,000 cycles for the 0.015 wt.% sulfur 

steel, and approximately 1,200 cycles for the 0.012 wt.% sulfur steel. 
89

At temperatures above 150°C, the logarithm of fatigue life decreased linearly with temperature; 

the decrease in fatigue life was greater at higher temperatures and DO levels. However, as 

mentioned earlier, the temperature range specified in the initial revision of NUREG/CR-6909 for 

environmental effects for carbon and low-alloy steels in LWR environments extended beyond 

the range of actual fatigue ε-N data. An insignificant amount of fatigue ε-N data were available 

at temperatures above 290°C. Consequently, in this report, the maximum temperature limit was 

set at 325°C as a reasonable bound to cover all anticipated LWR operating conditions. This is 

adequate for all expected operating LWR conditions considering the use of average 

temperature (as discussed in Section 4.1.11 and shown in Fig. 81).

Nearly all of the fatigue ε–N data available for evaluation for this report were obtained under 

loading histories with constant strain rates, temperatures, and strain amplitudes. However, the 

operating experience for U.S. LWRs indicates that the actual loading histories encountered 

during normal operation involves variable loading and environmental conditions. Some fatigue 

tests were conducted in Japan on 12-mm outside diameter tube specimens (1– and 3–mm wall 

thicknesses) of A333–Gr. 6 carbon steel in oxygenated water under combined mechanical and 

thermal cycling.21 Triangular waveforms were used for both strain and temperature cycling. 

Two sequences were selected for temperature cycling (Fig. 62): an in–phase sequence in which

the temperature cycling was synchronized with the mechanical strain cycling, and another 

sequence in which the temperature and strain cycling were out of phase, i.e., the maximum 

temperature occurred at the time of minimum strain level and vice versa. Three temperature 

ranges, 50–290°C, 50–200°C, and 200–290°C, were selected for the tests. The results are 

shown in Fig. 63; an average temperature was used to plot the thermal cycling tests. Because 

environmental effects on fatigue lives were moderate and independent of temperature below 

150°C, the temperatures for the tests cycled in the ranges of 50–290°C or 50–200°C were

Figure 61.

Change in fatigue life of A333–Gr. 6 

carbon steel and A508-Gr. 3 lowalloy steel with temperature and DO 

(Ref. 136).

0 50 100 150 200 250 300 350

>1 ppm

<0.05 ppm

Air

Air Predicted

0.01%/s (>1.0 ppm)

10 0.01%/s (0.05 ppm) 2

103

104

Temperature (°C)

A333–Gr 6 Carbon Steel

εa = 0.6%, S = 0.015 wt.%

Strain Rate = 0.01%/s

Fatigue Life (Cycles)

0 50 100 150 200 250 300 350

0.004%/s (>1 ppm DO)

0.002%/s (>1 ppm DO)

0.004%/s (0.05 ppm DO)

0.4%/s (Air)

Air Predicted

0.002%/s

0.004%/s

0.004%/s

102

103

104

Temperature (°C)

A333–Gr 6 Carbon Steel

εa = 0.6%, S = 0.012 wt.%

Fatigue Life (Cycles)

0 50 100 150 200 250 300 350

0.005 ppm

0.2 ppm

1.0-8.0 ppm

Air

102

103

104

Temperature (°C)

A508–Gr. 3 Low-Alloy Steel

εa = 0.6%, S = 0.003 wt.%

Strain Rate = 0.01%/s

Fatigue Life (Cycles)
90

determined from the average of the threshold temperature of 150°C and the maximum 

temperature of the test (i.e., 220°C and 175°C, respectively). The results (Fig. 63) indicated that 

load cycles involving variable temperature conditions represented by an average temperature, 

e.g., the fatigue lives from variable–temperature tests were comparable with those from 

constant–temperature tests.

Figure 63. Fatigue lives of A333–Gr. 6 carbon steel tube specimens under varying 

temperature conditions, as indicated by horizontal bars (Ref. 21).

However, nearly identical fatigue lives were obtained from the in–phase and out–of–phase tests. 

Assuming that the tensile–load cycle was primarily responsible for the observed environmentally 

assisted reductions in fatigue lives, and that the applied strains and temperatures must be 

above a minimum threshold value for environmental effects to occur, then the fatigue lives 

obtained from the out–of–phase tests were expected to be longer than those obtained from the 

in–phase tests. This expectation was based on the premised that the applied strains above the 

threshold strain occurred at temperatures above 150°C for the in–phase tests, whereas the 

applied strains above the threshold strain occurred at temperatures below 150°C for the out–of–

phase tests. Under the assumption that environmental effects on fatigue lives were considered 

to be minimal below the 150°C temperature and 0.28 % strain threshold values, the average 

temperatures for the out–of–phase tests at 50–290°C, 50–200°C, and 200–290°C were 195, 

160, and 236°C, respectively, instead of 220, 175, and 245°C, as plotted in Fig. 63. Thus, the 

fatigue lives from out–of–phase tests were expected to be at least 50% higher than those from 

the in–phase tests. Such differences in environmental conditions were therefore assumed to be

offset by the difference in the cyclic hardening behavior of the material for the out–of–phase and 

Figure 62. Waveforms for changes in temperatures and strains during exploratory 

fatigue tests (Ref. 21).
91

in-phase tests. From those observations, it was concluded that estimates of fatigue lives for 

actual nuclear power plant transients based on an average temperature may yield 

nonconservative estimates.

• The effects of temperature on the fatigue lives of carbon and low-alloy steels in LWR 

environments were explicitly considered in Fen defined in Eq. 41 (Section 4.1.11). For

simple, linear transients, an average temperature that considers the threshold temperature of 

150°C may be used to calculate Fen for a specific stress cycle or load set pair. Complex 

thermal transients that have multiple increasing and decreasing temperature excursions 

should be evaluated using the maximum temperature for the specific stress cycle or load set 

pair unless information is available to justify the use of an average temperature.

4.1.5 Dissolved Oxygen

The dependence of fatigue lives of carbon and low-alloy steels on the DO content in water is 

shown in Fig. 64.18,19,22 For the tests summarized in this figure, the temperatures, applied strain 

amplitudes, and sulfur contents in the steels tested were above, and the strain rates were 

below, the critical threshold values. The results indicated a minimum DO level of 0.04 ppm 

above which the environment decreased the fatigue lives of the steels tested. The effect of DO 

content on fatigue lives saturated at 0.5 ppm, i.e., increases in DO levels above 0.5 ppm did not 

cause further decreases in fatigue lives. In Fig. 64, for DO levels between 0.04 and 0.5 ppm, 

fatigue lives decreased logarithmically with DO. Estimates of fatigue lives from the trained ANN 

also showed a similar effect of DO on the fatigue lives of carbon steels and low–alloy steels.

Figure 64. Dependence on DO of the fatigue lives of carbon and low alloy steels in 

high-purity water (Ref. 18, 19, 22). 

Environmental effects on the fatigue lives of carbon and low-alloy steels were minimal at DO 

levels below 0.04 ppm, i.e., in low-DO PWR or HWC BWR environments. In contrast, 

environmental enhancement of CGRs was observed in low–alloy steels even in low–DO 

water.182 This apparent inconsistency of fatigue ε–N data with the CGR data was attributed to 

differences in the environmental conditions locally at the crack tip. As discussed earlier in 

Section 2.2.1.2, environmentally assisted enhancement of CGRs in low–alloy steels required a 

critical level of sulfides at the crack tip.182 The development of this critical sulfide concentration 

required a minimum crack extension of 0.33 mm and CGRs in the range of 1.3 x 10–4 to 

4.2 x 10–7 millimeters/second. These conditions were not achieved under the majority of the 

available ε-N tests. Thus, environmental effects on fatigue lives are expected to be insignificant 

in low–DO environments for carbon and low-alloy steels.
92

• The effects of DO levels on the fatigue lives of carbon and low-alloy steels n LWR 

environments were explicitly considered in the Fen, defined in Eq. 41 (Section 4.1.11). 

4.1.6 Water Conductivity

In most of the studies reviewed for this report, the DO level in water was considered as the key 

environmental parameter that affected the fatigue lives of materials in LWR environments. 

Studies on the effects of the concentration of anionic impurities in water (expressed as the 

overall conductivity of water) were limited. The limited data indicated that the fatigue lives of 

WB36 low–alloy steel at 177°C in water with approximately 8 ppm DO decreased by a factor of 

approximately 6 when the conductivity of the water was increased from 0.06 to 0.5 μS/cm.78,227 

Similar behavior was also observed in another study of the effects of conductivity on the 

initiation of short cracks.228

• U.S. LWRs are unlikely to accumulate significant fatigue cycles during off–normal water 

chemistry conditions. Thus, the effects of water conductivity on fatigue lives were not 

considered in the determination of Fen for carbon and low-alloy steels.

4.1.7 Sulfur Content in Steel

Sulfur content and morphology were the most important material–related parameters that 

determined susceptibility of low–alloy steels to environmentally enhanced fatigue CGRs.184–188 

A critical concentration of S2– or HS– ions was required at crack tips for environmental effects to 

occur. The corrosion fatigue CGRs and threshold stress intensity factor, ∆Kth, were both a 

function of the sulfur content in the range 0.003–0.019 wt.%.187 The probability of 

environmental enhancement of fatigue CGRs in precracked specimens of low–alloy steels,

diminished markedly for sulfur contents less than 0.005 wt.%.

The available fatigue ε–N data for carbon and low–alloy steels also indicated a dependence of 

fatigue lives on sulfur content. When all the threshold conditions were satisfied, the 

environmental effects on the fatigue lives of these materials increased with increased sulfur 

content. The fatigue lives of A508–Cl. 3 low-alloy steels with 0.003 and 0.008 wt.% sulfur and 

A333–Gr. 6 carbon steels with 0.008 and 0.016 wt.% sulfur were plotted as a function of strain 

rate, as shown in Fig. 65. The available data sets were too sparse to establish a functional form 

Figure 65. Effect of strain rate on fatigue life of low–alloy steels with different sulfur

contents (Refs. 10, 136).
93

for dependence of fatigue lives on sulfur content and to define either a threshold for sulfur

content below which environmental effects were unimportant or an upper limit above which the 

effects of sulfur on fatigue lives may saturate. A linear dependence of fatigue life versus sulfur 

content was assumed in proposed correlations for estimating the fatigue lives of carbon steels 

and low–alloy steels in LWR environments.10,118 The limited data indicated that in high-purity 

water with 0.2 ppm DO at 289°C, the fatigue lives of carbon steels with 0.016 and 0.026 wt.% 

sulfur at 0.001 %/s strain rate and 0.3 % strain amplitude were comparable. Similar behavior 

was observed for low-alloy steels with greater than 0.0125 wt.% sulfur. Therefore, fatigue lives 

of carbon and low-alloy steels were assumed to saturate at sulfur contents above 0.015 wt.%.10

The existing fatigue ε-N data also indicated significant reductions in fatigue lives for some heats 

of carbon steels with sulfur levels as low as 0.002 wt.%. The fatigue lives of several heats of 

A333–Gr. 6 carbon steels with sulfur contents of 0.002–0.016 wt.% in high-DO water at 288°C 

and 0.6% strain amplitude were plotted as a function of strain rate, as shown in Fig. 66.10 

Environmental effects on the fatigue lives of these steels were independent of sulfur contents in 

the range of 0.002–0.015 wt.%. The fatigue lives of carbon steel in air-saturated water 

(approximately 8 ppm DO) were relatively insensitive to sulfur contents in very high DO water. 

Under these conditions, the effects of DO dominated fatigue lives.

• The effects of steel sulfur content on the fatigue lives of carbon and low-alloy steels in LWR 

environments were explicitly considered in the Fen, defined in Eq. 41 (Section 4.1.11). 

Evaluation of experimental data on low-sulfur steels (less than 0.005 wt.% sulfur) in water 

with more than 1 ppm DO should be performed with caution because, in some cases, the 

effects of sulfur were observed to be larger than those predicted by Eq. 41. 

Figure 66.

Effect of strain rate on the 

fatigue lives of A333–Gr. 6 

carbon steels with different 

sulfur contents (Ref. 10). 

4.1.8 Hold Periods

Fatigue tests conducted using trapezoidal loading waveforms indicated that hold periods at 

peak tensile strains decreased the fatigue lives of carbon steels in high–DO water at 289°C.10,24 

However, examination of the data indicated that these results were caused by limitations of the 

test procedures or by frequency effects. Loading waveforms, hysteresis loops, and fatigue lives 

for the tests on A106–Gr B carbon steel in air and water environments were plotted, as shown in 

Fig. 67.10 A 300–s hold period was sufficient to reduce fatigue lives by approximately 50% 

(approximately 2,000 cycles without a hold period and approximately 1,000 cycles with a hold 

period); a longer hold period of 1800 s resulted in lower fatigue lives than those obtained with a 

300–s hold period. For example, two 300–s hold tests at 288°C and approximately 0.78% strain 
94

range in oxygenated water with 0.7 ppm DO yielded fatigue lives of 1,007 and 1,092 cycles; the 

fatigue life from a 1,800–s hold test was 840 cycles. These tests were conducted in stroke–

control mode and were different from conventional hold–time tests in a strain–controlled mode 

where the total strain in the sample was held constant during the hold period. However, a 

portion of the elastic strain was converted to plastic strain because of stress relaxation. In the

stroke–controlled tests, there were additional plastic strains in the samples due to relaxation of 

elastic strains from the load trains (Fig. 67). Consequently, significant strain changes occurred 

during the hold periods; the measured plastic strains during the hold periods were 

approximately 0.028% from relaxation of the gauge and 0.05–0.06% from relaxation of the load 

trains. These conditions resulted in strain rates of 0.005–0.02%/s during the hold periods. The 

reductions in fatigue lives were attributed to slow strain rates during the hold periods. Also, 

frequency effects decreased the fatigue lives obtained from hold time tests, e.g., in air, the 

fatigue lives of stroke-controlled tests with hold periods were approximately 50% lower than 

those without the hold periods. 

Strain or Stroke Control

Air: 4740±1250 cycles

PWR: 1965±385 cycles

High DO: 2077 cycles

Strain Control

Air: 6,275 cycles

Stroke Control (5–min hold)

Air: 2592 cycles

High DO: 1007, 1092 cycles

Stroke Control (30–min hold)

High DO: 840 cycles

Figure 67. Fatigue lives of A106–Gr B steel in air and water environments at 288°C, 

0.78% strain range, and hold periods at peak tensile strain (Ref. 10). 

Hysteresis loops are for tests in air.

Hold–time tests were also conducted on STS410 carbon steel at 289°C in water with 1 ppm DO 

(Fig. 68).24 The most significant observation was that, for strain hold periods at peak tensile 

strain, reduction in fatigue lives were significant in tests that were conducted at fast strain rates, 

e.g., at 0.4%/s. The reduction in fatigue lives with hold periods decreased at lower strain rates 

with insignificant reductions in fatigue lives at 0.004 %/s strain rate. The results also indicated 

that the decrease in fatigue lives with extended hold periods saturated at values that were 

comparable to fatigue lives at slow strain rates (e.g., 0.004 %/s).
95

The most significant observation of this data was that little or no decreases in fatigue lives were 

observed when the hold periods were below the peak strain during the decreasing strain 

portions of the fatigue cycles (i.e., 0.06% below the peak strain of 0.24%). Based on these 

results, Higuchi et al.24 concluded that the procedures for calculating Fen did not need revision.

The JNES report136 investigated hold time effects and reported that, in the high temperature 

water environments, the fatigue lives of carbon and low-alloy steels were reduced due to strain 

hold times at the peak (local maximum value). Fatigue life reductions due to strain hold times at 

the peak were significant at higher strain rates, but they were reduced as the strain rate 

decreased. There were little or no observed fatigue life reductions at strain rates of 0.004%/s or 

less. JNES concluded that the extent of fatigue life reduction depended on the length of the hold 

time, and that fatigue life reductions tended to be saturated as the hold time became longer. A 

threshold was observed at a strain rate of 0.004%/s. For carbon steels, the effects of strain hold 

times were negligible at strain rates of 0.004%/s or lower. Fatigue life reductions due to strain 

hold times in low-alloy steels were smaller than those in carbon steels. Although fatigue lives

were reduced due to strain hold times at the peak (local maximum value), when strain was held 

at 0.06% below the peak strain after overshoot showed no reductions in fatigue lives, although

tensile stresses corresponding to the yield point still remained. From these results, JNES 

concluded that the effects of strain hold times in the actual components was not necessary 

since the peak thermal stress generated by actual operating thermal transients is not 

considered to exceed the yield stress significantly but, for strain rates exceeding 0.004%/s,

evaluations should be performed assuming a threshold strain rate of 0.004%/s while considering 

fatigue life reduction due to strain holding when the strain is at the peak and held under the 

internal pressure condition that accompanies elastic follow-up.

As discussed in Section 4.1.11, the differences in fatigue lives observed in the JNES tests were 

generally within the data scatter for the fatigue ε–N data in LWR environments. Thus, the 

effects of hold time from available data are inconclusive and, until such time as sufficient data 

are available, these effects were not explicitly addressed in the updated Fen methodology. 

Further research of these effects is recommended.

• The available ε-N data investigated in this report were not fully conclusive with respect to the 

effects of hold time periods on the fatigue lives of carbon and low-alloy steels in LWR 

environments. Thus, hold time effects were not explicitly addressed in the updated Fen

methodology.

(a) (b)

Figure 68. Effect of hold periods on the fatigue lives of A333–Gr. 6 carbon steel at 

289°C in water with 1 ppm DO (Ref. 24).
96

4.1.9 Flow Rate

Nearly all of the laboratory fatigue ε–N data for LWR environments were obtained at very low 

water flow rates. Recent test data indicated that, under the environmental conditions typical for 

operating BWRs, environmental effects on the fatigue lives of carbon steels were lower at high 

flow rates (7 meters/second) compared to the fatigue lives under very low flow rate conditions 

similar to those flow rates where most of the data were obtained.25,26,55 The effects of water 

flow rate on the fatigue lives of high– and low–sulfur A333–Gr. 6 carbon steel and A533-Gr. B 

low-alloy steel in high–purity water at 289°C tested at different strain amplitudes and strain rates 

are shown in Fig. 69.

The results indicated that the effects of increased flow rates were modest. The benefits were 

greater for high–sulfur steels at high strain amplitudes and high strain rates (e.g., 0.4%/s).25,26 

At 0.3% strain amplitude and 0.01%/s strain rate, and for all DO levels, fatigue lives were 

increased by a factor of approximately 2 when the flow rate was increased from approximately 

10–5 to 7 meters/second. At 0.6% strain amplitude and 0.001%/s strain rate, fatigue lives were 

increased by a factor of approximately 6 in water with 0.2 ppm DO and by a factor of 

(a) (b)

(c) (d)

Figure 69. Effects of water flow rate on fatigue lives of A333–Gr. 6 and A508-Gr. 1 

carbon steels and A533-Gr. B low-alloy steel at 289°C and 0.3 or 0.6% strain 

amplitudes and various strain rates (Ref. 25,26).
97

approximately 3 in water with 1.0 or 0.05 ppm DO. Under similar loading conditions, i.e., 0.6% 

strain amplitude and 0.001%/s strain rate, a low–sulfur (0.008 wt.%) heat of A333–Gr. 6 carbon 

steel showed a factor of approximately 2 increase in fatigue life with increased flow rates. Note 

that the beneficial effects of flow rate were determined from a single test on each material at 

very low flow rates; data scatter in LWR environments is typically a factor of approximately 2. A 

factor of 2 increase in fatigue lives was observed (Fig. 70) at KWU during component tests with 

180° bends of carbon steel tubing (0.025 wt.% sulfur) when internal flow rates of up to 

0.6 meters/second were established.55 The tests were conducted at 240°C in water that 

contained 0.2 ppm DO.

• Because of the uncertainties in the flow conditions at or near the locations of crack initiation, 

the beneficial effects of flow rates on the fatigue lives of carbon and low-alloy steels were not 

explicitly considered in the updated Fen methodology.

Figure 70.

Effect of flow rate on low–cycle 

fatigue of carbon steel tube bends in 

high–purity water at 240°C (Ref. 55). 

RT = room temperature.

4.1.10 Fatigue Life Model

As discussed in the beginning of Section 4.1, the fatigue-life models for estimating the fatigue 

lives of carbon and low–alloy steels in LWR environments presented in the original revision of 

NUREG/CR-6909 were based on an analysis of the updated PVRC database. For this report, 

more recently available data were fit to a modified version of the Langer equation expressed by 

Eq. 6, which included a term for environmental effects on fatigue lives. The environmental term 

included the effects of key parameters, such as temperature, strain rate, DO content in the 

water, and sulfur content in the steel on the fatigue lives of carbon and low-alloy steels, and also 

considered revised constraints based on stakeholder comments and experience with 

implementation of the Fen methodology in industry analyses. The functional forms of these 

dependencies and constraints were based on the observed data trends. In LWR environments, 

the analysis concluded that the fatigue life, N, of carbon steels was best represented by

ln(N) = 5.951 – 1.975 ln(εa – 0.113) + 0.101 S* T* O* *, (39)

and that of low–alloy steels, by

ln(N) = 5.747 – 1.808 ln(εa – 0.151) + 0.101 S* T* O* *, (40)

where S*, T*, O*, and * represent the terms for transformed sulfur content, temperature, DO 

level, and strain rate, respectively, that are defined by Eqs. 35-38. These equations for carbon 
98

and low-alloy steels remain unchanged from those specified in the initial revision to 

NUREG/CR-6909. The predicted fatigue lives showed good agreement with the experimental 

values; the experimental and predicted values differed by a factor of 3 or less. A threshold 

strain amplitude (one-half of the applied strain range) was also defined, below which LWR 

coolant environments have an insignificant effect on fatigue lives, i.e., Fen = 1. The threshold 

strain amplitude was specified as 0.07%, or a 145 MPa (21 ksi) stress amplitude for both carbon 

and low–alloy steels.

• The ANL fatigue life models for carbon and low-alloy steels represent the mean values of 

fatigue life as a function of applied strain amplitude, temperature, strain rate, DO level in the 

water, and sulfur content of the steel. The effects of parameters (such as mean stress, 

surface finish, size and geometry, and loading history) known to influence fatigue lives were 

not included in the models; the effects of these parameters were considered in the 

development of the fatigue design curves, as discussed in Chapter 5.

4.1.11 Environmental Fatigue Correction Factor 

To incorporate environmental effects into ASME Code Section III fatigue evaluations, the initial 

revision to NUREG/CR-6909 specified that the fatigue usage for a specific stress cycle or load 

set pair based on the current ASME Code Section III fatigue design curves was multiplied by the 

environmental correction factor, Fen, given by Eqs. 33 and 34, respectively, for carbon steels 

and low-alloy steels. Further details for incorporating environmental effects into fatigue 

evaluations were presented in Appendix A of the initial revision to NUREG/CR-6909. 

The previous Fen expressions for carbon and low-alloy steels (i.e., Eqs. 33 and 34) were

updated in this report using the larger fatigue ε–N database described in Table 10 to remove 

some of the conservatism in the Fen methodology and to reflect the additional data available 

since the initial publication of NUREG/CR-6909. As discussed previously, an additional 

objective of the reevaluation was to investigate the significance of the constant terms in the 

previous expressions. The updated evaluation addressed stakeholders’ concerns related to: 

(a) the constants in the Fen expressions that result in Fen values of approximately 2 even when 

strain rate is very high or temperature is very low, and (b) the temperature dependence of Fen

for carbon and low-alloy steels. 

The available fatigue ε-N data for carbon and low-alloy steels were reanalyzed using a different 

dependence of fatigue lives on strain rate, dissolved oxygen, and temperature, such that Fen is 

equal to 1 at high strain rates (i.e., greater than 2.2%/s). A single Fen expression was 

developed for both carbon and low-alloy steels. The functional form of the new Fen expression 

and for the dependence of Fen on the sulfur content in the steel were comparable to the 

expressions proposed by the JNES.136 In addition, a maximum temperature limit was selected 

at 325°C as a reasonable extension to cover all anticipated LWR operating conditions. This is 

adequate for all expected operating LWR conditions considering the use of average 

temperature (as discussed in Section 4.1.11 and shown in Fig. 81). In addition, the limit for the 

saturation strain rate was decreased from 0.001 to 0.0004%/s. A best fit of the experimental 

data yielded the following expression for Fen for both carbon and low-alloy steels,

Fen = exp((0.003 – 0.031 *) S*T*O*), (41)

where S*, T*, O*, and * are the transformed sulfur content, temperature, DO level, and strain 

rate, respectively, defined as:
99

S* = 2.0 + 98 S (S ≤ 0.015 wt.%)

S* = 3.47 (S > 0.015 wt.%) (42)

T* = 0.395 (T < 150°C)

T* = (T – 75)/190 (150°C ≤ T ≤ 325°C) (43)

O* = 1.49 (DO < 0.04 ppm)

O* = ln(DO/0.009) (0.04 ppm ≤ DO ≤ 0.5 ppm)

O* = 4.02 (DO > 0.5 ppm) (44)

* = 0 ( > 2.2%/s)

* = ln( /2.2) (0.0004%/s ≤ ≤ 2.2%/s)

* = ln(0.0004/2.2) ( < 0.0004%/s). (45)

The experimental values of fatigue lives compared to those predicted by Eq. 41 and Eqs. 33 or 

34 were plotted, as shown in Figs. 71 and 72 for carbon and low-alloy steels, respectively. The 

results indicate that the new Fen expressions represent a better fit of the experimental data 

relative to the fit for the expressions in the original revision of NUREG/CR-6909; the regression 

(a) (b)

Figure 71.

Experimental fatigue lives of carbon 

steels in LWR environments vs. 

fatigue lives predicted from the 

(a) new expression, (b) JNES 

expression, and (c) the previous 

NUREG/CR-6909 expression.
100

(c)

(a) (b)

Figure 72.

Experimental fatigue lives of lowalloy steels in LWR environments 

vs. fatigue lives predicted from 

the (a) new expression, (b) JNES 

expression, and (c) the previous 

NUREG/CR-6909 expression.

(c)

(R-squared) values increased from 0.80 to 0.85 for carbon steels and from 0.83 to 0.84 for lowalloy steels. The new expressions typically underestimated environmental effects for operating 

conditions that resulted in very large Fen values (i.e., greater than 40) and in the high-cycle 

fatigue regime (i.e., fatigue lives above 50,000 cycles). However, such conditions are not 

typical of the thermal transients encountered during reactor operation or evaluated in most 

ASME Code CUF calculations.

A comparison was made of the fatigue lives predicted for carbon and low-alloy steels using the 

new Fen expressions and the JNES Fen expressions, and is shown in Fig. 73. In general, Fen

values calculated from the new ANL expression were marginally lower than those obtained from 

the JNES expression in Ref. 136; the fatigue lives predicted by the new ANL expressions were 

either comparable to or slightly longer than those predicted from the JNES expressions. 

However, there were a few data points for carbon steels and several data points for low-alloy 

steels for which the fatigue lives predicted by the JNES expression were significantly lower than 

those predicted by the new ANL expression (bottom left corner of the plots in Fig. 73). As 

discussed previously, the new ANL Fen expression was optimized under environmental and 
101

loading conditions that are anticipated during reactor operation (i.e., conditions that yield Fen

values less than 40). This optimization limitation explains the differences observed between the 

two expressions, as the predicted Fen values for nearly all of these data points were above 60. 

The tests associated with these points were conducted in air-saturated water (8 ppm DO) at 

very low strain rates. Considering this, the ANL and JNES expressions are in very good 

agreement, which is remarkable given that the development approaches used were different.

Figure 73. Comparison of the fatigue lives of carbon and low-alloy steels predicted 

from the new Fen expression and the JNES Fen expression.

Upon completion of the modeling phase, the residual errors (i.e., the Cartesian distance of each 

data point from the mean prediction curve) did not show significant patterns, such as 

heteroskedasticity (changing variance), or a nonzero slope. The residual errors for each 

variable, grouped by steel type, were plotted and are shown in Figs. 74 and 75 for carbon and 

low-alloy steels, respectively. The residuals were determined from the difference between the 

logarithms of the estimated lives and predicted lives. Thus, negative residual errors indicated 

conservative estimates of fatigue lives and positive residual errors indicated nonconservative 

estimates of fatigue lives (i.e., predicted lives were greater than the observed fatigue lives). 

However, if the residuals for a specific heat were not evenly distributed about zero, it did not 

necessarily indicate any deficiency in the predictive models. Such results indicated that the 

specific heat was either superior or inferior to the average behavior predicted by the model. For 

example, a positive residual indicated that the heat was inferior (i.e., the constant A from Eq. 6

for the heat was smaller than the median value of A determined for the model) and a negative 

residual indicated that the heat was superior to the average behavior for the material. This 

behavior is discussed further in Section 4.1.13.

The results presented in Figs. 74 and 75 did not show any unexplained patterns. In general, 

high variance tended to be associated with longer lives and lower strain amplitudes. 

Furthermore, biases were traceable to heat–to–heat variations. For example, the heats of 

A108-Gr. B, A508-Gr. 1, and A516-KC70 had inferior fatigue resistances and two heats of 

A333-Gr. 6 (ANL Material IDs 8 and 10 in Table 10) had superior fatigue resistances compared 

to the average behavior represented by the fatigue ε-N model (Eqs. 39 and 40). 

Some of the heats of carbon and low-alloy steels were also tested in air. The residual errors for 

the best fit of the fatigue ε-N data for carbon and low-alloy steels in air were plotted as a 

function of the ANL Material ID, as shown in Fig. 76. Most of the data subsets for fatigue tests 
102

in air followed the same trends observed in LWR environments; data subsets that yielded 

positive residuals in LWR environments also showed positive residuals in air, and vice versa. 

(a) (b)

(c) (d)

(e) (f)

Figure 74. Residuals for predicted fatigue lives of carbon steels as a function of 

(a) Material ID, (b) water dissolved oxygen content, (c) strain rate, 

(d) temperature, (e) steel sulfur content, and (f) strain amplitude.
103

(a) (b)

(c) (d)

(e) (f)

Figure 75. Residuals for predicted fatigue lives of low-alloy steels as a function of 

(a) Material ID, (b) water dissolved oxygen content, (c) strain rate, 

(d) temperature, (e) steel sulfur content, and (f) strain amplitude.
104

The exception was ANL Material ID 21, which yielded a positive residual in an LWR 

environment but a negative residual in an air environment. However, the total data in air were 

quite limited for this heat of A516-KC70 carbon steel, so quantitative conclusions were not 

made. 

• The Fen approach should be used to incorporate environmental effects into ASME Code, 

Section III fatigue evaluations for carbon and low-alloy steels. Appendix C of this report 

presents a sample application of the Fen methodology.

Figure 76. Residuals for predicted fatigue lives in air of carbon and low-alloy steels as 

a function of Material ID.

4.1.12 Surface Finish

Fatigue tests were conducted on specimens of carbon and low-alloy steels that were 

intentionally roughened in a lathe, under controlled conditions, with 50-grit sandpaper to 

produce circumferential scratches with an average roughness, Ra, of 1.2 μm and a root-meansquare, Rq, of 1.6 μm (approximately 62 micro in.).46 The results for A106–Gr B carbon steel 

and A533–Gr B low–alloy steel are shown in Fig. 77. In air, the fatigue lives of rough A106–

Gr B specimens were a factor of 3 lower than that of smooth specimens, and, in high–DO water, 

were the same as those of smooth specimens. In low–DO water, the fatigue lives of the 

roughened A106–Gr B specimen were slightly lower than those for smooth specimens. The 

effects of surface finish on the fatigue lives of A533–Gr B low–alloy steel were similar to those 

for A106–Gr B carbon steel; in high–DO water, the fatigue lives of both rough and smooth 

specimens were the same. The results in water were consistent with a mechanism of growth by 

a slip oxidation/dissolution process, which was not affected by surface finish. Surface 

roughness is expected to influence fatigue lives because environmental effects were moderate 

in low–DO water.
105

Figure 77. Effect of surface finish on the fatigue lives of (a) A106–Gr B carbon steel 

and (b) A533 low–alloy steel in air and high–purity water at 289°C (Ref. 46).

The potential additional impact of strain rate on the observed surface finish effects on the 

fatigue lives of low-alloy steels were also investigated (Fig. 78).144 The results showed a strong 

influence of strain rate on surface finish effects. At high strain rates, relative to smooth 

specimens, the fatigue lives of A533-B low-alloy steel decreased significantly even with slight 

increases in surface roughness, whereas at slow strain rates, since fatigue lives were already 

low, any further decrease in fatigue lives occurred only for very rough surfaces. The different 

behavior was attributed to the differences in the mechanism for corrosion fatigue of carbon and 

low-alloy steels in LWR environments. As discussed in Section 2.2.1.2, the corrosion fatigue 

mechanism changed from hydrogen-induced cracking to a slip-oxidation/dissolution mechanism 

with decreasing strain rates. During cyclic loading in high-temperature water, plastic 

deformation induced slip bands at the crack tip along the maximum shear directions or the 

preferred slip directions, which ruptured the protective oxide film at the crack tip. Furthermore, 

the slip bands were the favored paths for hydrogen transportation and the matrix/inclusion 

interfaces were the preferred traps for hydrogen. As a result, at high strain rates, fatigue 

cracking preferentially occurred along the slip bands as well as the matrix/inclusions interfaces, 

which resulted in macroscopically tortuous fatigue cracks and a rough fracture surface. 

However, at low strain rates, fatigue crack growth in high-temperature water was controlled by 

Figure 78.

Relationship between surface finish 

and fatigue life reduction fraction for 

A533-Gr. B low-alloy steel in water at 

288°C (Ref. 144).
106

the film-rupture/oxidation-dissolution mechanism, which resulted in a macroscopically straight, 

and relatively flat, featureless fracture surface.

The results in Fig. 77 were also observed to be consistent with strain rate effects; the surface 

finish of the specimens that were tested at slow strain rates were not sufficiently rough to further 

decrease the fatigue lives. 

• The effects of surface finish were not explicitly included in the environmental fatigue 

correction factor for carbon and low-alloy steels; instead, they were included in the subfactor 

for “surface finish and environment” that was applied to the mean data air curve to develop 

the fatigue design curve in air.

4.1.13 Heat-to-Heat Variability

The effects of material heat-to-heat variability and data scatter on the fatigue lives of carbon and 

low-alloy steels was evaluated for LWR environments. The fatigue behavior of each of the 

heats or loading conditions was characterized by the value of the constant A in the ANL models 

for carbon steels given by 

ln(N) = A – 1.975 ln(εa – 0.113) – ln(Fen), (46)

and in the ANL model for low-alloy steels by 

ln(N) = A – 1.808 ln(εa – 0.151) – ln(Fen), (47)

where Fen was determined from Eq. 41. The values of A, determined from Eqs. 46 and 47 for 

the various data sets in the larger, updated fatigue ε-N database used in this report were 

ordered, and median ranks were used to estimate the cumulative distribution of A for the 

population. The estimated cumulative distribution of constant A for heats of carbon and low–

alloy steels in water environments were plotted, and are shown in Fig. 79. The median value of 

constant A in water was slightly lower than that in air; the values of constant A in LWR and air 

environments, respectively, were 6.503 and 6.583 for carbon steels and 6.358 and 6.449 for 

low-alloy steels. The results of the analysis of the larger, updated fatigue ε-N database 

indicated that an increase in the fatigue data of more than 60% had an insignificant impact on 

the parameters in the ANL models for the fatigue lives of carbon and low-alloy steels.

The results also demonstrated that the Fen expression given in Eq. 41 adequately captured the 

effects of LWR environments on the fatigue lives of carbon and low-alloy steels. Since the 

actual heats of carbon and low-alloy steels that were tested in air and LWR environments were 

different, the location (percentile) of a specific heat on the distribution curve differed between 

the two environments. However, the estimated cumulative distribution of most of the heats of 

carbon steel and low-alloy steels that were tested in both air and LWR environments were 

comparable. However, a few exceptions showed significant differences. For example, for ANL 

heat designation A333-Gr. 6-3 (0.014 wt. % sulfur, ANL Material ID 10 in Tables 1 and 10), the 

updated ANL model underestimated environmental effects and the material ranked in the 97th

percentile in LWR environment and the 50th percentile in air. In contrast, for ANL heat 

designation A333-Gr. 6-7 (0.008 wt. % sulfur, ANL Material ID 14 in Tables 1 and 10), the model 

overestimated environmental effects and the material ranked 40th percentile in LWR 

environment and the 55th percentile in air. A similar contrasting behavior was observed in two 

heats of low-alloy steels, e.g., the environmental effects were overestimated for A302-Gr. B 

(0.027 wt. % sulfur, ANL Material ID 1 in Tables 1 and 10) and underestimated for A508-Gr. 3-1 

(0.003 wt. % sulfur, ANL Material ID 6 in Tables 1 and 10). 
107

Figure 79. Estimated cumulative distribution of parameter A in the ANL model for 

fatigue lives for heats of carbon and low–alloy steels in LWR environments. 

These results and evaluation indicated that, for carbon and low-alloy steels, the heat-to-heat 

variation in LWR environments were essentially the same as that established in air and 

presented in Section 3.1.7. Thus, the 95/95 values of the factors to account for material 

variability and data scatter were the same in air (i.e., presented in Tables 2 and 3 for carbon and 

low-alloy steels, respectively). These factors were required to provide 95% confidence that the 

resultant lives were greater than those observed for 95% of the materials of interest. 

• The effects of heat-to-heat variability were not explicitly included in the environmental fatigue 

correction factor for carbon and low-alloy steels; instead, they were included in the subfactor 

for “data scatter and material variability” that was applied to the mean data air curve to 

develop the fatigue design curve in air.

4.1.14 Modified Rate Approach

Most of the available fatigue ε–N data evaluated in this report were obtained under loading 

histories with constant strain rate, temperature, and strain amplitude. The actual loading 

histories encountered during service of nuclear power plants are far more complex. Exploratory 

fatigue tests were conducted with loading waveforms in which the test temperature and strain 

rate were varied.10,21,24 The results of such tests provided limited guidance for developing 

procedures and rules for fatigue evaluation of components under complex loading histories.

The modified rate approach was proposed to predict fatigue lives under changing test 

conditions.37,38 This approach provided methods for calculating Fen under conditions where 

temperature and strain rate were varied. In this approach, the correction factor, Fen( , T), is 

assumed to increase linearly from a minimum value of 1.0 with increments of strain from a 

minimum value, εmin (%), to a maximum value, εmax (%). Increments of Fen, dFen, during 

increments of increasing strain, dε, are calculated from

dFen = (Fen – 1) dε /( εmax – εmin). (48)
108

Integration of Eq. 48 from εmin to εmax (portion of loading where strain is increasing) provides the 

environmental fatigue correction factor under changing temperature and strain rate. The 

application of the modified rate approach to an increasing strain transient is illustrated in Fig. 80; 

at each strain increment, dε, the associated Fen( ,T) value for carbon and low-alloy steels is 

determined from Eq. 41. Thus, Fen for the total increasing strain transient is given by 

, (49)

where n is the total number of strain increments, and k is the subscript for the kth incremental 

segment. 

Figure 80.

Application of the modified rate approach 

to determine the environmental fatigue 

correction factor Fen during the increasing 

strain portion of a transient.

As discussed in Section 4.1.3, a minimum threshold strain, εth (one-half of the strain threshold of

0.14% strain for carbon and low-alloy steels considering a factor of 2 for data scatter), was 

required for an environmentally assisted decrease in fatigue life. Consideration of a strain 

threshold assumes that during a strain cycle, environmental effects are significant only after the 

applied strain level exceeds the threshold value. In application of the modified rate approach 

when a threshold strain, εth, is considered, Fen for the total strain transient is given by 

. (50)

The modified rate approach was used to evaluate fatigue lives under cyclic loading conditions 

where both temperature and strain rate were varied during the test.24,37,38 The studies 

demonstrated the applicability of the modified rate approach to variable loading conditions such 

as those that are typically present during actual plant transients. The following significant 

conclusions were made from those studies.

(a) The use of a strain threshold, εth, for calculating Fen by the modified rate approach (i.e.,

Eq. 50) was not necessary because it did not improve the accuracy of estimation.38 As 

discussed in Section 4.1.3, application of the modified rate approach, without the consideration 

of a strain threshold, gave the best estimates of fatigue lives.

(b) Under load cycles that involved variable strain rates, estimates of Fen based on an average 

strain rate [i.e., in Fig. 80, total strain (εmax – εmin) divided by the total time between εmin and 
109

(εmax] were the most conservative when the maximum transient temperature was used.24 

Thus, calculations of Fen based on an average strain rate for the transient are expected to 

yield conservative estimates of fatigue lives provided that appropriate temperatures are 

selected for use in the calculations. 

(c) An average temperature for the transient, considering the threshold temperature of 150°C, 

may be used to estimate Fen during a load cycle, i.e., average of the maximum temperature 

for the transient and the higher of the threshold temperature for the material under 

consideration and the minimum temperature for the transient. However, some limited NRC 

calculations indicated that using either an average transient temperature or an average of 

the transient maximum temperature and the Fen threshold temperature did not always yield 

a conservative Fen estimate when compared to the results obtained from an integrated Fen

using the modified rate approach, as shown in Fig. 81. If the integration time step is 

sufficiently small, there is an insignificant difference in Fen results for the modified rate 

approach when either average or maximum temperatures are used.

Figure 81. Example showing Fen values computed using average temperatures 

compared to the Fen computed using an integrated (modified rate) approach. 

• Where information is available regarding the transients associated with a specific stress cycle 

or load set pair, the modified rate approach may be used to determine Fen using Eq. 49. 

Average Transient 

Temperature = 385.1°F

Average of Max. Transient and 

Threshold Temps. = 435.6°F

0

100

200

300

400

500

600

700

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 100 200 300 400 500 600

Temperature (°F)

Strain (%)

Time (seconds)

(Material = SS, DO = 10 ppb)

Scaled Strain

Scaled Strain Used for Integrated Fen

Average Strain Rate

Metal Temperature

RESULTS: Integrated Fen = 1.822

Fen Based on Average Transient Temperature = 1.465

Fen Based on Average of Transient Maximum and Threshold Temperatures = 1.638
110

4.2 Wrought and Cast Austenitic Stainless Steels

Fatigue-life models for estimating the fatigue lives of wrought and cast austenitic SSs in LWR 

environments presented in the initial revision of NUREG/CR-6909 were based on the updated 

PVRC database available at that time. The effects of key parameters, such as temperature, 

strain rate, and the DO content in water were included in the correlations. The functional forms 

for the effects of these parameters were based on the observed data trends. For both wrought 

and cast austenitic SSs, the model assumed threshold and saturation values of 0.4 and 

0.0004%/s, respectively, for strain rate and a threshold value of 150°C for temperature. In 

addition, because of a lack of relevant fatigue data, the dependence of environmental effects on 

the DO level was not defined in the initial revision of NUREG/CR-6909. Lacking sufficient data 

to establish the effects of DO level on fatigue lives, those effects were assumed to be the same 

in low– and high–DO water for both wrought and cast austenitic SSs. The fatigue ε-N data for 

austenitic SSs in LWR environments were fitted to a modified version of Eq. 6 and expressed as 

ln(N) = A – B ln(εa – C) – T’ O’ ’

, (51)

where T’

, O’, and ’ are the transformed temperature, water DO level, and strain rate, 

respectively, which are defined in Eqs. 53-55. The least–squares fit of the experimental data in 

LWR environments yielded a steeper slope for the ε–N curve than the slope of the curve 

obtained in air.45,121 These results indicated that, for austenitic SSs, environmental effects were

less pronounced with increasing strain amplitudes above the threshold value of strain amplitude. 

Differing slopes for the ε–N curves in air and water environments added complexity to the 

determination of the environmental fatigue correction factor, Fen. Therefore, the slope, B, of the 

ε–N curve was assumed to be the same in LWR and air environments (i.e., the value of 

constant B was assumed to be 1.920 for both environments), and the constant C was also 

considered the same for both environments (i.e., constant C was assumed to be 0.112). A 

value of 6.157 for the constant A was determined from the best fit of the fatigue ε-N data in LWR 

environments. Note that the constant A in the ANL model for austenitic SSs presented in the 

initial revision of NUREG/CR-6909 differed from the values reported earlier in NUREG/CR–

5704, NUREG/CR–6815, and NUREG/CR–6878 because relative to the earlier expressions, the 

environmental fatigue correction factor, Fen, determined in the initial revision of NUREG/CR6909 was 45–60% lower. Thus, the environmental fatigue correction factor for wrought and cast 

austenitic SSs was given by

Fen = exp(0.734 – T' ' O'

), (52)

where T'

, ', and O' were defined as the transformed temperature, strain rate, and water DO

level, respectively, as follows:

T' = 0 (T < 150°C)

T' = (T – 150)/175 (150 ≤ T < 325°C)

T' = 1 (T ≥ 325°C) (53)

' = 0 ( > 0.4%/s) ' = ln( /0.4) (0.0004 ≤ ≤ 0.4%/s) ' = ln(0.0004/0.4) ( < 0.0004%/s) (54)

O' = 0.281 (all DO levels). (55)

The model was recommended for predicted fatigue lives equal to or less than 106 cycles. Note 

that Eq. 52 was based on the ANL model for austenitic SSs in air (Eq. 29) and the analysis 
111

presented in Section 5.2.11 of the initial revision of NUREG/CR-6909. A single expression was 

specified for Types 304, 304L, 316, 316L, and 316NG SSs. Equations 52–55 were also 

applicable to cast austenitic SSs such as CF-3, CF-8, and CF–8M. The initial revision of 

NUREG/CR-6909 noted that, because the influence of DO level on the fatigue lives of austenitic 

SSs were influenced by the material composition and heat treatment, the ANL fatigue life model 

was somewhat conservative for some SSs in high–DO water. 

Since the initial publication of NUREG/CR-6909, comments received from stakeholders focused 

on two areas. First, the constant value of 0.734 in the Fen expression, which resulted in an Fen

of approximately 2.5 even at very low temperatures (i.e., below the threshold temperature of 

150°C) or at very high strain rates (e.g., during seismic or similar loadings). The other area

concerned the absence of DO dependence on environmental effects. As a result, the Fen

expression given by Eq. 52 yielded conservative estimates of Fen for some materials (e.g., for 

low-carbon or nonsensitized high-carbon wrought SSs). 

In this report, the Fen expressions (i.e., Eqs. 52-55) for incorporating environmental effects on 

the fatigue life of wrought and cast austenitic SSs were updated to address the stakeholder

comments as well as to incorporate data from the much larger database described in Section 

4.2.1. In addition, the dependence of environmental effects on the DO level in the reactor 

coolant environment was included in the revised expression. 

4.2.1 Experimental Data

The relevant fatigue ε–N data for wrought and cast austenitic SSs in LWR environments include 

the large JNES database;136 tests performed by GE in a test loop at the Dresden 1 reactor;14,15

work sponsored by EPRI at GE;58-60 and the data developed at ANL.45 The data that was used 

in the evaluation consisted of 683 tests; 193 tests on 11 heats of Type 304 SS, 255 tests on 8 

heats of Type 316 SS, 115 tests on 7 heats of CF-8M cast austenitic SSs, and 120 tests on 6 

compositions of SS weld metals. Both low-carbon and high-carbon grades of Types 304 and 

316 SSs were included in the database. For all of the SS data, 15% of the tests were 

conducted at temperatures of 100-200°C, 39% at 250–290°C, 44% at 300–325°C, and 1% (10 

tests) at 360°C. A summary of the data sources for the updated database used in this report, as 

categorized by material type and test environment, is shown in Table 11. Other material 

information such as chemical composition, heat treatment, and room temperature tensile 

properties of the various types and heats of materials is given in Appendix B.

The data indicated that the fatigue lives of austenitic SSs were decreased in LWR 

environments; an example of environmental effects on the fatigue lives of Types 304 and 

316NG SSs in high-purity water at 288°C is shown in Fig. 82. The ε–N curves based on the 

ANL model (Eqs. 29 and 52) are also included in this figure. The fatigue lives were decreased 

significantly when three threshold conditions were satisfied simultaneously, viz., when both the 

applied strain range and the service temperature were above minimum threshold levels, and the 

loading strain rate was below a threshold value. The DO level in the water and, to some extent, 

the composition and heat treatment of the steel were important parameters for environmental 

effects on fatigue lives. For some steels, fatigue lives were longer in high-DO water than in lowDO PWR environments. Although the fatigue lives in air of Type 316NG SSs were slightly 

longer than those of Types 304 and 316 SSs, the effects of LWR environments were

comparable for wrought Types 304, 316, and 316NG SSs. In addition, as discussed later in 

Section 4.2.13, available data indicated that the fatigue lives of cast austenitic SSs in both lowDO and high-DO environments were comparable to those of wrought SSs in low-DO 

environments.
112

Table 11. Sources of the fatigue ε–N data for cast and austenitic stainless steels in LWR 

environments.

ANL 

Mat. 

IDa

Material 

Heat 

Designationa

Carbon 

Content 

(wt.%)

Dissolved 

Oxygen 

(ppm)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

Type 304 Stainless Steels

1 304-1 0.050 0.02, 8.0 288 12, 5 JNES (Hasegawa, 

Fukakura) 136

3 304-3 0.060 0.2 288 7 JNES (Enomoto), 136

9 304-9T 0.070 8.0 300 22 (15 aged) JNES (Endo) 136

20 304-G 0.070 0.2 260 7 GE 14,15

21 304-A2 0.060 0.003, 

0.8 288 14, 5b ANL 45

22 304-21T 0.060 0.005 100-360 58 (4 aged), 

6

JNES (Kanasaki, 

Tsutsumi) 136

24 304-35 0.070 0.01-0.2 289 15 (4 aged) JNES (Hirano) 136

25 304-36T 0.050 0.005 325 4 JNES (Nomura) 136

28 304L-E 0.039 0.09 150, 300 8, 20 Solomon 58-60

29 304L-1 0.017 0.01-0.2 289 6 JNES (Hirano) 136

30 304L-G 0.017 0.2 260 4 GE 14,15

Type 316 Stainless Steels

42 316-12T 0.060

0.005, 

8.0 100-325 45, 6 JNES (Kanasaki, Tsutsumi) 136

43 316-13T 0.070 0.005 325 4 JNES (Tsutsumi) 136

44 316-14T 0.060 0.005 325 8 (4 aged) JNES (Tsutsumi) 136

45 316-15T 0.040 0.005 100-325 61c JNES (EFT) 136

48 316N-1 0.010 0.01-0.2, 

8.0

150-289, 288 65, 30

JNES (Nakao, 

Higuchi, Hirano, 

Fukakura)

136

49 316N-2 0.009 0.2 288 9 JNES (Asano) 136

51 316N-4 0.008 0.01, 8.0 290 11 JNES (Higuchi) 136

54 316N-A 0.013 0.004-0.75 288 16 ANL 45

Stainless Steel Weld Metals

56a 308-WM-1 0.050 0.005 100, 200, 325 6, 6, 14 JNES (Tsutsumi) 136

56b 308-WM-2 0.034 0.005 325 9 JNES (Nomura) 136

57a 316 WM 0.039 0.005 100, 200, 325 4, 4, 24d JNES (Tsutsumi) 136

57c 316TP-WM 0.070 0.005 100, 200, 325 3, 3, 11 JNES (Nomura) 136

58 316N-WM-1 0.018 0.01, 8.0 290 4, 8 JNES (Higuchi) 136

59 316N-WM-2 0.017 0.01-8.0 150-289 24 JNES (Hirano) 136

Cast Austenitic Stainless Steels 

61 CF–8M-1 0.050 0.01-1.0 289 26 (4 aged) JNES (Hirano) 136

62 CF–8M-2T 0.050 0.005 325 36 (21 aged) JNES (Tsutsumi) 136

63 CF–8M-3T 0.050 0.005 325 4 JNES (Tsutsumi 136

64 CF–8M-4T 0.050 0.005 325 4 JNES (Tsutsumi) 136

65 CF–8M-5T 0.050 0.005 325 38 (4 aged) JNES (Nomura) 136

68 CF–8M-8 0.064 0.006-1.0 288 5 ANL 45

69 CF–8M-9 0.065 0.008-1.0 288 2 ANL 45 a T at the end of the number designates a tube specimen. b Six specimens were sensitized. c Twelve specimens had 2% mean strain. d Six specimens were aged for 25,200 h at 465°C.
113

(a) (b)

Figure 82. Strain amplitude vs. fatigue life data for (a) Type 304 and (b) Type 316NG 

SSs in water at 288°C (JNUFAD and Refs. 13,45). 

Furthermore, the existing fatigue data indicated that a slow strain rate applied during the 

tensile–loading cycle (i.e., up–ramp with increasing strain) was primarily responsible for the 

environmentally assisted reduction in fatigue lives. Slow loading rates applied during both 

tensile– and compressive–loading cycles (i.e., up– and down–ramps) did not further decrease 

fatigue lives compared with those observed for tests with only slow tensile–loading cycles

(Fig. 82b). Consequently, loading and environmental conditions during the tensile–loading cycle 

(strain rate, temperature, and DO level) are important for environmentally assisted reduction of 

the fatigue lives of these steels.

It is important to note for evaluation of experimental fatigue ε-N data that although most of the 

data were obtained from strain-controlled fatigue tests, some data, particularly at low strain 

amplitudes, were obtained from load-controlled fatigue tests. Caution should be exercised 

when comparing such data to the ASME Code fatigue design curve for austenitic SSs. For 

example, the applied stress amplitude vs. fatigue life data from load-controlled tests on Type 

304L SSs, with or without a 100 MPa mean stress, in air and PWR primary water environments 

at 150 and 300°C are shown in Fig. 83. The results indicated that, for tests conducted at 

applied stress amplitudes of 80-170 MPa with 100 MPa mean stress, the fatigue lives in PWR 

water relative to fatigue lives in air were significantly decreased at 150°C, while the fatigue lives 

were increased at 300°C. Some investigators have incorrectly interpreted these results and 

indicated that a combination of mean stress and PWR environment decreased the 107 cycles 

fatigue limit of austenitic SSs at 150°C.

As discussed earlier, the ASME Code fatigue design curves were based on fully reversed (i.e., 

R ratio equal to -1) strain-controlled fatigue tests. The stress amplitude used to develop the 

stress-life (S-N) fatigue design curves was a pseudo-stress defined as Sa = E εa, where E is 

the elastic modulus. Therefore, for all fatigue tests conducted at strain amplitudes beyond the 

elastic limit (i.e., with some plastic strain), the experimental stress amplitudes were lower than 

the stress amplitudes plotted for use in developing the ASME Code fatigue design curves. 

Furthermore, as discussed earlier, at low strain amplitudes, based on the chemical composition 

of the material, the effects of DSA may affect the cyclic hardening behavior of austenitic SSs. 

Therefore, depending on the temperature and strain rate, the cyclic stress amplitudes during 

strain-controlled tests or total strain amplitudes during load-controlled tests, may vary 

significantly during tests. These differences have significant effects of the fatigue lives of SS 

materials.
114

The fatigue lives of some load-controlled tests were plotted as a function of total strain 

amplitude in Fig. 84. Note that these results may also be plotted as stress amplitude, Sa vs. 

fatigue life, where Sa is obtained by multiplying the total strain amplitudes by the elastic 

modulus, E. The best-fit air curve and the mean-stress adjusted curve of the fatigue ε-N data 

and the ASME Code Section III fatigue design curve are also shown in the figure. Fatigue ε-N 

data from other strain-controlled-tests performed by the same authors on Type 304L SSs are 

also included for comparison.60 The results indicated that the load-controlled data show 

excellent agreement with the strain-controlled test results. Unfortunately, data for the loadcontrolled tests that showed significant reductions in fatigue lives (i.e., tests with 100 MPa 

mean stress in PWR water at 150°C) were not included in this comparison because the actual 

strain amplitudes for these tests were not specified. In general, at a strain rate of 0.4%, 

environmental effects decreased fatigue lives at 300°C, and had insignificant effects at 150°C. 

The results also indicated that, for Type 304L SSs, the slope of the fatigue ε-N curve was 

steeper than that of the best-fit air curve based on the ANL model for austenitic SSs. This 

behavior was consistent with the best-fit curves developed in NUREG/CR-5704 for Types 

304316, and 316NG SSs. In general, the slope of the curve for low-carbon grades of austenitic 

SSs (e.g., Type 316NG or 304L) was steeper than the slope of the curve for high-carbon SSs 

(Types 304 or 316). For fatigue lives greater than 105 cycles, the fatigue data for Type 304L 

SSs were all below the best-fit air curve. The fatigue lives of tests in air at 150 or 300°C with 

100 MPa mean stress were significantly below those predicted using the mean-stress adjusted 

curve. However, all data were above the ASME Code Section III fatigue design curve, without 

adjusting for environmental effects. Consequently, the potential effects of differences in the 

cyclic hardening behavior of austenitic SSs, particularly at low strain amplitudes, should be 

considered while establishing the factors in the ASME Code Section III fatigue design curves to 

account for the effects of data scatter, heat-to-heat variability, component size and geometry, 

and surface roughness.

• When interpreting load-controlled fatigue tests, care should be taken, particularly when 

comparing the experimental stress amplitudes from such tests to stress amplitudes from the 

ASME Code Section III fatigue design curve. In addition, the potential effects of differences 

in the cyclic hardening behavior should be considered when establishing the factors in ASME 

Code Section III fatigue design curves.

Figure 83. Fatigue stress - life data from load-controlled tests on Type 304L SSs, with 

and without mean stress, in air and PWR water (Ref. 60).
115

(a) (b)

(c) (d)

Figure 84. Fatigue strain - life data from load-controlled tests on Type 304L SSs, with 

and without mean stress, in air (a, c) and PWR water (b, d) (Refs. 58,60). 

4.2.2 Strain Rate

The fatigue lives of Types 304L and 316 SSs in low-DO water were plotted as a function of 

tensile strain rate, as shown in Fig. 85. The lines in the two plots of this figure were based on

the best-fit air curve for austenitic SSs given by Eq. 29 and the Fen expressions given in Eqs. 61

and 58-60. The results of the reanalysis of the larger database indicated that in low–DO PWR 

environments, the fatigue lives of austenitic SSs decreased with decreasing strain rates below 

approximately 10%/s; the effects of environment on fatigue lives saturated at approximately 

0.0004%/s (Fig. 85).13,24,27-31,34,35,45-47 Environmental effects did not occur at strain rates 

greater than 10%/s (i.e., Fen = 1). Decreases in the strain rate from 10 to 0.0004%/s reduced 

the fatigue lives by more than a factor of 10.

In high-DO water at 288°C, the effects of strain rate were less pronounced than in low–DO 

water (Fig. 86). For example, for Heat 30956 of Type 304 SS, strain rate had no effect on the 

fatigue lives in high–DO water, whereas fatigue lives decreased linearly with strain rate in low–

DO water (Fig. 86a). For Heat D432804 of Type 316NG, some effect of strain rate was 

observed in high–DO water, although it was smaller than that in low–DO water (Fig. 86b).

• The effects of strain rate on the fatigue lives of austenitic SSs in LWR environments were 

explicitly considered in the Fen expression defined in Eq. 61 (Section 4.2.13). 
116

Figure 85. Dependence of fatigue lives of austenitic stainless steels on strain rate in 

low–DO water (Refs. 13,45,47,60).

 

(a) (b)

Figure 86. Dependence of fatigue lives of Types (a) 304 and (b) 316NG SSs on strain 

rate in high– and low–DO water at 288°C (Ref. 13,45,47). 

4.2.3 Strain Amplitude

As in the case of the carbon and low–alloy steels, a minimum threshold strain range was 

required for the environmentally induced decrease in fatigue lives of SSs to occur. Exploratory 

fatigue tests were conducted on austenitic SSs to determine the threshold strain range beyond 

which environmental effects were significant during a fatigue cycle.30,35 The tests were 

performed with loading waveforms in which the slow strain rate was applied during only a 

fraction of the tensile loading cycle. The results indicated that a minimum threshold strain was 

necessary to produce an environmentally assisted decrease in the fatigue lives of SSs (Fig. 87). 

The threshold strain range, ∆εth, was independent of material type (weld or base metal) and 

temperature in the range of 250–325°C, but it tended to decrease as the strain range was 

decreased.30,35 The threshold strain range was expressed in terms of the applied strain range,

∆ε, by the equation 

∆εth/∆ε = – 0.22 ∆ε + 0.65. (56)
117

The results suggested that the threshold strain range, ∆εth, was related to the elastic strain 

range of the test, and it did not correspond to the strain at which the crack closed. The 

threshold value was attributed to the rupture strain of the surface oxide film; limited data 

suggested that the threshold strain was between 0.32 and 0.36%. The above expression yields 

a value of 0.31% at a strain range of 0.6%. 

Since the contribution of strain threshold was relatively more significant at low strain amplitudes, 

a strain threshold value of 0.32% (or a strain amplitude of 0.16%) was identified in the original 

version of NUREG/CR-6909. This value was adjusted for the effects of mean stress and 

uncertainties due to material and loading variability. The threshold strain amplitude was 

decreased by approximately 10% to account for mean stress effects and by a factor of 1.5 to 

account for uncertainties in fatigue lives associated with material and loading variability. Thus, a 

threshold strain amplitude of 0.10% (stress amplitude of 195 MPa, or 28.3 ksi) was selected, 

below which environmental effects on fatigue lives were considered insignificant. 

Some stakeholders identified that the strain amplitude threshold of 0.10% was based on a factor

of 1.7 on strain instead of the factor of 2 proposed in the criteria document for developing the 

ASME Code Section III fatigue design curves.8 The threshold value of 0.10% was endorsed by 

the PVRC Steering Committee for Cyclic Life Environmental Effects (CLEE).* Based on 

experimental data, the CLEE proposed a strain threshold for environmental effects; a lower 

strain amplitude below which environmental effects were considered to be insignificant, a 

slightly higher strain amplitude above which environmental effects decreased fatigue lives, and 

a linear variation between these two values. The two strain amplitudes were 0.10 and 0.11% for 

both wrought and cast austenitic SSs. For simplicity, in the initial revision of NUREG/CR-6909, 

a single value of 0.10% was proposed for the strain amplitude threshold. 

The same procedure is appropriate for defining a value of strain threshold that maintains the 

factor of 2 on strain proposed by ASME Code Section III. However, since the effects of mean 

stress on fatigue lives are accounted for in the mean-stress adjustment to the best-fit mean data 

curve using the Modified Goodman relation, only the effects of material and loading variability 

were addressed in defining the strain threshold for environmental effects to avoid double 

counting mean stress effects.

 * Welding Research Council Progress Report, Vol. LIX No. 5/6, May/June 1999.

Figure 87.

Results of strain rate change tests on 

Type 316 SSs in low–DO water at 325°C. 

Low strain rate was applied during only 

a fraction of the tensile loading cycle. 

Fatigue life is plotted as a function of 

fraction of strain at high strain rate 

(Refs. 30,35).
118

• The procedure for calculating Fen, defined in Eq. 61 (Section 4.2.13), includes a threshold 

strain amplitude of 0.10% below which LWR coolant environments do not affect fatigue lives, 

i.e., Fen = 1. However, this threshold strain amplitude should not be considered when the 

modified rate approach is used to determine Fen for a stress cycle or a load set pair. 

4.2.4 Temperature

The changes in fatigue lives of austenitic SSs with test temperatures at two strain amplitudes 

and two strain rates were plotted and are shown in Fig. 88. The results indicated a threshold 

temperature of 100°C, above which the environment decreased fatigue lives in low–DO water if 

the strain rate was below the threshold value. In the range of 100–325°C, the logarithm of 

fatigue life decreased linearly with temperature. Environmental effects either did not occur or 

were insignificant at temperatures below the threshold value of 100°C. 

Figure 88. Change in fatigue lives of austenitic stainless steels in low–DO water with 

temperature (Refs. 13,29–31,34,45–47).

Fatigue tests were conducted at MHI in Japan on Type 316 SSs under combined mechanical 

and thermal cycling.29,30 Triangular waveforms were used for both strain and temperature 

cycling. The strain rate for the tests was 0.002%/s. Two sequences were selected for 

temperature cycling: (i) an in–phase sequence, in which temperature cycling was synchronized 

with mechanical strain cycling, and (ii) a sequence in which temperature and strain were out of 

phase, i.e., maximum temperature occurred at minimum strain level and vice versa. Two 

temperature ranges, 100–325°C and 200–325°C, were selected for the tests. The results are 

shown in Fig. 89, along with data obtained from tests at constant temperature at a strain rate of 

0.01%/s. An average temperature was used in Fig. 89 for the thermal cycling tests. The 

average temperature was determined by considering that environmental effects were 

insignificant below threshold values of 100°C for temperature and 0.32% for strain. Thus, the 

average temperature for the thermal cycling tests was determined from the higher value 

between 100°C and the temperature at the threshold strain for the in–phase tests, and the lower 

value between the maximum temperature and the temperature at the threshold strain for the 

out–of–phase tests. The solid and chain-dash lines in the figure were based on the best-fit air 

curve (Eq. 29) and the updated Fen expression for austenitic SSs (Eq. 61). 

103

104

50 100 150 200 250 300 350 400

0.4%/s

Fatigue Life (Cycles)

0.01%/s

Temperature (°C)

Austenitic SSs

εa = 0.3%, DO  0.005 p

Open Symbols: Type 304

Closed Symbols: Type 316 & 316NG

103

104

50 100 150 200 250 300 350 400

0.4%/s

0.01%/s

Fatigue Life (Cycles)

Temperature (°C)

Austenitic SSs

εa = 0.6%, DO  0.005 p

Open Symbols: Type 304

Closed Symbols: Type 316 & 316NG
119

Figure 89.

Fatigue lives of Type 316 SSs 

under constant and varying 

test temperatures (Ref. 29,30).

The results in Fig. 89 indicated that for the variable temperature tests, fatigue lives estimated 

using an average temperature, determined by taking into consideration the threshold values of 

temperature and strain, showed good agreement with the experimental fatigue lives. As 

expected, the predicted fatigue lives of the in–phase tests were shorter than those for the out–

of–phase tests. The reason fatigue lives were longer for out–of–phase tests compared to in–

phase tests was that applied strains above the threshold strain occurred at higher temperatures 

for the in–phase tests, whereas they occurred at lower temperatures for the out–of–phase tests. 

The results from the thermal cycling tests (triangles) agreed well with the estimated values 

shown by the chain-dash line, and those from the constant–temperature tests (open circles) 

agreed well with the estimated values shown by the solid line. 

Another study conducted by JNES on Type 316 SSs under combined mechanical and thermal 

cycling in PWR water showed similar results; the in–phase tests had lower fatigue lives than the 

out–of–phase tests.36,38 These results indicated that load cycles involving simple linear

temperature transients were represented by an average temperature determined by taking into 

consideration the threshold values of temperature and strain. However, the use of an average 

temperature for more complex temperature transients requires verification.

• The effects of temperature on the fatigue lives of austenitic SSs in LWR environments were 

explicitly considered in Fen, defined in Eq. 61 (Section 4.2.13). In addition, guidance was 

developed to define the temperature used to calculate Fen for actual reactor transients.

4.2.5 Dissolved Oxygen

In contrast to the behavior of carbon and low–alloy steels, the fatigue lives of austenitic SSs 

decreased significantly in low–DO (i.e., less than 0.05 ppm DO) water. In low–DO water, the 

fatigue lives were not influenced by the material composition or heat treatment. The fatigue 

lives, however, continued to decrease with decreasing strain rate in the range of 10 –

0.0004%/s and increasing temperature in the range of 100 – 325°C.13,24,29–31,34,35,45–47 As 

discussed in Sections 4.2.2 and 4.2.4, environmental effects saturated at a strain rate of 

0.0004%/s and a temperature of 325°C.

In high–DO water, the fatigue lives of austenitic SSs were either comparable to29,34 or, in some 

cases, higher13,45,47 than those in low–DO water, i.e., for some SSs, environmental effects were 

lower in high–DO water compared to low–DO water. The results (Figs. 86a and 86b) indicated

that, in high–DO water, environmental effects on the fatigue lives of austenitic SSs were 

influenced by the material composition and heat treatment. For example, for high–carbon Type 
120

304 SS, environmental effects in high-DO water were insignificant for mill–annealed (MA) 

material (Fig. 86a), whereas the effects of environment were the same for sensitized material in 

high– and low–DO water. For low–carbon Type 316NG SSs, some effects of strain rate were

apparent in high–DO water, although they were smaller than those in low–DO water (Fig. 86b). 

The effects of material heat treatment on the fatigue lives of Type 304 SSs is discussed further

in Section 4.2.7. 

• The effects of DO on the fatigue lives of austenitic SSs in LWR environments were explicitly 

considered in Fen, defined in Eq. 61 (Section 4.2.13). In high-DO water, the material 

composition and heat treatment affected the fatigue lives of austenitic SSs. 

4.2.6 Water Conductivity

The studies performed at ANL indicated that, for fatigue tests in high–DO water, the conductivity 

of water and the ECP of steel were important parameters that must be held constant.13,45,47 

During laboratory tests, the time to reach stable environmental conditions depended on the 

autoclave volume, DO level, flow rate, etc. In the ANL test facility, fatigue tests on austenitic 

SSs in high–DO water required a soaking period of 5–6 days for the ECP of the steel to 

stabilize. The steel ECP increased from zero or a negative value to above 150 mV during this 

period. The results shown in Fig. 86a for Type 304 MA Heat 30956 SS in high–DO water 

(closed circular symbols) were obtained for specimens that were soaked for 5–6 days prior to 

testing. The same material tested in high–DO water after soaking for 24 h showed a significant 

reduction in fatigue life, as indicated by Fig. 90. At conductivity values of 0.05-0.1 μS/cm, the 

fatigue lives of specimens that were soaked for 24 h (shown as solid symbols) were a factor of 

approximately 3 lower than those of specimens soaked for 120 h (shown as open symbols).

Figure 90.

Effects of water conductivity and 

soaking period on fatigue lives of 

Type 304 SSs in high–DO water 

(Ref. 13,45). 

The effects of water conductivity and the ECP of the steel on the fatigue lives of austenitic SSs 

were determined, as shown in Fig. 90. In high–DO water, the fatigue lives were decreased by a 

factor of approximately 2 when the conductivity of the water was increased from approximately 

0.05 to 0.4 μS/cm. Note that environmental effects appeared more significant for the specimens 

that were soaked for only 24 h. For these tests, the ECP of the steel was initially very low and 

increased during testing (i.e., the DO level in the test autoclave was lower than the target DO 

level of 0.7 ppm). 

• The effects of water conductivity on the fatigue lives of austenitic SSs were not explicitly 

included in the determination of the environmental fatigue correction factor, Fen. Additional 
121

guidance was therefore not included to address excursions from normal water chemistry 

conditions.

4.2.7 Material Heat Treatment

Limited small-scale laboratory fatigue test data indicated that, although heat treatment had little 

or no effects on the fatigue lives of austenitic SSs in low–DO and air environments, fatigue lives 

in high–DO environments were longer for nonsensitized or slightly sensitized SSs.47 The 

effects of heat treatment on the fatigue lives of Type 304 SSs in air, BWR, and PWR 

environments are shown in Fig. 91. Fatigue lives were plotted as a function of EPR 

(electrochemical potentiodynamic reactivation) values for various material conditions. The 

results indicated that heat treatment had little or no effects on the fatigue lives of Type 304 SSs 

in air and PWR environments. In a BWR environment, fatigue lives were lower for the 

sensitized SSs; fatigue lives decreased with increasing EPR values.

Figure 91.

The effects of material heat treatment 

on fatigue lives of Type 304 SSs in air, 

BWR and PWR environments at 289°C, 

approximately 0.38% strain amplitude, 

sawtooth waveform loading, and 

0.004%/s tensile strain rate (Ref. 47). 

These results are consistent with the data obtained at MHI on solution–annealed and sensitized 

Types 304 and 316 SSs.27,31 In low–DO (less than 0.005 ppm) water at 325°C, sensitization 

annealing had no effects on the fatigue lives of these steels. In high–DO (8 ppm) water at 

300°C, the fatigue lives of sensitized Type 304 SSs were a factor of approximately 2 lower than 

those of solution–annealed steels. However, sensitization annealing had little or no effect on 

the fatigue lives of low-carbon Type 316NG SSs in high–DO water at 288°C, and the fatigue 

lives of solution–annealed and sensitized Type 316NG SSs were comparable.

• The effects of heat treatment was not explicitly included in the environmental fatigue 

correction factor; estimates of Fen based on Eq. 61 (Section 4.2.13) are therefore

conservative for some SSs in high–DO water.

4.2.8 Cast Austenitic Stainless Steels

The fatigue lives of cast austenitic SSs were lower in LWR coolant environments. The available 

data also indicated that the fatigue lives of cast SSs in high–DO water were the same as those 

in low–DO water. The fatigue lives of CF-8M cast austenitic SSs in high-purity water at 289°C 

and 0.3 and 0.6% strain amplitudes were plotted as a function of DO (Fig. 92). The results 

showed no fatigue life dependency on water DO levels. In both NWC and HWC BWR 

environments, the fatigue lives of cast austenitic SSs were well represented by the Fen

expressions for wrought austenitic SSs in low–DO PWR environments. 
122

Figure 92.

Fatigue lives of cast austenitic 

SSs in high-purity water at 

289°C and 0.3% and 0.6% strain 

amplitude plotted as a function 

of DO content (Ref. 136). 

In addition, the existing data indicated that the fatigue lives of cast austenitic SSs were relatively 

insensitive to changes in ferrite content in the range of 12–28%.29,34 The fatigue ε-N data for a 

heat of CF-8M cast SS (with 19.7% ferrite) at 325°C in PWR water containing 0.005 ppm DO 

were plotted (Fig. 93) at various strain rates. The best-fit air curve at room temperature and the 

estimated fatigue lives for the tests at 0.4 and 0.01%/s strain rates were also included. The 

results showed a gradual decrease in fatigue lives with decreasing strain rates. The results also 

indicated that thermal aging for 25,200 h at 465°C had little or no effect on fatigue lives. The 

experimental data showed good agreement with the estimated fatigue ε-N curves. However, 

the fatigue ε-N data for unaged and aged (for 10,000 h at 400°C) material from two heats of CF8M cast SSs, shown in Fig. 94a, indicated potential effects of thermal aging. Some of the data 

shown in Fig. 93 were plotted as a function of strain rate (Fig. 94a). The limited data for Heat 

CF8M-8 (shown as open and closed circular symbols in Fig. 94a) indicated that, unlike the 

thermal aging effects of cast SSs aged at 450°C or higher, thermal aging for 10,000 h at 400°C 

decreased the fatigue lives of the material by a factor of 2.45 

Figure 93.

Strain amplitude vs. fatigue life 

data for cast austenitic SSs at 

325°C and various strain rates in 

water with 0.005 ppm DO content 

(Ref. 29,34). 
123

(a) (b)

Figure 94. Dependence of fatigue lives of CF–8M cast SSs on strain rate in low–DO 

water at various strain amplitudes (Refs. 136,43,45).

The different thermal aging effects observed for the cast austenitic SSs in Figs. 94a are 

attributed to differences in the microstructure produced after thermal aging at 400°C as opposed 

to 465°C. Available data indicated that thermal aging at temperatures between 300 and 400°C 

resulted in a spinodal decomposition of the ferrite phase which strengthened the ferrite phase 

and increased cyclic hardening.229-232 In contrast, thermal aging at 465°C resulted in the 

nucleation and growth of large α’ particles and other phases such as a sigma phase, which did

not change the tensile or cyclic hardening properties of the material.230 

The results also showed that the effects of strain rate on the fatigue lives of cast SSs were 

similar to those for wrought SSs. However, for the cast SS unaged Heat CF8M-2, 

environmental effects on life did not appear to saturate even at strain rates as low as 

0.00001%/s.29,34 Similar results were also reported for unaged CF–8M steels in low–DO water 

at 325°C.233 Based on these results, JNES136 recommended a lower threshold value for the 

saturation strain rate for cast austenitic SSs. The saturation strain rate of 0.0004%/s, 

recommended for wrought SSs, was decreased to 0.00004%/s for cast SSs. 

As shown in Fig. 94, the fatigue data obtained at 289°C were in good agreement with estimates 

based on the Fen expressions for wrought austenitic SSs. Even the data at 325°C at strain rates 

equal to or greater than 0.001%/s were in agreement with the estimated curves. However, the 

strain rate dependence of the data obtained on unaged material at low strain rates increased at 

strain rates below 0.0005%/s (i.e., the slope of the log-log plot of fatigue lives vs. strain rates 

was steeper). The reasons for this behavior of the unaged cast austenitic SSs were not 

determined. Until more data are available, the effects of strain rate on the fatigue lives of cast 

austenitic SSs were assumed similar to those for wrought SSs in low-DO PWR environments. 

Furthermore, strain rates less than 0.0004%/s are either not expected for typical reactor 

operation, or the total strain accumulated under these transients is expected to be insignificant. 

Limited data indicated that the effects of temperature on the fatigue lives of cast austenitic SSs 

were also similar to those for wrought SSs in low-DO PWR environments, as shown in Fig. 95. 

The data showed good agreement with the estimated values.

• The effects of LWR environments on the fatigue lives of cast austenitic SSs was represented 

by the same Fen expression (i.e., Eq. 61 in Section 4.2.13) developed for wrought SSs in 

low-DO PWR environments.
124

Figure 95.

Change in fatigue lives of cast 

austenitic SSs in low–DO water 

with temperature (Ref. 136). 

4.2.9 Stainless Steel Weld Metals

As discussed in Section 3.2.9, the available fatigue ε-N data indicated that the best-fit mean 

data curve for wrought austenitic SSs in air may be used for the fatigue ε-N behavior of SS weld 

metals. In addition, the plots of the estimated cumulative distribution of constant A for the mean 

data curve for wrought SSs in air (i.e., Fig. 45) showed that the constant A for the few heats of 

SS weld metals for which fatigue data were available were evenly distributed about the median 

value of constant A. The available fatigue ε–N data for austenitic SS weld metals also indicated 

that environmental effects in LWR environments could be estimated from the Fen expression 

given by Eq. 61 in Section 4.2.13 for cast and wrought austenitic SSs. The fatigue ε-N data for 

Type 308 and 316TP SS weld metals at 325°C in PWR water containing 0.005 ppm DO were 

plotted, and are shown in Fig. 96 at various strain rates. The fatigue lives estimated from 

Eqs. 29 (Section 3.2.6) and 61 (Section 4.2.13) for the tests at various strain rates were also 

included as shown in the figure. The experimental fatigue lives were in good agreement with 

the estimated ε–N curves; the fatigue lives decreased gradually with decreasing strain rates. 

Figure 96. Strain amplitude vs. fatigue lives for Types 308 and 316TP SS weld metals 

at 325°C and various strain rates in water with 0.005 ppm DO content

(Ref. 136). 

The experimental fatigue lives of SS weld metals at 0.6% strain amplitude were compared with 

the estimated fatigue lives (using Eqs. 29 and 61) at various strain rates and temperatures, as 

102

103

104

50 100 150 200 250 300 350 400

0.4

0.02

CF8M-2

CF8M-3

CF8M-4

CF8M-5

Fatigue Life (Cycles)

Temperature (°C)

CF-8M Cast Austenitic SSs

εa = 0.6%, DO  0.005 ppm

Heat Id. CF8M-5

Strain Rate (%/s)

Heat Id.

Strain Rate 0.01 %/s
125

shown in Fig. 97. The results indicated that the estimates based on the expressions for wrought 

austenitic SSs yielded either comparable or slightly lower fatigue lives compared to the 

experimental values. The fatigue ε-N data also indicated that changes in the water DO content 

had little or no effects on fatigue lives; the fatigue lives in 8 or 0.2 ppm water were comparable 

to those in 0.005 ppm water. 

• The effects of LWR environments on the fatigue lives of austenitic SS weld metals were

represented by the same Fen expression (i.e., Eq. 61 in Section 4.2.13) developed for 

wrought SSs in low-DO PWR environments.

Figure 97. Change in fatigue lives of SS weld metals in LWR environments with strain 

rate and temperature (Ref. 136).

4.2.10 Hold Periods

Environmental effects on fatigue lives occurred primarily during tensile–loading cycles and at 

strain levels greater than the threshold strain value. Information on the effects of hold periods 

on the fatigue lives of austenitic SSs in water was limited. In high–DO water, the fatigue lives of 

Type 304 SSs tested with a trapezoidal waveform (i.e., hold periods at peak tensile and 

compressive strain)14 were comparable to those tested with a triangular waveform,31 as shown 

in Fig. 98. As discussed in Section 4.1.8, a similar behavior was observed for carbon and low–

alloy steels: the data showed little or no effects of hold periods on fatigue lives of the steels in 

102

103

104

50 100 150 200 250 300 350 400

316N-WM, 0.05 ppm

316N-WM, 0.2 ppm

316TP-WM, 0.005 ppm

Fatigue Life (Cycles)

Temperature (°C)

Stainless Steel Weld Metals, εa = 0.6%

Open Symbols: 0.001%/s

Closed Symbols: 0.4%/s

Weld Metal, DO (ppm) 0.001%/s

0.4%/s

Figure 98.

Fatigue lives of Type 304 SSs tested 

in high–DO water at 260–288°C with 

trapezoidal or triangular waveform 

loadings (Refs. 14,31).
126

high–DO water. The effects of hold periods as long as 2,000 s at peak tensile strains are shown 

in Fig. 99. The results indicated little or no effects of hold periods at peak tensile strains on the 

fatigue lives of austenitic SSs. 

• The available fatigue ε-N data did not demonstrate that hold periods at peak tensile strains 

affected the fatigue lives of austenitic SSs in LWR environments. Therefore, the effects of 

hold times were not explicitly included in the Fen expression (i.e., Eq. 61 in Section 4.2.13) 

developed for austenitic SSs.

Figure 99. Effect of hold periods on the fatigue lives of Types 316NG and 316 SSs in 

LWR environments at various strain rates (Ref. 136).

4.2.11 Flow Rate

Flow rate affects the fatigue lives of LWR materials because it causes differences in local 

environmental conditions in the enclaves of the microcracks formed during the early stages of a 

fatigue ε–N test. As discussed in Section 4.1.9, data obtained under typical operating 

conditions for BWRs indicated that environmental effects on the fatigue lives of carbon steels 

were a factor of approximately 2 lower at high flow rates (7 meters/second) compared to those 

at low flow rates (0.3 meters/second or lower).25,26 However, similar tests in both low–DO and 

high–DO environments indicated that increasing flow rates had either no effects or detrimental 

effects on the fatigue lives of austenitic SSs. The potential effects of water flow rate on the 

fatigue lives of Types 304, 304L, and 316NG wrought austenitic SSs and CF-8M cast austenitic 

SSs at 289°C in high-purity water containing 0.05 to 0.2 ppm DO were plotted, and are shown in 

Fig. 100. Similarly, the effects of flow rate on the fatigue lives of austenitic SSs in PWR primary 

water environment at 325°C were plotted, and are shown in Fig. 101. Under all test conditions, 

the fatigue lives of these steels were either the same or slightly lower at high flow rates 

compared to those at lower rates or semi–stagnant conditions. 

Fatigue tests conducted on SS pipe bend specimens in simulated PWR primary water at 240°C 

also indicated that water flow rate had no effects on the fatigue lives of austenitic SSs.131 

Increasing the flow rate from 0.005 meters/second to 2.2 meters/second had no effects on 

fatigue crack initiation in approximately 26.5–mm diameter tube specimens. These results were 

consistent with the notion that, in LWR environments, the mechanism of fatigue crack initiation 

in austenitic SSs differs from that in carbon and low–alloy steels. 
127

• Because of the uncertainties in the flow conditions at or near the locations of crack initiation 

and the observations of the insignificant effects of flow rate, flow rate effects were not 

explicitly included in the Fen expression (i.e., Eq. 61 in Section 4.2.13) developed for 

austenitic SSs. 

Figure 100. Effects of water flow rate on the fatigue lives of Types 304, 304L, 316NG 

and CF-8M cast SSs in high-purity water at 289°C (Ref. 136). 

Figure 101.

Effects of water flow rates on the 

fatigue lives of Type 304 and 316 

austenitic SSs in PWR primary 

water at 325°C (Ref. 136). 

4.2.12 Fatigue Life Model

The fatigue life models for estimating the fatigue lives of austenitic SSs in LWR environments 

were presented in the initial revision of NUREG/CR-6909, and were based on an analysis of the 

updated PVRC database. The data were fitted to a modified version of the Langer equation 

expressed by Eq. 6, which included a term for environmental effects. The environmental term 

included the effects of key parameters, such as strain rate, water DO content, and temperature. 

The functional forms of these dependencies were based on the data trends. For both wrought 

and cast austenitic SSs, the model assumed threshold and saturation values of 0.4 and 

0.0004%/s, respectively, for strain rate and a threshold value of 150°C for temperature. 

However, because of insufficient data, the dependencies of environmental effects on water DO 
128

content were not included. The results of the analysis indicated that the fatigue lives of 

austenitic SSs in LWR environments were best represented by the following expression 

ln(N) = A – 1.920 ln(εa – 0.112) + T' ' O'

, (57)

where constant A was determined to be 6.157 and the transformed temperature, T'

, the 

transformed strain rate, ’, and the transformed DO content, O'

, were defined by Eqs. 53-55. 

The experimental and predicted values differed by a factor of less than 3 for most heats of 

austenitic SSs. The experimental fatigue lives for a few tests on Type 304 SSs were up to a 

factor of approximately 4 lower than the predicted values; all of these tests were on tube 

specimens with 1– or 3–mm wall thicknesses. A threshold strain amplitude (one-half of the 

applied strain range) was defined, below which LWR coolant environments had no effects on 

fatigue lives, i.e., Fen = 1. The threshold strain amplitude was specified as 0.10%, or a 195 MPa 

(28.3 ksi) stress amplitude for wrought and cast austenitic SSs. 

• The ANL model represented the mean values of fatigue lives as a function of applied strain 

amplitude, temperature, strain rate, and water DO content. The effects of parameters such 

as mean stress, surface finish, size and geometry, and loading history, which are known to 

influence fatigue lives, were not included in the model; the effects of these parameters were 

considered in the development of the fatigue design curve, as discussed in Chapter 5.

4.2.13 Environmental Correction Factor

As discussed at the beginning of Section 4.2, the ANL model for incorporating environmental 

effects on the fatigue lives of austenitic SSs (i.e., Eq. 57) resulted in approximately a factor of 

2.5 decrease in fatigue lives relative to those in air, even when the environmental term of the 

expression is neglected (i.e., when either the temperature was below the threshold value of 

150°C or the strain rate was above the threshold strain rate value). In addition, Eq. 57 did not 

consider the dependence of environmental effects on DO and the temperature dependency was 

not consistent with the available fatigue ε-N data. As discussed in Section 4.2.5, the fatigue 

lives of austenitic SSs were decreased significantly in low–DO water, whereas in high–DO water 

they were either comparable or, for some steels, lower than those in low–DO water. In high–DO 

water, the material composition and heat treatment influenced the magnitude of environmental 

effects on austenitic SSs (refer to Section 4.2.7). Therefore, the Fen expression given by Eq. 52

yielded very conservative estimates of Fen for some materials (e.g., for low-carbon or 

nonsensitized high-carbon wrought SSs).

The fatigue life model for incorporating environmental effects on the fatigue lives of wrought and 

cast austenitic SSs in LWR environments was updated in this report to address the foregoing 

concerns using a much larger database that is described in Section 4.2.1. As discussed earlier, 

in the initial revision of NUREG/CR-6909, the least–squares fit of the experimental data for 

austenitic SSs in LWR environments yielded a steeper slope for the ε–N curve compared to the 

slope of the curve obtained in air.45,121 These results indicated that environmental effects may 

be more pronounced at low strain amplitudes compared to high strain amplitudes. However, 

differing slopes for the ε–N curves in air and water environments added complexity to the 

determination of the environmental fatigue correction factor, Fen. Therefore, the ANL model 

slope of the ε–N curve was assumed to be the same in both LWR and air environments. 

Furthermore, the reevaluation of the fatigue ε-N data assumed that the constant A under 

environmental conditions was also the same as the value in air. 

In addition, a review of the updated fatigue database indicated that the results from the EdFsponsored study at GE on Type 304L SSs tested in PWR water at 150°C showed significant 
129

environmental effects in the high-cycle regime (i.e., greater than 104 cycles). However, the Fen

expression in the initial revision of NUREG/CR-6909 included a temperature threshold of 150°C 

below which environmental effects were considered insignificant. The Fen expressions 

developed by JNES did not consider a temperature threshold. Therefore, to better represent 

the existing fatigue ε-N data, the temperature dependence relationships in the Fen expression 

was modified and the temperature threshold was decreased from 150 to 100°C. In addition, a 

maximum temperature limit was selected at 325°C as a reasonable extension to cover all 

anticipated LWR operating conditions. This is adequate for all expected operating LWR 

conditions considering the use of average temperature (as discussed in Section 4.1.11 and 

shown in Fig. 81). The dependency of fatigue lives on strain rate was also modified, and the 

threshold strain rate below which environmental effects were significant was increased from 0.4 

to 10%/s. In addition, the dependence of environmental effects on water DO content was also 

included; it was based on the material composition and heat treatment. 

Using Eq. 51 and values of constants A, B, and C that are the same as those obtained for the 

best-fit air curve for austenitic SSs (i.e., Eq. 29), a least-squared fit of the much larger fatigue 

ε-N database in LWR environments yielded the following expressions for the transformed 

parameters T’, ’

, and O’:

T' = 0 (T < 100°C)

T' = (T – 100)/250 (100°C ≤ T ≤ 325°C) (58)

' = 0 ( > 10%/s) ' = ln( /10) (0.0004%/s ≤ ≤ 10%/s) ' = ln(0.0004/10) ( < 0.0004%/s) (59)

For DO less than 0.1 ppm, i.e., PWR of BWR HWC water, 

O' = 0.29 (all wrought and cast SSs and heat treatments and SS weld metals)

For DO greater than or equal to 0.1 ppm, i.e., NWC BWR water, 

O' = 0.29 (sensitized high-carbon wrought and cast SSs) 

O' = 0.14 (all wrought SSs except sensitized high-carbon SSs). (60)

The reevaluation of the updated fatigue ε-N data for austenitic SSs using the updated

expressions yielded a good fit of the data, particularly in the low-cycle regime. The R-squared 

values for the best fit of the data to minimize the error in the values of fatigue lives and the 

values of the shortest distance between the data points and the best fit ε-N curve improved from 

0.83 to 0.86 and 0.92 to 0.93, respectively. This updated model is recommended for predicting

fatigue lives up to 106 cycles. A single expression was used for Types 304, 304L, 316, 316L, 

and 316NG SSs, and Eqs. 57–60 also apply to cast austenitic SSs such as CF-3, CF-3M, CF-8, 

and CF–8M as well as SS weld metals. 

The effects of reactor coolant environments on fatigue lives were expressed in terms of a 

fatigue life correction factor, Fen, which was defined as the ratio of fatigue life in air at room 

temperature to that in water at the service temperature. The Fen for austenitic SSs in LWR 

environments is given by

Fen = exp(– T' ' O'), (61)

where the constants T', ', and O' are defined in Eqs. 58–60. To incorporate environmental 

effects into an ASME Code Section III fatigue evaluation, the fatigue usage in air for a specific 

stress cycle is multiplied by the environmental correction factor, Fen. Further details for 

incorporating environmental effects into fatigue evaluations are presented in Appendix A.
130

Comparisons of the experimental fatigue lives of wrought and cast austenitic SSs, as well as 

their associated weld metals in LWR environments, were compared to those predicted by the 

updated Fen expression (i.e., from Eqs. 61 and 29), the JNES expression,136 and the expression

in the initial revision of NUREG/CR-6909, as shown in Fig. 102. The results indicated that the 

updated Fen expression represented a better fit to the larger experimental database relative to 

the fit for the expression in the initial revision of NUREG/CR-6909. Typically, for fatigue lives 

less than 3 x 104 cycles, the predicted values were within a factor of 3 to the experimental 

values. Also, compared to the estimates based on the expressions in the initial revision of 

NUREG/CR-6909, the R-squared values for the best-fit of the data were slightly higher. 

(a) (b)

(c) (d)

Figure 102. Experimental fatigue lives of wrought and cast austenitic SSs in LWR 

environments vs. fatigue lives predicted from (a) the updated ANL

expression, (b) the JNES expression, (c) the previous NUREG/CR-6909 

expression, and (d) fatigue lives of SS weld metals predicted from the 

updated ANL expression.
131

A comparison of the fatigue lives predicted using the updated Fen expression and the JNES Fen

expression was also made, as shown in Fig. 103. In general, the Fen values calculated from the 

updated expression were marginally lower for fatigue lives less than 104 cycles and slightly 

longer than those predicted from the JNES expression for fatigue lives greater than 104 cycles. 

Some significant differences remain in the predicted lives obtained from the updated Fen

expression for SS compared to those obtained from the JNES expression for BWR 

environments. The reasons for these differences are not fully understood, but appear to be 

predominantly associated with the DO and temperature relationships. Further investigation of 

these differences is recommended as a part of any future research activities.

Figure 103.

Fatigue lives of wrought and 

cast austenitic SSs in LWR 

environments estimated from 

the new Fen expressions vs. 

those estimated from the 

JNES expression.

The experimental fatigue lives were compared with the estimated values using the updated Fen

expression and the JNES expression for a smaller dataset of Types 304L and 316N SSs and 

cast and wrought austenitic SSs in water containing greater than 0.1 ppm DO, as shown in 

Figs. 104 and 105, respectively. The results indicated that, in general, the estimates based on 

the updated expression were slightly better than those from the JNES expression. However, 

the data scatter for high-carbon Type 304 SSs in high-DO water (i.e., greater than 0.1 ppm DO 

in water) is larger than that for the other grades of SSs.
132

(a) (b)

Figure 104. Experimental fatigue lives of Types 304L and 316N austenitic SSs in LWR 

environments vs. fatigue lives predicted from (a) the updated ANL 

expression and (b) the JNES expression.

(a) (b)

Figure 105. Experimental fatigue lives of wrought and cast austenitic SSs in water 

containing greater than 0.1 ppm DO vs. fatigue lives predicted from (a) the 

updated ANL expression and (b) the JNES expression.
133

As observed in Section 4.1.11 for carbon and low-alloy steels, upon completion of the modeling 

phase, the residual errors did not show significant patterns, such as changing variance or a 

nonzero slope. The residual errors for each variable, grouped by steel type, were plotted, as 

shown in Fig. 106 for wrought and cast austenitic SSs in LWR environments. The residuals 

were determined from the difference between the logarithms of the estimated lives and 

predicted lives. Thus, negative residual errors corresponded to conservative estimates of 

fatigue lives and positive residual errors corresponded to nonconservative estimates of fatigue 

lives (i.e., predicted lives were greater than observed fatigue lives). However, predominantly 

positive or negative residuals did not necessarily indicate any deficiency in the predictive 

models. Such results indicated that the specific heat was either superior or inferior to the 

average behavior predicted by the model. For example, a positive residual indicated that the

heat was inferior (i.e., the constant A for the heat was smaller than the median value of constant 

A in the model) and a negative residual indicated that the heat was superior to the average 

behavior for the material. This behavior is discussed further in Section 4.2.15.

The results presented in Fig. 106 did not reveal any unexplained patterns. In general, high 

observed variances tended to be associated with longer lives and lower strain amplitudes. 

Furthermore, any observed biases were traceable to heat–to–heat variations. For example, 

heats of Type 304 SSs with Mat. ID #9, Type 316 SSs with Mat. ID #49, and cast austenitic 

SSs with Mat. ID #61 had inferior fatigue resistance, and heats of Type 304 SSs with Mat. ID 

#1 and 21 and of Type 316 SSs with Mat. ID #51 had superior fatigue resistance than the 

average behavior represented by the fatigue ε-N model (Eqs 61 and 29).

Some of the heats of austenitic SSs that were tested in LWR environments were also tested in 

air. The residual errors for the best fit of the fatigue ε-N data for austenitic SSs in air were 

plotted as a function of the ANL Material ID, as shown in Fig. 107. Most of the data subsets for 

fatigue tests in air followed the same trends as those observed in LWR environments. For 

example, data subsets for Mat. ID #21 and 51 yielded predominantly negative residuals in both 

environments and predominantly positive residuals for Mat. ID #61. The one exception was 

material ID #9, which yielded positive residuals in air and marginally negative residuals in LWR 

environments. These results indicated that environmental effects on fatigue lives in LWR 

environments were accurately estimated by the updated Fen expression.
134

(a) (b)

(c) (d)

Figure 106.

Residuals for predicted fatigue 

lives of wrought and cast austenitic 

SSs as a function of (a) ANL 

Material ID, (b) water DO content, 

(c) strain rate, (d) temperature, and 

(e) strain amplitude.

(e)
135

Figure 107.

Residuals for predicted fatigue lives 

of wrought and cast austenitic SSs in 

air as a function of ANL Material ID.

 

• The Fen approach should be used to incorporate environmental effects into ASME Code 

Section III fatigue evaluations for cast and wrought austenitic SSs and their associated weld 

metals. Appendix C of this report presents a sample application of the Fen methodology.

4.2.14 Surface Finish

Austenitic SSs tended to develop a corrosion scale in high–temperature water thereby 

eliminating any apparent effects of surface finish in LWR environments. Therefore, the fraction 

of the adjustment factor related to surface finish that was applied to the best-fit mean data curve 

to obtain the fatigue design curve was assumed to be 1.5 or lower. Fatigue tests were 

conducted on Types 304 and 316NG SSs that were intentionally roughened in a lathe, under 

controlled conditions, with 50-grit sandpaper to produce circumferential cracks with an average 

surface roughness of 1.2 μm. The results are shown in Fig. 108 for Types 316NG and 304 SSs. 

For both steels, the fatigue lives of roughened specimens were up to a factor of 3 lower than 

those of the smooth specimens in both air and low–DO water environments. However, the 

results of a single test on Heat P91576 of Type 316NG in high–DO water did not show any 

effects of surface finish; the fatigue lives were the same for rough and smooth specimens 

(shown as open and closed diamond symbols in Fig. 108a). 

Similar tests conducted on Type 304L SSs in air and PWR water environments155-157 also 

indicated a factor of approximately 2 decrease in fatigue lives of the ground specimens relative 

to those of the polished specimens, as shown in Fig. 109. The tests were conducted with a 

triangular waveform loading with a strain rate of 0.4%/s and a complex waveform loading that 

simulated a PWR safety injection transient. The tests were conducted under strain control and 

the strain rates associated with the safety injection transient ranged from 0.08 to 0.00013%/s. 

Note that the strain accumulated under specific strain rates decreased with decreasing strain 

rates.

Thus, the available small-scale laboratory fatigue ε-N data indicated decrease in fatigue lives of 

up to a factor of up to 2.5 for the roughened specimens relative to the lives of polished 

specimens in both air and LWR environments. Limited data also indicated that for some lowcarbon heats of austenitic SSs, surface finish did not have any effects on the fatigue lives of 

SSs in LWR environments. However, the data were very limited, so additional data are needed 

to validate this behavior.
136

(a) (b)

Figure 108. Effect of surface finish on fatigue life of (a) Type 316NG and (b) Type 304 

stainless steels in air and high–purity water at 289°C. 

 

Figure 109.

Effects of surface finish on the fatigue 

lives of Type 304L SSs in air and PWR 

primary water environments at 300°C 

(Refs. 155,157). 

• The effects of surface finish were not explicitly included in the environmental fatigue 

correction factor; instead, they were included in the subfactor for “surface finish and 

environment,” which was applied to the mean data air curve to develop the fatigue design 

curve in air.

4.2.15 Heat-to-Heat Variability

The effects of material variability and data scatter on the fatigue lives of austenitic SSs were

evaluated for data in LWR environments. The fatigue behavior of each of the heats or loading 

conditions was characterized by the value of the constant A in the ANL model (e.g., Eq. 6). The 

values of A were determined from Eq. 57 for the various data sets in the larger, updated fatigue 

ε-N database used in this report. The values of constant A were ordered, and median ranks 

were used to estimate the cumulative distribution of A for the population. If the Fen expression 

given in Eq. 57 adequately captured the effects of LWR environments on the fatigue lives of 

wrought and cast austenitic SSs, the reanalysis should have yielded a median value of constant 

A that is the same as in an air environment. 
137

The estimated cumulative distribution of constant A is shown in Fig. 110. The results yielded a 

median value of A of 6.800 for all the data sets for cast and wrought austenitic SSs and their 

associated weld metals, and a value of 6.749 without the datasets for weld metals. These 

values of constant A are slightly lower than that in air (e.g., the difference is less than 10%). 

These results demonstrate that the Fen expressions for cast and wrought austenitic SSs 

adequately capture the environmental effects in LWR environments. 

The heat-to-heat variation in LWR environments differed insignificantly from that in air and 

presented in Section 3.2.7. The 95/95 values of the factors to account for material variability 

and data scatter were the same in air (i.e., presented in Table 7 for austenitic SSs). These 

factors provide 95% confidence that the resultant lives are greater than those observed for 95% 

of the materials of interest.

• Heat-to-heat variability was not explicitly included in the environmental fatigue correction 

factor for austenitic SSs; instead, it was included in the subfactor for “data scatter and 

material variability” that was applied to the room-temperature mean data air curve to develop 

the fatigue design curve in air. 

Figure 110.

Estimated cumulative distribution of 

constant A in the ANL model for 

fatigue lives of heats of austenitic 

SSs in LWR environments. 
138

4.3 Ni-Cr-Fe Alloys

The relevant fatigue ε–N data for Ni-Cr-Fe alloys and associated weld metals in LWR 

environments evaluated in this report included the data compiled in the JNES database from 

Japan136 and the tests performed by Van Der Sluys et al.75 The database was composed of 

162 tests; 87 tests on 5 heats of Alloy 600, 21 tests on 2 heats of Alloy 690, and 54 tests on 6 

heats of Ni-Cr-Fe alloy weld metals, which included Alloys 82, 182, 132, 152, and 690. Out of 

these, 7 tests were conducted at 100°C (one at 54°C), 10 tests at 200°C, 88 tests at 288/289°C, 

10 tests at 315°C, and 47 tests at 325°C. A summary of the data sources for the updated 

database used in this report, as categorized by material type and test environment, is shown in

Table 12. Other material information such as chemical composition, heat treatment, and room 

temperature tensile properties for the Ni-Cr-Fe alloys and associated weld metals evaluated is 

given in Appendix B. 

Table 12. Sources of the fatigue ε–N data for Ni-Cr-Fe alloys and their weld metals in 

LWR environments.

ANL 

Mat. 

ID

Material 

Heat 

Designation

Carbon 

Content 

(wt.%)

Dissolved 

Oxygen 

(ppm)

Test 

Temperature 

(°C)

No. of 

Data Points

Source Applicable 

Reference

Alloy 600

1 Alloy 600-1 0.07 0.2 288 12 JNES (Higuchi) 39, 136

2 Alloy 600-2 0.07 0.2 288 16 JNES (Nakao) 136

5 Alloy 600-3 0.01 0.01, 0.05, 

0.2, 8.0 289 (4 at 200) 11, 1, 14, 4 JNES (Hirano) 136

3 Alloy 600-4 0.07 0.01, 0.2 289 2, 6 JNES (Hirano) 136

4 Alloy 600-5 0.03 0.005 100, 200, 325 6, 6, 9 JNES (Nomura) 136

Alloy 690

9 Alloy 690-1 0.03 0.005 325 20 JNES (Nomura) 136

12 Alloy 690-3 0.02 0.01 315 1 PVP (Van der Sluys) 75

Ni-Cr-Fe Alloy Weld Metals

10 Alloy 152 WM 0.037 0.005 325 9 JNES (Kanasaki) 136

6 Alloy 182-1 0.06 0.2 288 14 JNES (Higuchi) 136

7 Alloy 182-2 0.038 0.2 288 12 JNES (Nakao) 136

11 Alloy 82-5 0.04 0.01, 

0.007

315 4,a 5 PVP (Van der Sluys) 75

8 Alloy 132 0.04 0.005 325 9 JNES (Nomura) 136

13 Alloy 152-2 0.032 0.01 315 1 PVP (Van der Sluys) 75

a One test in 0.01 ppm DO water was performed at 54°C.

4.3.1 Experimental Data

Similar to carbon, low-alloy and austenitic SSs, the fatigue lives of Ni-Cr-Fe alloys and their 

welds were also decreased in LWR environments; the fatigue ε-N data for various Ni-Cr-Fe 

alloys in simulated BWR water at approximately 289°C and PWR water at 315-325°C are shown 

in Figs. 111 and 112, respectively. The ε–N air curve based on the ANL model for austenitic 

SSs (Eq. 29 discussed in Section 3.2.6) is also included on the plots in these figures. The 

results indicated that environmental effects on the fatigue lives of Ni-Cr-Fe alloys were also 

dependent on key parameters such as strain rate, temperature, and the DO level in the water. 

Similar to SSs, the effects of coolant environments on the fatigue lives of Ni-Cr-Fe alloys were 
139

greater in low–DO PWR environments than they were in the high–DO BWR environments. 

However, under similar loading and environmental conditions, the extent of the effects of 

environment was considerably less for the Ni-Cr-Fe alloys compared to that for austenitic SSs. 

In general, environmental effects on fatigue lives were the same for wrought and weld Ni-Cr-Fe 

alloys. 

Figure 111. Fatigue ε–N behavior for Alloy 600 and its weld alloys in simulated BWR 

water at approximately 289°C (Refs. 136, 39).

Figure 112.

Fatigue ε–N behavior for Alloys 600 

and 690 and associated weld metals 

in simulated PWR water at 325°C

(Refs. 136, 75).

0.1

1.0

102 103 104 105 106 107 108

A690 (0.01 ppm)

A152 (0.01 ppm)

A82 (0.01 ppm)

A82 (0.007 ppm)

A82 (0.01 ppm)

Strain Amplitude, εa (%)

Fatigue Life (Cycles)

Alloy 690 & Alloys 82 & 152 Weld Metals

325°C, PWR Water 

Best–Fit Air

ANL Model

Austenitic SSs

Alloy (DO Content )

Strain Rate (%/s)

Open Symbols: 0.01

Closed Symbols: 0.1
140

4.3.2 Effects of Key Parameters

The effects of the key loading and environmental parameters (e.g., strain rate, temperature, and 

DO level) on the fatigue lives of Ni-Cr-Fe alloys in LWR environments were evaluated using the 

limited fatigue ε-N data that were available. The fatigue lives of Alloys 600 and 690 and their 

weld metals (e.g., Alloys 132 and 152) in simulated PWR and BWR water at different strain 

amplitudes were plotted as a function of strain rate, as shown in Fig. 113. The fatigue lives of 

these alloys decreased logarithmically with decreasing strain rate. Since there were little or no 

data at strain rates below 0.001%/s, the effects of strain rate on Ni-Cr-Fe alloys were assumed 

to be similar to those for austenitic SSs. The effects were assumed to saturate at a strain rate 

of 0.0004%/s.

Furthermore, the threshold strain rate below which environmental effects were insignificant 

could not be sufficiently determined from the available data. Higuchi et al.39 defined a threshold 

strain rate of 1.8%/s in high-DO BWR water and 26.1%/s in low-DO PWR water. As discussed 

in the next section, an average threshold value of 5%/s provided good estimates of fatigue lives 

of Ni-Cr-Fe alloys in LWR environments. The results also indicated that the effects of 

environment were greater in low–DO PWR water than in high–DO BWR water. For example, a 

three-orders-of-magnitude decrease in strain rate decreased the fatigue lives of these alloys by 

a factor of approximately 3 in PWR water and by a factor of approximately 2 in BWR water. 

The fatigue lives of Alloy 600 in PWR environments at three different strain amplitudes were 

plotted as a function of temperature, as shown in Fig. 114. The results indicated a decrease in 

fatigue lives with increasing temperature. Because of very limited fatigue data for Ni-Cr-Fe 

alloys, the effects of temperature on the fatigue lives of these materials were also assumed to 

be similar to those observed in austenitic SSs. Environmental effects on fatigue lives were 

considered to be insignificant below a threshold temperature of 50°C. In addition, it was 

assumed that a slow strain rate applied during the tensile–loading cycle (i.e., up–ramp with 

increasing strain) was primarily responsible for the environmentally assisted reduction in fatigue 

lives. Slow rates applied during both tensile– and compressive–loading cycles (i.e., up– and 

down–ramps) did not further decrease fatigue lives compared with those observed for tests with 

only a slow tensile–loading cycle. Thus, loading and environmental conditions during the 

tensile–loading cycle were important for an environmentally assisted reduction in the fatigue 

lives of Ni-Cr-Fe alloys. The available fatigue ε-N data for Ni-Cr-Fe alloys in LWR environments 

Figure 113. Dependence of fatigue lives of Alloys 690 and 600 and associated weld 

metals on strain rate in PWR and BWR environments (Refs. 39, 75, 136). 
141

were inadequate to define the threshold strain amplitude below which environmental effects on 

fatigue lives did not occur.

As discussed in Section 4.2.13, some significant differences remain in the predicted lives 

obtained from the updated Fen expression for austenitic SSs compared to those obtained from 

the JNES expression for BWR environments. These differences may also impact the relations

for Ni-Cr-Fe alloys. The reasons for these differences are not fully understood, but appear to be 

predominantly associated with the DO and temperature relationships. Further investigation of 

these differences is recommended as a part of any future research activities.

4.3.3 Environmental Correction Factor

The effects of reactor coolant environments on the fatigue lives of Ni-Cr-Fe alloys were also 

expressed in terms of a fatigue life correction factor, Fen. The available fatigue data were very 

limited to develop a fatigue life model for Ni-Cr-Fe alloys in LWR environments. However, as 

discussed in Section 4.3.2, environmental effects for these alloys showed the same trends as 

those observed for austenitic SSs. Environmental effects increased with increasing temperature 

and decreasing strain rate. Based on the available fatigue ε-N data, the effects of temperature 

on the fatigue lives were considered to be insignificant below 50°C and saturated at 325°C. A

maximum temperature limit was selected at 325°C as a reasonable extension to cover all 

anticipated LWR operating conditions. This is adequate for all expected operating LWR 

conditions considering the use of average temperature (as discussed in Section 4.1.11 and 

shown in Fig. 81). Similarly, the effects of strain rate were considered insignificant at strain 

rates above 5%/s and they saturated at 0.0004%/s. Thus, the Fen relationship for Ni-Cr-Fe 

alloys was expressed as

Fen = exp(-T’ ’ O’

), (62)

where T’

, ’, and O’ are transformed temperature, strain rate, and DO, respectively. The 

functional forms for these transformed parameters were obtained from the best fit of the 

experimental data and were defined as follows:

T’ = 0 (T < 50°C)

T’ = (T-50)/275 (50°C ≤ T ≤ 325°C) (63)

’ = 0 ( > 5.0%/s) ’ = ln( /5.0) (0.0004%/s ≤ ≤ 5.0%/s) ’ = ln(0.0004/5.0) ( < 0.0004%/s) (64)

Figure 114.

Dependence of fatigue lives of Alloy 

600 on temperature in a PWR 

environment (Refs. 39, 75, 136). 
142

O’ = 0.06 (NWC BWR water, i.e., ≥ 0.1 ppm DO)

O’ = 0.14 (PWR or HWC BWR water, i.e., < 0.1 ppm DO). (65)

The fatigue lives of Ni-Cr-Fe alloys in LWR environments were estimated from Eqs. 29 and 62–

65. The experimental fatigue lives of various Ni-Cr-Fe alloys in BWR NWC (i.e., ≥ 0.1 ppm DO) 

and PWR or HWC BWR (i.e., < 0.1 ppm DO) environments estimated using the updated Fen

expression, the original NUREG/CR-6909 expression, and the JNES expression were plotted, 

as shown in Figs. 115-117, respectively. The results indicated that the updated expression 

represented a better fit to the larger database compared to the expression in the initial revision 

of NUREG/CR-6909. The R-squared values for the best-fit of the data were slightly higher for 

the updated expression compared to those obtained from the original NUREG/CR-6909 Fen

expression. In general, the estimated values were either comparable (within a factor of 2) or 

longer (conservative) than those observed experimentally.

(a) (b)

Figure 115. Experimental fatigue lives vs. fatigue lives predicted from the updated Fen

expression for Ni-Cr-Fe alloys and weld metals in simulated (a) BWR and 

(b) PWR environments.
143

(a) (b)

Figure 116. Experimental fatigue lives vs. fatigue lives predicted from the Fen

expression in the original revision of NUREG/CR-6909 for Ni-Cr-Fe alloys 

and weld metals in simulated (a) BWR and (b) PWR environments. 

(a) (b)

Figure 117. Experimental fatigue lives vs. fatigue lives predicted from the JNES Fen

expression for Ni-Cr-Fe alloys and associated weld metals in simulated 

(a) BWR and (b) PWR environments.

For Ni-Cr-Fe alloys, the residual errors did not show significant patterns such as changing 

variances or nonzero slopes. The residual errors for each variable, grouped by steel type, were 

plotted, as shown in Fig. 118 for Ni-Cr-Fe wrought and weld alloys in LWR environments. The 

residuals were determined from the difference between the logarithms of the estimated lives 

and the predicted lives. Therefore, negative residual errors corresponded to conservative 

estimates of fatigue lives and positive residual errors corresponded to nonconservative 

estimates of fatigue lives. The results did not reveal any unexplained patterns. In general, high 

observed variances tended to be associated with longer lives and lower strain amplitudes. 

Furthermore, any observed biases were traceable to heat–to–heat variations. For example, the 
144

negative residuals for Alloy 82 weld metal were likely due to superior fatigue properties of the 

material relative to that of Alloy 600. Most of the compositions of Ni-Cr-Fe alloys that were 

tested in LWR environments were also tested in air. The residual errors for the best fit of the 

fatigue ε-N data for Ni-Cr-Fe alloys in air were plotted as a function of the material ID, as shown 

in Fig. 119. Most of the data subsets for fatigue tests in air followed the same trends as those 

observed in LWR environments. For example, except for the data subset associated with 

Material ID #42, the other four data subsets for Alloy 82, including Material ID #51, yielded 

predominantly negative residuals in air. These results indicated that environmental effects on 

the fatigue lives of Ni-Cr-Fe alloys in LWR environments were reasonably estimated by the 

updated Fen expression.

A threshold strain amplitude (one-half of the applied strain range) was also defined, below which 

LWR coolant environments had insignificant effects on fatigue lives, i.e., Fen = 1. The threshold 

value for strain amplitude was assumed to be the same as that for austenitic SSs, or 0.10% 

(195 MPa, or 28.3 ksi). Further details for incorporating environmental effects into fatigue 

evaluations for Ni-Cr-Fe materials are presented in Appendix A.

• Due to significantly less available data for Ni-Cr-Fe materials compared to carbon and lowalloy steels and austenitic SSs, the updated austenitic SS Fen expression may be used to

incorporate environmental effects into ASME Code Section III fatigue evaluations for Ni-CrFe materials. The modified rate approach may also be used for Ni-Cr-Fe materials. 

Appendix C of this report presents a sample application of the Fen methodology.
145

(a) (b)

(c) (d)

Figure 118.

Residuals for predicted fatigue lives of 

Ni-Cr-Fe alloys and associated weld 

metals as a function of (a) material ID, 

(b) water DO content, (c) strain rate, 

(d) temperature, and (e) strain 

amplitude.

(e)
146

Figure 119.

Residuals for predicted fatigue lives of 

Ni-Cr-Fe alloys and associated weld 

metals in air as a function of ANL 

Material ID.
147

5 ADJUSTMENT FACTORS IN ASME CODE FATIGUE DESIGN 

CURVES

Conservatisms in ASME Code Section III fatigue evaluations typically arise from (a) the fatigue 

evaluation procedures and assumptions implemented by the analyst, and/or (b) the fatigue 

design curves. The overall conservatisms in ASME Code Section III fatigue evaluations were 

demonstrated in fatigue tests on components. 234,235 Mayfield et al.234 showed that, in air, the 

factors on the number of cycles to failure for elbows and tees ranged from 40 to 310 and 104 to 

510, respectively, for austenitic SSs and 118 to 2,500 and 123 to 1,700, respectively, for carbon 

steels. The factors for girth butt welds were significantly lower, ranging from 6 to 77 for SSs and 

from 14 to 128 for carbon steels. Data obtained by Heald and Kiss235 on 26 piping components 

at room temperature and 288°C showed that the adjustment factors for cracking exceeded a 

factor of 20, and for most of the components, it was greater than a factor of 100. In these tests, 

fatigue lives were expressed as the number of cycles for the crack to penetrate through the wall 

thickness of the test specimens, which ranged in thicknesses from 6 to 18 mm. Consequently, 

depending on the wall thickness, the actual factors to initiate a finite crack (e.g., to form a 3–

mm-deep crack) were estimated to be a factor of 2 to 3 lower. 

Deardorff and Smith236 discussed the types and extent of conservatisms present in ASME Code 

Section III fatigue evaluation procedures and the effects of LWR environments on fatigue 

adjustment factors. The sources of conservatisms in the procedures included (a) the use of 

design transients that were significantly more severe than those experienced in service, 

(b) conservative grouping of transients, and (c) the use of simplified elastic–plastic analyses that 

led to higher stresses. The authors estimated that the ratio of the CUFs computed with the 

mean experimental air fatigue curve for test specimen data in air to those obtained using more 

accurate values of the stresses and calculated CUFs using the ASME Code Section III air 

fatigue design curve were approximately 60 and 90, respectively, for PWR and BWR nozzles. 

The reductions in these factors caused by environmental effects were estimated to be factors of 

5.2 and 4.6 for PWR and BWR nozzles, respectively. Thus, Deardorff and Smith236 argued that, 

after accounting for environmental effects, factors of 12 and 20 on life for PWR and BWR 

nozzles, respectively, were available to account for uncertainties due to material variability, 

surface finish, size, mean stress, and loading sequence. 

However, other studies on piping and components indicated that the ASME Code Section III 

fatigue design procedures do not always contain large conservatisms.237,238 Southwest 

Research Institute performed fatigue tests in room–temperature water on 0.91–m (36-in) 

diameter carbon and low–alloy steel vessels.237 In the low–cycle regime, approximately 5–mm

(0.2-in) deep cracks were initiated slightly above the number of cycles predicted by the ASME 

Code Section III fatigue design curve (Fig. 120a). Battelle–Columbus conducted tests on 203–

mm (8.0-in) and 914–mm (36.0-in) carbon steel pipe welds at room temperature in an inert 

environment, and Oak Ridge National Laboratory (ORNL) performed four–point bend tests on a 

406–mm (16.0-in) diameter Type 304 SS pipe removed from the C–reactor at the Savannah 

River site.238 The results showed that the number of cycles to produce leaks was lower than 

predicted from calculations using the ASME Code Section III fatigue design curves (Fig. 120). 

In the case of the ORNL “tie–in” and flawed “test” welds, the specimens cracked completely 

through the 12.7–mm (0.5-in) wall thickness, and the number of cycles to initiate a 3-mm crack 

was shorter than the cycles predicted using the ASME Code Section III fatigue design curve. 

These and other similar tests indicate that other factors, such as environmental effects, may 

eliminate much of the conservatism that may be present in ASME Code calculations. 

Much of the margin in ASME Code Section III fatigue evaluations arises from design procedures 

(e.g., stress analysis rules and assumptions) that, as discussed by Deardorff and Smith,236 are 
148

quite conservative. However, the Section III of the ASME Code is not fully prescriptive, so there 

is a wide variation in the specific procedures that are applied to fatigue evaluations by different 

analysts. For example, modern computer capabilities, particularly modern finite element 

methods, fatigue monitoring, and improved Ke factors, allow for evaluation refinements that 

significantly decrease the conservatisms traditionally applied in fatigue evaluation procedures 

performed in the past. 

(a) (b)

Figure 120. Fatigue data for (a) carbon and low–alloy steel and (b) Type 304 stainless 

steel components (Refs. 237,238). 

The factors of 2 on stress and 20 on cycles used in the ASME Code Section III air fatigue 

design curves were intended to cover the effects of variables that influence fatigue lives but 

were not investigated in the laboratory tests that provided the data for the curves. It is therefore 

not clear how much conservatism is embedded in the particular values of 2 and 20. A study 

sponsored by the PVRC to assess the factors of 2 and 20 used in the development of the ASME 

Code Section III air fatigue design curves concluded that these factors should not be changed 

due to their being too many unknowns.239 

The variables that can affect fatigue lives in air and LWR environments are broadly classified 

into three groups:

(a) Material

(i) Composition 

(ii) Metallurgy: grain size, inclusions, orientation within a forging or plate

(iii) Processing: cold work, heat treatment

(iv) Size and geometry

(v) Surface finish: fabrication surface condition

(vi) Surface preparation: surface work hardening

(b) Loading

(i) Strain rate: rise time

(ii) Sequence: cycle counting, linear damage summation or Miner's rule

(iii) Mean stress

(iv) Biaxial effects: constraints

(c) Environment

(i) Water chemistry: DO, lithium hydroxide, boric acid concentrations

(ii) Temperature

(iii) Flow rate
149

The existing fatigue ε–N database covers an adequate range of material parameters (a(i–iii)), 

one loading parameter (b(i)), and environmental parameters (c(i–ii)); therefore, the variability 

and uncertainty in fatigue lives due to these parameters were incorporated into the revised ANL 

models described in Chapter 4. The existing data are conservative with respect to the effects of 

surface preparation because the fatigue ε–N data were obtained for specimens that were free of 

surface cold work, which tends to improve fatigue performance due to the introduction of 

favorable compressive surface residual stresses. Fabrication procedures for fatigue test 

specimens generally followed American Society for Testing and Materials (ASTM) guidelines, 

which required that the final polishing of the specimens avoided surface work–hardening. 

Biaxial effects were covered by design procedures and were not considered in the ASME Code 

Section III fatigue design curves. 

As discussed in Sections 4.1.9 and 4.2.11, under conditions that were typical of operating 

BWRs, environmental effects on the fatigue lives were a factor of approximately 2 lower at high 

flow rates (7 meters/second) compared to those at very low flow rates (0.3 meters/second or 

lower) for carbon and low–alloy steels and were independent of flow rate for austenitic SSs.25,26 

However, because of the uncertainties in the flow conditions at or near the locations of crack 

initiation, the beneficial effects of flow rate on the fatigue lives of carbon and low-alloy steels 

was not included in the revised ANL models described in Chapter 4. 

Thus, the contributions of four groups of variables, namely, material variability and data scatter, 

specimen size and geometry, surface finish, and loading sequence (Miner's rule), were 

considered in the ANL investigations for developing revised fatigue design curves applicable to 

components. 

5.1 Material Variability and Data Scatter

The effects of material variability and data scatter were included in the ANL investigations to 

ensure that the design curves encompass the available test data well and adequately describe 

the fatigue lives of the much larger number of heats of material that are found in the field. The 

effects of material variability and data scatter were evaluated for various materials by 

considering the best–fit curves determined from tests on individual heats of materials or loading 

conditions as samples of the much larger population of heats of materials and service conditions 

of interest. The fatigue behaviors of each of the heats or loading conditions were characterized 

by the values of the constant A in Eq. 6. The values of A for the various data sets were ordered, 

and median ranks were used to estimate the cumulative distribution of A for the entire 

population. The distributions were fit to lognormal curves. Further details of heat-to-heat 

variability of fatigue lives in air and LWR environments are discussed, respectively, in Sections 

3.1.7 and 4.1.13 for carbon and low-alloy steels and in Sections 3.2.7 and 4.2.15 for cast and 

wrought austenitic SSs. The results indicated that the revised Fen expressions presented in this 

report adequately capture the effects of LWR environments on the fatigue lives of carbon and 

low-alloy steels and austenitic SSs. After accounting for the environmental effects from the 

experimental fatigue lives in LWR environments, the resultant fatigue lives showed good 

agreement with the fatigue lives that are expected for the materials in air. The results also 

indicated that the statistical data presented in the original revision to NUREG/CR-6909 remain 

valid and were therefore not updated. 

The median values of A and the standard deviations for the sample of data available for each 

material that were presented in the original version of NUREG/CR-6909 are listed in Table 13. 

These values did not change significantly based on the reevaluation of the larger database used 

for this report so they were not changed. The 95/95 values of the factors on the median values 

to account for material variability and data scatter for the samples of heats of materials used in 
150

the present evaluation were determined as 2.8, 2.1, and 2.3 for carbon steels, low-alloy steels, 

and austenitic SSs, respectively. These factors applied to the mean values of fatigue lives

determined from the ANL models provide 95% confidence that the fatigue lives of the 95th

percentile of the materials of interest were greater than the resultant values estimated from the 

ANL model. 

Table 13. Statistical information for the constant A used to 

evaluate material variability and data scatter. 

Air Environment

Median 

Value of A

Standard 

Deviation

Number of 

Data Sets

Carbon Steel 6.583 0.477 17

Low-Alloy Steel 6.449 0.375 32

Stainless Steel 6.891 0.417 51

5.2 Size and Geometry

The effect of specimen size on fatigue lives were reviewed in earlier reports.12,46 Various 

studies concluded that “size effects” are not significant in the design curve factors when the 

fatigue curves were based on data from axial strain controlled specimens rather than bending 

test specimens. No intrinsic size effects were observed for smooth specimens tested in axial 

loading or plain bending. However, size effects did occur in rotating bending test specimens; 

the fatigue endurance limits decreased by approximately 25% if the specimen sizes were 

increased from 2 to 16 mm, but the limits did not decrease further with larger sizes. Also, some 

effects of size and geometry were observed on small–scale–vessel tests conducted at the Ecole 

Polytechnique in conjunction with the large–size–pressure–vessel tests carried out by the 

Southwest Research Institute.237 The tests at the Ecole Polytechnique were conducted in 

room–temperature water on 19–mm (0.75-in) thick shells with a 305–mm (12.0-in) inner 

diameter that contained nozzles made of machined bar stock. The results indicated that the 

fatigue lives determined from tests on the small–scale–vessels were 30–50% lower than those 

obtained from tests on small, smooth fatigue specimens. However, the differences in fatigue 

lives in these tests were not attributed to specimen size alone; rather, they were attributed to the 

effects of both size and surface finish. 

During cyclic loading, cracks generally form at surface irregularities either already in existence 

or produced by slip bands, grain boundaries, second phase particles, etc. In smooth 

specimens, formation of surface cracks is affected by the specimen size; crack initiation is 

easier in larger specimens because of the increased surface areas and, therefore, an increased 

numbers of sites for crack initiations. However, specimen sizes are not likely to influence crack 

initiation in specimens with rough surfaces because cracks already initiate at existing 

irregularities on the rough surface. As discussed in the next section, surface roughness has 

large effects on fatigue lives. Consequently, for rough surfaces, the effects of specimen sizes 

are not appropriate for consideration in the factor of 12 applied to the fatigue design curves 

developed in this report. Therefore, considering all of the foregoing, a factor ranging from 1.0 to 

1.4 on fatigue lives was used to incorporate size effects on fatigue lives in the low–cycle regime. 

This range is slightly improved over the range used in the original revision to NUREG/CR-6909 

(1.2 to 1.4) to account for the fact that, in some cases, size effects were observed to be 

negligible.
151

5.3 Surface Finish

The effects of surface finish were considered to account for the differences in fatigue lives 

expected in actual components with industrial–grade surface finishes compared to the smooth 

polished surfaces of test specimens. Fatigue lives are sensitive to surface finish; cracks are 

more likely to initiate at surface irregularities that act as stress risers. The height, spacing, 

shape, and distribution of surface irregularities are important for crack initiation. The effects of 

surface finish on crack initiation are expressed by Eq. 26 in terms of the RMS value of surface 

roughness (Rq). 

The roughnesses of machined surfaces or natural finishes typically range from approximately 

0.8 to 6.0 μm.219 Typical surface finishes for various machining processes are in the range of 

0.2 to 1.6 μm for cylindrical grinding, 0.4 to 3.0 μm for surface grinding, 0.8 to 3.0 μm for finish 

turning and drilling, and 1.6 to 4.0 μm for milling. For fabrication processes, roughnesses range 

from 0.8 to 3.0 μm for extrusion and 1.6 to 4.0 μm for cold rolling. Thus, from Eq. 26, the fatigue 

lives of components with such surface roughnesses can be a factor of 2 to 3.5 lower than those 

of smooth specimens. 

Limited data in LWR environments on specimens that were intentionally roughened indicated 

that the effects of surface roughness on fatigue lives were the same in air and water 

environments for austenitic SSs, but were insignificant in water for carbon and low-alloy steels, 

particularly in NWC BWR environments. However, the results for surface finish effects on 

carbon and low-alloy steels were limited. Therefore, additional data are needed to better define 

surface finish effects for carbon and low alloy steels in LWR environments. Until additional data 

are available to verify that surface finish effects for carbon and low-alloy steels are insignificant 

in LWR environments, a factor of 2.0 to 3.5 was used in the ANL investigations to account for 

the effects of surface finish on the fatigue lives of carbon and low-alloy steels and wrought and 

cast austenitic SSs. This range is slightly improved over the range used in the original revision 

to NUREG/CR-6909 (2.0 to 3.5) to account for the fact that, in some cases, surface finish 

effects of as low as a factor of 1.5 have been observed. 

5.4 Loading Sequence

The effects of variable amplitude loading of smooth specimens were also reviewed in an earlier 

report.46 A few cycles at high strain amplitude loading introduced into a small strain amplitude 

load history resulted in significantly lower fatigue lives compared to constant–amplitude loading, 

i.e., the fatigue limits of the materials were lower under variable loading histories.

As discussed in Section 2.1, fatigue life is conventionally divided into two stages: initiation, 

expressed as the number of cycles required to form MSCs on the surface, and initial 

propagation, expressed as the number of cycles required to propagate the MSCs to engineering 

size (≈3 mm) – the depth at which most crack propagation analyses take over and crack 

initiation is considered complete. The transition from the initiation stage to the propagation 

stage strongly depends on the applied stress amplitude; at stress levels above the fatigue limit 

of the material, tests showed that the transition from the initiation stage to the propagation stage 

occurred at crack depths in the range of 150 to 250 μm. However, under constant loading at 

stress levels below the fatigue endurance limit of the material (∆σ1 in Fig. 8), although 

microcracks approximately 10 μm formed early in life, they did not grow to an engineering size. 

Under the variable loading conditions typically encountered during the operation of nuclear 

power plants, cracks created by growth of MSCs at high stresses (∆σ3 in Fig. 8) with depths 

larger than the transition crack depth grew to an engineering size even at continued stress 

levels below the fatigue limit of the material tested. Therefore, because the fatigue ε-N data 
152

used to develop the ASME Code Section III fatigue design curves were obtained from fatigue 

tests at constant strain amplitudes, the effects of loading sequence on the fatigue lives and the 

fatigue limits of materials were included in the ASME air design curves. These effects were also 

included in the ANL air design curves.

Studies on fatigue damage in Type 304 SS under complex loading histories240 indicated that the 

loading sequences for decreasing strain levels (i.e., high strain levels followed by low strain 

levels) were more damaging than those of increasing strain levels. The fatigue lives of the 

steels at low strain levels decreased by factors of 2 to 4 under decreasing strain sequences. In 

another study, the fatigue endurance limits of medium carbon steels were lowered even after 

low–stress high–cycle fatigue; higher applied stresses caused greater decreases in the fatigue 

thresholds.241 A study on Type 316NG and Ti-stabilized Type 316 SS on strain-controlled tests 

in air and PWR environments with constant or variable strain amplitudes reported factors of 3 or 

more decreases in fatigue lives under variable amplitude loading compared with constant 

amplitude loading.158 Although the strain spectrum used in the study was not intended to be 

representative of actual operating plant transients, it represented a generic loading case and

demonstrated the effects of variable strain amplitudes on the fatigue lives of materials.

Because variable loading histories primarily influence fatigue lives at low strain levels, the mean 

fatigue ε–N curves were lowered to account for damaging cycles that occur below the constant–

amplitude fatigue limits of the materials tested. Factors ranging from 1.0 to 2.0 were used to 

incorporate the possible effects of variable strain amplitudes on fatigue lives in the low–cycle 

regime. This range is slightly improved over the range used in the original revision to 

NUREG/CR-6909 (1.2 to 2.0) to account for the fact that, in some cases, loading sequence 

effects were observed to be negligible.

5.5 Air Fatigue Design Curve Adjustment Factors Summarized

The ASME Code Section III air fatigue design curves were obtained from the mean data curves 

by first adjusting for the effects of mean stress using the modified Goodman relationship, and 

then reducing the life at each point of the adjusted curve by a factor of 2 on strain or 20 on life, 

whichever was more conservative. The factors on strain were needed to account for the 

variation in the fatigue limit of the material caused by material variability and data scatter, 

component size, surface finish, and load history. Because these variables affect life through 

their influence on the growth of short cracks (less than 100 μm), the adjustment on strain to 

account for such variations is typically not cumulative. Thus, the adjustment on strain is 

controlled by the variable that has the largest effect on fatigue life. In relating the fatigue lives of 

laboratory test specimens to those of actual reactor components, the factor of 2 on strain used 

to develop the ASME Code Section III air design curves was adequate to account for the 

uncertainties associated with material variability, component size, surface finish, and load 

history.

The factors on life are needed to account for variations in fatigue lives in the low–cycle regime. 

Based on the previous discussions, the effects of various material, loading, and environmental 

parameters on fatigue lives may be summarized as follows: 

(a) The results presented in Table 13 were used to determine the factors that were applied to 

the mean value of fatigue life to ensure that the resultant value of fatigue life bounded 

the 95th percentile of the materials and loading conditions of interest.

(b) For rough surfaces, specimen size does not significantly influence fatigue lives. However, 

specimen size does, in some cases, significantly affect fatigue lives for smooth specimens. 
153

Absent additional test data that indicate otherwise, factors ranging from 1.0 to 1.4 on fatigue 

lives were used in the reanalysis of the larger fatigue database to incorporate size effects on 

fatigue lives.

(c) Factors ranging from 1.5 to 3.5 were used to incorporate the effects of surface finish on 

fatigue lives in air. Limited data indicate that, for carbon and low-alloy steels, the effects of 

surface roughness on fatigue lives may be insignificant in LWR environments. Therefore, a 

lower factor of 2.0 was used for carbon and low-alloy steels in water environments instead 

of the factors ranging from 1.5 to 3.5 that were used for these steels in air. A factor of 2.0 

was used for austenitic SSs in both air and water environments for surface finish effects. 

(d) Variable loading histories primarily influence fatigue lives at low strain levels (i.e., in the 

high–cycle regime), so the mean air fatigue ε–N curves were adjusted by a factor of 2.0 on 

strain to account for damaging cycles that occur below the constant–strain fatigue limit of 

the material. Factors ranging from 1.0 to 2.0 were used to incorporate the possible effects 

of load histories on fatigue lives in the low–cycle regime. 

The subfactors needed to account for the effects of the various material, loading, and 

environmental parameters on fatigue lives are summarized in Table 14. The total adjustment on 

life varies from 4.7 to 27.4. However, because the maximum value represents relatively poor 

heats of materials and assumes the maximum effects of size, surface finish, and loading history, 

the maximum value of 27.4 is overly conservative to apply depending on the confidence bounds 

desired. A value of 12 was used to develop the air design curves from the mean-data air curves

to be consistent with the initial version of this report. However, based on Monte Carlo statistical 

evaluation, a value of 10 was justified as discussed below.

Table 14. Factors on life applied to the mean fatigue ε–N air curve to account for the 

effects of various material, loading, and environmental parameters.

Parameter Section III Criterion Document Present Report

Material Variability and Data Scatter 

(minimum to mean) 2.0 2.1–2.8

Size Effect 2.5 1.0–1.4

Surface Finish, etc. 4.0 1.5–3.5

Loading History – 1.0–2.0 

Total Adjustment 20 4.7–27.4 

To determine the most appropriate value for the adjustment factor on fatigue life, Monte Carlo 

simulations were performed using the material variability and data scatter results given in 

Table 13, and the factors needed to account for the effects of size, surface finish, and loading 

history listed in Table 14. A lognormal distribution was assumed for the effects of size, surface 

finish, and loading history, and 5th and 95th percentile values were assumed to represent the 

minimum and maximum values of the adjustment factors (i. e., 1.0 and 1.4 for size, 1.5 and 3.5 

for surface finish, and 1.0 and 2.0 for loading history, respectively). A total of 25,000 

simulations were performed for each material. The median value, standard deviation, and 95th

percentile values for the factor were, respectively, 5.037, 3.159, and 10.233 for carbon steels, 

4.830, 2.558, and 9.037 for low-alloy steels, and 4.932, 2.864, and 9.643 for austenitic SSs. 

The 95th percentile values for the factors that were applied to the best-fit mean air data curves to 

obtain the design fatigue ε–N air curves are given in Table 15. The factor that was applied to 

the mean data curves for test specimens to obtain component curves that bounded 95% of the 

population ranged from 9.0 to 10.2 for carbon, low-alloy, and austenitic stainless steels, 
154

respectively, as shown in Table 15. Plots of the cumulative distribution of the values of constant 

A for best-fit mean data air curves and for the adjusted design air curves are shown in Fig. 121

for carbon, low–alloy, and austenitic stainless steels.

The average value for the factor for application to the best-fit mean air curves for the three 

materials to obtain air fatigue design curves that are applicable for reactor components is 9.6. 

Note that the selection of 95th percentile value for the factor was arbitrary, but is consistent with 

NRC practice. As a comparison, the corresponding 98th percentile values for the factors are 

11.5, 10.1, and 10.8, respectively, for carbon, low-alloy, and austenitic stainless steels (or an 

average value of 10.8).

The results of the reanalysis of the fatigue adjustment factors indicate that, for all materials, the 

current ASME Code Section III use of a factor of 20 on cycles to account for the effects of 

material variability and data scatter, as well as specimen size, surface finish, and loading 

history, may contain as much as a factor of 2.0 conservatism (i.e., 20/10 considering the 

average factor of 9.6 obtained from Table 15). To reduce this conservatism, fatigue design air 

curves were derived from the mean data curves by first correcting for mean stress effects using 

the modified Goodman relationship, and then reducing the mean–stress adjusted curve by a 

factor of 2 on stress and 12 on cycles, whichever was more conservative. Fatigue design 

curves that were developed from the ANL fatigue life models using this procedure for carbon 

and low–alloy steels are presented in Section 3.1.11 and for wrought and cast austenitic SSs in 

Section 3.2.11. The selection of bounding the 95th percentile of the population for a design 

curve was made under the presumption that the design curve controls fatigue initiation, not 

failure. The choice also recognized that there were conservatisms implied in the choice of log 

normal distributions, which have infinite tails, and in the identification of values of the effects as 

95th percentile values. Finally, the results of the present analysis indicate that the conservatism 

in the ASME Code Section III fatigue design air curves may be further reduced by using a factor 

of 10 on life instead of the factor of 12 on life used in the fatigue design air curves presented in 

this report for carbon, low-alloy, and wrought and cast austenitic stainless steels.

Table 15. Factor applied to the mean values of fatigue life to 

bound 95% of the data population.

Material Air Environment

Carbon Steels 10.2

Low–Alloy Steels 9.0 

Austenitic Stainless Steels 9.6
155

Figure 121.

Estimated cumulative distribution of 

parameter A in the ANL models that 

represent the fatigue lives of test 

specimens and actual components in air.

0.0

0.2

0.4

0.6

0.8

1.0

3 4 5 6 7

Components

Test Specimens

Cumulative Distribution F

Constant A

95th Percentile

Component

Median

Test Specimens

Carbon Steel, Air

Margin of 

20 on life

Constant A 

6.583

Constant A 

4.966

Margin of 

10.233 on life

Constant A 

4.257

0.0

0.2

0.4

0.6

0.8

1.0

3 4 5 6 7

Components

Test Specimens

Cumulative Distribution F

Constant A

95th Percentile

Component

Median

Test Specimens

Low-Alloy Steel, Air

Margin of 

20 on life

Constant A 

6.449

Constant A 

4.248

Margin of 

9.037 on life

Constant A 

4.874

0.0

0.2

0.4

0.6

0.8

1.0

4 5 6 7 8

Components

Test Specimens

Cumulative Distribution F

Constant A

95th Percentile

Component

Median

Test Specimens

Stainless Steel, Air

Margin of 

20 on life

Constant A 

6.891

Constant A 

4.625

Margin of 

9.643 on life

Constant A 

5.295

157

6. VALIDATION OF FEN EXPRESSIONS

The updated Fen expressions were validated by comparing calculated results from six 

experimental data sets with estimates of fatigue lives based on the updated Fen expressions. 

The intent of the calculations was only to validate the accuracy of the revised Fen expressions. 

The experimental data sets evaluated included the following:

1. Tests with changing strain rates within each strain cycle.136

2. Tests performed by VTT on small specimens with either constant or spectrum strain 

cycling (i.e., an amplitude sequence of a narrow band randomized block of 50 strain 

cycles that was repeated until specimen failure).158,159

3. Tests performed by Areva on small specimens with triangular and complex strain cycles 

of cold and hot thermal shock associated with a simulated safety injection transient.155-157

4. EPRI U-bend tests in inert (dry nitrogen) and PWR environments.97-99

5. Tests with changing strain rate and temperature within each strain cycle.154

6. Bettis laboratory thermal fatigue tests of a stepped pipe of differing thicknesses exposed 

to temperature cycles between 38 and 343°C (100 and 650°F).160

Since the experimental data sets were tested to crack initiation (i.e., CUF greater than unity), 

the goal of these evaluations was to benchmark the Fen methodology against the predictions of 

failures and, if warranted, make appropriate adjustments to the Fen expressions. In the tests 

evaluated, fatigue failure was defined as the number of cycles to (a) form a finite crack or 

(b) decrease the cyclic tensile stress by 25% from its peak (steady-state) value. The following 

three methods were used to calculate the environmental correction factor, Fen, which was 

applied to the number of loading cycles in air to estimate the number of loading cycles in the 

environment. 

Strain-Integrated Method: In this method, the applied strain cycle was divided into small time 

intervals, and the environmental correction factor, Fen, was determined at each time interval 

using the modified rate approach and the updated Fen expressions. In addition, Fen was 

calculated using expressions presented in the initial version of NUREG/CR-6909 for 

comparative purposes. In these calculations, the overall integrated Fen was expressed as

, (66)

where εmin and εmax, respectively, are the minimum and maximum values of strain, and εi and 

Fen,i are the strain and Fen at the ith increment of strain. The summation was only applied when 

the strain increment was positive. In addition, a threshold strain, εth, was also considered to 

compute the overall Fen. Consideration of a threshold strain assumes that, during a strain cycle, 

environmental effects are significant only after the applied strain exceeds the threshold value. 

Thus, 

. (67)

Simplified Method: In this method the overall Fen was determined for the entire period of the 

strain cycle where the strain rate was greater than zero (i.e., increasing strain) and used the 

average temperature and average strain rate for the interval. The average values were 

determined using an average (i.e., straight line) from the valley to adjacent peak strain. As 
158

before, the overall Fen was computed from both the updated Fen expressions and the 

expressions in the initial version of NUREG/CR-6909. 

Multi-Linear Strain Based Method: This method is a modified version of the simplified method. 

Depending on the strain-time profile, the applied strain cycle was divided into two or more linear 

ramps within which the strain rate was positive. The overall Fen was determined for each ramp 

using the updated and the original NUREG/CR-6909 Fen expressions. Also, average values of 

temperature and strain rate were used in the Fen calculations for each ramp. The overall Fen

was defined as

, (68)

where ∆ε1 and ∆ε2 are the first and second strain increments, and Fen,1 and Fen,2 are the Fen

values for the first and second strain increments. Overall Fen values were calculated for each 

dataset using the foregoing three methods. The results were compared with the experimental 

values to benchmark the revised Fen methodology and to provide insights as to which 

computational methods yielded the most consistent and reliable results. The results associated 

with the changing strain rates within each cycle were presented in Section 4.1.3 as a part of the 

discussion associated with the threshold strain amplitude and, therefore, are not duplicated in 

this section. In addition, the assessments to estimate the overall Fen for the thermal fatigue 

tests of a stepped pipe indicated that the reported estimates of the total applied strain (elastic 

and plastic) were not reliable. NRC was not able to complete additional finite element analyses 

to provide meaningful thermal strain values for use in the evaluation. As a result, the dataset for 

the stepped pipe thermal fatigue tests was not considered further and those results are not 

included in this report. The results of the remaining four datasets are discussed in the following 

sections.

6.1 Spectrum Straining

Low-cycle, strain-controlled, completely-reversed fatigue tests were conducted on Type 316NG 

and Ti-stabilized 316 (O8X8H10T steel) austenitic SSs in air and simulated PWR environments 

using cylindrical specimens with a 4-mm diameter and a 10-mm gage length.158 Test 

specimens were fabricated from a 12-mm diameter round bar of Type 316NG SS. A 300-mm 

diameter, 16-mm thickness pipe was fabricated from the Ti-stabilized 316 material. The test 

specimens were smooth, but not polished. The chemical composition and tensile properties of 

the two materials are given Table 16. Pneumatic bellows, designed and developed by Valtion 

Teknillinen Tutkimuskeskus (VTT), which is the Technical Research Centre of Finland, were 

used for accurate control of strain. Fatigue tests were conducted on the Type 316NG SS 

specimens in a simulated PWR environment at 320°C. For the Ti-stabilized 316 SS specimens, 

fatigue tests were conducted in a simulated Voda-Vodyanoi Energetichesky Reaktor (VVER) 

Russian reactor environment at 293°C. Both steels were also tested in air at room temperature 

(25°C). Further details of the environmental conditions are given in Table 17. 

Table 16. Chemical composition and tensile strength of test materials for the constant 

and spectrum strain amplitude fatigue tests. 

Material Chemical Composition (wt. %) Min. YS 

(MPa)

Min. UTS 

(MPa)

Min. 

C Si Mn Ni Cr Mo V Cu Ti Elong. (%)

316NG 0.01 0.60 1.40 11.2 16.9 2.60 - - - 250 570 -

Ti-stab. 0.08 0.39 1.36 10.5 18.2 0.17 0.05 0.18 0.62 330 595 -
159

Table 17. Environmental conditions for the constant and spectrum 

strain amplitude fatigue tests.

Test Condition For Type 316NG SS For Ti-Stabilized 316 SS

Temperature 320°C 293°C

Pressure 125 bar 100 bar

pH at RT 5.1 7.2

Conductivity 2 to 40 μmho/cm 80 to 90 μmho/cm

Dissolved Oxygen < 0.01 ppm < 0.01 ppm

Chlorides < 0.15 ppm < 0.05 ppm

Fluorides < 0.15 ppm < 0.01 ppm

Dissolved Hydrogen 25 to 35 cm3/kg 30 to 35 cm3/kg

Boric Acid 2500 ppm 2750 ppm

To adjust pH 7.0 Lithium Kalium

Constant and variable strain amplitude fatigue tests were performed using a sinusoidal 

waveform. For spectrum loading, an amplitude sequence of a narrow-band, randomized block 

of 50 strain cycles, as shown in Fig. 122, was repeated until specimen failure occurred, which 

was defined as a 25% decrease in load from the steady state value. The spectrum straining 

data were transformed to equivalent constant amplitude ε-N data as follows: 

, , (69)

where and are, respectively, the equivalent number of cycles and strain amplitude 

under constant strain loading, and is the number of cycles at strain amplitude under 

spectrum loading and Di is an arbitrary damage function associated with that fatigue loading, 

and is given by 

. (70)

Figure 122.

Schematic of the repeated sequence 

of randomized block of 50 strain 

cycles (Ref. 158). 

The results yielded an equivalent strain amplitude at the mean damage level representative of 

the spectrum straining and the number of equivalent cycles that provided an identical damage 

sum (i.e., usage factor) for the equivalent straining and the original spectrum straining. Thus, 

the results were directly comparable and, therefore, were plotted on common graphs. The test 

conditions and a summary of the results are given in Table 18. The fatigue ε-N data on Type 
160

316NG and Ti-stabilized 316 SSs in air and PWR environments using constant and spectrum 

strain amplitude loading are shown in Fig. 123.

Table 18. The conditions and results of fatigue tests on austenitic SSs obtained under 

constant and spectrum strain amplitude loading.

Environment

Strain Rate 

(%/s)

εa

(%)

Equiv.

εa (%) Nf Neq

Estimateda

Nair

Estimated 

Fen

Predicted

b Nf

Type 316NG SS

Air 25°C 1.020 0.510 0.510 6,120 6,120 5,767 - 9,227

Air 25°C 0.620 0.310 0.310 47,000 47,000 22,036 - 35,257

Air 100°C 0.170 0.420 0.420 15,600 15,600 9,434 - 15,095

Air 25°C 0.800 0.20-0.80 0.535 9,650 3,260 5,130 - 4,104

PWR 320°C 0.020 0.508 0.508 1,400 1,400 5,823 4.88 1,908

PWR 320°C 0.016 0.040 0.400 2,650 2,650 10,732 5.17 3,321

PWR 320°C 0.013 0.315 0.315 6,660 6,660 21,005 5.45 6,165

PWR 320°C 0.013 0.315 0.315 7,800 7,800 21,005 5.45 6,165

PWR 320°C 0.065 0.19-0.78 0.529 1,250 384 5,273 3.62 1,167

PWR 320°C 0.039 0.11-0.48 0.359 4,600 883 14,413 4.12 2,799

Ti-Stabilized 316 SS

Air 25°C 1.000 0.500 0.500 4,590 4,590 6,056 - 9,689

Air 25°C 0.980 0.350 0.350 26,700 26,700 15,477 - 24,764

Air 25°C 0.920 0.230 0.230 362,900 362,900 59,526 - 95,242

Air 25°C 1.000 0.20-0.80 0.536 6,900 2,282 5,107 - 4,086

Air 25°C 1.000 0.12-0.50 0.359 21,900 4,367 14,413 - 11,530

Air 25°C 1.000 0.12-0.50 0.372 36,350 7,250 13,061 - 10,449

Air 25°C 1.000 0.072-0.30 0.238 450,000 84,437 52,482 - 41,986

VVER 293°C 0.020 0.500 0.500 1,734 1,734 6,056 4.02 2,410

VVER 293°C 0.011 0.283 0.283 12,256 12,256 29,199 4.60 10,165

VVER 293°C 0.060 0.18-0.77 0.523 2,150 641 5,422 3.14 1,380

VVER 293°C 0.030 0.09-0.39 0.302 14,400 2,492 23,852 3.67 5,197

VVER 293°C 0.024 0.08-0.31 0.247 95,500 17,847 45,971 3.86 9,529

a Fatigue lives estimated using Eq. 29.

b For constant strain amplitude loading, fatigue lives were determined from the estimated lives in air by multiplying by a factor of 1.6 

to account for heat-to-heat variability. For fatigue lives in a PWR environment, the adjusted values were divided by Fen. For 

spectrum loading, the effects of loading sequence were also included by dividing the values determined for the constant strain 

amplitude loading by a factor of 2.
161

Figure 123.

Fatigue strain-life data for Type 

316NG SS in PWR water at 320°C 

and for Ti-stabilized 316 SS in VVER 

water at 293°C (Refs. 158,159). 

The results indicated that, for the two heats of Type 316NG and Ti-stabilized 316 SSs tested, 

the slope of the fatigue ε-N data obtained under the constant strain amplitude loading was less 

steep than that of the ANL best-fit mean data curve. For fatigue lives greater than 104 cycles, 

the experimental fatigue lives were greater than those estimated from the ANL best fit air curve. 

For the Ti-stabilized steel, the experimental fatigue life was a factor of 6 greater than the fatigue 

life estimated using the best-fit mean data curve. For both steels, the measured fatigue lives at 

strain amplitudes between 0.3 and 0.5% were approximately 60% greater than the estimated 

values. Thus, a subfactor of 1.6 was used to account for heat-to-heat variability. Note that, 

since all tests were conducted on smooth rather than polished specimens, this subfactor 

included some effects of surface finish.

The results also indicated that the fatigue ε-N data obtained under spectrum strain amplitude 

loading were up to a factor of 5 lower than those obtained under constant strain amplitude 

loading. The actual differences between spectrum and constant strain amplitude loading in air 

and PWR environments, respectively, were factors of 2.4 and 4.4 for Type 316NG, and 3.4 and 

5.2 for Ti-stabilized 316 SS. The differences were greater for a PWR environment, most likely 

because these tests were conducted using a sine wave loading and the estimated values were 

based on average strain rates. Therefore, the environmental effects were likely underestimated. 

However, these results demonstrated the potential effects of loading sequence, which are 

discussed in Section 5.4. 

The predicted fatigue lives for the constant and spectrum strain loading fatigue tests are listed in 

the last column of Table 18. These values were determined from the fatigue lives in air (Nair) 

estimated from Eq. 29 (seventh column of Table 18). Since these tests were conducted at 

constant strain rate and temperature, the predicted fatigues lives were determined by 

multiplying Nair by a factor of 1.6 to account for heat-to-heat variability (and potential effects of 

surface finish), and dividing the adjusted values by Fen to account for environmental effects. 

Furthermore, for spectrum loading, the effects of loading sequence were included by dividing 

the values determined for the constant strain amplitude loading by a factor of 2, which is the 

maximum subfactor proposed in Table 14 (Section 5.5) to account for the effects of loading 

sequence. A subfactor of 2 was used instead of the values of 3.4–5.2 measured in these tests 

because these tests were conducted using a sinusoidal waveform instead of a triangular 

waveform. Therefore, the experimental environmental effects were greater because of 

differences in strain rates. The subfactor to account for the effects of surface finish was not 

used to determine the fatigue lives, even though the test specimens were “smooth” but not 

polished, because the effects of surface finish were already included in the heat-to-heat 
162

adjustment factor of 1.6 used to determine the predicted fatigue lives from the best-fit mean 

data curve. 

The measured fatigue lives, Neq., and the predicted fatigue lives for the constant and spectrum 

strain loading tests are plotted in Fig. 124. The results for the constant strain amplitude loading 

showed very good agreement with the experimental values; the predicted fatigue lives were 

within a factor of 2 (i.e., within the factor for data scatter). The predicted fatigue lives for the 

spectrum strain amplitude loading were generally greater than the measured values because of 

differences in the loading waveform (sinusoidal or triangular waveforms). 

• The predicted fatigue lives showed very good agreement with the experimental values. The 

loading sequence effects observed in the spectrum loading tests were greater than those 

proposed in this study; the differences were attributed to differences in the loading waveform 

(e.g., sinusoidal or triangular waveforms) and the methods used to determine equivalent 

strain amplitude and fatigue lives. 

Figure 124. Experimental and estimated fatigue lives for Type 316NG and Ti-stabilized 

316 SS tested with constant and spectrum strain loading (Refs. 158,159).

6.2 Complex Loading – Safety Injection Transient

Low-cycle, strain-controlled, completely-reversed fatigue tests were conducted on Type 304L 

austenitic SSs in a simulated PWR environment using cylindrical specimens with a 9-mm 

diameter and a 13.5-mm gage length.155-157 The test specimens were fabricated from a 590 x 

450 x 103 mm rolled plate that was water quenched. The chemical composition and tensile 

properties of the Type 304L SS are given Table 19. Fatigue tests were conducted on both 

polished and ground specimens in air and the simulated PWR environment at 300°C using a 

triangular loading waveform and a waveform that simulated the typical strain history of cold and 

hot thermal shocks associated with a PWR safety injection transient. The actual strain cycle 

used in this study is shown in Fig. 125. The specimen surface finish was specified as 40 μm, 

which corresponded to the material surface height between the maximum peak and minimum 

valley measured over a length of 4 mm. The authors noted that the machining process induced 

a superficial hardened layer which was not totally removed by the polishing process. The 

environmental conditions for the tests in the PWR environment are given in Table 20.
163

Table 19. Chemical composition and tensile strength of Type 304L SS.

Material Chemical Composition (wt. %) Min. YS 

(MPa)

Min. UTS 

(MPa)

Min. 

C Si Mn Ni Cr Mo V Cu Ti Elong. (%)

304L 0.025 0.37 1.687 9.12 18.3 0.38 - 0.217 - 255 573 64

Figure 125.

Typical strain cycle of cold and hot 

thermal shocks corresponding to a 

PWR safety injection transient 

(Ref. 155). 

Table 20. Environmental conditions for fatigue tests in 

simulated PWR environment.

Test Condition Value

Temperature 300°C

Pressure 140 bar

Conductivity 2 to 40 μS/cm

Dissolved Oxygen < 0.1 ppm

Chlorides, Fluorides < 0.15 ppm

Dissolved Hydrogen 25 to 35 cm3/kg

Boron 1000 ppm (adjusted by boric acid)

Lithium ~ 2 ppm (adjustment for pH)

Strain-controlled fatigue tests were conducted in both air and the PWR environment at 300°C 

using a triangular waveform to obtain the baseline data for the Type 304L SS material.155-157 

The results are shown on Fig. 126. The tests in air were used to establish the heat-to-heat 

variation of the material and surface finish effects, and the tests in the PWR environment were 

used to validate the estimates of fatigue lives calculated using the updated Fen expressions. 

The results indicated a small heat-to-heat variation; the fatigue lives for the heat of Type 304L 

SS used for these tests were 12% lower than those predicted by the best-fit mean data curve. 

The results also indicated that in air, fatigue lives of the ground specimens relative to those of 

polished specimens were decreased by a factor of 1.7. 

In addition, the effects of the PWR environment on the fatigue lives of Type 304L SS at 300°C 

and 0.01%/s strain rate were determined from a comparison of the fatigue ε-N behavior of the 

polished specimens in air versus those in the PWR environment. The experimental data yielded 

a Fen of 3.62 (i.e., the fatigue lives in the PWR environment were decreased by a factor of 3.62 

relative to those in air). The experimental data also indicated that surface finish effects were 

smaller in the PWR environment than those in air. For example, the reductions in the fatigue 

lives of the ground specimens in a PWR environment compared to those in an air environment 

were a factor of 2.90 instead of the factor of 3.62 obtained for the polished specimens.
164

Figure 126.

Fatigue strain-life data for Type 304L

SS in air and PWR environments at 

300°C (Refs. 155-157).

For the tests performed with a complex strain loading cycle, Fen values were determined using 

the three methods and the modified rate approach as described previously. The test conditions 

and results for these tests are given in Table. 21. The predicted fatigue lives were determined 

from the estimated fatigue lives in air (using Eq. 29) by multiplying the values by 0.88 to account 

for the effects of heat-to-heat variability, dividing by 1.7 to account for the effects of surface 

finish, and dividing by Fen to account for environmental effects. The overall Fen values were 

computed using the strain-integrated method (i.e., Eqs. 66 and 67 for the values without and 

with a strain threshold of 0.32%, respectively).

The measured fatigue lives and the predicted fatigue lives for the triangular and complex 

loading tests are plotted in Fig. 127. The results indicate that the predicted fatigue lives from 

the tests with a triangular loading waveform were in good agreement with the experimental 

values. The differences were within a factor of 2 (i.e., within data scatter). The predicted 

fatigue lives for the tests with the complex strain loading cycle were approximately a factor of 

2.5 lower than the experimental values; this difference was less than a factor of 2 when the 

strain threshold was included in the computation of Fen. This behavior is considered unique to 

this specific strain loading cycle. Fatigue tests with other strain loading cycle profiles should be 

conducted to provide a better understanding of possible effects of complex loading patterns on 

the fatigue lives of materials. However, although the predicted lives were generally lower, the 

estimated values were within the range of data scatter.

For the PWR safety injection transient, the predicted fatigue lives estimated using the simplified 

method were 25% lower than those obtained from the modified rate approach. The predicted 

lives estimated using the multi-linear method (using 3 ramps) were marginally (3%) lower. 

• The predicted fatigue lives were generally lower than the experimental values; however, the 

values were within the range of data scatter. 
165

Table 21. The conditions and results of fatigue tests on Type 304L austenitic SS at 300°C 

in air and PWR environments using a triangular or complex strain cycle.

Without Strain Threshold With Strain Threshold

Environment / 

Surface Finish

Strain Rate 

(%/s)

εa

(%)

Measured 

Nf

Estimateda

Nair

Estimated 

Fen

Predictedb

Nf

Estimated 

Fen

Predicted 

Nf

Triangular Waveform

Air, Polished 0.40 0.550 6,000 4,798 1.00 4,223 - -

Air, Polished 0.40 0.380 11,325 12,323 1.00 10,844 - -

Air, Polished 0.40 0.187 83,500 142,104 1.00 125.051 - -

Air, Ground 0.40 0.560 3,891 4,595 1.00 2,379 - -

Air, Ground 0.40 0.370 9,464 13,256 1.00 6,862 - -

Air, Ground 0.40 0.190 36,552 131,796 1.00 68,224 - -

Air, Ground 0.40 0.190 48,717 131,796 1.00 68,224 - -

PWR, Polished 0.01 0.540 1,002 5,016 4.97 889 - -

PWR, Polished 0.01 0.540 1,200 5,016 4.97 889 - -

PWR, Polished 0.01 0.280 9,000 30,209 4.97 5,353 - -

PWR, Ground 0.01 0.550 890 4,798 4.97 500 - -

PWR, Ground 0.01 0.550 1,000 4,798 4.97 500 - -

PWR, Ground 0.01 0.270 4,500 33,986 4.97 3,543 - -

Complex Strain Cycle

PWR, Polished variable 0.570 1,588 4,404 5.92 655 5.37 722

PWR, Polished variable 0.570 1,936 4,404 5.92 655 5.37 722

PWR, Polished variable 0.490 2,900 6,367 6.10 919 5.35 1,047

PWR, Polished variable 0.290 8,318 27,034 6.73 3,535 4.35 5,469

PWR, Polished variable 0.290 8,810 27,034 6.73 3,535 4.35 5,469

PWR, Ground variable 0.570 895 4,404 5.92 385 4.60 425

PWR, Ground variable 0.570 960 4,404 5.92 385 3.14 425

PWR, Ground variable 0.290 7,330 27,034 6.73 2,079 3.86 3,217 a Fatigue lives estimated using Eq. 29. b The predicted fatigue lives were obtained from the estimated lives in air by multiplying by a factor of 0.88 to account for heat-toheat variability, dividing by 1.7 to account for surface finish effects, and dividing by Fen to include environmental effects. The 

differences between the Fen values in 6th and 8th columns are due to the consideration of a threshold strain value of 0.32% as part 

of the calculation of the Fen values shown in the 8th column.

Figure 127. The experimental and estimated fatigue lives for Type 304L SS tested at 

300°C in air and a PWR environment using triangular and complex loading 

that simulated a PWR safety injection transient (Refs. 155-157).
166

6.3 U-Bend Tests in Inert and PWR Water Environments

Low-cycle, corrosion-fatigue tests were conducted on Type 304L SS tube U-bend specimens in 

an inert (pressurized nitrogen) environment and a simulated PWR primary water environment at 

240°C.97-99 The primary focus of the tests was to study the effects of flow rate on fatigue crack 

initiation. Initially straight tubing of nominal 33.4 mm outer diameter (OD) and 3.38 mm wall 

thickness was used for the tests. The tubing was manufactured by cold rolling followed by 

solution annealing at 1100°C and water quenching. The tubing was subsequently subjected to 

a pickling and passivation process. The tubing material was procured from Tubacex, Spain, 

meeting the compositional and mechanical property requirements of SA 312 Grade Type 304L 

low-carbon austenitic SS. A qualified, reproducible bending procedure was used by Babcock 

and Wilcox, Canada, to deform the tubing into a 180° U-bend using a cold die bend with an

internal mandrel. A total of ten U-bend test specimens were fabricated. A typical, as-received 

U-bend test specimen and the nomenclature adopted for the orientation around the 

circumference at the apex of the bend are shown in Fig. 128. The tensile yield strength, 

ultimate tensile strength, and total elongation of the material were, respectively, 245 MPa, 

607 MPa, and 76.5% at room temperature and 168 MPa, 476 MPa, and 41.5% at 240°C. 

Measurements made to characterize the as-received condition indicated that, as expected, the 

U-bend specimens exhibited a non-uniform wall thickness that was thinner at the extrados 

(0° circumferential position) and thicker at the intrados (180° position) in the apex region. The 

“neutral” bend positions (90° and 270°) retained the original wall thickness of the tubing. 

Furthermore, the stress-states at all locations along the outer surface of the bend were 

predominantly tensile in nature with the exception of the circumferential stress at the intrados, 

which was compressive throughout most of the evaluation depth. This stress state implied 

tensile residual stress for this location at the water-wetted, internal surface. The macroscopic 

external and internal surface condition of the bends was generally good, except for some 

shallow linear indications. Both the outer and internal surfaces exhibited mild pickling attack. 

For some tests, the outer surface was mechanically polished and the inside surface was 

electropolished. All U-bend specimens were pre-conditioned by lengthy exposure to simulated 

PWR primary water before testing. 

Low-cycle fatigue tests were carried out using fully-reversed cycling (R = -1) and a triangular 

loading waveform. Both load and axial strain gauge response at the 0, 90 and 180° positions 

were continuously monitored during the cycling. All fatigue tests were allowed to continue until 

failure, defined as a through-wall crack leading to a loss of internal pressure within the U-bend 

specimens. Strain control was used for the first 12 loading cycles to allow for shakedown, with 

the remainder of the test performed under displacement control. An axial strain gauge at the 

bend intrados was used as the leading strain gauge to establish the desired strain amplitudes of 

Figure 128. U-bend test specimen and nomenclature (Ref. 97).
167

either 0.6% or 0.4%. A series of baseline tests involving U-bends instrumented with numerous 

strain gauges were carried out in an inert environment at both room temperature and 240°C to 

establish both the basic fatigue behavior of the bend specimens and the appropriate load 

control sequence for subsequent testing in a simulated PWR primary water environment. 

The simulated PWR primary water environment consisted of high purity water with less than 

10 ppb DO, 1200 ppm boron as boric acid, and 2 ppm Li as LiOH. The combined chloride, 

fluoride, and sulfate impurities in water were less than 100 ppb. The tests were performed with 

either a low flow rate of 0.005 meters/second (10 liters/hour) or a high flow rate of 

2.2 meters/second (4400 liters/hour) for the 26.5-mm internal diameter (ID) tube. To facilitate 

proper evaluation of interim fatigue results, the following loading considerations were originally 

expected to be appropriate for the U-bend tests:

• The bend test was effectively strain controlled, with the axial strain at the outside surface 

of the bend intrados (180° position) acting as the control strain. 

• Despite the reduced wall thickness from fabrication at the bend extrados (0° position), 

axial strains at the outer surface of that location were anticipated to be considerably

smaller than at the intrados because of bend radius effects. 

• Under the push-pull of the bend legs, compressive/tensile, cyclic, axial strains were also 

created at the inside surface of the intrados, but their maximum values were expected to 

be about 35% lower than the control strain at the outer surface. 

• As a result of ovalization at the apex of the bend during cycling, the circumferential 

strains expected at the inside surface in the 90° and 270° locations were estimated to be 

approximately 75% of the axial control strain, and slightly higher than the circumferential 

strains at the outer surface. 

• The strains resulting from cyclic loading at the various locations around the bend apex 

were not expected to be entirely symmetrical because of factors such as “out-ofroundness” and wall thickness variations arising from the tube manufacturing and 

bending processes, as well as the bend residual stress. 

From these considerations, mechanically-dominated fatigue was expected to lead to 

circumferential cracking, starting at the outside surface of the intrados, whereas environmental 

effects were expected to manifest themselves primarily as axial cracking at the inside surface in 

the “neutral” bend positions (i.e., 90° and 270°) at the apex of the test specimens. The key 

conditions and results of the U-bend tests are summarized in Table 22. All tests were 

conducted at a strain rate of 0.01 %/s, except Tests 3a and 3b, which were performed at a 

strain rate of 0.0005 %/s. The dominant failures were through-wall cracks that led to a loss of 

internal pressure in the U-bend tube specimens. The results also showed that fatigue cracks on 

the outer surfaces were typically circumferential and on the inner surfaces were axial. An 

overview of the extent and location of the fatigue cracking in the U-bend tests at strain 

amplitude of 0.6 and 0.4% is presented in Figs. 129 and 130, respectively.

The predicted fatigue lives for the U-bend tests were obtained by dividing the estimated fatigue 

lives in air, Nair (determined from Eq. 29) by Fen to account for environmental effects. 

Furthermore, since the tests were conducted using constant strain rate and temperature, the 

modified rate approach was not considered and the Fen was determined using the simplified 

method. However, since the estimates of fatigue lives based on Eq. 29 represent small, 

polished test specimens, and the U-bend test results were obtained on larger U-bend tube 

specimens with a mechanically polished or pickled surface, the U-bend test results were 

adjusted for the effects of surface finish, size, and heat-to-heat variability. An adjustment for 

loading sequence was not included because all tests were conducted at constant strain 

amplitude. A value of 2.3 for the combined adjustment factor to account for the effects of 
168

surface finish, size, and heat-to-heat variability was determined by comparing the predicted 

fatigue lives with the results for the two tests in the inert environment (i.e., tests BLT2 and 

BLT3). The estimated fatigue lives were further adjusted by dividing by a factor of 2.3 to obtain 

the predicted fatigue lives for the various U-bend test datasets.

Table 22. Summary of the key conditions and results of the U-bend tests at 240°C.

Test

Strain 

amplitude

(%)

Displace

-ments

(mm)

Surface Condition Flow 

Rate Nf

Failure 

location & 

mechanism

Striation spacing 

mid fracture area

Crack 

depth 180° 

position

Crack 

depth 90° 

Outer Internal Env. Mech.(1) position

BLT2 0.60 +6.90 

-4.70 As pickled Stagnant N2

1705 180° OD 

mechanical - (2) 2.0 μm - (2) - (2)

2a 0.60 +6.50 

-4.85 As pickled Low 1520 180° OD mechanical 1 μm 5.0 μm >1000 μm N/A(3)

2b 0.60 +7.15 

-5.40 As pickled High 1238 at notch

180° OD 

mechanical 1 μm 2.5 μm 400 μm N/A(3)

BLT3 0.40 +4.90 

-4.92

Mech. 

polished

As 

pickled

Stagnant N2

4995 180° OD 

mechanical - (2) 3.0 μm - (2) - (2)

4a 0.40 +4.82 

-5.25 As pickled Low 3609 270° ID environ. 3 μm

1 μm 

(180°) 580 μm 1700 μm

4a’ 0.40 +4.91 

-5.07

Mech. 

polished

As 

pickled Low 3437 270° ID environ. 1 μm

N/A(3)

(180°) 500 μm 1050 μm

4b 0.40 +5.07 

-5.08

Mech. 

polished

As 

pickled High 3616 270° ID environ. 1 μm - (2) 1000 μm 750 μm

4d 0.40 +4.83 

-5.03

Mech. 

polished

electro 

polished High 3835 270° ID environ. 1 μm

N/A(3)

(180°) 680 μm 2600 μm

3a 0.40 +4.88 

-5.07

Mech. 

polished

As 

pickled Low 1939 270° ID environ. 2 μm - (2) 200 μm 2900 μm

3b 0.40 +4.67 

-4.71

Mech. 

polished

As 

pickled High 1517 270° ID environ. 2 μm - (2) 210 μm Through wall 

1 OD crack initiation.

2 Crack did not exist. 3 Crack existed but was not examined.

Figure 129. Overview of the extent and location of fatigue cracking in Ubend tests at strain amplitude of 0.6% (Ref. 97).
169

Figure 130. Overview of the extent and location of fatigue cracking in Ubend tests at strain amplitude of 0.4% (Ref. 97).

The experimental and predicted fatigue lives for the Type 304L SS U-bend specimens at 240°C 

in inert and simulated PWR primary water environments are plotted in Fig. 131. As mentioned 

before, the data in an inert environment (stagnant N2) were used to determine the adjustment 

factor to account for the effects of surface finish, size, and heat-to-heat variability on fatigue life. 

Consequently, the data in the inert environment (solid circles in Fig. 131) lie on the diagonal 

line, as expected. The results indicated that the predicted fatigue lives for axial cracks that 

initiated at the neutral bend positions (90° and 270°) in the PWR primary water environment 

showed very good agreement compared to the experimental fatigue lives. The predicted lives 

were within a factor of ±1.5 compared to the measured values. However, in the PWR 

environment, the predicted lives for the cracks at the intrados position (180°) were significantly 

lower than the experimental values. The lack of agreement for these cracks was most likely 

related to the concurrent dominant mechanical cracking from the OD at the same location. This 

is observed from the information presented in Fig. 130 for Tests 4a, 4a’, and 4d where several 

200 to 700-mm deep circumferential cracks initiated at the OD intrados position. 

The U-bend test results also indicated that, in contrast to the results for carbon steels, no 

beneficial effects of higher flow rates on fatigue lives were observed for Type 304L austenitic 

SS. The fatigue lives at high flow rates were lower than those at low flow rates for some tests 

and greater for other tests (diamonds and triangle symbols in Fig. 131). Furthermore, the 

results indicated little or no effects of electro-polished and pickled surface finishes on fatigue 

lives; the fatigue lives of U-bend specimens with pickled surfaces (Test 4b) or electro-polished 

surfaces were comparable.

• The predicted fatigue lives were within a factor of ±1.5 of the experimental values (i.e., within 

the range of data scatter). The results did not indicate any beneficial effects of higher flow 

rates on the fatigue lives of austenitic SSs. 
170

Figure 131.

The experimental and predicted 

fatigue lives for Type 304L SS 

U-bend specimens at 240°C in 

inert and PWR environments 

(Refs. 97-99). 

6.4 Simulation of Actual Plant Conditions

As discussed in Section 4.1.14, a modified rate approach was proposed for estimating fatigue 

lives of materials in LWR environments under varying temperature and strain rate conditions. 

The applicability of the modified rate approach was validated using fatigue ε-N data obtained 

under varying temperature and strain rate conditions. However, actual operating plant 

transients involve not only varying temperatures and strain rates, but also varying strain 

amplitudes. Therefore, to validate the applicability of the modified rate approach together with 

CUF evaluations that account for varying strain amplitudes, fatigue tests were conducted in a 

simulated PWR environment by combining loading cycle blocks of different strain amplitudes, 

which included changes in both temperature and strain rate. 

Tests were conducted on Type 316 austenitic SS hollow, cylindrical specimens with a 12 mm 

outside diameter, a 3 mm wall thickness and a 24 mm gauge length. The material was obtained 

from a Type 316 SS pipe with a 355.7 mm outside diameter and a 35.7 mm wall thickness. The 

material was heat treated for 30 minutes at 1055°C, followed by water quenching. The chemical 

composition and mechanical properties are given in Table 23. 

Table 23. Chemical composition and tensile strength of Type 316 SS material.

Material Chemical Composition (wt. %) Min. YS 

(MPa)

Min. UTS 

(MPa)

Min. 

C Si Mn Ni Cr Mo V Cu Ti Elong. (%)

316 SS 0.04 0.37 1.55 12.55 16.5 2.10 - - - 247 531 54

The tubular specimens were machined from the piping material such that the specimen gauge 

lengths were in the axial direction of the pipe. The outer and inner surfaces of the specimens 

were polished in the axial direction using emery papers up to 800 grit to remove machining 

scratches. All fatigue tests were conducted in a simulated PWR primary water environment 

under axial strain control using an extensometer attached to the outer surface of the specimens. 

The test environment consisted of 500 ppm boron added as boric acid, 2 ppm Li added as 

LiOH, less than 0.005 ppm DO, and dissolved hydrogen was maintained at 30 cc/kg of water. 

The fatigue loading consisted of two blocks of differing strain amplitude and temperature 

ranges, in which either the strain rate changed in response to the temperature or the 
171

temperature was changed in response to strain rate (in phase or out-of-phase). Examples of 

the loading cycles are shown in Fig. 132. The test matrix for the combined two-block cumulative 

fatigue damage test is given in Table 24. Fatigue life was defined as the number of cycles at 

which a fatigue crack penetrated through the wall thickness of the specimen, Nleak.

The measured fatigue lives and the predicted fatigue lives for the simulated actual plant 

conditions tests are plotted in Fig. 133. The predicted fatigue lives for these tests were obtained 

by dividing the estimated fatigue lives in air, Nair (determined from Eq. 29), by Fen to account for 

environmental effects. In addition, since the tests were conducted using linear changes in strain 

rate and temperature, the multi-linear method was used to determine the Fen. The predicted 

and experimental fatigue lives and the associated number of number of blocks and Fen values 

are listed in Table 25. The fatigue usage per block was determined from the ratio of cycles per 

block and the predicted fatigue life for the loading and environmental conditions for that block.

The results show very good agreement between the predicted and experimental fatigue lives for 

all tests; the difference is within a factor of ±2 (i.e., within the range of material variability and 

data scatter).

• The predicted fatigue lives for all block loading tests were within a factor of ±2.0 of the 

experimental values (i.e., within the range of material variability and data scatter).

Test No. 1

Test No. 7

Figure 132. Loading waveforms for Fatigue Test Nos. 1 and 7 (Ref. 154).
172

Table 24. Test matrix for the two blocks fatigue damage tests.

Test 

No.

Block 1 Block 2

εa

(%)

Pattern Temp. 

(°C)

Strain Rate 

(%/s)

Cycles 

/Block

εa

(%)

Pattern Temp. 

(°C)

Strain Rate 

(%/s)

Cycles 

/Block

1 0.6 In phase 100-325 0.002 275 0.3 In phase 100-325 0.001 379a

2 0.6 In phase 100-325 0.002 27 0.3 In phase 100-325 0.001 379

3 0.6 Out of phase 100-325 0.002 311 0.6 In phase 200-325 0.002 152

4 0.6 Out of phase 100-325 0.002 311 0.6 In phase 200-325 0.002 15

5 0.6 In phase 200-325 0.4-0.001 77 0.6 In phase 200-325 0.001-0.4 70

6 0.6 Out of phase 200-325 0.4-0.001 70 0.6 Out of phase 200-325 0.001-0.4 77

7 0.6 In phase 200-325 0.4-0.001 77 0.6 Out of phase 200-325 0.001-0.4 77 a The second block stopped after 129 cycles.

Figure 133.

The experimental and predicted 

fatigue lives of Type 316 SS tested in 

PWR primary water using two blocks 

of fatigue cycles of different strain 

amplitudes and varying temperature 

and strain rate (Ref. 154). 

Table 25. Results of the two blocks fatigue damage tests.

Test 

No. 

εa

(%)

Temp. 

(°C)

Strain Rate 

(%/s)

Cycles 

/Block

Nleak (cycles) Nair

(cycles) Fen

Usage 

/Block

Predicted 

Blocks

Nestd (cycles)

Partial Total Partial Total

1 0.6 100-325 0.002 275 1,108 1,995 3,899 3.039 0.214 3.302 908 1,795

0.3 100-325 0.001 379 887 24,341 3.327 0.052 887

2 0.6 100-325 0.002 27 216 3,100 3,899 3.039 0.021 13.729 378 5,574

0.3 100-325 0.001 379 2,884 24,341 3.327 0.052 5,196

3 0.6 100-325 0.002 311 699 1,003 3,899 3.039 0.242 2.291 757 1,061

0.6 200-325 0.002 152 304 3,899 4.980 0.194 304

4 0.6 100-325 0.002 311 1,915 2,005 3,899 3.039 0.242 3.823 1,201 1,246

0.6 200-325 0.002 15 90 3,899 4.980 0.019 45

5 0.6 200-325 0.4-0.001 77 1,001 1,857 3,899 4.779 0.094 6.695 539 984

0.6 200-325 0.001-0.4 70 856 3,899 3.063 0.055 445

6 0.6 200-325 0.4-0.001 70 777 1,624 3,899 3.063 0.055 6.695 490 984

0.6 200-325 0.001-0.4 77 847 3,899 4.779 0.094 494

7 0.6 200-325 0.4-0.001 77 539 1,046 3,899 4.779 0.094 5.298 431 816

0.6 200-325 0.001-0.4 77 507 3,899 4.779 0.094 385
173

7. SUMMARY

The comprehensive review of the available fatigue ε–N data for nuclear power plant piping and 

pressure vessel steels presented in the original version of NUREG/CR-6909 was reevaluated 

using a much larger database, and the results were updated to address feedback from 

interested stakeholders regarding the Fen methodology for incorporating environmental effects 

into ASME Code Section III fatigue CUF evaluations.

In this report, fatigue life is described as the number of cycles of a specified strain amplitude 

that a specimen can sustain before the formation of a 3-mm-deep crack (i.e., an “engineering 

crack”). This equates to a 25% load drop in test specimens, and is assumed to equate to crack 

initiation in an actual component. Using this definition, a calculated fatigue CUF less than unity 

provides reasonable assurance that a fatigue crack has not formed in a component, and 

indicates that the probability of forming a crack in the component is low.

In the original version of NUREG/CR-6909, the existing fatigue ε–N data for carbon and low–

alloy steels, wrought and cast austenitic SSs, and Ni-Cr-Fe alloys were evaluated to identify the 

various material, environmental, and loading parameters that influenced fatigue crack initiation, 

and to establish the effects of key parameters on the fatigue lives of these steels. The fatigue 

lives of these materials were decreased in LWR environments; the magnitude of the reduction 

depended on temperature, strain rate, DO level in the water, and, for carbon and low–alloy 

steels, the sulfur content of the steel. For all steels, environmental effects on fatigue lives were 

significant only when critical parameters (temperature, strain rate, DO level, and strain 

amplitude) met certain threshold values. Environmental effects were moderate, e.g., less than a 

factor of 2 decrease in lives, when any one of the threshold conditions was not satisfied. The 

threshold values of the critical parameters and the effects of other parameters (such as water 

conductivity, water flow rate, and material heat treatment) on the fatigue lives of the steels were 

also discussed. In this updated report, all of these evaluations were updated and reevaluated, 

and the results are summarized below.

Carbon and Low-Alloy Steels

In air, the fatigue lives of carbon and low–alloy steels depended on steel type, temperature, 

specimen orientation, and strain rate. The fatigue lives of carbon steels were a factor of 

approximately 1.5 lower than those of low–alloy steels. For both steels, fatigue lives decreased 

with an increase in temperature. Some heats of carbon and low–alloy steels exhibited effects of 

strain rate and specimen orientation. For these heats, fatigue lives decreased with decreasing 

strain rate. In addition, the data indicated significant heat–to–heat variation; the distribution and 

morphology of sulfides had a significant effect on the fatigue lives of these materials. The 

results also indicated that, in room-temperature air, the ASME Code Section III mean curve for 

low–alloy steels was in good agreement with the available experimental data, and the mean 

curve for carbon steels was somewhat conservative in the high-cycle regime (i.e., fatigue lives 

greater than 104 cycles. Revised fatigue design curves based on the ANL models were 

developed in the initial version of NUREG/CR-6909. Those curves extended up to 1011 cycles. 

In the present report, the extension of the fatigue design curves beyond 106 cycles was modified 

to be consistent with the current ASME Code Section III fatigue design air curve to better 

accommodate the field vibration data.

The fatigue lives of both carbon and low–alloy steels were decreased in LWR environments; the 

amount of reduction depended on temperature, strain rate, DO level in the water, and sulfur 

content of the steel. The results indicated that a minimum threshold strain was required for an 

environmentally-assisted decrease in the fatigue lives of these steels. In addition, 
174

environmental effects occurred primarily during the tensile–loading cycles and at strain levels 

greater than a threshold value. The fatigue lives were decreased significantly when all four 

conditions were satisfied simultaneously, viz., the strain amplitude, temperature, and DO in the 

water were above minimum levels, and the strain rate was below a threshold value. The sulfur 

content in the steel was also important; its effect on fatigue lives depended on the DO level in 

the water. 

Although the microstructures and cyclic–hardening behavior of carbon and low–alloy steels 

differed significantly, environmental degradation of the fatigue lives of these steels was very 

similar. The available fatigue ε–N data were reviewed to establish the critical parameters that 

influenced fatigue lives and updated definitions were developed for their threshold and limiting 

values within which environmental effects were significant. In the original version of 

NUREG/CR-6909, the Fen expressions for both steels predicted a moderate decrease in fatigue 

lives (i.e., by about a factor of 2) when any one of the threshold conditions was not satisfied, 

e.g., a low–DO BWR HWC or PWR environment, temperatures less than 150°C, or vibratory 

fatigue. In the present report, the Fen expressions for carbon and low-alloy steels were revised 

so that the value of Fen was 1 (i.e., no environmental effects) when any one of the threshold 

conditions was not satisfied. The impact of this revision on fatigue CUF values relative to the 

Fen expressions in the original version of NUREG/CR-6909 is that the updated Fen values are 

generally lower under certain environmental and loading conditions compared to the previous 

expressions. 

Austenitic Stainless Steels

In air, the fatigue lives of Types 304 and 316 SS were comparable; those of Type 316NG were 

superior to those of Types 304 and 316 SS at high strain amplitudes (i.e., the slope of the 

fatigue ε–N curve was steeper). The fatigue lives of austenitic SSs in air were independent of 

temperature in the range from room temperature to 427°C. Also, variations in strain rate in the 

range of 0.4–0.008%/s had no effect on the fatigue lives of SSs at temperatures up to 400°C. 

The fatigue ε–N behavior of cast SSs was similar to that of wrought austenitic SSs. The results 

indicated that the experimental data at strain amplitudes less than 0.5% or 975 MPa (141 ksi) 

were not consistent with the mean-data curve for SSs corresponding to the fatigue design 

curves in editions of Section III of the ASME Code prior to the 2009b Addenda; the ASME Code 

Section III mean air curve predicted significantly longer lives than those observed 

experimentally. The fatigue design air curve in editions of Section III of the ASME Code later 

than the 2009b Addenda was based on the ANL model and is consistent with the available 

fatigue ε–N data. 

The fatigue lives of cast and wrought austenitic SSs decreased in LWR environments compared 

to those in air. The decrease depended on the strain rate, the DO level in the water, and 

temperature. Similar to the behavior of carbon and low-alloy steels, a minimum threshold strain 

was required for environmental effects on fatigue lives of SSs to occur, and this strain was 

independent of material type (weld or base metal) and temperature in the range of 250–325°C. 

Furthermore, environmental effects were significant only during the tensile–loading cycles. 

Strain rates and temperatures had strong effects on fatigue lives in LWR environments. Fatigue 

lives decreased with decreasing strain rates below 0.4%/s; the effects saturated at 0.0004%/s. 

In the original version of NUREG/CR-6909, a threshold temperature of 150°C was defined 

below which environmental effects were insignificant; in the range of 150–325°C, the logarithm 

of fatigue lives decreased linearly with temperature. However, to better represent all of the 

more recently available fatigue ε–N data, the temperature dependence relationships in the Fen

expressions were modified and the temperature threshold decreased from 150 to 100°C. The 

dependency of fatigue lives on strain rate was also modified, and the threshold strain rate above 
175

which environmental effects were considered insignificant was increased from 0.4 to 10%/s. 

The impact of these revisions on fatigue CUF values relative to the Fen expressions in the 

original version of NUREG/CR-6909 was that Fen values using the updated expressions are 

lower under many environmental and loading conditions, but are marginally higher for some 

conditions. 

The effects of DO levels were different for different steels. In low–DO water (i.e., less than 

0.01 ppm DO), the fatigue lives for all wrought and cast austenitic SSs were decreased 

significantly; compositions or heat treatments of the steels had little or no effects on fatigue 

lives. However, in high–DO water, the environmental effects on fatigue lives were influenced by 

the composition and heat treatment of the steels. For example, for high–C Type 304 SSs, 

environmental effects were significant only for sensitized steels. For low–C Type 316NG SSs, 

some effects of environment were observed even for mill–annealed (nonsensitized) steels in 

high–DO water, although the effects were smaller than those observed in low–DO water. 

Limited fatigue ε–N data indicated that the fatigue lives of cast SSs were approximately the 

same in low– and high–DO water and were comparable to those observed for wrought SSs in 

low–DO water. As such, in the initial version of NUREG/CR-6909, environmental effects on the 

fatigue lives of wrought and cast austenitic SSs were considered to be identical in high-DO and 

low-DO environments. However, based on the more recently available fatigue ε–N data, the 

dependency of environmental effects on water DO content was included in this report; that 

dependency was based on the material composition and heat treatment. 

Ni-Cr-Fe Alloy Steels

The available fatigue ε–N data for Ni-Cr-Fe alloys indicated that, although the data for Alloys 

690 and 800 were very limited, the fatigue lives of these alloys were comparable to those of 

Alloy 600. In addition, the fatigue lives of the Ni-Cr-Fe alloy weld metals were comparable to 

those of the wrought Alloy 600 and 690 materials in the low–cycle regime (i.e., less than 

105 cycles), and were slightly superior in the high–cycle regime. The data for Ni-Cr-Fe alloys 

also indicated that the fatigue resistance of Inconel 718 was superior to that of Alloy 600, 690, 

and 800 materials. For Inconel 718, the slope of the fatigue ε–N curve was flatter and the 

fatigue limit (i.e., fatigue life at 106 cycles) was higher than those for austenitic SSs. 

The available laboratory fatigue data for Ni-Cr-Fe alloys in LWR environments were very limited. 

However, the available data indicated that the effects of key loading and environmental 

parameters on fatigue lives are similar to those for austenitic SSs. For example, the fatigue 

lives of these steels decreased logarithmically with decreasing strain rates. Also, the effects of 

environment were greater in low-DO PWR water compared to those in high-DO BWR water. 

However, environmental effects on the fatigue lives of Ni-Cr-Fe alloys were lower than those for 

austenitic SSs. Therefore, in this report, the temperature dependency of the Fen expression for 

Ni-Cr-Fe alloys was revised; the effects of temperature on fatigue lives of these materials were 

considered to be insignificant below 50°C and they saturated at temperatures above 325°C. 

The impact of this revision on fatigue evaluations is that updated Fen values are typically lower 

relative to those based on Fen expressions in the initial version of NUREG/CR-6909. 

Model Validation

The updated Fen methodology proposed in this revised report was validated by comparing 

evaluation of the results of several experimental data sets obtained from fatigue tests that 

simulated actual plant conditions with estimates of fatigue usage using the updated Fen

expressions. The data sets represented fatigue tests with changing strain rates and/or 

temperatures, complex loadings that simulated a PWR safety injection transient, spectrum 
176

loadings (i.e., random strain amplitudes), and pipe U-bend tests. In all cases, the results 

indicated that the predicted fatigue lives were in good agreement with the experimental values; 

the differences between the experimental and predicted fatigue lives were within a factor of 2, 

which is within data scatter. However, the predicted fatigue lives for the tests with the complex 

strain loading cycles were all lower than the experimental values by a factor of about 2. The 

reason for this one exception was not clear. This behavior may have been unique to the 

specific strain loading cycles used in the test. Fatigue tests with other strain loading cycle 

profiles are recommended to provide further understanding of possible effects of complex 

loading patterns on the fatigue lives of materials. Nonetheless, although the predicted lives 

were lower, the estimated values were within the range of data scatter.

Fatigue Design Curve Adjustment Factors

This updated report also presented a critical review of the ASME Code Section III fatigue 

adjustment factors of 2 on stress and 20 on life, and assessed the possible conservatisms in the 

choice of these adjustment factors. These factors covered the effects of variables that influence 

fatigue lives, but were not investigated in the tests that provided the data for the ASME Code 

Section III air design curves. These variables included material variability and data scatter, size, 

surface finish, and loading sequence. Although the factors of 2 and 20 used by ASME were 

intended to be conservative, they are not considered to be safety margins because they were 

intended to account for variables that are known to affect fatigue lives. Data available in the 

literature were reviewed to evaluate the factors on cycles and stress that are needed to account 

for the differences and uncertainties caused by the four parameters that were not considered in 

the fatigue test data. Monte Carlo simulations were performed to determine the factor on cycles 

needed to obtain fatigue design air curves that provide conservative estimates of the number of 

cycles to initiate a fatigue crack in reactor components. 

The results presented in the initial version of NUREG/CR-6909 indicated that, for carbon and 

low–alloy steels and austenitic SSs, the current ASME Code Section III requirements for a 

factor of 20 on cycles to account for the effects of material variability and data scatter, as well as 

size, surface finish, and loading history, were conservative by at least a factor of 1.7. Thus, to 

reduce this conservatism, fatigue design curves were developed from the ANL model by first 

correcting for mean stress effects, and then reducing the mean–stress adjusted curve by a 

factor of 2 on stress and 12 on cycles, whichever was more conservative. In this updated 

report, the range of the subfactors for material variability and data scatter, size, surface finish, 

and loading sequence were examined and modified, and Monte Carlo simulations were 

performed to determine the factor on cycles needed to obtain fatigue design air curves with 95% 

confidence bounds. The results indicated that for these materials, a factor of 2 on stress and 10 

on cycles were adequate to develop the fatigue design curves from the best-fit mean air curves. 

However, until these results are further validated with applicable fatigue data ε–N data, the 

fatigue design curves presented in this report were based on factors of 2 on stress and 12 on 

life.

A detailed procedure for incorporating environmental effects into ASME Code Section III fatigue 

evaluations is presented in Appendix A. The methodology is identical to that presented in the 

initial version of NUREG/CR-6909, except that the Fen expressions were updated based on the 

analyses presented in this report. In addition, the updated methodology described in this report 

applies to any component exposed to the LWR environment that requires an ASME CUF 

calculation as part of its design, or if required by the safety basis for the component, or if 

required by the plant current licensing basis, unless otherwise justified. Appendix C of this 

report presents a sample application of the Fen methodology.
177

8. REFERENCES

1. ASTM Designation E 1823-09a, “Standard Terminology Relating to Fatigue and Fracture

Testing,” American Society for Testing and Materials, Philadelphia, PA, March 2009.

2. ASTM Designation E 606-04, “Standard Practice for Strain-Controlled Fatigue Testing,”

American Society for Testing and Materials, Philadelphia, PA, July 2005.

3. ASTM Designation E 468-90, “Standard Practice for Presentation of Constant Amplitude 

Fatigue Test Results for Metallic Materials,” Philadelphia, PA, October 2004.

4. ASTM Designation E 739-91, “Standard Practice for Statistical Analysis of Linear or 

Linearized Stress-Life (S-N) and Strain-Life (ε-N) Fatigue Data,” American Society for 

Testing and Materials, Philadelphia, PA, May 2006.

5. Rice, R. C., “Fatigue Data Analysis,” Metals Handbook, Vol. 8, American Society for Metal, 

Materials Park, OH, pp. 695-720, 1985. 

6. ASTM Designation E 1823-09a, “Standard Terminology Related to Fatigue and Fracture 

Testing,” American Society for Testing and Materials, Philadelphia, PA, March 2009. 

7. Langer, B. F., “Design of Pressure Vessels for Low–Cycle Fatigue,” ASME J. Basic Eng. 

84, 389–402, September 1962.

8. “Criteria of the ASME Boiler and Pressure Vessel Code for Design by Analysis in Sections 

III and VIII, Division 2,” The American Society of Mechanical Engineers, New York, 1969.

9. Cooper, W. E., “The Initial Scope and Intent of the Section III Fatigue Design Procedure,” 

Welding Research Council, Inc., Technical Information from Workshop on Cyclic Life and 

Environmental Effects in Nuclear Applications, Clearwater, Florida, Jan. 22-21, 1992.

10. Chopra, O. K., and W. J. Shack, “Effects of LWR Coolant Environments on Fatigue Design 

Curves of Carbon and Low–Alloy Steels,” NUREG/CR–6583, ANL–97/18, March 1998.

11. Gavenda, D. J., P. R. Luebbers, and O. K. Chopra, “Crack Initiation and Crack Growth 

Behavior of Carbon and Low–Alloy Steels,” Fatigue and Fracture 1, Vol. 350, S. Rahman, 

K. K. Yoon, S. Bhandari, R. Warke, and J. M. Bloom, eds., American Society of 

Mechanical Engineers, New York, pp. 243–255, 1997.

12. Chopra, O. K., and W. J. Shack, “Environmental Effects on Fatigue Crack Initiation in 

Piping and Pressure Vessel Steels,” NUREG/CR–6717, ANL–00/27, May 2001.

13. Chopra, O. K., “Mechanisms and Estimation of Fatigue Crack Initiation in Austenitic 

Stainless Steels in LWR Environments,” NUREG/CR–6787, ANL–01/25, Aug. 2002.

14. Hale, D. A., S. A. Wilson, E. Kiss, and A. J. Giannuzzi, “Low–Cycle Fatigue Evaluation of 

Primary Piping Materials in a BWR Environment,” GEAP–20244, U.S. Nuclear Regulatory 

Commission, Sept. 1977.

15. Hale, D. A., S. A. Wilson, J. N. Kass, and E. Kiss, “Low Cycle Fatigue Behavior of 

Commercial Piping Materials in a BWR Environment,” J. Eng. Mater. Technol. 103, 15–25, 

1981.
178

16. Ranganath, S., J. N. Kass, and J. D. Heald, “Fatigue Behavior of Carbon Steel 

Components in High–Temperature Water Environments,” BWR Environmental Cracking 

Margins for Carbon Steel Piping, EPRI NP–2406, Appendix 3, Electric Power Research 

Institute, Palo Alto, CA, May 1982.

17. Ranganath, S., J. N. Kass, and J. D. Heald, “Fatigue Behavior of Carbon Steel 

Components in High–Temperature Water Environments,” Low–Cycle Fatigue and Life 

Prediction, ASTM STP 770, C. Amzallag, B. N. Leis, and P. Rabbe, eds., American 

Society for Testing and Materials, Philadelphia, pp. 436–459, 1982.

18. Nagata, N., S. Sato, and Y. Katada, “Low–Cycle Fatigue Behavior of Pressure Vessel 

Steels in High–Temperature Pressurized Water,” ISIJ Intl. 31 (1), 106–114, 1991.

19. Higuchi, M., and K. Iida, “Fatigue Strength Correction Factors for Carbon and Low–Alloy 

Steels in Oxygen–Containing High–Temperature Water,” Nucl. Eng. Des. 129, 293–306, 

1991.

20. Katada, Y., N. Nagata, and S. Sato, “Effect of Dissolved Oxygen Concentration on Fatigue 

Crack Growth Behavior of A533 B Steel in High Temperature Water,” ISIJ Intl. 33 (8), 

877–883, 1993.

21. Kanasaki, H., M. Hayashi, K. Iida, and Y. Asada, “Effects of Temperature Change on 

Fatigue Life of Carbon Steel in High Temperature Water,” Fatigue and Crack Growth: 

Environmental Effects, Modeling Studies, and Design Considerations, PVP Vol. 306, S. 

Yukawa, ed., American Society of Mechanical Engineers, New York, pp. 117–122, 1995.

22. Nakao, G., H. Kanasaki, M. Higuchi, K. Iida, and Y. Asada, “Effects of Temperature and 

Dissolved Oxygen Content on Fatigue Life of Carbon and Low–Alloy Steels in LWR Water 

Environment,” Fatigue and Crack Growth: Environmental Effects, Modeling Studies, and 

Design Considerations, PVP Vol. 306, S. Yukawa, ed., American Society of Mechanical 

Engineers, New York, pp. 123–128, 1995.

23. Higuchi, M., K. Iida, and Y. Asada, “Effects of Strain Rate Change on Fatigue Life of 

Carbon Steel in High–Temperature Water,” Fatigue and Crack Growth: Environmental 

Effects, Modeling Studies, and Design Considerations, PVP Vol. 306, S. Yukawa, ed., 

American Society of Mechanical Engineers, New York, pp. 111–116, 1995; also Proc. of 

Symp. on Effects of the Environment on the Initiation of Crack Growth, ASTM STP 1298, 

American Society for Testing and Materials, Philadelphia, 1997.

24. Higuchi, M., K. Iida, and K. Sakaguchi, “Effects of Strain Rate Fluctuation and Strain 

Holding on Fatigue Life Reduction for LWR Structural Steels in Simulated PWR Water,” 

Pressure Vessel and Piping Codes and Standards, PVP Vol. 419, M. D. Rana, ed., 

American Society of Mechanical Engineers, New York, pp. 143–152, 2001.

25. Hirano, A., M. Yamamoto, K. Sakaguchi, T. Shoji, and K. Iida, “Effects of Water Flow Rate 

on Fatigue Life of Ferritic and Austenitic Steels in Simulated LWR Environment,” Pressure 

Vessel and Piping Codes and Standards – 2002, PVP Vol. 439, M. D. Rana, ed., 

American Society of Mechanical Engineers, New York, pp. 143–150, 2002.
179

26. Hirano, A., M. Yamamoto, K. Sakaguchi, and T. Shoji, “Effects of Water Flow Rate on 

Fatigue Life of Carbon and Stainless Steels in Simulated LWR Environment,” Pressure 

Vessel and Piping Codes and Standards – 2004, PVP Vol. 480, American Society of 

Mechanical Engineers, New York, pp. 109–119, 2004. 

27. Fujiwara, M., T. Endo, and H. Kanasaki, “Strain Rate Effects on the Low–Cycle Fatigue 

Strength of 304 Stainless Steel in High–Temperature Water Environment, Fatigue Life: 

Analysis and Prediction,” Proc. Intl. Conf. and Exposition on Fatigue, Corrosion Cracking, 

Fracture Mechanics, and Failure Analysis, ASM, Metals Park, OH, pp. 309–313, 1986.

28. Mimaki, H., H. Kanasaki, I. Suzuki, M. Koyama, M. Akiyama, T. Okubo, and Y. Mishima, 

“Material Aging Research Program for PWR Plants,” Aging Management Through 

Maintenance Management, PVP Vol. 332, I. T. Kisisel, ed., American Society of 

Mechanical Engineers, New York, pp. 97–105, 1996.

29. Kanasaki, H., R. Umehara, H. Mizuta, and T. Suyama, “Fatigue Lives of Stainless Steels 

in PWR Primary Water,” Trans. 14th Intl. Conf. on Structural Mechanics in Reactor 

Technology (SMiRT 14), Lyon, France, pp. 473–483, 1997.

30. Kanasaki, H., R. Umehara, H. Mizuta, and T. Suyama, “Effects of Strain Rate and 

Temperature Change on the Fatigue Life of Stainless Steel in PWR Primary Water,” 

Trans. 14th Intl. Conf. on Structural Mechanics in Reactor Technology (SMiRT 14), Lyon, 

France, pp. 485–493, 1997.

31. Higuchi, M., and K. Iida, “Reduction in Low–Cycle Fatigue Life of Austenitic Stainless 

Steels in High–Temperature Water,” Pressure Vessel and Piping Codes and Standards, 

PVP Vol. 353, D. P. Jones, B. R. Newton, W. J. O'Donnell, R. Vecchio, G. A. Antaki, 

D. Bhavani, N. G. Cofie, and G. L. Hollinger, eds., American Society of Mechanical 

Engineers, New York, pp. 79–86, 1997.

32. Hayashi, M., “Thermal Fatigue Strength of Type 304 Stainless Steel in Simulated BWR 

Environment,” Nucl. Eng. Des. 184, 135–144, 1998. 

33. Hayashi, M., K. Enomoto, T. Saito, and T. Miyagawa, “Development of Thermal Fatigue 

Testing with BWR Water Environment and Thermal Fatigue Strength of Austenitic 

Stainless Steels,” Nucl. Eng. Des. 184, 113–122, 1998. 

34. Tsutsumi, K., H. Kanasaki, T. Umakoshi, T. Nakamura, S. Urata, H. Mizuta, and 

S. Nomoto, “Fatigue Life Reduction in PWR Water Environment for Stainless Steels,” 

Assessment Methodologies for Preventing Failure: Service Experience and Environmental 

Considerations, PVP Vol. 410-2, R. Mohan, ed., American Society of Mechanical 

Engineers, New York, pp. 23–34, 2000.

35. Tsutsumi, K., T. Dodo, H. Kanasaki, S. Nomoto, Y. Minami, and T. Nakamura, “Fatigue 

Behavior of Stainless Steel under Conditions of Changing Strain Rate in PWR Primary 

Water,” Pressure Vessel and Piping Codes and Standards, PVP Vol. 419, M. D. Rana, 

ed., American Society of Mechanical Engineers, New York, pp. 135–141, 2001. 
180

36. Tsutsumi, K., M. Higuchi, K. Iida, and Y. Yamamoto, “The Modified Rate Approach to 

Evaluate Fatigue Life under Synchronously Changing Temperature and Strain Rate in 

Elevated Temperature Water,” Pressure Vessel and Piping Codes and Standards – 2002, 

PVP Vol. 439, M. D. Rana, ed., American Society of Mechanical Engineers, New York, pp. 

99–107, 2002.

37. Higuchi, M., T. Hirano, and K. Sakaguchi, “Evaluation of Fatigue Damage on Operating 

Plant Components in LWR Water,” Pressure Vessel and Piping Codes and Standards –

2004, PVP Vol. 480, American Society of Mechanical Engineers, New York, pp. 129–138, 

2004.

38. Nomura, Y., M. Higuchi, Y. Asada, and K. Sakaguchi, “The Modified Rate Approach 

Method to Evaluate Fatigue Life under Synchronously Changing Temperature and Strain 

Rate in Elevated Temperature Water in Austenitic Stainless Steels,” Pressure Vessel and 

Piping Codes and Standards – 2004, PVP Vol. 480, American Society of Mechanical 

Engineers, New York, pp. 99–108, 2004.

39. Higuchi, M., K. Sakaguchi, A. Hirano, and Y. Nomura, “Revised and New Proposal of 

Environmental Fatigue Life Correction Factor (Fen) for Carbon and Low–Alloy Steels and 

Nickel Alloys in LWR Water Environments,” Proc. of the 2006 ASME Pressure Vessels 

and Piping Conf., July 23–27, 2006, Vancouver, BC, Canada, paper # PVP2006–ICPVT–

93194.

40. Chopra, O. K., and W. J. Shack, “Evaluation of Effects of LWR Coolant Environments on 

Fatigue Life of Carbon and Low–Alloy Steels,” Effects of the Environment on the Initiation 

of Crack Growth, ASTM STP 1298, W. A. Van Der Sluys, R. S. Piascik, and 

R. Zawierucha, eds., American Society for Testing and Materials, Philadelphia, pp. 247–

266, 1997.

41. Chopra, O. K., and W. J. Shack, “Low–Cycle Fatigue of Piping and Pressure Vessel 

Steels in LWR Environments,” Nucl. Eng. Des. 184, 49–76, 1998. 

42. Chopra, O. K., and D. J. Gavenda, “Effects of LWR Coolant Environments on Fatigue 

Lives of Austenitic Stainless Steels,” J. Pressure Vessel Technol. 120, 116–121, 1998.

43. Chopra, O. K., and J. L. Smith, “Estimation of Fatigue Strain–Life Curves for Austenitic 

Stainless Steels in Light Water Reactor Environments,” Fatigue, Environmental Factors, 

and New Materials, PVP Vol. 374, H. S. Mehta, R. W. Swindeman, J. A. Todd, S. Yukawa, 

M. Zako, W. H. Bamford, M. Higuchi, E. Jones, H. Nickel, and S. Rahman, eds., American 

Society of Mechanical Engineers, New York, pp. 249–259, 1998.

44. Smith, J. L., and O. K. Chopra, “Crack Initiation in Smooth Fatigue Specimens of 

Austenitic Stainless Steel in Light Water Reactor Environments,” in Operations, 

Applications, and Components – 1999, PVP Vol. 395, I. T. Kisisel, ed., American Society 

of Mechanical Engineers, New York, pp. 235–242, 1999.

45. Chopra, O. K., “Effects of LWR Coolant Environments on Fatigue Design Curves of 

Austenitic Stainless Steels,” NUREG/CR–5704, ANL–98/31, 1999.

46. Chopra, O. K., and W. J. Shack, “Review of the Margins for ASME Code Design Curves –

Effects of Surface Roughness and Material Variability,” NUREG/CR–6815, ANL–02/39, 

Sept. 2003.
181

47. Chopra, O. K., B. Alexandreanu, and W. J. Shack, “Effect of Material Heat Treatment on 

Fatigue Crack Initiation in Austenitic Stainless Steels in LWR Environments,” NUREG/CR–

6878, ANL–03/35, July 2005. 

48. Terrell, J. B., “Fatigue Life Characterization of Smooth and Notched Piping Steel 

Specimens in 288°C Air Environments,” NUREG/CR–5013, EM–2232 Materials 

Engineering Associates, Inc., Lanham, MD, May 1988.

49. Terrell, J. B., “Fatigue Strength of Smooth and Notched Specimens of ASME SA 106–B 

Steel in PWR Environments,” NUREG/CR–5136, MEA–2289, Materials Engineering 

Associates, Inc., Lanham, MD, Sept. 1988.

50. Terrell, J. B., “Effect of Cyclic Frequency on the Fatigue Life of ASME SA–106–B Piping 

Steel in PWR Environments,” J. Mater. Eng. 10, 193–203, 1988.

51. O’Donnell, W. James and W. John O’Donnell, “Temperature Dependence of Reactor 

Water Environmental Fatigue Effects on Carbon, Low-Alloy and Austenitic Stainless 

Steels,” Proc. of the 2008 ASME Pressure Vessels and Piping Division Conf., July 27–31, 

2008, Chicago, IL, paper # PVP2008–61917.

52. Takahashi, Y. and T. Nakamura, “Statistical Analyses of In-Air and In-Water Fatigue Test 

Data of Austenitic Stainless Steels and Ferritic Steels,” Pressure Vessel and Piping Codes 

and Standards – 2003, PVP Vol. 453, American Society of Mechanical Engineers, 

New York, pp. 113–122, 2003, paper # PVP2003-1775. 

53. Nomura, Y., S. Asada, T. Nakamura, and M. Tanaka, “Effects of Continuous Strain Rate 

Changing on Environmental Fatigue for Stainless Steels in PWR Environment,” Proc. of 

the ASME 2010 Pressure Vessels and Piping Division/K-PVP Conf., July 18–22, 2010, 

Bellevue, Washington, DC, paper # PVP2010–25194.

54. Le Duff, J. A., A. Lefrancois, J. P. Vernot, and D. Bossu, “Effect of Loading Signal Shape 

and of Surface Finish on the Low Cycle Fatigue Behavior of 304L Stainless Steel in PWR 

Environment,” Proc. of the ASME 2010 Pressure Vessels and Piping Division/K-PVP 

Conf., July 18–22, 2010, Bellevue, Washington, DC, paper # PVP2010–26027.

55. Lenz, E., N. Wieling, and H. Muenster, “Influence of Variation of Flow Rates and 

Temperature on the Cyclic Crack Growth Rate under BWR Conditions,” Environmental 

Degradation of Materials in Nuclear Power Systems – Water Reactors, The Metallurgical 

Society, Warrendale, PA, 1988.

56. Garud, Y. S., S. R. Paterson, R, B, Dooley, R. S. Pathania, J. Hickling, and A. Bursik, 

“Corrosion Fatigue of Water Touched Pressure Retaining Components in Power Plants,” 

EPRI TR–106696, Final Report, Electric Power Research Institute, Palo Alto, Nov. 1997.

57. Amzallag, C., P. Rabbe, G. Gallet, and H.–P. Lieurade, “Influence des Conditions de 

Sollicitation Sur le Comportement en Fatigue Oligocyclique D'aciers Inoxydables 

Austénitiques,” Memoires Scientifiques Revue Metallurgie Mars, pp. 161–173, 1978. 

58. Solomon, H. D., C. Amzallag, A. J. Vallee, and R. E. De Lair, “Influence of Mean Stress on 

the Fatigue Behavior of 304L SS in Air and PWR Water,” Proc. of the 2005 ASME 

Pressure Vessels and Piping Conf., July 17–21, 2005, Denver, CO, paper # PVP2005–

71064.
182

59. Solomon, H. D., C. Amzallag, R. E. De Lair, and A. J. Vallee, “Comparison of the Fatigue 

Life of Type 304L SS as Measured in Load and Strain Controlled Tests,” Proc. of the 12th

Intl. Conf. on Environmental Degradation of Materials in Nuclear Power Plants – Water 

Reactors, T. R. Allen, P. J. King, and L. Nelson, eds., The Minerals, Metals and Materials 

Society, 2004.

60. Solomon, H. D., C. Amzallag, R. E. De Lair, and A. J. Vallee, “Strain Controlled Fatigue of 

Type 304L SS in Air and PWR Water,” Proc. Third Intl. Conf. on Fatigue of Reactor 

Components, Seville, Spain, Oct. 3–6, 2004.

61. Jaske, C. E., and W. J. O’Donnell, “Fatigue Design Criteria for Pressure Vessel Alloys,” 

Trans. ASME J. Pressure Vessel Technol. 99, 584–592, 1977.

62. Conway, J. B., R. H. Stentz, and J. T. Berling, “Fatigue, Tensile, and Relaxation Behavior 

of Stainless Steels,” TID–26135, U.S. Atomic Energy Commission, Washington, DC, 1975.

63. Keller, D. L., “Progress on LMFBR Cladding, Structural, and Component Materials Studies 

During July, 1971 through June, 1972, Final Report,” Task 32, Battelle–Columbus 

Laboratories, BMI–1928, 1977. 

64. Smith, R. W., M. H. Hirschberg, and S. S. Manson, “Fatigue Behavior of Materials Under 

Strain Cycling in Low and Intermediate Life Range,” NASA TN D-1574, Lewis Research 

Center, April 1963.

65. Krempl, E., “Low Cycle Fatigue Crack Initiation in the Presence of Stress/Strain 

Concentration,” in Reactor Primary Coolant System Rupture Study, Quarterly Progress 

Report No. 3, GEAP-5082, General Electric, San Jose, CA, pp. 6-6 to 6-23, Jan. 1966.

66. Jacko, R. J., “Fatigue Performance of Ni–Cr–Fe Alloy 600 under Typical PWR Steam 

Generator Conditions,” EPRI NP–2957, Electric Power Research Institute, Palo Alto, CA, 

March 1983.

67. Dinerman, A. E., “Cyclic Strain Fatigue of Inconel at 75 to 600°F,” KAPL–2084, Knolls 

Atomic Power Laboratory, Schenectady, NY, August 1960.

68. Mowbray, D. F., G. J. Sokol, and R. E. Savidge, “Fatigue Characteristics of Ni–Cr–Fe 

Alloys with Emphasis on Pressure–Vessel Cladding,” KAPL–3108, Knolls Atomic Power 

Laboratory, Schenectady, NY, July 1965.

69. Jaske, C. E., H. Mindlin, and J. S. Perrin, “Low-Cycle Fatigue of Incoloy Alloy 800,” 

Topical Report BMI-1921, Battelle’s Columbus Laboratories, Feb. 1972.

70. McGowan, E. J., and J. W. Faber, “Effects of Electric Discharge and Electrochemical 

Machining on the Fatigue Strength of Selected Structural Materials,” WAPD-TM-787, 

Bettis Atomic Power Laboratory, Jan. 1969.

71. Conway, J. B., “Short Term tensile and Low-Cycle Fatigue Studies of Incoloy 800,” GEMP732, General Electric Company, Dec. 1969.

72. Miller, J., “Low Cycle Fatigue Under Biaxial Strain Controlled Conditions,” J. of Materials,

Vol. 7, No. 3, 307-314, Sept. 1972.
183

73. Nachtigall, A. J., “Strain Cycling Fatigue Behavior of Ten Structural Metals Tested in 

Liquid Helium (4K), in Liquid Nitrogen (78K), and in Ambient Air (300K),” 

NASA TN D-7532, Lewis Research Center, Feb. 1974.

74. Brinkman, C. R., and G. E. Korth, “Strain Fatigue and Tensile Behavior of Inconel 718 

from Room Temperature to 650°C,”J. of Testing and Evaluation, Vol. 2, No. 4, 249-259, 

July 1974.

75. Van Der Sluys, W. A., B. A. Young, and D. Doyle, “Corrosion Fatigue Properties on Alloy 

690 and Some Nickel–Based Weld Metals,” Assessment Methodologies for Preventing 

Failure: Service Experience and Environmental Considerations, PVP Vol. 410-2, R. 

Mohan, ed., American Society of Mechanical Engineers, New York, pp. 85–91, 2000.

76. Faidy, C., T. Le Courtois, E. de Fraguier, J–A Leduff, A. Lefrancois, and J. Dechelotte, 

“Thermal Fatigue in French RHR System,” Int. Conf. on Fatigue of Reactor Components, 

Napa, CA, July 31–August 2, 2000. 

77. Kussmaul, K., R. Rintamaa, J. Jansky, M. Kemppainen, and K. Törrönen, “On the 

Mechanism of Environmental Cracking Introduced by Cyclic Thermal Loading,” in IAEA 

Specialists Meeting, Corrosion and Stress Corrosion of Steel Pressure Boundary 

Components and Steam Turbines, VTT Symp. 43, Espoo, Finland, pp. 195–243, 1983. 

78. Hickling, J., “Strain Induced Corrosion Cracking of Low-Alloy Reactor Pressure Vessel 

Steels under BWR Conditions,” Proc. 10th Intl. Symp. on Environmental Degradation of 

Materials in Nuclear Power Systems – Water Reactors, F. P. Ford, S. M. Bruemmer, and 

G. S. Was, eds., The Minerals, Metals, and Materials Society, Warrendale, PA, CD-ROM, 

paper 0156, 2001. 

79. Hickling, J., “Research and Service Experience with Environmentally Assisted Cracking of 

Low–Alloy Steel,” Power Plant Chem., 7 (1), 4–15, 2005.

80. Iida, K., “A Review of Fatigue Failures in LWR Plants in Japan,” Nucl. Eng. Des. 138, 297–

312, 1992. 

81. NRC IE Bulletin No. 79–13, “Cracking in Feedwater System Piping,” U.S. Nuclear 

Regulatory Commission, Washington, DC, June 25, 1979.

82. NRC Information Notice 93–20, “Thermal Fatigue Cracking of Feedwater Piping to Steam 

Generators,” U.S. Nuclear Regulatory Commission, Washington, DC, March 24, 1993.

83. Kussmaul, K., D. Blind, and J. Jansky, “Formation and Growth of Cracking in Feed Water 

Pipes and RPV Nozzles,” Nucl. Eng. Des. 81, 105–119, 1984.

84. Gordon, B. M., D. E. Delwiche, and G. M. Gordon, “Service Experience of BWR Pressure 

Vessels,” Performance and Evaluation of Light Water Reactor Pressure Vessels, PVP 

Vol.–119, American Society of Mechanical Engineers, New York, pp. 9–17, 1987. 

85. Lenz, E., B. Stellwag, and N. Wieling, “The Influence of Strain–Induced Corrosion 

Cracking on the Crack Initiation in Low–Alloy Steels in HT–Water – A Relation Between 

Monotonic and Cyclic Crack Initiation Behavior,” in IAEA Specialists Meeting Corrosion 

and Stress Corrosion of Steel Pressure Boundary Components and Steam Turbines, VTT 

Symp. 43, Espoo, Finland, pp. 243–267, 1983. 
184

86. Hickling, J., and D. Blind, “Strain–Induced Corrosion Cracking of Low–Alloy Steels in LWR 

Systems – Case Histories and Identification of Conditions Leading to Susceptibility,” Nucl. 

Eng. Des. 91, 305–330, 1986. 

87. Hirschberg, P., A. F. Deardorff, and J. Carey, “Operating Experience Regarding Thermal 

Fatigue of Unisolable Piping Connected to PWR Reactor Coolant Systems,” Int. Conf. on 

Fatigue of Reactor Components, Napa, CA, July 31–August 2, 2000. 

88. Shah, V. N., M. B. Sattison, C. L. Atwood, A. G. Ware, G. M. Grant, and R. S. Hartley, 

“Assessment of Pressurized Water Reactor Primary System Leaks,” NUREG/CR–6582, 

INEEL/EXT–97–01068, Dec. 1998. 

89. NRC Information Notice 88–01, “Safety Injection Pipe Failure,” U.S. Nuclear Regulatory 

Commission, Washington, DC (Jan. 27, 1988).

90. NRC Bulletin No. 88–08, “Thermal Stresses in Piping Connected to Reactor Coolant 

Systems,” U.S. Nuclear Regulatory Commission, Washington, DC, June 22; Suppl. 1, 

June 24; Suppl. 2, Aug. 4, 1988; Suppl. 3, April 1989.

91. Sakai, T., “Leakage from CVCS Pipe of Regenerative Heat Exchanger Induced by High–

Cycle Thermal Fatigue at Tsuruga Nuclear Power Station Unit 2,” Int. Conf. on Fatigue of 

Reactor Components, Napa, CA, July 31–August 2, 2000. 

92. Hoshino, T., T. Ueno, T. Aoki, and Y. Kutomi, “Leakage from CVCS Pipe of Regenerative 

Heat Exchanger Induced by High–Cycle Thermal Fatigue at Tsuruga Nuclear Power 

Station Unit 2,” Proc. 8th Intl. Conf. on Nuclear Engineering, 1.01 Operational 

Experience/Root Cause Failure Analysis, Paper 8615, American Society of Mechanical 

Engineers, New York, 2000.

93. NRC Bulletin No. 88–11, “Pressurizer Surge Line Thermal Stratification,” U.S. Nuclear 

Regulatory Commission, Washington, DC, Dec. 20, 1988. 

94. Daret, J., J. M. Boursier, and J. M. Olive, “Cracking of Stainless Steel Channel Heads in a 

Primary Water Experimental Loop,” in Proc. Tenth Intl. Symp. on Environmental 

Degradation of Materials in Nuclear Power Systems – Water Reactors, The Metallurgical 

Society, Warrendale, PA, Paper #0089, Lake Tahoe, NV, Aug. 5-9, 2001.

95. Stephan, J.–M., and J. C. Masson, “Auxiliary Feedwater Line Stratification and Coufast 

Simulation,” Int. Conf. on Fatigue of Reactor Components, Napa, CA, July 31–August 2, 

2000. 

96. Lenz, E., A. Liebert, and N. Wieling, “Thermal Stratification Tests to Confirm the 

Applicability of Laboratory Data on Strain–Induced Corrosion Cracking to Component 

Behavior,” in 3rd IAEA Specialists Meeting on Sub–Critical Crack Growth, Moscow, pp. 

67–91, 1990. 

97. Kilian, R., J. Hickling, and R. Nickell, “Environmental Fatigue Testing of Stainless Steel 

Pipe Bends in Flowing, Simulated PWR Primary Water at 240°C,” Third Intl. Conf. Fatigue 

of Reactor Components (MRP-151), EPRI Report 1011958, Electric Power Research 

Institute, Palo Alto, CA, Aug. 2005.
185

98. Kilian, R., “Environmental Fatigue Testing of Type 304L Stainless Steel U-Bends in 

Simulated PWR Primary Water (MRP-188),” Materials Reliability Program, EPRI Report 

1013028, Electric Power Research Institute, Palo Alto, CA, Jan. 2006.

99. Hickling, J., R. Kilian, L. Spain, and J. Carey, “Environmental Fatigue Testing of Type 

304L Stainless Steel U-Bends in Simulated PWR Primary Water,” Proc. of the 2006 ASME 

Pressure Vessels and Piping Conf., July 23–27, 2006, Vancouver, BC, Canada, paper # 

PVP2006–ICPVT11–93318.

100. Shahinian, P., H. E. Watson, and H. H. Smith, “Effect of Neutron Irradiation on Fatigue 

Crack Propagation in Types 304 and 316 Stainless Steels at High Temperature,” NRL 

Report 7446, Naval Research Laboratory, Washington, DC, July 1972.

101. James, L. A., and R. L. Knecht, “Fatigue-Crack Propagation in Fast-Neutron-Irradiated 

Types-304 and -316 Stainless Steels,” Nucl. Technol. 19, 148–155, 1973. 

102. James, L. A., “The Effect of Fast Neutron Irradiation Upon the Fatigue-Crack Propagation 

Behavior of Two Austenitic Stainless Steels,” J. Nucl. Mater. 59, 183–191, 1975.

103. Michel, D. J., “Irradiation Effects on Fatigue Crack Propagation in Austenitic Stainless 

Steels,” NRL Memorandum Report 3610, Naval Research Laboratory, Washington, DC, 

Sept. 1977.

104. Michel, D. J., and H. H. Smith, “Fatigue Crack Propagation in Neutron Irradiated Type 304 

and Type 308 Stainless Steel Plate and Weld Materials,” J. Nucl. Mater. 71, 173–177, 

1977.

105. Shahinian, P., H. E. Watson, and H. H. Smith, “Neutron Irradiation Effects on Fatigue 

Crack Growth in Types 304 and 316 Stainless Steels,” in Irradiation Effects on Reactor 

Structural Materials, Quarterly Progress Report 1 May – 31 July 1972, Section II Advance 

Reactor Materials (LMFBR), NRL Memorandum Report 2505, Naval Research Laboratory, 

Washington, DC, Aug. 1972.

106. Fyfitch, S., H. Xu, K. Moore, and R. Gurdal, “PWR Internals Materials Aging Degradation 

Mechanism Screening and Threshold Values (MRP-175),” Materials Reliability Program, 

EPRI Report 1012081, Electric Power Research Institute, Palo Alto, CA, December 2005.

107. Edwards, D., E. Simonen, S. Bruemmer, and P. Efsing, “Microstructural Evolution in 

Neutron- Irradiated Stainless Steels: Comparison of LWR and Fast-Reactor Irradiations,” 

Proc. 12th Intl. Conf. on Environmental Degradation of Materials in Nuclear Power System 

- Water Reactors, T. R. Allen, P. J. King, and L. Nelson, eds., Minerals, Metals, & 

Materials Society, pp. 419-428, 2005.

108. Korth, G. E., and M. D. Harper, “Fatigue and Creep-Fatigue Behavior of Irradiated and 

Unirradiated Type 308 Stainless Steel Weld Metal at Elevated Temperatures,” Properties 

of Reactor Structural Alloys After Neutron or Particle Irradiation, ASTM STP 570, 

American Society for Testing and Materials, Philadelphia, PA 175-190, 1975.

109. Kangilaski, M., and F. R. Shober, “Effect of Neutron Irradiation on Mechanical Properties 

of AISI Type 347 Stainless Steel,” Effects of Radiation on Structural Metals, ASTM STP 

426, American Society for Testing and Materials, 487-510, 1967.
186

110. Kanasaki, H., I. Satoh, M. Koyama, T. Okubo, T. R. Mager, and R. G. Lott, “Fatigue and 

Stress Corrosion Cracking Behaviors of Irradiated Stainless Steels in PWR Primary 

Water,” Proc. of the 5th Intl. Conf. on Nuclear Engineering (ICONE 5), Nice, France, May 

26-30, 1997.

111. Ware, A. G., D. K. Morton, and M. E. Nitzel, “Application of NUREG/CR–5999 Interim 

Design Curves to Selected Nuclear Power Plant Components,” NUREG/CR–6260, INEL–

95/0045, March 1995.

112. NUREG-0933, Main Report with Supplements 1–34 “Resolution of Generic Safety Issues,” 

Section 3 “New Generic Issues,” Issues 78, 166, and 190, March 29, 2012.

113. SECY-95-245, “Completion of Fatigue Action Plan,” Sept. 25,1995.

114. Khaleel, M. A., F. A. Simonen, H. K. Phan, D. O. Harris, and D. Dedhia, “Fatigue Analysis 

of Components for 60-Year Plant Life,” NUREG/CR-6674, PNNL-13227, June 2000.

115. Van Der Sluys, W. A., and S. Yukawa, “Status of PVRC Evaluation of LWR Coolant 

Environmental Effects on the S–N Fatigue Properties of Pressure Boundary Materials,” 

Fatigue and Crack Growth: Environmental Effects, Modeling Studies, and Design 

Considerations, PVP Vol. 306, S. Yukawa, ed., American Society of Mechanical 

Engineers, New York, pp. 47–58, 1995.

116. Van Der Sluys, W. A., “PVRC’s Position on Environmental Effects on Fatigue Life in LWR 

Applications,” Welding Research Council Bulletin 487, Welding Research Council, Inc., 

New York, Dec. 2003.

117. Memorandum for W. Travers from A. Thadani, "Closeout of Generic Safety Issue 190, 

'Fatigue Evaluation of Metal Components for 60-Year Plant Life,'" December 26, 1999.

118. Iida, K., T. Bannai, M. Higuchi, K. Tsutsumi, and K. Sakaguchi, “Comparison of Japanese 

MITI Guideline and Other Methods for Evaluation of Environmental Fatigue Life 

Reduction,” Pressure Vessel and Piping Codes and Standards, PVP Vol. 419, M. D. Rana, 

ed., American Society of Mechanical Engineers, New York, pp. 73–81, 2001. 

119. Chopra, O. K., and W. J. Shack, “Overview of Fatigue Crack Initiation in Carbon and Low–

Alloy Steels in Light Water Reactor Environments,” J. Pressure Vessel Technol. 121, 49–

60, 1999. 

120. Higuchi, M., “Revised Proposal of Fatigue Life Correction Factor Fen for Carbon and Low 

Alloy Steels in LWR Water Environments,” Assessment Methodologies for Preventing 

Failure: Service Experience and Environmental Considerations, PVP Vol. 410-2, R. 

Mohan, ed., American Society of Mechanical Engineers, New York, pp. 35–44, 2000.

121. Leax, T. R., “Statistical Models of Mean Stress and Water Environment Effects on the 

Fatigue Behavior of 304 Stainless Steel,” Probabilistic and Environmental Aspects of 

Fracture and Fatigues, PVP Vol. 386, S. Rahman, ed., American Society of Mechanical 

Engineers, New York, pp. 229–239, 1999. 

122. Mehta, H. S., and S. R. Gosselin, “Environmental Factor Approach to Account for Water 

Effects in Pressure Vessel and Piping Fatigue Evaluations,” Nucl. Eng. Des. 181, 175–

197, 1998.
187

123. Mehta, H. S., and S. R. Gosselin, “An Environmental Factor Approach to Account for

Reactor Water Effects in Light Water Reactor Pressure Vessel and Piping Fatigue,” EPRI 

Report TR-105759, Electric Power Research Institute, Palo Alto, CA, Dec. 1995.

124. Mehta, H. S., “An Update on the Consideration of Reactor Water Effects in Code Fatigue 

Initiation Evaluations for Pressure Vessels and Piping,” Assessment Methodologies for 

Preventing Failure: Service Experience and Environmental Considerations, PVP Vol. 410-

2, R. Mohan, ed., American Society of Mechanical Engineers, New York, pp. 45–51, 2000.

125. O’Donnell, W. J., W. J. O’Donnell, and T. P. O’Donnell, “Proposed New Fatigue Design 

Curves for Austenitic Stainless Steels, Alloy 600, and Alloy 800,” Proc. of the 2005 ASME 

Pressure Vessels and Piping Conf., July 17–21, 2005, Denver, CO, paper # PVP2005–

71409.

126. O’Donnell, W. J., W. J. O’Donnell, and T. P. O’Donnell, “Proposed New Fatigue Design 

Curves for Carbon and Low–Alloy Steels in High Temperature Water,” Proc. of the 2005 

ASME Pressure Vessels and Piping Conf., July 17–21, 2005, Denver, CO, paper # 

PVP2005–71410.

127. Park, H. B., and O. K. Chopra, “A Fracture Mechanics Approach for Estimating Fatigue 

Crack Initiation in Carbon and Low-Alloy Steels in LWR Coolant Environment,” 

Assessment Methodologies for Preventing Failure: Service Experience and Environmental 

Considerations, PVP Vol. 410-2, R. Mohan, ed., American Society of Mechanical 

Engineers, New York, pp. 3–11, 2000.

128. O’Donnell, T. P., and W. J. O’Donnell, “Stress Intensity Values in Conventional S-N 

Fatigue Specimens,” Pressure Vessels and Piping Codes and Standard: Volume 1 –

Current Applications, PVP Vol. 313–1, K. R. Rao and Y. Asada, eds., American Society of 

Mechanical Engineers, New York, pp. 191–192, 1995.

129. Majumdar, S., O. K. Chopra, and W. J. Shack, “Interim Fatigue Design Curves for Carbon, 

Low–Alloy, and Austenitic Stainless Steels in LWR Environments,” NUREG/CR–5999, 

ANL–93/3, 1993.

130. Keisler, J., O. K. Chopra, and W. J. Shack, “Fatigue Strain–Life Behavior of Carbon and 

Low–Alloy Steels, Austenitic Stainless Steels, and Alloy 600 in LWR Environments,” 

NUREG/CR–6335, ANL–95/15, 1995.

131. Higuchi, M., K. Sakaguchi, Y. Nomura, and A. Hirano, “Final Proposal of Environmental 

Fatigue Life Correction Factor (Fen) for Structural Materials in LWR Water Environment,”

Proc. of the 2007 ASME Pressure Vessels and Piping Division Conf., July 22–26, 2007, 

San Antonio, TX, paper # PVP2007–26100.

132. Higuchi, M., “Comparison of Environmental Fatigue Evaluation Methods in LWR Water,” 

Proc. of the 2008 ASME Pressure Vessels and Piping Division Conf., July 27–31, 2008, 

Chicago, IL, paper # PVP2008–61087.

133. Nakamura, T., M. Iwasaki, and S. Asada, “Optimization of Environmental Fatigue 

Evaluation (Step 1),” Proc. of the 2007 ASME Pressure Vessels and Piping Division Conf., 

July 22–26, 2007, San Antonio, TX, paper # PVP2007–26247.
188

134. Nomura, Y., K. Tsutsumi, T., Inoue, S. Asada, and T. Nakamura, “Optimization of 

Environmental Fatigue Evaluation (Step 2),” Proc. of the 2009 ASME Pressure Vessels 

and Piping Division Conf., July 26–30, 2009, Prague, Czech Republic, paper # PVP2009–

77115. 

135. Higuchi, M., T. Nakamura, and Y. Sugie, “Updated Knowledge Implemented to the 

Revision of Environmental Fatigue Evaluation Method for Nuclear Power Plants in JSME 

Code,” Proc. of the 2009 ASME Pressure Vessels and Piping Division Conf., July 26–30, 

2009, Prague, Czech Republic, paper # PVP2009–77077. 

136. JNES-SS Report, “Environmental Fatigue Evaluation Method for Nuclear Power Plants,” 

JNES-SS-1005, Nuclear Energy System Safety Division, Japan Nuclear Energy Safety 

Organization, March 2011.

137. Chopra, O. K., and W. J. Shack, “Effect of LWR Coolant Environments on the Fatigue Life 

of Reactor Materials – Final Report,” NUREG/CR–6909, ANL–06/08, Feb. 2007.

138. Wu, X. Q., and Y. Katada, “Influence of Cyclic Strain Rate on Environmentally Assisted 

Cracking Behavior of Pressure Vessel Steel in High-Temperature Water,” Mater. Sci. Eng. 

A379, 58–71, 2004.

139. Wu, X., and Y. Katada, “Corrosion Fatigue Behavior of Low-Alloy Pressure Vessel Steels 

in High Temperature Water under Multi-Factor Conditions,” J. Pressure Vessel Technol. 

Trans. ASME, Vol. 126, 466–472, 2004.

140. Wu, Q. X., and Y. Katada, “Influence of Strain Rate Change on Corrosion Fatigue 

Behavior of A533B Steel in Simulated BWR Water,” J. Mater. Sci. 39, 2519–2522, 2004.

141. Wu, Q. X., and Y. Katada, “Strain-Amplitude Dependent Fatigue Resistance of Low-Alloy 

Pressure Vessel Steels in High-Temperature Water,” J. Mater. Sci. 40, 1953–1958, 2005.

142. Wu, X., and Y. Katada, “Strain-Rate Dependence of Low Cycle Fatigue Behavior in a 

Simulated BWR Environment,” Corros. Sci. 47, 1415–1428, 2005.

143. Wu, X., E. Han, W. Ke, and Y. Katada, “Effects of Loading Factors on Environmental 

Fatigue Behavior of Low-Alloy Pressure Vessel Steels in Simulated BWR Water,” Nucl. 

Eng. Des. 237, 1452–1459, 2007.

144. Wu, X., H. Guan, E. H. Han, W. Ke, and Y. Katada, “Influence of Surface Finish on 

Fatigue Cracking Behavior of Reactor Pressure Vessel Steel in High Temperature Water,” 

Mater. Corros. 57 (11), 868–871, 2006.

145. Solomon, H. D., R. E. De Lair, and H. Hoffmann, “Influence of Environment and Strain 

Rate on the Low Cycle Fatigue Crack Initiation in Low Alloy Steel 15NiCuMoNb5 in High 

Temperature Water,” Proc. of the 11th Intl. Conf. on Environmental Degradation of 

Materials in Nuclear Systems, Stevenson, WA, Aug. 10-14, 2004.

146. Roth, A., and J. Hickling, “Crack Initiation due to Environmentally Assisted Cracking in 

Carbon and Low-Alloy Steels Exposed to High-Temperature Water,” Proc. of the 13th Intl. 

Conf. on Environmental Degradation of Materials in Nuclear Power Systems, Whistler, BC, 

Canada, Aug. 19-23, 2007.
189

147. Devrient, B., A. Roth, K. Kuster, U. Ilg, and M. Widera, “Effect of Dynamic Strain Ageing 

on the Environmentally Assisted Cracking of Low-Alloy Steels in Oxygenated HighTemperature Water,” Proc. of the 13th Intl. Conf. on Environmental Degradation of 

Materials in Nuclear Power Systems, Whistler, BC, Canada, Aug. 19-23, 2007.

148. Devrient, B., A. Roth, K. Kuster, M. Widera, and U. Ilg, “Influence of Dynamic Strain 

Ageing on the Crack Growth Rates and Crack Tip Plasticity of Low-Alloy Steels in 

Oxygenated High-Temperature Water,” Proc. of the 14th Intl. Conf. on Environmental 

Degradation of Materials in Nuclear Power Systems, Virginia Beach, VA, Aug. 23-27, 

2009.

149. Hanninen, H., Y. Yagodzinskyy, O. Tarasenko, U. Ehrnsten, and P. Aaltonen, H.-P. 

Seifert, “Effects of Dynamic Strain Ageing on Environmentally Assisted Cracking of LowAlloy Pressure Vessel and Piping Steels,” Proc. of the Tenth Intl. Conf. on Environmental 

Degradation of Materials in Nuclear Power Systems – Water Reactors, The Metallurgical 

Society, Warrendale, PA, Paper #0047, Lake Tahoe, NV, Aug. 5-9, 2001.

150. Seifert, H.-P., and S. Ritter, “Strain-Induced Corrosion Cracking Behavior of Low-Alloy 

Steels under Boiling Water Reactor Conditions,” J. Nucl. Mater. 378, 312–326, 2008. 

151. Wu, Q. X., and Y. Katada, “Role of Dynamic Strain Aging in Corrosion Fatigue of LowAlloy Pressure Vessel Steel in High Temperature Water,” J. Mater. Sci. 42, 633–639, 

2007.

152. Lee, B. H., and I. S. Kim, “Dynamic Strain Aging in High-Temperature Low-Cycle Fatigue 

of SA508 Cl. 3 Forging Steel,” J. Nucl. Mater. 226, 216–225, 1995. 

153. Huang, J. Y., J. R. Hwang, J. J. Yeh, C. Y. Chen, R. C. Kuo, and J. G. Huang, “Dynamic 

Strain Aging and Grain Size Reduction Effects on the Fatigue Resistance of SA533B3 

Steels,” J. Nucl. Mater. 324, 140–151, 2004. 

154. Sakaguchi, Y. Nomura, S. Suzuki, and H. Kanasaki, “Applicability of the Modified Rate 

Approach Method Under Various Conditions Simulating Actual Plant Conditions,” Proc. of 

the 2006 ASME Pressure Vessels and Piping Conf., July 23–27, 2006, Vancouver, BC, 

Canada, paper # PVP2006–ICPVT–11-93220.

155. Le Duff, J. A., A. Lefrancois, and J. P. Vernot, “Effect of Surface Finish and Loading 

Conditions on the Low Cycle Fatigue Behavior of Austenitic Stainless Steel in PWR 

Environment Comparison of LCF Test Results with NUREG/CR-6909 Life Estimates,” 

Proc. of the 2008 ASME Pressure Vessels and Piping Division Conf., July 27–31, 2008, 

Chicago, IL, paper # PVP2008–61894. 

156. Le Duff, J. A., A. Lefrancois, J. P. Vernot, and D. Bossu, “Effect of Loading Signal Shape 

and of Surface Finish on the Low Cycle Fatigue Behavior of 304L Stainless Steel in PWR 

Environment,” Proc. of the 2010 ASME Pressure Vessels and Piping Division/K-PVP 

Conf., July 18–22, 2010, Bellevue, WA, paper # PVP2010–26027.

157. Le Duff, J. A., A. Lefrancois, and J. P. Vernot, “Effect of Surface Finish and Loading 

Conditions on the Low Cycle Fatigue Behavior of Austenitic Stainless Steel in PWR 

Environment for Various Strain Amplitude Levels,” Proc. of the ASME 2009 Pressure 

Vessels and Piping Division Conf., July 26–30, 2009, Prague, Czech Republic, paper # 

PVP2009–78129.
190

158. Solin, J. P., “Fatigue of Stabilized SS and 316NG Alloy in PWR Environment,” Proc. of the 

2006 ASME Pressure Vessels and Piping Conf., July 23–27, 2006, Vancouver, BC, 

Canada, paper # PVP2006–ICPVT–93833.

159. Solin, J. P., S. Reese, and W. Mayinger, “Discussion on Fatigue Design Curves for 

Stainless Steels,” Proc. of the ASME 2011 Pressure Vessels and Piping Division Conf., 

July 17–21, 2011, Baltimore, MD, paper # PVP2011–57943.

160. Jones, D. P., J. E. Holliday, T. R. Leax, and J. L. Gordon, “Analysis of a Thermal Fatigue 

Test of a Stepped Pipe,” PVP Vol. 482, Computer Technology and Applications, July 25-

29, 2004, San Diego, CA, paper # PVP2004–2748.

161. Stevens, G. L., and J. M. Davis, “Guidelines for Addressing Fatigue Environmental Effects 

in a License Renewal Application (MRP-47 Revision 1),” Industry Guidance Document TR1012017, Electric Power Research Institute, Palo Alto, CA, April 2005.

162. Laird, C., “The Influence of Metallurgical Structure on the Mechanism of Fatigue Crack 

Propagation,” in Fatigue Crack Propagation, ASTM STP 415, American Society for 

Testing and Materials, Philadelphia, PA, 131-180, 1967.

163. Miller, K. J., “Initiation and Growth Rates of Short Cracks,” in Fundamentals of 

Deformation and Fracture, B. A. Bilby, K. J. Miller, and J. R. Willis, eds., Cambridge United 

Press, 476–500, 1984. 

164. Miller, K. J., “Damage in Fatigue: A New Outlook,” in Pressure Vessels and Piping Codes 

and Standard: Volume 1 – Current Applications, PVP Vol. 313–1, K. R. Rao and Y. Asada, 

eds., American Society of Mechanical Engineers, New York, 191–192, 1995. 

165. Suh, C. M., R. Yuuki, and H. Kitagawa, “Fatigue Microcracks in a Low Carbon Steel,”

Fatigue Fract. Eng. Mater. Struct. 8, 193–203, 1985. 

166. Tokaji, K., T. Ogawa, and S. Osako, “The Growth of Microstructurally Small Fatigue 

Cracks in a Ferritic–Pearlitic Steel, Fatigue Fract.” Eng. Mater. Struct. 11, 331–342, 1988. 

167. Dowling, N. E., “Crack Growth During Low–Cycle Fatigue of Smooth Axial Specimens,” in 

Cyclic Stress–Strain and Plastic Deformation Aspects of Fatigue Crack Growth, ASTM 

STP 637, American Society for Testing and Materials, Philadelphia, PA, 97–121, 1977.

168. Suresh, S., and R. O. Ritchie, “Propagation of Short Fatigue Cracks,” Int. Metals Reviews 

29, 445–476, 1984. 

169. Tokaji, K., and T. Ogawa, “The Growth of Microstructurally Small Fatigue Cracks in 

Metals,” in Short Fatigue Cracks, ESIS 13, M. J. Miller and E. R. de los Rios, eds., 

Mechanical Engineering Publication, London, 85–99, 1992. 

170. de los Rios, E. R., Z. Tang, and K. J. Miller, “Short Crack Fatigue Behavior in a Medium 

Carbon Steel,” Fatigue of Engineering Materials and Structures 7, 97–108, 1984. 

171. de los Rios, E. R., A. Navarro, and K. Hussain, “Microstructural Variations in Short Fatigue 

Crack Propagation of a C–Mn Steel,” in Short Fatigue Cracks, ESIS 13, M. J. Miller and E. 

R. de los Rios, eds., Mechanical Engineering Publication, London, pp. 115–132, 1992.
191

172. Chopra, O. K., Michaud, W. F. and Shack, W. J., “Environmentally Assisted Cracking in 

Light Water Reactors, Semiannual Report, October 1992–March 1993,” NUREG/CR–4667 

Vol. 16, ANL–93/27, pp. 3–19, September 1993.

173. Mizuno, T., Pednekar, S., Smialowska, S. and Macdonald, D. D., “Corrosion Behavior of 

Carbon Steel in Oxygenated Water Environments,” EPRI NP–2853, Electric Power 

Research Institute, Palo Alto, CA, Section 2, February 1983.

174. Choi, H., Smialowska, S. and Macdonald, D. D., “Stress Corrosion Cracking of ASME 

SA508–Cl2 Pressure Vessel Steel,” EPRI NP–2853, Electric Power Research Institute, 

Palo Alto, CA, Section 4, February 1983. 

175. Wranglen, G., “Pitting and Sulphide Inclusions in Steel,” Corr. Sci. 14, 331–349 (1974). 

176. Chopra, O. K., Michaud, W. F., Shack, W. J. and Soppet, W. K., “Environmentally Assisted 

Cracking in Light Water Reactors, Semiannual Report, April–September 1993,”

NUREG/CR–4667 Vol. 17, ANL–94/16, pp. 1–22, June 1994.

177. James, L. A., “The Effect of Temperature and Cyclic Frequency Upon Fatigue Crack 

Growth Behavior of Several Steels in Elevated Temperature Aqueous Environment,” J. 

Pressure Vessel Technol. 116, 122-127, 1994. 

178. James, L. A., “The Initiation of Environmentally–Assisted Cracking in Semi–Elliptical 

Surface Cracks,” in Pressure Vessel and Piping Codes and Standards, PVP Vol. 353, 

T. C. Esselman, ed., American Society of Mechanical Engineers, New York, pp. 125–139, 

1997.

179. Bulloch, J. H., “A Review of the Fatigue Crack Extension Behaviour of Ferritic Reactor 

Pressure Vessels Materials in Pressurized Water Reactor Environments,” Res. Mech. 26, 

95–172, 1989.

180. Lenz, E., N. Wieling, and H. Munster, “Influence of Variation of Flow Rates and 

Temperature on the Cyclic Crack Growth Rate under BWR Conditions,” in Proc. 3rd Int. 

Symp. on Environmental Degradation of Materials in Nuclear Power Systems – Water 

Reactors, G. J. Theus and J. R. Weeks, eds., The Metallurgical Society, Warrendale, PA, 

pp. 283–288, 1988.

181. James, L. A., G. L. Wire, and W. H. Cullen, “The Effect of Water Flow Rate Upon the 

Environmentally–Assisted Cracking Response of a Low–Alloy Steel,” J. Pressure Vessel 

Technol. 117 (3), 238–244, 1995.

182. Wire, G. L., and Y. Y. Li, “Initiation of Environmentally–Assisted Cracking in Low–Alloy 

Steels,” Fatigue and Fracture Vol. 1, PVP Vol. 323, H. S. Mehta, ed., American Society of 

Mechanical Engineers, New York, pp. 269–289, 1996.

183. Van Der Sluys, W. A., and R. H. Emanuelson, “Environmentally Acceleration of Fatigue 

Crack Growth in Reactor Pressure Vessel Materials,” EPRI Report TR-102796, Electric 

Power Research Institute, Palo Alto, CA, Aug. 1993.

184. Cullen, W. H., M. Kemppainen, H. Hänninen, and K. Törrönen, “The Effects of Sulfur 

Chemistry and Flow Rate on Fatigue Crack Growth Rates in LWR Environments,” 

NUREG/CR–4121, 1985.
192

185. Van Der Sluys, W. A., and R. H. Emanuelson, “Environmental Acceleration of Fatigue 

Crack Growth in Reactor Pressure Vessel Materials and Environments,” Environmentally 

Assisted Cracking: Science and Engineering, ASTM STP 1049, W. B. Lisagor, T. W. 

Crooker, and B. N. Leis, eds., American Society for Testing and Materials, Philadelphia, 

PA, pp. 117–135, 1990.

186. Atkinson, J. D., and J. E. Forrest, “The Role of MnS Inclusions in the Development of 

Environmentally Assisted Cracking of Nuclear Reactor Pressure Vessel Steels,” in Proc. 

2nd Int. Atomic Energy Agency Specialists' Meeting on Subcritical Crack Growth, 

NUREG/CP–0067, MEA–2090, Vol. 2, pp. 153–178, April 1986.

187. Atkinson, J. D., J. Yu, and Z.–Y. Chen, “An Analysis of the Effects of Sulfur Content and 

Potential on Corrosion Fatigue Crack Growth in Reactor Pressure Vessel Steels,” Corros. 

Sci. 38 (5), 755–765, 1996.

188. Auten, T. A., S. Z. Hayden, and R. H. Emanuelson, “Fatigue Crack Growth Rate Studies of 

Medium Sulfur Low Alloy Steels Tested in High Temperature Water,” Proc. 6th Int. Symp. 

on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors, 

R. E. Gold and E. P. Simonen, eds., The Metallurgical Society, Warrendale, PA, pp. 35–

40, 1993.

189. Ford, F. P., and P. L. Andresen, “Stress Corrosion Cracking of Low–Alloy Pressure Vessel 

Steel in 288°C Water,” Proc. 3rd Int. Atomic Energy Agency Specialists' Meeting on 

Subcritical Crack Growth, NUREG/CP–0112, Vol. 1, pp. 37–56, Aug. 1990.

190. Ford, F. P., “Overview of Collaborative Research into the Mechanisms of Environmentally 

Controlled Cracking in the Low Alloy Pressure Vessel Steel/Water System,” Proc. 2nd Int. 

Atomic Energy Agency Specialists' Meeting on Subcritical Crack Growth, NUREG/CP–

0067, MEA–2090, Vol. 2, pp. 3–71, April 1986.

191. Ford, F. P., D. F. Taylor, and P. L. Andresen, “Corrosion-Assisted Cracking of Stainless 

and Low-Alloy Steels in LWR Environments,” EPRI NP-5064S, Electric Power Research 

Institute, Palo Alto, CA, Feb. 1987.

192. Ford, F. P., S. Ranganath, and D. Weinstein, “Environmentally Assisted Fatigue Crack 

Initiation in Low–Alloy Steels - A Review of the Literature and the ASME Code Design 

Requirements,” EPRI Report TR-102765, Electric Power Research Institute, Palo Alto, 

CA, Aug. 1993.

193. Ford, F. P., “Prediction of Corrosion Fatigue Initiation in Low–Alloy and Carbon Steel/

Water Systems at 288°C,” Proc. 6th Intl. Symp. on Environmental Degradation of 

Materials in Nuclear Power Systems – Water Reactors, R. E. Gold and E. P. Simonen, 

eds., The Metallurgical Society, Warrendale, PA, pp. 9–17, 1993.

194. Hänninen, H., K. Törrönen, and W. H. Cullen, “Comparison of Proposed Cyclic Crack 

Growth Mechanisms of Low Alloy Steels in LWR Environments,” in Proc. 2nd Int. Atomic 

Energy Agency Specialists' Meeting on Subcritical Crack Growth, NUREG/CP–0067, 

MEA–2090, Vol. 2, pp. 73–97, April 1986.

195. Hänninen, H., K. Törrönen, M. Kempainen, and S. Salonen, “On the Mechanisms of 

Environment Sensitive Cyclic Crack Growth of Nuclear Reactor Pressure Vessel Steels,” 

Corros. Sci. 23, 663–679, 1983. 
193

196. Törrönen, K., M. Kempainen, and H. Hänninen, “Fractographic Evaluation of Specimens of 

A533B Pressure Vessel Steel,” EPRI Report NP–3483, Project 1325–7, May 1984. 

197. Oriani, R. A., “A Mechanistic Theory of Hydrogen Embrittlement of Steels,” Ber. 

Bunsenges. Phys. Chem. 76, 848–857, 1972.

198. Beachem, C. D., “A New Model for Hydrogen Assisted Cracking,” Met. Trans. 3A (2), 437–

451, 1972.

199. Kim, Y. J., “Characterization of the Oxide Film Formed on Type 316 Stainless Steel in 

288°C Water in Cyclic Normal and Hydrogen Water Chemistries,” Corrosion 51 (11), 849–

860, 1995.

200. Kim, Y. J., “Analysis of Oxide Film Formed on Type 304 Stainless Steel in 288°C Water 

Containing Oxygen, Hydrogen, and Hydrogen Peroxide,” Corrosion 55 (1), 81–88, 1999. 

201. Tapping, R. L., Davidson, R. D., McAlpine, E. and Lister, D. H., “The Composition and 

Morphology of Oxide Films Formed on Type 304 Stainless Steel in Lithiated High–

Temperature Water,” Corrosion Sci. 26 (8), 563–576 (1986).

202. Lister, D. H., Davidson, R. D. and McAlpine, E., “The Mechanism and Kinetics of 

Corrosion Product Release from Stainless Steel in Lithiated High–Temperature Water,” 

Corrosion Sci. 27 (2), 113–140 (1987).

203. Belo, M. Da Cunha, M. Walls, M., Hakiki, N. E., Corset, J., Picquenard, E., Sagon, G. and 

Neol, D., “Composition, Structure and Properties of the Oxide Films Formed on the 

Stainless Steel 316L in a Primary Type PWR Environment,” Corrosion Sci. 40 (2/3), 447–

463 (1998).

204. Stellwag, B., “The Mechanism of Oxide Film Formation on Austenitic Stainless Steels in 

High–Temperature Water,” Corrosion Sci. 40 (2/3), 337–370 (1998).

205. Nakayama, T. and Oshida, Y., “Identification of the Initial Oxide Films on 18–8 Stainless 

Steel in High–Temperature Water,” Corrosion NACE 24 (10), 336–337 (1968). 

206. Srinivasan, V. S., M. Valsan, R. Sandhya, K. Bhanu Sankara Rao, M. L. Mannan, and D. 

H. Sastry, “High Temperature Time-Dependent Low Cycle Fatigue Behavior of a Type 

316L(N) Stainless Steel, Intl. J. Fatigue 21, 11–21, 1999.

207. Obrtlik, K., J. Polák, M. Hájek, and A. Vasek, “Short Fatigue Crack Behavior in 316L 

Stainless Steel,” Intl. J. Fatigue 19, 471–475, 1997. 

208. Shack, W. J., and T. F. Kassner, “Review of Environmental Effects on Fatigue Crack 

Growth of Austenitic Stainless Steels,” NUREG/CR-6176, ANL-94/1, May 1994.

209. Chopra, O. K., W. K. Soppet, and W. J. Shack, “Effects of Alloy Chemistry, Cold Work, 

and Water Chemistry on Corrosion Fatigue and Stress Corrosion Cracking of Nickel Alloys 

and Welds,” NUREG/CR-6721, ANL-01/07, April 2001.

210. Private communication from M. Higuchi, Ishikawajima-Harima Heavy Industries Co. 

Japan, to M. Prager of the Pressure Vessel Research Council, 1992. The old database 

“FADAL” has been revised and renamed “JNUFAD.” 
194

211. Abdel–Raouf, H., A. Plumtree, and T. H. Topper, “Effects of Temperature and Deformation 

Rate on Cyclic Strength and Fracture of Low–Carbon Steel,” Cyclic Stress–Strain 

Behavior – Analysis, Experimentation, and Failure Prediction, ASTM STP 519, American 

Society for Testing and Materials, Philadelphia, pp. 28–57, 1973.

212. Lee, B. H., and I. S. Kim, “Dynamic Strain Aging in the High–Temperature Low–Cycle 

Fatigue of SA 508 Cl. 3 Forging Steel,” J. Nucl. Mater. 226, 216–225, 1995. 

213. Manjoine, M. J., and R. L. Johnson, “Fatigue Design Curves for Carbon and Low Alloy 

Steels up to 700°F (371°C),” Material Durability/Life Prediction Modeling: Materials for the 

21st Century, PVP–Vol. 290, American Society of Mechanical Engineers, New York, 1994.

214. Johnson, L. G., “The Median Ranks of Sample Values in Their Population with an 

Application to Certain Fatigue Studies,” Ind. Math. 2, 1–9, 1951.

215. Lipson, C., and N. J. Sheth, “Statistical Design and Analysis of Engineering Experiments,”

McGraw Hill, New York, 1973. 

216. Beck, J., and K. Arnold, “Parameter Estimation in Engineering and Science,” J. Wiley, 

New York, 1977. 

217. Maiya, P. S., and D. E. Busch, “Effect of Surface Roughness on Low–Cycle Fatigue 

Behavior of Type 304 Stainless Steel,” Met. Trans. 6A, 1761–1766, 1975.

218. Maiya, P. S., “Effect of Surface Roughness and Strain Range on Low–Cycle Fatigue 

Behavior of Type 304 Stainless Steel,” Scripta Metall. 9, 1277–1282, 1975.

219. Stout, K. J., “Surface Roughness – Measurement, Interpretation, and Significance of 

Data,” Mater. Eng. 2, 287–295, 1981.

220. Iida, K., “A Study of Surface Finish Effect Factor in ASME B & PV Code Section III,” 

Pressure Vessel Technology, Vol. 2, L. Cengdian and R. W. Nichols, eds., Pergamon 

Press, New York, pp. 727–734, 1989.

221. Stambaugh, K. A., D. H. Leeson, F. V. Lawrence, C. Y. Hou, and G. Banas, “Reduction of 

S-N Curves for Ship Structural Details,” Welding Research Council 398, January 1995.

222. Miller, K. J. and W. J. O’Donnell, “The Fatigue Limit and its Elimination,” Fatigue Fract. 

Eng. Mater. Struct. 22, 545-557, 1999. 

223. Wire, G. L., T. R. Leax, and J. T. Kandra, “Mean Stress and Environmental Effects on 

Fatigue in Type 304 Stainless Steel,” in Probabilistic and Environmental Aspects of 

Fracture and Fatigues, PVP Vol. 386, S. Rahman, ed., American Society of Mechanical 

Engineers, New York, pp. 213–228, 1999.

224. Diercks, D. R., “Development of Fatigue Design Curves for Pressure Vessel Alloys Using 

a Modified Langer Equation,” Trans. ASME J. Pressure Vessel Technol. 101, 292–297, 

1979.

225. Solomon, H. D., and C. Amzallag, “Comparison of Models Predicting the Fatigue Behavior 

of Austenitic Stainless Steels,” Proc. of the 2005 ASME Pressure Vessels and Piping 

Conf., July 17–21, 2005, Denver, CO, paper # PVP2005–71063.
195

226. Pleune, T. T., and O. K. Chopra, “Artificial Neural Networks and Effects of Loading 

Conditions on Fatigue Life of Carbon and Low–Alloy Steels,” Fatigue and Fracture Vol. 1, 

PVP Vol. 350, S. Rahman, K. K. Yoon, S. Bhandari, R. Warke, and J. M. Bloom, eds., 

American Society of Mechanical Engineers, New York, pp. 413–423, 1997.

227. Solomon, H. D., R. E. DeLair, and A. D. Unruh, “Crack Initiation in Low-Alloy Steel in HighPurity Water,” Effects of the Environment on the Initiation of Crack Growth, ASTM STP 

1298, W. A. Van Der Sluys, R. S. Piascik, and R. Zawierucha, eds., American Society for 

Testing and Materials, Philadelphia, pp. 135–149, 1997.

228. Solomon, H. D., R. E. DeLair, and E. Tolksdorf, “LCF Crack Initiation in WB36 in HighTemperature Water,” Proc. 9th Intl. Symp. on Environmental Degradation of Materials in 

Nuclear Power Systems – Water Reactors, F. P. Ford, S. M. Bruemmer, and G. S. Was, 

eds., The Minerals, Metals, and Materials Society, Warrendale, PA, pp. 865–872, 1999.

229. Chopra, O. K., “Estimation of Fracture Toughness of Cast Stainless Steels During Thermal 

Aging in LWR Systems,” NUREG/CR–4513, ANL–93/22, Aug. 1994. 

230. Chopra, O. K., and A. Sather, “Initial Assessment of the Mechanisms and Significance of 

Low-Temperature Embrittlement of Cast Stainless Steels in LWR Systems,” NUREG/CR–

5385, ANL–89/17, Aug. 1990.

231. Michaud, W. F., P. T. Toben, W. K. Soppet, and O. K. Chopra, “Tensile Property 

Characterization of Thermally Aged Cast Stainless Steels,” NUREG/CR–6142, ANL–

93/35, Feb. 1994.

232. Chopra, O. K., “Effect of Thermal Aging on Mechanical Properties of Cast Stainless 

Steels,” in Proc. of the 2nd Int. Conf. on Heat–Resistant Materials, K. Natesan, P. 

Ganesan, and G. Lai, eds., ASM International, Materials Park, OH, pp. 479–485, 1995. 

233. Higuchi, M., “Review and Consideration of Unsettled Problems on Evaluation of Fatigue 

Damage in LWR Water,” Proc. of the 2005 ASME Pressure Vessels and Piping Conf., July 

17–21, 2005, Denver, CO, paper # PVP2005–71306.

234. Mayfield, M. E., E. C. Rodabaugh, and R. J. Eiber, “A Comparison of Fatigue Test Data on 

Piping with the ASME Code Fatigue Evaluation Procedure,” ASME Paper 79–PVP–92, 

American Society of Mechanical Engineers, New York, 1979.

235. Heald, J. D., and E. Kiss, “Low Cycle Fatigue of Nuclear Pipe Components,” J. Pressure 

Vessel Technol. 74, PVP–5, 1–6, 1974.

236. Deardorff, A. F., and J. K. Smith, “Evaluation of Conservatisms and Environmental Effects 

in ASME Code, Section III, Class 1 Fatigue Analysis,” SAND94–0187, prepared by 

Structural Integrity Associates, San Jose, CA, under contract to Sandia National 

Laboratories, Albuquerque, NM, 1994. 

237. Kooistra, L. F., E. A. Lange, and A. G. Pickett, “Full–Size Pressure Vessel Testing and Its 

Application to Design,” J. Eng. Power 86, 419–428, 1964.
196

238. Scott, P. M., and G. M. Wilkowski, “A Comparison of Recent Full–Scale Component 

Fatigue Data with the ASME Section III Fatigue Design Curves,” in Fatigue and Crack 

Growth: Environmental Effects, Modeling Studies, and Design Considerations, PVP Vol. 

306, S. Yukawa, ed., American Society of Mechanical Engineers, New York, pp. 129–138, 

1995.

239. Hechmer, J., “Evaluation Methods for Fatigue - A PVRC Project,” in Fatigue, 

Environmental Factors, and New Materials, PVP Vol. 374, H. S. Mehta, R. W. Swindeman, 

J. A. Todd, S. Yukawa, M. Zako, W. H. Bamford, M. Higuchi, E. Jones, H. Nickel, and 

S. Rahman, eds., American Society of Mechanical Engineers, New York, pp. 191–199, 

1998.

240. Manjoine, M. J., “Fatigue Damage Models for Annealed Type 304 Stainless Steel under 

Complex Strain Histories,” Trans. 6th Intl. Conf. on Structural Mechanics in Reactor 

Technology (SMiRT), Vol. L, 8/1, North–Holland Publishing Co., pp. 1–13, 1981. 

241. Nian, L., and Du Bai–Ping, “The Effect of Low–Stress High–Cycle Fatigue on the 

Microstructure and Fatigue Threshold of a 40Cr Steel,” Int. J. Fatigue 17 (1), 43–48, 1995. 
A-1

APPENDIX A INCORPORATING ENVIRONMENTAL EFFECTS INTO

FATIGUE EVALUATIONS

A1 Scope

This Appendix provides the environmental fatigue correction factor (Fen) methodology that is 

considered acceptable for incorporating the effects of reactor coolant environments in fatigue 

usage factor evaluations of metal components. The methodology for performing fatigue 

evaluations for the four major categories of structural materials, e.g., carbon steels, low-alloy 

steels, wrought and cast austenitic stainless steels, and Ni-Cr-Fe alloys, is described.

A2 Environmental Correction Factor (Fen)

The effects of reactor coolant environments on the fatigue lives of structural materials are 

expressed in terms of a nominal environmental fatigue correction factor, Fen,nom, which is 

defined as the ratio of fatigue life in air at room temperature (Nair,RT) to that in water at the 

service temperature (Nwater): 

Fen,nom = Nair,RT/Nwater (A.1)

The nominal environmental fatigue correction factor, Fen,nom, for both carbon and low-alloy 

steels is expressed as 

Fen,nom = exp((0.003 – 0.031 *) S*T*O*) (A.2)

where S*, T*, O*, and * are transformed sulfur (S) content, material temperature, dissolved 

oxygen (DO) level, and strain rate, respectively, defined as:

S* = 2.0 + 98 S (S ≤ 0.015 wt. %)

S* = 3.47 (S > 0.015 wt. %) (A.3)

T* = 0.395 (T < 150 °C)

T* = (T – 75)/190 (150°C ≤ T ≤ 325 °C) (A.4)

O* = 1.49 (DO < 0.04 ppm)

O* = ln(DO/0.009) (0.04 ppm ≤ DO ≤ 0.5 ppm)

O* = 4.02 (DO > 0.5 ppm) (A.5)

* = 0 ( * > 2.2%/s)

* = ln( */2.2) (0.0004%/s ≤ * ≤ 2.2%/s)

* = ln(0.0004/2.2) ( * < 0.0004%/s) (A.6)

For carbon and low-alloy steels, a threshold value of 0.07% for strain amplitude (one-half the 

strain range for the cycle) is defined, below which environmental effects on the fatigue lives of 

these steels may not occur. Thus, 

Fen,nom = 1 (εa ≤ 0.07%) (A.7)
A-2

Note that the strain amplitude threshold should not be applied when using a modified rate 

approach, as it may yield non-conservative results.

For wrought and cast austenitic stainless steels,

Fen,nom = exp(– T' O' '

) (A.8)

where T'

, ', and O' are transformed temperature, strain rate, and DO level, respectively, 

defined as:

T' = 0 (T ≤ 100°C)

T' = (T – 100)/250 (100°C ≤ T < 325°C) (A.9)

' = 0 ( ' > 10%/s) ' = ln( /10) (0.0004%/s ≤ ' ≤ 10%/s) ' = ln(0.0004/10) ( ' < 0.0004%/s) (A.10)

For DO less than 0.1 ppm, i.e., for PWR or BWR HWC water:

O' = 0.29 (all wrought and cast SSs and heat treatments and SS weld 

metals)

For DO greater than or equal to 0.1 ppm (i.e., for BWR NWC water):

O' = 0.29 (sensitized high-carbon wrought and cast SSs) 

O' = 0.14 (all wrought SSs except sensitized high-carbon SSs) (A.11)

For wrought and cast austenitic stainless steels, a threshold value of 0.10% for strain amplitude 

(one-half the strain range for the cycle) is defined, below which environmental effects on the 

fatigue lives of these steels do not occur. Thus,

Fen,nom = 1 (εa ≤ 0.10%) (A.12)

Note that the strain amplitude threshold should not be applied when using a modified rate 

approach, as it may yield non-conservative results.

For Ni-Cr-Fe alloys,

Fen,nom = exp(– T’ ’ O’

) (A.13)

where T’

, ’, and O’ are transformed temperature, strain rate, and DO, respectively, defined as:

T’ = 0 (T < 50°C)

T’ = (T – 50)/275 (50°C ≤ T ≤ 325°C) (A.14)

’ = 0 ( > 5.0%/s) ’ = ln( /5.0) (0.0004%/s ≤ ≤ 5.0%/s) ’ = ln(0.0004/5.0) ( < 0.0004%/s) (A.15)

O’ = 0.06 (NWC BWR water, i.e., ≥ 0.1 ppm DO)

O’ = 0.14 (PWR or HWC BWR water, i.e., < 0.1 ppm DO) (A.16)
A-3

For Ni-Cr-Fe alloys, a threshold value of 0.10% for strain amplitude (one-half the strain range for 

the cycle) is defined, below which environmental effects on the fatigue lives of these alloys do 

not occur. Thus,

Fen,nom = 1 (εa ≤ 0.10%) (A.17)

Note that the strain amplitude threshold should not be applied when using a modified rate 

approach, as it may yield non-conservative results.

For all materials, a maximum temperature limit was selected at 325°C as a reasonable 

extension to cover all anticipated LWR operating conditions. This is adequate for all expected 

operating LWR conditions considering the use of average temperature.

A3 Fatigue Evaluation Procedure

The environmental fatigue evaluation method uses as its input the partial fatigue usage factors 

U1, U2, U3, ...Un, determined in fatigue evaluations. To incorporate environmental effects into 

the fatigue evaluation, the partial fatigue usage factor for a specific stress cycle or load set pair, 

based on the fatigue design curves, is multiplied by the environmental fatigue correction factor: 

Uen,1 = U1·Fen,1 (A.18)

In the ASME Code Section III design–by–analysis (NB-3200) methods, the partial fatigue usage 

factors are calculated for each type of stress cycle in Subparagraph NB-3222.4(e)(5). For 

piping products designed using NB–3600 methods, Paragraph NB-3653 provides the 

procedures for the calculation of partial fatigue usage factors for each of the load set pairs. The 

partial usage factors are obtained from the fatigue design curves provided they are consistent, 

or conservative, with respect to the existing fatigue ε–N data. For example, the ASME Code 

Section III fatigue design curve for austenitic SSs developed in the 1960s (i.e., the design curve 

in Code editions prior to 2009b Addenda) is not consistent with the fatigue database used to 

develop the environmental factors in this report and, therefore, may give non-conservative 

estimates of environmental fatigue usage factors for most heats of austenitic SSs used in the 

construction of nuclear reactor components. The current ASME Code fatigue design curve (i.e., 

the design curve in Code editions as of the 2009b Addenda) is consistent with the ANL fatigue

life model (presented in Fig. 49), and is consistent with the fatigue ε–N database used in this 

report. Examples of calculating partial usage factors are as follows: 

(1) For carbon and low–alloy steels with ultimate tensile strengths less than 552 MPa (80 ksi), 

the partial fatigue usage factors are obtained from the ASME Code fatigue design curve, 

i.e., Fig. I–9.1 of Mandatory Appendix I to Section III of the ASME Code. As an alternative, 

to reduce conservatism in the current Code fatigue design curve for carbon steel and the 

Code requirement of a factor of 20 on life, partial usage factors may be determined from the 

fatigue design curves developed from the ANL fatigue life model, i.e., Figs. A.1 and A.2 and 

Table A.1. 

(2) For wrought or cast austenitic SSs and Ni-Cr-Fe alloys, the partial fatigue usage factors are 

obtained from the fatigue design curve in the 2009b Addenda or later editions of the ASME 

Code, i.e., Fig. I–9.2 of Mandatory Appendix I to Section III of the ASME Code, which is the 

same as the ANL fatigue design curve. The ANL fatigue design curve is based on the ANL 

fatigue life model and was developed using a factor of 12 on life, i.e., Fig. A.3 and Table A.2.
A-4

The cumulative fatigue usage factor, Uen, considering the effects of reactor coolant 

environments is then calculated as follows:

Uen = U1·Fen,1 + U2·Fen,2 + U3·Fen,3 + Ui

·Fen,i ...+ Un·Fen,n (A.19)

 

Figure A.1.

Fatigue design curves for 

carbon steels in air. The 

curve developed from the 

ANL model is based on 

factors of 12 on life and 2 

on stress.

 

Figure A.2.

Fatigue design curves

for low-alloy steels in air. 

The curve developed 

from the ANL model is 

based on factors of 12 on 

life and 2 on stress. 
A-5

 

Figure A.3.

Fatigue design curve 

for austenitic stainless 

steels in air. The curve 

developed from the 

ANL model is based on 

factors of 12 on life and 

2 on stress.

Table A.1. Fatigue design curves for carbon and low-alloy steels in air.

Stress Amplitude, MPa (ksi) Stress Amplitude, MPa (ksi)

Cycles

ASME 

Code Curve

Carbon

Steel

Low-Alloy 

Steel Cycles

ASME 

Code Curve

Carbon

Steel

Low-Alloy 

Steel

1 E+01 3999 (580) 5355 (777) 5467 (793) 2 E+05 114 (16.5) 176 (25.5) 141 (20.5)

2 E+01 2827 (410) 3830 (556) 3880 (563) 5 E+05 93.1 (13.5) 154 (22.3) 116 (16.8)

5 E+01 1896 (275) 2510 (364) 2438 (354) 1 E+06 86.2 (12.5) 142 (20.6) 106 (15.4)

1 E+02 1413 (205) 1820 (264) 1760 (255) 2 E+06 130 (18.9) 98 (14.2)

2 E+02 1069 (155) 1355 (197) 1300 (189) 5 E+06 120 (17.4) 94 (13.6)

5 E+02 724 (105) 935 (136) 900 (131) 1 E+07 76.8 (11.1) 115 (16.7) 91 (13.2)

1 E+03 572 (83) 733 (106) 720 (104) 2 E+07 110 (16.0) 88 (12.7)

2 E+03 441 (64) 584 (84.7) 576 (83.5) 5 E+07 105 (15.2) 84 (12.2)

5 E+03 331 (48) 451 (65.4) 432 (62.7) 1 E+08 68.5 (9.9) 101 (14.7) 81 (11.8)

1 E+04 262 (38) 373 (54.1) 342 (49.6) 1 E+09 61.1 (8.8) 90 (13.1) 72.3 (10.5)

2 E+04 214 (31) 305 (44.2) 276 (40.0) 1 E+010 54.4 (7.9) 81 (11.7) 64.4 (9.3)

5 E+04 159 (23) 238 (34.5) 210 (30.5) 1 E+011 48.5 (7.0) 72 (10.4) 57.4 (8.3)

1 E+05 138 (20.0) 201 (29.2) 172 (24.9)

Table A.2. Fatigue design curves for austenitic stainless steels in air.

Stress Amplitude, MPa (ksi) Stress Amplitude, MPa (ksi)

Cycles New Design Curve Cycles New Design Curve

1 E+01 6000 (870) 2 E+05 168 (24.4)

2 E+01 4300 (624) 5 E+05 142 (20.6)

5 E+01 2748 (399) 1 E+06 126 (18.3)

1 E+02 1978 (287) 2 E+06 113 (16.4)

2 E+02 1440 (209) 5 E+06 102 (14.8)

5 E+02 974 (141) 1 E+07 99 (14.4)

1 E+03 745 (108) 1 E+08 97.1 (14.1)

2 E+03 590 (85.6) 1 E+09 95.8 (13.9)

5 E+03 450 (65.3) 1 E+10 94.4 (13.7)

1 E+04 368 (53.4) 1 E+11 93.7 (13.6)

2 E+04 300 (43.5)

5 E+04 235 (34.1)

1 E+05 196 (28.4)

where Fen,i is the nominal environmental fatigue correction factor for the “ith” stress cycle (NB3200) or load set pair (NB-3600). Because environmental effects on fatigue lives occur 

primarily during the tensile-loading cycle (i.e., up-ramp with increasing strain or stress), this 

calculation is performed only for the tensile stress producing portion of the stress cycle 
A-6

constituting a load pair. Also, the values for key parameters such as strain rate, material 

temperature, DO in the water, and for carbon and low–alloy steels S content, are needed to 

calculate Fen for each stress cycle or load set pair. As discussed in Section 4 of this report, the 

following guidance may be used to determine these parameters:

(1) An average strain rate for the transient typically yields a conservative estimate of Fen. For 

complex loading conditions, the strain rates used in the calculations should produce results 

that are consistent with the results that would be obtained using the modified rate approach 

described in Section 4.1.14 of this report. The lower bound or saturation strain rate of 

0.0004%/s can be used to perform the most conservative evaluation.

(2) For the case of a constant strain rate and a linear temperature response, an average 

temperature (i.e., average of the maximum temperature for the transient and the higher of 

the threshold temperature for the material under consideration and the minimum 

temperature for the transient) may be used to calculate Fen. In general, the “average” 

temperature used in the calculations should produce results that are consistent with the 

results that would be obtained using the modified rate approach described in Section 4.1.14 

of this report. The maximum temperature can be used to perform the most conservative 

evaluation.

(3) The DO value is obtained from each transient constituting the stress cycle. For carbon and 

low-alloy steels, the DO content associated with a stress cycle is the highest oxygen level in 

the transient, and for austenitic stainless steels, it is the lowest DO level in the transient. A 

value of 0.5 ppm for carbon and low-alloy steels and 0.05 ppm for austenitic stainless steels 

and Ni alloys can be used for the DO content to perform a conservative evaluation.

(4) The sulfur content, S, in terms of weight percent might be obtained from the certified 

material test report or an equivalent source. If the sulfur content is unknown, then its value 

shall be assumed as the maximum value specified in the procurement specification or the 

applicable construction Code.

The detailed procedures for incorporating environmental effects into the Code fatigue 

evaluations have been presented in several articles and reports. The following are just two 

examples of such documents that may be used for guidance:

(1) Mehta, H. S., “An Update on the Consideration of Reactor Water Effects in Code Fatigue 

Initiation Evaluations for Pressure Vessels and Piping,” Assessment Methodologies for 

Preventing Failure: Service Experience and Environmental Considerations, PVP Vol. 410-2, 

R. Mohan, ed., American Society of Mechanical Engineers, New York, pp. 45–51, 2000.

(2) Nakamura, T., M. Higuchi, T. Kusunoki, and Y. Sugie, “JSME Codes on Environmental 

Fatigue Evaluation,” Proc. of the 2006 ASME Pressure Vessels and Piping Conf., July 23–

27, 2006, Vancouver, BC, Canada, paper # PVP2006–ICPVT11–93305.

In addition, Appendix C of this report presents a sample application of the Fen methodology.
B-1

APPENDIX B MATERIAL INFORMATION

The various grades, heat treatment, chemical composition, and mechanical properties of the carbon and low-

stainless steels, and Ni-Cr-Fe alloy steels used in this report are provided in this appendix. 

B1 Carbon and Low-Alloy Steels Included in the Fatigue Database

The various grades, heat treatment, chemical composition, and mechanical properties of the carbon and low-a

report are listed in the following table. 

Mat. 

ID

Heat 

Designation Heat Treatment

Chemical Composition (wt.%) YS 

(MPa)

UTS 

(MPa)

E

C Si Mn P S Ni Cr Mo

Carbon Steels

1 A106-Gr.B-A - 0.29 0.25 0.88 0.013 0.015 0.09 0.19 0.05 301 572 

2 A106-Gr.B-H - 0.24 0.29 0.91 0.01 0.007 - - - 333 559 

3 A106-Gr.B-T - 0.26 0.28 0.92 0.008 0.020 0.002 0.015 0.003 300 523 

4 A106-Gr.C-1 - 0.24 0.27 1.27 0.022 0.006 - - - 340 520 

5 A106-Gr.C-2 - 0.21 0.24 1.25 0.003 0.020 - - - 390 533 

6 A106-Gr.C-3 - 0.27 0.29 0.87 0.012 0.007 - - - 323 519 

7 A226-Cl.4 650°C×1.5hr 0.19 0.23 1.24 0.005 0.004 - - - 347 501 

8 A333-Gr.6-1 900°C×10hxA 0.16 0.14 1.2 0.026 0.015 - - - 353 539 

9 A333-Gr.6-2 900°C×0.5hxAC 0.20 0.31 0.93 0.020 0.015 - - - 302 490 

10 A333-Gr.6-3 900°C ×2hxA 0.16 0.29 1.26 0.02 0.014 - - - 297 426 

11 A333-Gr.6-4 - 0.15 0.2 1.25 0.019 0.006 314 490 

12 A333-Gr.6-5 - 0.21 0.31 1.14 0.016 0.012 383 549 

13 A333-Gr.6-GE - 0.12 0.23 1.05 0.010 0.030 - - - 309 427 

14 A333-Gr.6-7 As received 0.21 0.27 1.29 0.01 0.008 - - - 310 531 

15 A333-Gr.6-8 900°C×0.5hxAC 0.20 0.26 1.14 0.01 0.016 - - - 348 509 

16 A333-Gr.6-9 650°C×1.5hr 0.21 0.27 1.29 0.011 0.026 - - - 278 524 

17 A508-Gr.1-1 870°C×6.0h×W, 620°C×1.0h×AC, 

635°C×46.0h×FC 0.20 0.26 1.31 0.008 0.008 0.35 0.06 0.02 335 503 

18 A508-Gr.1-2 - 0.19 0.23 1.24 0.005 0.004 0.32 0.21 0.02 347 501 

19 A508-Gr.1-3 - 0.21 0.30 1.25 0.011 0.008 - - - 350 540 

20 A216-Gr.WCC - 0.22 0.40 0.90 0.013 0.015 0.14 0.20 0.17 316 500 

21 A516-KC70- - 0.26 0.28 0.95 0.017 0.033 - - - 331 514 

22 A516-G70 As received 0.23 0.24 1.11 0.012 0.002 - 0.05 - 330 526 

23 CS Tube - - - - - - - - - - - 
B-2

Mat. 

ID

Heat 

Designation Heat Treatment

Chemical Composition (wt.%) YS 

(MPa)

UTS 

(MPa)

E

C Si Mn P S Ni Cr Mo

24 CS - - - - - - - - - - - 

Low-Alloy Steels

1 A302-Gr.B 899-927°Cx4hxWQ to 538°CxA:649-

tempered @ 677°C:621-649°Cx6hxA 0.21 0.22 1.34 0.021 0.027 0.23 0.14 0.51 389 552 

2 A508-Gr.2 880°CX4.5hXWC+665°CX4.3hXAC+62

0°CX46.2hXFC 0.21 0.25 0.88 0.007 0.003 0.86 0.42 0.66 521 673 

3 A508-Gr.2 - 0.21 0.25 0.68 0.01 0.011 0.84 0.36 0.65 469 629 

4 A508-Gr.2 880°CX6hXWC+660°CX10hXAC+620°C

X45hXFC 0.18 0.31 0.77 0.008 0.008 0.74 0.36 0.6 510 637 

5 A508-Gr.2 880°CXWC+660°CXAC+620°CXFC 0.20 0.26 0.94 0.006 0.008 0.78 0.36 0.6 583 655 

6 A508-Gr.3 880°CX7hXWC+654°CX8hXWC 0.17 0.28 1.38 0.003 0.003 0.74 0.15 0.48 447 598 

7 A508-Gr.3 900°C×16.7hxA:650°C×16.5hxF:890°C×

9.1hxW:660°C×9.0hxA 0.20 0.26 1.42 0.004 0.002 0.74 0.11 0.5 453 605 

8 A508-Gr.3 900°C×8.3hxA:650°C×8.0hx:880°C×4.8h

xW:660°C×4.1hxA 0.23 0.27 1.5 0.004 0.003 0.77 0.13 0.52 503 637 

9 A508-Gr.3 910°C×8hxA:660°C×7.0hxA:890°C×8.0h

xW:650°C×8.0hxA 0.18 0.22 1.46 0.003 0.005 0.69 0.15 0.57 476 602 

10 A508-Gr.3 910°CX8.0hXAC+660°CX7.0hXAC+890

°CX8.0hXWC+650°CX8.0hXAC 0.20 0.29 1.45 0.003 0.003 0.68 0.12 0.55 476 611 

11 A508-Gr.3 930°C×8hxA:660°C×5.0hxA:890°C×6.0h

xW:660°C×8.0hxA 0.19 0.2 1.46 0.003 0.003 0.76 0.15 0.48 456 596 

12 A508-Gr.3 910°C×8hxA:660°C×7.0hxA:890°C×8.0h

xW:650°C×8.0hxA 0.20 0.29 1.45 0.003 0.003 0.68 0.12 0.55 476 611 

13 A508-Gr.3 - 0.20 0.26 0.94 0.006 0.008 0.78 0.36 0.6 533 655 

14 A508-Gr.3 880°C x 7h water quenching, 655°C x 

9h air cooling 0.21 0.25 1.24 0.007 0.002 0.88 0.21 0.47 461 593 

15 A508-Gr.3 - - - - - 0.018 - - - - - 

16 A533-Gr.B 871-899°Cx5.5hxBQ:649-

663°Cx5.5hxBQ:607°Cx23.8hxA 0.22 0.19 1.3 0.01 0.012 0.51 0.18 0.48 431 602 

17 A533-Gr.B 880°CX0.0hXWC+660°CX5.0hXFC 0.19 0.24 1.28 0.008 0.007 0.64 0.19 0.45 454 601 

18 900°C×5.0hxA:640°C×5.0hxA:880°C×4.

0hxW:660°C×4.0hxA 0.17 0.27 1.32 0.004 0.001 0.65 0.13 0.55 518 647 

19 A533-Gr.B 900°C×8.0hxA:635°C×12.3hxA:880°C×8

.0hxW:655°C×6.2hxA 0.18 0.27 1.39 0.008 0.003 0.61 0.15 0.54 580 647 

20 A533-Gr.B 900°C×3.3hxA:880°C×3.3hxW::655°C×3

.3hxA 0.18 0.22 1.42 0.004 0.002 0.69 0.09 0.49 443 597 

21 A533-Gr.B 880°CX5.6hXWC+660°CX4.9hXAC+61

5°CX45.9hXFC 0.19 0.27 1.45 0.02 0.010 0.60 0.13 0.52 488 630 
B-3

Mat. 

ID

Heat 

Designation Heat Treatment

Chemical Composition (wt.%) YS 

(MPa)

UTS 

(MPa)

E

C Si Mn P S Ni Cr Mo

22 A533-Gr.B 880°C×5.6hxW:660°C×4.9hxA:615°C×4

5.9hxF:375°C×480.0hxF 0.18 0.31 0.77 0.008 0.008 0.74 0.36 0.6 510 637 

23 A533-Gr.B

900°C x 3h water quenching, 660°C x 

3h air cooling, then 600°C x 25h to 

relieve stress 

0.17 0.25 1.39 0.003 0.013 0.59 0.004 0.46 483 584 

24 A533-Gr.B

900°C x 3h water quenching, 660°C x 

3h air cooling, then 600°C x 25h to 

relieve stress 

0.17 0.24 1.38 0.003 0.025 0.60 0.004 0.47 488 582 

25 A533-Gr.B - 0.17 0.24 0.36 0.003 0.038 0.59 0.009 0.47 - - 

26 A533- Gr. B

(SQV2A) - 0.22 0.28 1.43 0.021 0.021 0.51 0.1 0.49 481 617 

27 A533-Gr.B 

Cl.2 - 0.18 0.24 1.43 0.003 <0.001 0.66 - 0.57 548 679 

28 A533-Gr.B - - - - - 0.014 - - - - - 

29 LAS - - - - - - - - - - - 

30 15MnNi63 - - - - - - - - - - - 

31 17MNMoV64 - - - - - - - - - - - 
B-4

B2 Wrought and Cast Austenitic Stainless Steels and Welds

The various grades, heat treatment, chemical composition, and mechanical properties of the wrought and ca

steels and associated weld metals used in this report are listed in the following table. 

Mat.

ID

Heat 

Designation

Chemical Composition (wt.%) YS 

(MPa)

UTS 

(MPa)

Elong. 

(%)

C Si Mn P S Ni Cr Mo N

Type 304 Stainless Steel

1 304-1 0.050 0.50 1.52 0.028 0.001 9.45 18.35 - - 253 570 66.3 

2 304-2H 0.050 0.26 0.74 0.032 0.022 8.21 18.14 0.15 - 252 605 78.8 

3 304-3, 3H 0.060 0.50 1.55 0.023 0.001 9.35 18.35 - - 260 573 59.7 

4 304-4B 0.050 0.51 0.15 0.035 0.004 9.04 18.52 - - - - - 

5 304-5B 0.060 0.54 0.11 0.027 0.008 8.87 18.51 - - - - - 

6 304-6B 0.060 0.56 0.16 0.040 0.005 9.20 18.35 - - - - - 

7 304-7B 0.059 0.69 0.08 0.025 0.005 8.89 18.28 - - - - - 

8 304-8B 0.060 0.54 0.09 0.025 0.007 8.69 18.15 - - - - - 

9 304-9T 0.070 0.27 1.69 0.033 0.009 8.15 18.16 223 602 63.0 

10 304-10 0.060 0.50 0.80 0.032 0.010 8.82 18.35 0.19 0.019 222 667 72.9 

11 304-11H 0.070 0.56 1.60 0.023 0.007 9.40 18.30 - - 237 628 53.0 

12 304-12 - - - - - - - - - - 600 - 

13 304-13 0.026 0.40 0.45 0.030 0.014 8.50 18.67 0.02 - 255 745 - 

14 304-14 0.026 0.40 0.45 0.030 0.014 8.50 18.67 0.02 - 745 951 - 

15 304-15 - - - - - - - - - - - - 

16 304-16 0.060 0.31 1.89 0.026 0.025 9.96 19.92 0.15 - 305 632 60.9 

17 304-17 - - - - - - - - - - - - 

18 304-18 0.020 0.49 1.78 0.014 0.011 9.78 18.50 - - 276.5 572.2 - 

19 304-19 - - - - - - - - - - - - 

20 304-G 0.070 0.54 1.63 0.016 0.013 9.50 18.57 - - 251 561 64.0 

21 304-A2 0.060 0.48 1.54 0.019 0.007 8.00 18.99 0.44 - - - - 

22 304-21T 0.060 0.59 0.83 0.023 0.002 9.17 18.89 - 0.040 246 604 57.4 

23 304-32 0.070 0.27 1.69 0.033 0.009 8.15 18.16 - - 221 616 62.0 

24 304-35 0.070 0.65 0.91 0.022 0.002 8.09 18.48 - - 245 682 59.0 

25 304-xxT 0.050 0.48 1.72 0.027 0.003 9.23 18.12 - - 274 580 60.0 

26 304HP-1 0.050 0.54 0.88 0.029 0.010 9.10 18.53 0.12 - 242 666 68.0 

27 304HP-2 0.060 0.45 0.82 0.029 0.006 8.61 18.38 - 0.052 275 618 68.0 
B-5

Mat.

ID

Heat 

Designation

Chemical Composition (wt.%) YS 

(MPa)

UTS 

(MPa)

Elong. 

(%)

C Si Mn P S Ni Cr Mo N

28 304L-E 0.039 0.36 1.82 0.030 0.006 10.38 18.50 0.06 0.055 - - - 

29 304L-1 0.017 0.29 1.19 0.024 0.002 9.15 18.05 - - 245 574 61.0 

30 304L-G 0.017 0.51 1.72 0.018 0.013 10.16 19.09 - - 259 339 63.3 

31 304L 0.013 0.61 0.90 0.020 0.080 9.30 18.50 - 0.090 235 588 65.0 

Type 316 Stainless Steel

32 316-1H 0.055 0.52 1.51 0.027 0.005 13.20 16.25 2.12 - 177 465 43.5 

33 316-2 0.050 0.70 1.10 0.034 0.003 12.60 17.05 2.24 0.017 257 606 67 

34 316-3H 0.040 0.76 1.63 0.030 0.007 11.57 17.44 2.47 - - - 58 

35 316-4 0.060 0.40 1.72 0.012 0.007 13.30 17.30 2.33 - - - - 

36 316-5 - - - - - - - - - - - - 

37 316-6 - - - - - - - - - - - - 

38 316-7 - - - - - - - - - - - - 

39 316-8 - - - - - - - - - - - - 

40 316-9 - - - - - - - - - - - - 

41 316-10 - - - - - - - - - - - - 

42 316-12T 0.060 0.61 1.69 0.025 0.010 13.06 16.55 2.08 234 550 63 

43 316-13T 0.070 0.50 1.50 0.031 0.010 11.10 17.60 2.30 - 264 569 58.5 

44 316-14T 0.060 0.60 1.60 0.026 0.010 13.00 16.50 2.07 - 250 555 50.5 

45 316-15T, 27T 0.040 0.37 1.55 0.025 0.001 12.55 16.50 2.10 - 247 531 54 

46 316-26T 0.057 0.64 1.64 0.026 0.005 13.02 16.48 2.07 - 250 555 50 

47 316L-1H 0.040 0.37 1.55 0.025 0.001 12.55 16.50 2.10 - 154 406 43 

48 316N-1 0.015 0.39 1.66 0.025 0.003 14.90 17.25 2.32 - 259 555 60.7 

49 316N-2 0.010 0.51 1.67 0.027 0.001 13.25 17.50 2.50 0.106 264 574 63.9 

50 316N-3H 0.009 0.65 1.55 0.023 0.002 12.70 17.60 2.74 - 168 454 43.7 

51 316N-6 0.012 0.45 1.58 0.024 0.004 12.60 17.15 2.46 0.102 310 710 44.2 

52 316N-7 0.007 0.36 0.51 0.002 0.001 74.95 16.01 - 300 588 55 

53 316N-8 0.008 0.56 1.46 0.028 0.001 12.11 17.73 2.60 0.090 252 558 62 

54 316N-A 0.011 0.61 0.91 0.017 0.004 11.18 16.26 2.17 - - - - 

Stainless Steel Welds

55 304HP-WM-1 0.058 0.68 1.78 0.026 0.005 9.62 19.98 0.06 0.039 - - - 

56a 308-WM-1 0.050 0.56 1.39 0.022 0.004 10.30 19.90 - - - - - 
B-6

Mat.

ID

Heat 

Designation

Chemical Composition (wt.%) YS 

(MPa)

UTS 

(MPa)

Elong. 

(%)

C Si Mn P S Ni Cr Mo N

56b 308-WM-2 0.034 0.71 1.93 0.022 0.007 9.78 19.60 0.08 - 414 578 38.0 

57a 316 WM 0.039 0.39 1.31 0.011 0.005 11.60 19.60 2.20 - - - - 

57b 316TP WM-1 0.020 0.41 1.90 0.013 0.006 12.20 18.80 2.20 - - - - 

57c 316TP WM-2 0.070 0.40 1.82 0.011 0.006 12.50 18.50 2.19 - - - - 

57 316N-WM-1 0.018 0.39 1.70 0.010 0.007 11.47 19.75 2.27 0.075 - - - 

59 316N-WM-2 0.017 0.43 1.86 0.011 0.006 12.01 19.49 2.39 - 489 615 30.0 

60 316N-WM-3 0.002 0.44 1.46 0.026 0.001 13.14 17.21 2.43 0.078 254 548 57.0 

Cast Austenitic Stainless Steel

61 CF–8M-1 0.053 0.95 0.80 0.030 0.005 9.52 20.52 2.20 0.045 300 611 45.3 

62 CF–8M-2 0.050 1.17 0.86 0.021 0.006 10.03 20.59 2.28 - 308 619 51.0 

63 CF–8M-3 0.050 0.79 0.74 0.026 0.009 9.66 18.86 2.23 - 232 561 49.0 

64 CF–8M-4 0.050 1.00 0.80 0.030 0.010 9.52 20.50 2.20 - 300 611 45.3 

65 CF–8M-5 0.050 1.30 0.80 0.280 0.020 9.32 20.80 2.30 - 352 644 43.3 

66 CF–8M-6 0.050 0.60 0.80 0.280 0.010 10.50 20.20 2.16 - 259 521 48.6 

67 CF–8M-7 0.050 0.79 0.74 0.026 0.009 9.66 18.86 2.23 - 252 498 50.0 

68 CF–8M-8 0.064 0.73 0.54 0.022 0.016 9.03 19.11 2.51 0.048 273 537 63.0 

69 CF–8M-9 0.065 0.67 0.53 0.022 0.012 9.12 20.86 2.58 0.0523 322 601 43.6 
B-7

B3 Ni-Cr-Fe Alloys and Welds

The various grades, heat treatment, chemical composition, and mechanical properties of the Ni-Cr-Fe Alloys 

metals used in this report are listed in the following table.

Mat. 

ID

Heat 

Designation

Chemical Composition (wt.%) YS

(MPa)

UTS

(MPa)

Elon

(%

C Si Mn P S Ni Cr Fe Other

1 Alloy 600-1 0.070 0.32 0.51 0.002 0.001 74.86 15.95 8.13 - 310 710 44.

2 Alloy 600-2 0.070 0.29 0.37 0.006 0.001 76.07 15.46 7.12 0.01 Cu 294 686 42.

3 Alloy 600-3 0.010 0.17 0.21 0.007 0 73.33 16.60 6.95 2.56 Nb+Ta 279 677 54.

4 Alloy 600-4 0.010 0.17 0.21 0.007 0 73.33 16.60 6.95 2.56 Nb+Ta 289 693 63.

5 Alloy 600-5 0.070 0.34 0.37 0.007 0.001 73.56 15.64 9.46

0.16 Nb, 

0.01 Ta, 

0.27 Ti

303 696 39.

6 Alloy 600-6 0.030 0.05 0.49 0.004 0.001 74.50 16.00 8.37 - 264 635 55.

7 Alloy 600-7 0.020 0.17 0.13 0.017 0.010 75.85 15.54 6.81

0.06 Cu,

0.01 Co,

0.18 Al,

0.11 Ti,

0.096 Cb

253 612 50.

8 Alloy 600-8 0.080 0.19 0.13 - 0.007 77.31 15.70 6.52

0.04 Cu,

0.23 Ti,

0.05 Co,

0.14 Al

567 745 - 

9 Alloy 600-9 0.060 0.25 0.20 - 0.007 76.67 15.45 7.24

0.06 Cu,

0.21 Ti,

0.09 Co,

0.13 Al

256 651 - 

10 Alloy 600-10 0.080 0.48 0.46 0.010 0.008 73.63 15.72 9.40

0.08 Cu,

0.12 Ti,

0.05 Co,

0.02 Al

267 656 - 

11 Alloy 600-11 0.030 1.20 0.99 - 0.012 73.76 15.52 7.58

0.12 Cu,

0.05 Ti,

0.08 Co,

0.009 Al,

253 538 - 
B-8

Mat. 

ID

Heat 

Designation

Chemical Composition (wt.%) YS

(MPa)

UTS

(MPa)

Elon

(%

C Si Mn P S Ni Cr Fe Other

0.65 Cb+Ta

12 Alloy 600-12 0.070 0.73 0.78 - 0.005 74.40 16.00 7.70

0.01 Cu,

0.01 Ti,

0.11 Co,

0.01 Al

170 374 - 

13 Alloy 600-13 0.051 0.31 0.25 0.010 0.0012 73.72 15.80 8.86

0.021 Cu,

0.24 Ti,

0.05 Co,

0.21 Al,

0.0010 B

237 654 45.

14 Alloy 600-14 0.050 0.20 0.20 - 0.007 78.04 15.37 6.03 0.08 Cu 312 685 45.

15 Alloy 600-15 - - 0.24 - 0.008 74.21 - - 0.13 Cu 403 721 43.

16 Alloy 600-16 0.050 0.20 0.20 - 0.007 78.04 15.37 6.03 0.08 Cu 312 685 45.

16 Alloy 600-16 0.060 0.25 0.20 - 0.007 76.67 15.45 7.24

0.06 Cu,

0.21 Ti,

0.09 Co,

0.13 Al

256 651 - 

17 Alloy 600-17 0.020 0.17 0.13 0.017 0.010 75.85 15.54 6.81

0.06 Cu,

0.11 Ti,

0.01 Co,

0.18 Al,

0.096 Cb

245 595 48.

20 Alloy 690-1 0.030 0.11 0.27 0.007 0.001 60.1 29.50 9.44 - 280 691 46.

21 Alloy 690-2 - - - - - - - - - - - - 

22 Alloy 690-3 0.020 0.09 0.15 - <0.001 61.58 29.15 9.00 <0.01 Cu,

0.007 Co 247 643 52.

25 Alloy 800-1 0.060 0.38 0.90 - 0.007 32.11 20.35 45.17

0.25 Cu,

0.39 Ti,

0.36 Al

190 546 - 

26 Alloy 800-2 0.060 0.38 0.90 - 0.007 32.11 20.35 45.17

0.25 Cu,

0.39 Ti,

0.36 Al

158 499 - 

26 Alloy 800-2 - - - - - - - - - 212 515 - 
B-9

Mat. 

ID

Heat 

Designation

Chemical Composition (wt.%) YS

(MPa)

UTS

(MPa)

Elon

(%

C Si Mn P S Ni Cr Fe Other

30 Inconel 718-1 - - - - - - - - - - - - 

31 Inconel 718-2 - - - - - - - - - 1200 1515 - 

32 Inconel 718-3 - - - - - - - - - - - - 

33 Inconel 718-4 - - - - - - - - - - - - 

34 Inconel 718-5 - - - - - - - - - - - - 

35 Inconel 718-6 0.030 0.35 0.18 - 0.007 52.64 18.59 18.94

0.36 Al,

0.03 Cu,

2.96 Mo,

0.91 Ti

4.98 Cb+Ta

1110 1304 - 

36 Inconel 718-7 - - - - - - - - - - - - 

38 Alloy 690 WM 0.037 0.32 4.47 <0.005 0.001 55.60 29.20 8.71 - 431 656 39.

39 Alloy 62 * 0.070 0.175 0.325 - 0.006 73.50 17.75 6.90

1.0 Cb,

0.01 Cu,

0.05 Co

- - - 

40 Alloy 82-1 0.040 0.10 2.80 - 0.017 63.50 17.28 13.56

0.02 Co,

0.004 Al,

0.01 Cu,

0.044 Mo,

0.08 Ti

1.92 Cb+Ta

353 606 - 

41 Alloy 82-2 0.040 0.86 2.54 - 0.014 65.05 20.00 8.60

0.10 Co,

1.75 Mo,

0.03 Ti

1.46 Cb+Ta

322 633 - 

42 Alloy 82-3 0.070 0.30 2.48 0.005 0.015 54.70 13.95 25.70

0.02 Co,

0.05 Al,

0.02 Cu,

0.01 Mo,

0.25 Ti

1.77 Cb+Ta

0.01 V,

0.01 W,

355 573 - 
B-10

Mat. 

ID

Heat 

Designation

Chemical Composition (wt.%) YS

(MPa)

UTS

(MPa)

Elon

(%

C Si Mn P S Ni Cr Fe Other

0.002 Mg

43 NiCrFe WM-1 - - - - - - - - - - - - 

44 Arcaloy 8N12 - - - - - - - - - - - - 

45 NiCrFe WM-2 - - - - - - - - - - - - 

46 Alloy 82-4 0.040 0.10 2.80 - 0.017 63.50 17.28 13.56

0.02 Co,

0.004 Al,

0.01 Cu,

0.044 Mo,

0.08 Ti

1.92 Cb+Ta

353 606 - 

47 Alloy 182-1 0.060 0.61 5.56 0.004 0.006 68.20 15.50 7.25 0.14 Cu, 

0.52 Ti 456 698 35.

48 Alloy 182-2 0.060 0.61 5.56 0.004 0.006 68.20 15.50 7.25 0.14 Cu, 

0.52 Ti 456 698 35.

49 Alloy 182-3 0.038 0.25 2.50 0.004 0.005 73.00 15.10 7.20 - 405 667 38.

50 Alloy 182-4 0.040 0.21 2.76 <0.005 0.004 72.50 15.00 7.99 - 409 623 34.

51 Alloy 82-5 0.040 0.12 2.92 0.003 0.001 72.85 20.64 0.65

0.03 Cu,

0.04 Co,

0.27 Ti

339 565 56.

52 Alloy 152 - - - - - - - - - - - - 

53 Alloy 132 0.040 0.21 2.76 <0.005 0.004 72.50 15.0 7.99 <0.01 Cu 409 623 34.

* Average composition of first and second layers.
C-1

APPENDIX C SAMPLE PROBLEM

C1 Background

This Appendix provides the cumulative usage factor (CUF), environmental fatigue multiplier

(Fen), and environmentally assisted fatigue cumulative usage factor (CUFen) solution for a 

sample problem. The sample problem was obtained from Appendix B of Reference [C-1]. The 

purpose of this sample problem solution is to demonstrate one example of the use of the 

methodology described in this report to calculate the environmental fatigue multiplier (Fen) and 

environmentally assisted fatigue cumulative usage factor (CUFen) for a relatively simple 

problem. The sample problem is not intended to be an exhaustive treatment of more 

comprehensive component assessments that may be present in operating nuclear power plants.

The sample problem selected for solution in this appendix was the second example problem 

developed and solved by several industry participants. The purpose of the industry’s sample 

problem efforts was to evaluate the effectiveness of some American Society of Mechanical 

Engineers (ASME) Code Cases in providing sufficient guidance for environmentally assisted 

fatigue (EAF) evaluations, and to identify any related guidelines that may be useful for industry 

applications. The main intentions of the second sample problem were to ensure that transient 

pairs occurred between peaks and valleys from different transients, to include a complex 

transient with multiple peaks and valleys, to incorporate a dynamic load event, and to include 

dissolved oxygen variations between transients and during at least one transient.

During the industry’s solution of their first sample problem (documented in Appendix A of 

Reference [C-1]), considerable time was spent standardizing input parameters and stresses for 

the fatigue evaluation that preceded the environmental calculations. Those iterations yielded 

insight into the impact of certain modeling and analysis choices and the resulting differences in 

the fatigue results, which could be further magnified in the environmental fatigue analysis. 

Based on that insight, and to minimize differences in the stress and fatigue portions of the 

analysis, a standard set of stress histories for all transients was provided for all participants to 

use in the second sample problem. Those stress histories were used as the starting point for 

the calculations in this appendix. As a result, only minimal portions of the content for the 

sample problem statement and finite element modeling details used to derive the stresses for 

the sample problem are included in this appendix. The reader is referred to Appendix B of 

Reference [C-1] for those details.

C2 Problem Description

The full problem statement and definitions for the sample problem are provided in Appendix B of 

Reference [C-1].

The geometry evaluated in the sample problem is shown in Figure C.1. The geometry 

represents a typical vessel nozzle with attached piping.

The transients evaluated in the sample problem are shown in Table C.1. The transient

temperature, pressure, and dissolved oxygen (DO) time histories are plotted in Figure C.2.

The transient stress component histories that were obtained from finite element analysis were 

provided for the sample problem for both stress cut lines (SCLs) shown in Figure C.1. The 
C-2

SCL 2 stresses are plotted in Figures C.3 and C.4. Only the stresses for SCL 2 were evaluated 

in this appendix; calculations for SCL 1 would be performed in a similar manner with 

consideration given to the different material. The transients were linked in sequential order to 

obtain the overall stress histories used in the evaluation, as shown in Figure C.5. The OBE 

stresses were assumed to occur coincident with the peak stresses associated with Transient #2, 

which had the highest total stresses of any of the four thermal transients evaluated.

11.188 D

14.00 D

5.00

7.906

4.00

8.50 10.5

R 1.9

TP316 SA-508

DM

Weld

CL

SS

Weld

CL

1.00

TP316 SA-508

DM

Weld

CL

SCL 1 SCL 2

SS

Weld

CL

1.0

1.906

(Note: All dimensions are in inches. Sketches are not to scale.)

Figure C.1. Sample Problem Geometry

Pipe

Safe End

Nozzle
C-3

Table C.1. Sample Problem Transient Definitions

Transient

No.

Time

(sec)

Fluid Temperature

(°F)

Heat Transfer Coefficient, h

(BTU/s-in2-°F)

Pressure

(psi)

Resultant Moment

(in-kips)

DO 

(ppm)

1

(20 cycles)

0 450 0.003 2,250 -3,000 0.150

100 450 0.003 2,250 -3,000 0.150

450 100 0.003 1,000 1,000 0.150

1510 100 0.003 1,000 1,000 0.150

1710 600 0.003 2,250 -3,000 0.150

3210 600 0.003 2,250 -3,000 0.150

2

(50 cycles)

0 500 0.003 1,500 -2,500 0.550

100 500 0.003 1,500 -2,500 0.550

260 100 0.003 2,250 1,000 0.550

1290 100 0.003 2,250 1,000 0.550

1540 350 0.003 2,000 -2,500 0.550

3240 350 0.003 2,000 -2,500 0.550

3

(20 cycles)

0 300 0.003 1,600 0 0.050

50 650 0.003 1,600 0 0.050

250 650 0.003 1,600 0 0.050

275 400 0.003 1,600 0 0.050

400 400 0.003 1,600 0 0.050

600 550 0.003 1,600 0 0.050

700 550 0.003 1,600 0 0.050

900 350 0.003 1,600 0 0.050

1000 350 0.003 1,600 0 0.050

1200 400 0.003 1,600 0 0.050

1300 400 0.003 1,600 0 0.050

1500 70 0.003 1,600 0 0.050

1600 70 0.003 1,600 0 0.050

2000 300 0.003 1,600 0 0.050

3800 300 0.003 1,600 0 0.050

4

(100 cycles)

0 70 0.003 400 -3000 0.55

100 70 0.003 400 -3000 0.55

3700 170 0.003 400 -2100 0.442

7300 270 0.003 400 -1200 0.334

8272 297 0.003 580.32 -957 0.30484

10072 347 0.003 914.26 -507 0.25084

13672 447 0.003 1582.13 393 0.14284

17272 547 0.003 2250 1293 0.3484

18100 547 0.003 2250 1500 0.01

26000 547 0.003 2250 1500 0.01

5

(5 events;

10 cycles 

per event)

Operating Basis Earthquake (OBE) Transient

OBE loading was defined by resultant moment loads. The resultant moment load was specified as +/- 2000 inkips. Each OBE event was assumed to occur at any time during any of the transients. DO= 0.100 ppm.
C-4

Figure C.2. Sample Problem Transient Time Histories

0.600

0.500

0.400

0.300

0.200

0.100

0.000 0

500

2,500

2,000

1,500

1,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Dissolved Oxygen (ppm)

Pressure (psig)

F) ° Fluid Temperature (

Time (seconds)

Transient #1 - Pressure, Temperature and Dissolved Oxygen Histories

Pressure

Fluid Temperature

Dissolved Oxygen

0

500

2,500

2,000

1,500

1,000

0 500 1,000 1,500 2,00

Pressure (psig)

F) ° Fluid Temperature (

Time (seconds)

Transient #2 - Pressure, Temperature and 

0.600

0.500

0.400

0.300

0.200

0.100

0.000 0

500

2,500

2,000

1,500

1,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Dissolved Oxygen (ppm)

Pressure (psig)

F) ° Fluid Temperature (

Time (seconds)

Transient #3 - Pressure, Temperature and Dissolved Oxygen Histories

Pressure

Fluid Temperature

Dissolved Oxygen

0

500

2,500

2,000

1,500

1,000

0 5,000 10,000 15,000 

Pressure (psig)

F) ° Fluid Temperature (

Time (seconds)

Transient #4 - Pressure, Temperature and 
C-5

Figure C.3. Sample Problem Transient Membrane Plus Bending Stress Histories for SC

-20,000

-40,000

-60,000

0

60,000

40,000

20,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Stress (psi)

Time (seconds)

Primary Plus Secondary Stress Histories for Transient #1

Sx

Sy

Sz

Sxy

-20,000

-40,000

0

80,000

60,000

40,000

20,000

0 500 1,000 1,500 2

Stress (psi)

Time (seconds

Primary Plus Secondary Stress Histo

-20,000

-40,000

-60,000

0

60,000

40,000

20,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Stress (psi)

Time (seconds)

Primary Plus Secondary Stress Histories for Transient #3

Sx

Sy

Sz

Sxy

-10,000

-15,000

-20,000

-5,000

0

5,000

20,000

15,000

10,000

0 5,000 10,000 15,000 

Stress (psi)

Time (seconds

Primary Plus Secondary Stress Histo
C-6

Figure C.4. Sample Problem Transient Total Stress Histories for SCL 2

-20,000

-40,000

-60,000

-80,000

0

60,000

40,000

20,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Stress (psi)

Time (seconds)

Total Stress Histories for Transient #1

Sx

Sy

Sz

Sxy

-20,000

-40,000

0

80,000

60,000

40,000

20,000

0 500 1,000 1,500 2

Stress (psi)

Time (seconds

Total Stress Histories for Tr

-20,000

-40,000

-60,000

0

60,000

40,000

20,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Stress (psi)

Time (seconds)

Total Stress Histories for Transient #3

Sx

Sy

Sz

Sxy

-10,000

-15,000

-20,000

-5,000

0

5,000

20,000

15,000

10,000

0 5,000 10,000 15,000 

Stress (psi)

Time (seconds

Total Stress Histories for Tr
C-7

Figure C.5. Sample Problem Combined Transient Stress History for SCL 2

End of

Trans. 1

End of

Trans. 2

End of

Trans. 3T

-20,000

-40,000

-60,000

-80,000

0

80,000

60,000

40,000

20,000

100,000

0 5,000 10,000 15,000 20,000 25,000 30,000 35,

Stress (psi)

Time (seconds)

Total Stress Histories for All Transients (includes OBE)

Sx

Sy

Sz

Sxy
C-8

C3 Evaluation

The CUF for the sample problem was calculated in accordance with the ASME Boiler and 

Pressure Vessel Code (Code), Subsection NB [C-2] using the provisions of Subarticle NB-3200, 

“Design by Analysis.” A summary of the steps used to calculate the CUF is as follows:

A. The alternating stress intensities, Salt, were calculated for the input stress history (Table 

C.2) using the following steps (follows ASME Code NB-3216.2 methodology for varying 

principal stress direction):

a. NB-3216.2(a) requires that six components of stress be considered taking into 

account both gross and local structural discontinuities and the thermal effects 

which vary during the cycle. The stresses shown in Table C.2 satisfy this 

requirement and were used as input to the calculation.

b. NB-3216.2(b) requires selection of a point in time where conditions are at an 

extreme (either maximum or minimum algebraically). The maximum total stress 

values for each of the six stress components were found and identified as SXi

, 

SYi

, SZi, etc.

c. NB-3216.2(c) requires calculation of the stress differences for the entire stress 

history for every point in time. These differences were computed as S’X = (SXSXi

), S’Y = (SY-SYi), S’Z = (SZ-SZi), etc.

d. NB-3216.2(d) requires calculation of the principal stresses for the entire stress 

history for every point in time from the stress differences calculated in Step c. 

These differences were computed as S’1, S’2, and S’3 using the six stress 

differences (i.e., S’X, S’Y, S’Z, etc.).

e. Principal stresses were calculated for the entire stress history by solving a cubic 

equation for the six component stress differences from Step d.

f. NB-3216.2(e) requires calculation of the principal stress differences for the entire

stress history for every point in time as S'12 = (S'1-S'2), S'23 = (S'2-S'3), and S'31 = 

(S'3-S'1) and finding the largest absolute magnitudes of these three differences 

based on their variations throughout the stress history. Salt values were 

calculated as one-half of all of these largest stress amplitudes based on rangepair cycle counting for the entire stress intensity history to identify stress “peaks” 

(points of local stress maxima) and “valleys” (points of local stress minima).

g. The Salt values were adjusted for the effects of Young’s Modulus (per NB3222.4(e)(4)) and for the effects of simplified elastic-plastic analysis, i.e., Ke (per 

NB-3228.5).

h. Since it was not obvious which case led to the highest Salt values, all six of the 

following cases were evaluated1:

i. Based on maximum total SX stress.

ii. Based on maximum total SY stress.

 1 Since the shear stress components (SXY, SYZ, and SZX) have significantly lower values compared to the primary stress 

components (SX, SY, and SZ), they do not lead to a maximum Salt situation. As a result, they were not considered in the 

maximum Salt selection process.
C-9

iii. Based on maximum total SZ stress.

iv. Based on maximum membrane plus bending SX stress.

v. Based on maximum membrane plus bending SY stress.

vi. Based on maximum membrane plus bending SZ stress.

i. The Salt values counted for each case in Step h were designated as Salt 1, Salt 2, 

Salt 3, ..., Salt n. The number of times that each Salt value occurred during the 

entire principal stress difference history was determined, and these were 

designated as n1, n2, n3, ..., nn, respectively.

j. From the Salt 1, Salt 2, Salt 3, ..., Salt n values calculated for each case in Step h, the 

applicable design fatigue curve from Appendix A was used to determine the 

maximum number of allowable cycles, N1, N2, N3, ..., Nn.

k. Partial usage factors, U1, U2, U3, ..., Un, were calculated as U1 = n1/N1, U2 = 

n2/N2, U3 = n3/N3, ..., Un = nn/Nn.

l. The total CUF was calculated as U1 + U2 + U3 +...+ Un.

m. The highest CUF resulting from all of the six cases identified in Step h was used 

as the final reported CUF value.

Only CUF and Fen calculations were performed for the sample problem. Therefore, the results 

of stress limit checks required as a part of ASME Code design calculations are not included in 

this appendix.

Calculations for CUFen were performed for the limiting CUF value. Strain rates were calculated 

based on the total S'31 history which was the limiting CUF case. Fen was computed using the 

equations in Appendix A of this report using two approaches:

A. Average Strain Rate Approach: In this approach, the Fen for each peak and valley 

resulting from the Salt calculation process was computed as follows:

i. The strain rate was based on the total stress component principal stress 

difference, S’31, which was used to compute CUF. For simplicity, Ke was 

conservatively not included in the calculation of strain rate.

ii. The strain rate was calculated between each adjacent valley and peak with 

increasing stress, as:

ε̇ = (S’31-peak – S’31-valley) / (∆t x E x 100)

where: ε̇ = strain rate (%/sec)

S’31-peak = S’31 stress intensity value at the peak (psi)

S’31-valley = S’31 stress intensity value at the valley (psi)

∆t = time increment between the valley and peak (seconds)

E = the Young's Modulus determined at the maximum metal 

temperature of the peak and valley (psi)

iii. To neglect compressive loading in the determination of Fen, the Fen value was set 

to 1.0 for any valley-to-peak interval where ε̇ was less than zero.

iv. The Fen was calculated between each valley and peak using the appropriate 

equation from Appendix A for the material evaluated, and using the maximum 

metal temperature of the peak and valley.
C-10

v. The Fen was assigned to both the peak and valley for use in the CUFen

calculations.

vi. The above steps were repeated for all valley-peak intervals for the entire 

principal stress intensity history.

B. Modified Strain Rate Approach: In this approach, the Fen for each peak and valley 

resulting from the Salt calculation process was computed using the Modified Rate 

Approach described in Section 4.1.14, as follows:

i. The strain rate was based on the total stress component principal stress 

difference, S’31, which was used to compute CUF. For simplicity, Ke was 

conservatively not included in the calculation of strain rate.

ii. The Fen integration was set up and performed between each valley and peak with 

increasing stress, as follows (refer to Figure 80):

ε̇

i = S’31 i+1 – S’31 i

100 ∆t E

where: ε̇

i = strain rate at any point, i, between the valley and peak 

(%/sec)

S’31 i+1 = S’31 stress intensity value at point i+1 (psi)

S’31 i = S’31 stress intensity value at point i (psi)

∆t = time increment between points i and i+1 (seconds)

E = the Young's Modulus determined at the maximum metal 

temperature of points i and i+1 (psi)

iii. To neglect compressive loading in the determination of Fen, the Fen value was set 

to 1.0 for any point interval where ε̇ was less than zero.

iv. The Fen,i was calculated between for point i and I=1 using the appropriate 

equation from Appendix A for the material evaluated, and using the maximum 

metal temperature of points i and i+1.

v. The integrated Fen-n for the valley-peak load pair was calculated as:

Fen−n = �Fen,i

k

i=1

εi

εmax − εmin

where: Fen-n = integrated Fen for valley-peak load pair n

k = number of integration points between valley and peak

εi = strain at any point, i, between the valley and peak

computed as S’31 i divided by E evaluated at the metal 

temperature of point i

εmax = maximum strain at the peak computed as S’31-peak divided 

by E evaluated at the metal temperature of the peak

εmin = minimum strain at the valley computed as S’31-valley divided 

by E evaluated at the metal temperature of the valley

E = the Young's Modulus determined at the maximum metal 

temperature of points i and i+1 (psi)

vi. The Fen calculated in Step B(v) was assigned to both the peak and valley for use 

in the CUFen calculations.
C-11

vii. The above steps were repeated for all valley-peak intervals for the entire 

principal stress intensity history.

viii. The total CUFen was calculated as Fen-1 U1 + Fen-2 U2 + Fen-3 U3 +...+ Fen-n Un.

C4 Results

The highest CUF calculated for the sample problem from Step A(m) in Section C3 is shown in 

Table C.2. The highest CUF resulted from the using the S’31 membrane plus bending principal 

stress differences (Case (v) for maximum membrane plus bending SY stress in Step A(h) in 

Section C3). The entire principal stress difference time history for this case is also plotted in 

Figure C.6. The peaks and valleys identified in the Table C.2 CUF calculation are also indicated 

on the plot in Figure C.6.

The CUFen calculated for the sample problem using the Average Strain Rate Approach is shown 

in Table C.3.

The CUFen calculated for the sample problem using the Modified Strain Rate Approach is shown 

in Table C.4.

The entire principal stress difference time history for this case, as calculated in Step A(f) in 

Section C3, is provided in Table C.5.
C-12

Table C.2. Limiting CUF Results for Sample Problem for SCL 2

Pair A Pair B

Applied

Cycles 

A

Applied

Cycles 

B

M+B 

STRESS

(psi) Ke

Total 

Stress

(psi)

Salt

(psi) Nn nn U

694 447 5 20 125542.9 2.580 144164.4 220490.4 140.005 5 0.03

699 447 50 15 121622.8 2.405 139047.0 198300.6 178.958 15 0.08

699 1021 35 20 104691.5 1.653 126037.5 124507.0 582.468 20 0.03

699 899 15 50 89695.4 1.000 102302.8 57864.5 6339.47 15 0.00

695 899 5 35 84993.9 1.000 98798.6 55882.4 7027.83 5 0.00

185 899 20 30 68222.2 1.000 76465.1 43250.2 15549.1 20 0.00

1432 899 20 10 66665.7 1.000 83098.8 47002.3 11892.7 10 0.00

1432 1653 10 100 49437.0 1.000 61950.9 33687.5 35734.8 10 0.00

1296 1653 20 90 32478.6 1.000 38719.1 22025.4 154852 20 0.00

1136 1653 20 70 27045.6 1.000 33751.1 19388.7 258499 20 0.00

2215 1653 100 50 25255.9 1.000 25668.1 15147.6 1.15E+06 50 0.00

2215 1213 50 20 22343.7 1.000 25298.3 14929.4 1.30E+06 20 0.00

2215 1562 30 20 22047.7 1.000 24970.1 14735.7 1.46E+06 20 0.00

2215 1 10 20 11956.0 1.000 12255.6 7232.5 1.00E+11 10 0.00

1347 1 20 10 3786.5 1.000 4173.0 2412.1 1.00E+11 10 0.00

1347 1595 10 20 3408.0 1.000 3430.2 1963.3 1.00E+11 10 0.00

960 1595 20 10 241.8 1.000 259.9 146.0 1.00E+11 10 0.00

960 960 5 5 0.0 1.000 0.0 0.0 1.00E+11 10 0.00

TOTAL CUF = 0.15
C-13

Figure C.6. Principal Stress Intensity Histories and Peaks and Valleys Used in Limiting CUF Calcula

Problem for SCL 2

185

1

447

694

695

699

899

960

1021

1136

1213

1296

1347

1432

1562

1595

1653

2215

-100,000

-120,000

-140,000

-20,000

-40,000

-60,000

-80,000

0

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 

Stress Difference (psi)

Time (seconds)

Peaks and Valleys Based on P+Q Principal Stress Differences

Sigma3-Sigm

Peaks and V
C-14

Table C.3. CUFen Results Based for Sample Problem for SCL 2

(Average Strain Rate Approach)

Pair A Pair B Fen-n Un CUFen-n

694 447 49.107 0.0357 1.7538

699 447 3.156 0.0838 0.2645

699 1021 3.156 0.0343 0.1084

699 899 3.156 0.0024 0.0075

695 899 1.000 0.0007 0.0007

185 899 15.763 0.0013 0.0203

1432 899 2.802 0.0008 0.0024

1432 1653 2.802 0.0003 0.0008

1296 1653 5.418 0.0001 0.0007

1136 1653 5.865 0.0001 0.0005

2215 1653 198.536 0.0000 0.0086

2215 1213 198.536 0.0000 0.0030

2215 1562 198.536 0.0000 0.0027

2215 1 198.536 0.0000 0.0000

1347 1 1.000 0.0000 0.0000

1347 1595 2.231 0.0000 0.0000

960 1595 10.531 0.0000 0.0000

960 960 10.531 0.0000 0.0000

TOTAL CUFen = 2.1738 (Overall Fen = 13.6174)
C-15

Table C.4. CUFen Results Based for Sample Problem for SCL 2

(Modified Strain Rate Approach)

Pair A Pair B Fen-nA Fen-nB Un Fen-n CUFen-n

694 447 45.1590 1.0000 0.0357 45.159 1.6128

699 447 2.2180 1.0000 0.0838 2.218 0.1859

699 1021 2.2180 1.0000 0.0343 2.218 0.0762

699 899 2.2180 1.0000 0.0024 2.218 0.0052

695 899 1.0000 1.0000 0.0007 1.000 0.0007

185 899 7.2220 1.0000 0.0013 7.222 0.0093

1432 899 2.0700 1.0000 0.0008 2.070 0.0017

1432 1653 2.0700 1.0000 0.0003 2.070 0.0006

1296 1653 4.3530 1.0000 0.0001 4.353 0.0006

1136 1653 5.5320 1.0000 0.0001 5.532 0.0004

2215 1653 24.7870 1.0000 0.0000 24.787 0.0011

2215 1213 24.7870 1.0000 0.0000 24.787 0.0004

2215 1562 24.7870 1.0000 0.0000 24.787 0.0003

2215 1 24.7870 1.0000 0.0000 24.787 0.0000

1347 1 1.0000 1.0000 0.0000 1.000 0.0000

1347 1595 1.0000 2.2310 0.0000 2.231 0.0000

960 1595 12.1020 2.2310 0.0000 12.102 0.0000

960 960 12.1020 12.1020 0.0000 12.102 0.0000

TOTAL CUFen = 1.8952 (Overall Fen = 11.8726)
C-16

Table C.5. Principal Stress Intensity Histories Used in Limiting CUF Calculation for 

Sample Problem for SCL 2

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1 0.00 34007.5 29079.5 -63087.0 45032.0 27828.0 -72859.9 450.0 20 0.150

2 10.00 33994.5 29077.5 -63072.0 45002.0 27826.0 -72827.9 449.9 20 0.150

3 20.00 33977.5 29071.5 -63049.0 44976.0 27821.0 -72796.9 449.7 20 0.150

4 30.00 33961.5 29064.5 -63025.9 44954.0 27814.0 -72767.9 449.6 20 0.150

5 40.00 33946.5 29057.5 -63003.9 44934.0 27807.0 -72740.9 449.5 20 0.150

6 60.00 33920.5 29040.5 -62960.9 44899.9 27792.0 -72691.9 449.2 20 0.150

7 80.00 33898.4 29023.4 -62921.9 44873.0 27776.0 -72648.9 448.9 20 0.150

8 100.00 33880.4 29005.4 -62885.9 44850.9 27758.9 -72609.9 448.6 20 0.150

9 103.00 33902.5 28926.5 -62829.1 44871.9 27678.9 -72550.8 448.6 20 0.150

10 105.00 33857.6 28864.6 -62722.2 44605.8 27617.8 -72223.6 447.2 20 0.150

11 107.00 33752.7 28792.7 -62545.3 44275.7 27545.7 -71821.4 445.7 20 0.150

12 109.00 33614.7 28711.7 -62326.4 43940.6 27466.6 -71407.2 444.1 20 0.150

13 111.00 33454.8 28622.8 -62077.5 43606.5 27380.5 -70987.0 442.4 20 0.150

14 113.00 33282.8 28526.8 -61809.6 43276.4 27289.4 -70565.8 440.8 20 0.150

15 115.00 33096.9 28424.9 -61521.7 42952.3 27191.3 -70143.6 439.1 20 0.150

16 117.00 32906.9 28317.9 -61224.8 42634.2 27087.2 -69721.4 437.3 20 0.150

17 119.00 32712.9 28203.9 -60916.9 42321.1 26979.1 -69300.2 435.6 20 0.150

18 121.00 32518.0 28085.0 -60602.9 42015.1 26866.1 -68881.1 433.9 20 0.150

19 123.00 32319.0 27962.0 -60281.0 41715.0 26747.0 -68461.9 432.1 20 0.150

20 125.00 32121.0 27835.0 -59956.1 41421.9 26624.9 -68046.8 430.3 20 0.150

21 127.00 31924.1 27703.1 -59627.1 41132.8 26499.8 -67632.7 428.5 20 0.150

22 129.00 31728.1 27568.1 -59296.2 40850.8 26370.8 -67221.6 426.7 20 0.150

23 131.00 31534.1 27429.1 -58963.2 40576.7 26237.7 -66814.5 424.9 20 0.150

24 133.00 31341.1 27287.1 -58628.3 40306.7 26101.7 -66408.3 423.1 20 0.150

25 135.00 31151.2 27142.1 -58293.3 40042.6 25962.6 -66005.2 421.3 20 0.150

26 137.00 30964.2 26994.2 -57958.3 39783.5 25821.5 -65605.1 419.5 20 0.150

27 139.00 30780.2 26845.2 -57625.4 39531.5 25677.5 -65209.0 417.7 20 0.150

28 141.00 30598.2 26693.2 -57291.4 39283.4 25532.4 -64815.9 415.8 20 0.150

29 143.00 30419.2 26539.2 -56958.5 39041.4 25384.4 -64425.8 414.0 20 0.150

30 145.00 30243.2 26382.2 -56625.5 38804.3 25234.3 -64038.7 412.2 20 0.150

31 147.00 30071.3 26224.3 -56295.5 38573.3 25082.3 -63655.6 410.3 20 0.150

32 149.00 29901.3 26065.3 -55966.5 38346.3 24929.3 -63275.5 408.5 20 0.150

33 151.00 29734.3 25904.3 -55638.6 38123.2 24775.2 -62898.4 406.6 20 0.150

34 153.00 29570.3 25742.3 -55312.6 37904.1 24620.2 -62524.3 404.8 20 0.150

35 155.00 29409.3 25580.3 -54989.6 37691.1 24464.1 -62155.2 402.9 20 0.150

36 157.00 29251.3 25416.3 -54667.6 37481.1 24306.1 -61787.1 401.1 20 0.150
C-17

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

37 159.00 29096.3 25251.3 -54347.7 37276.0 24148.0 -61424.0 399.2 20 0.150

38 161.00 28943.3 25085.3 -54028.7 37075.0 23988.0 -61062.9 397.3 20 0.150

39 163.00 28794.4 24918.4 -53712.7 36877.9 23827.9 -60705.8 395.5 20 0.150

40 165.00 28648.4 24751.4 -53399.7 36685.9 23667.9 -60353.7 393.6 20 0.150

41 167.00 28503.4 24584.4 -53087.7 36495.8 23506.8 -60002.6 391.7 20 0.150

42 169.00 28362.4 24415.4 -52777.8 36309.8 23344.8 -59654.6 389.8 20 0.150

43 171.00 28222.4 24247.4 -52469.8 36127.7 23182.7 -59310.5 388.0 20 0.150

44 173.00 28085.4 24078.4 -52163.8 35948.7 23019.7 -58968.4 386.1 20 0.150

45 175.00 27952.4 23909.4 -51861.8 35773.6 22857.6 -58631.3 384.2 20 0.150

46 177.00 27820.4 23739.4 -51559.8 35601.6 22694.6 -58296.2 382.3 20 0.150

47 179.00 27691.4 23569.4 -51260.8 35433.5 22530.6 -57964.1 380.4 20 0.150

48 181.00 27564.4 23399.4 -50963.8 35267.5 22367.5 -57635.0 378.5 20 0.150

49 183.00 27440.4 23229.4 -50669.9 35106.5 22203.5 -57309.9 376.6 20 0.150

50 185.00 27319.4 23058.4 -50377.9 34948.4 22039.4 -56987.8 374.7 20 0.150

51 187.00 27199.4 22888.4 -50087.9 34792.4 21875.4 -56667.7 372.9 20 0.150

52 189.00 27081.4 22718.5 -49799.9 34639.3 21711.3 -56350.6 371.0 20 0.150

53 191.00 26965.5 22549.4 -49514.9 34489.3 21547.2 -56036.5 369.1 20 0.150

54 193.00 26851.5 22379.5 -49230.9 34341.2 21384.2 -55725.4 367.2 20 0.150

55 195.00 26741.5 22208.5 -48949.9 34198.2 21220.1 -55418.3 365.3 20 0.150

56 197.00 26631.5 22039.5 -48671.0 34056.1 21056.1 -55112.2 363.4 20 0.150

57 199.00 26524.5 21869.5 -48393.9 33917.1 20892.1 -54809.1 361.4 20 0.150

58 201.00 26418.5 21700.5 -48119.0 33780.0 20730.0 -54510.0 359.5 20 0.150

59 203.00 26315.5 21530.5 -47846.0 33647.0 20566.0 -54212.9 357.6 20 0.150

60 205.00 26215.5 21361.5 -47577.0 33515.9 20402.9 -53918.8 355.7 20 0.150

61 207.00 26115.5 21192.5 -47308.0 33386.9 20240.9 -53627.8 353.8 20 0.150

62 209.00 26017.5 21024.5 -47042.0 33260.8 20076.8 -53337.7 351.9 20 0.150

63 211.00 25921.5 20855.5 -46777.0 33135.8 19915.8 -53051.5 350.0 20 0.150

64 213.00 25828.5 20687.5 -46516.0 33014.7 19753.7 -52768.4 348.1 20 0.150

65 215.00 25735.5 20519.5 -46255.0 32895.7 19590.7 -52486.4 346.1 20 0.150

66 217.00 25644.5 20352.5 -45997.1 32778.6 19429.6 -52208.3 344.2 20 0.150

67 219.00 25555.5 20185.5 -45741.1 32663.6 19268.6 -51932.1 342.3 20 0.150

68 221.00 25468.5 20018.5 -45487.1 32551.5 19106.5 -51658.0 340.4 20 0.150

69 223.00 25384.5 19851.5 -45236.1 32441.5 18946.5 -51388.0 338.5 20 0.150

70 225.00 25300.6 19685.5 -44986.1 32333.4 18786.4 -51119.9 336.6 20 0.150

71 227.00 25218.5 19519.5 -44738.1 32227.4 18626.4 -50853.7 334.6 20 0.150

72 229.00 25137.6 19354.6 -44492.1 32122.3 18467.3 -50589.7 332.7 20 0.150

73 231.00 25057.6 19190.6 -44248.1 32019.3 18308.3 -50327.5 330.8 20 0.150

74 233.00 24980.6 19025.6 -44006.1 31919.2 18149.2 -50068.4 328.9 20 0.150

75 235.00 24903.6 18861.6 -43765.2 31819.2 17991.2 -49810.3 326.9 20 0.150
C-18

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

76 237.00 24827.6 18698.6 -43526.2 31722.1 17832.1 -49554.2 325.0 20 0.150

77 239.00 24753.6 18535.6 -43289.2 31626.1 17675.1 -49301.1 323.1 20 0.150

78 241.00 24681.6 18372.6 -43054.2 31532.0 17518.0 -49050.0 321.1 20 0.150

79 243.00 24610.6 18210.6 -42821.2 31439.0 17362.0 -48800.9 319.2 20 0.150

80 245.00 24540.6 18048.6 -42589.2 31347.9 17204.9 -48552.8 317.3 20 0.150

81 247.00 24471.6 17886.6 -42358.2 31258.9 17048.9 -48307.7 315.4 20 0.150

82 249.00 24403.6 17726.6 -42130.3 31170.8 16893.8 -48064.6 313.4 20 0.150

83 251.00 24338.6 17565.6 -41904.3 31085.8 16738.8 -47824.5 311.5 20 0.150

84 253.00 24273.6 17405.7 -41679.3 31000.7 16584.7 -47585.4 309.6 20 0.150

85 255.00 24209.7 17246.7 -41456.3 30917.7 16430.6 -47348.3 307.6 20 0.150

86 257.00 24147.7 17086.7 -41234.3 30836.6 16276.6 -47113.2 305.7 20 0.150

87 259.00 24087.7 16928.7 -41016.3 30758.5 16122.5 -46881.1 303.7 20 0.150

88 261.00 24027.7 16770.7 -40798.4 30680.5 15970.5 -46651.0 301.8 20 0.150

89 263.00 23969.7 16612.7 -40582.4 30604.4 15817.4 -46421.9 299.9 20 0.150

90 265.00 23912.7 16455.7 -40368.4 30529.4 15666.4 -46195.8 297.9 20 0.150

91 267.00 23856.7 16298.7 -40155.4 30456.3 15514.3 -45970.7 296.0 20 0.150

92 269.00 23801.7 16143.7 -39945.5 30384.3 15364.3 -45748.5 294.0 20 0.150

93 271.00 23747.7 15987.7 -39735.5 30313.2 15213.2 -45526.5 292.1 20 0.150

94 273.00 23693.7 15832.8 -39526.5 30243.2 15063.2 -45306.3 290.1 20 0.150

95 275.00 23640.8 15677.8 -39318.5 30173.1 14914.1 -45087.2 288.2 20 0.150

96 277.00 23589.8 15523.8 -39113.6 30106.1 14765.1 -44871.1 286.2 20 0.150

97 279.00 23538.8 15369.8 -38908.6 30039.0 14616.0 -44655.0 284.3 20 0.150

98 281.00 23488.8 15215.8 -38704.6 29971.9 14467.9 -44439.9 282.4 20 0.150

99 283.00 23438.8 15063.8 -38502.6 29906.9 14319.9 -44226.8 280.4 20 0.150

100 285.00 23390.8 14911.8 -38302.7 29842.8 14172.8 -44015.7 278.5 20 0.150

101 287.00 23342.8 14759.8 -38102.7 29779.8 14025.8 -43805.6 276.5 20 0.150

102 289.00 23295.9 14607.9 -37903.7 29716.7 13879.7 -43596.5 274.6 20 0.150

103 291.00 23248.9 14456.9 -37705.8 29655.7 13732.7 -43388.4 272.6 20 0.150

104 293.00 23203.9 14306.9 -37510.8 29595.6 13587.6 -43183.3 270.6 20 0.150

105 295.00 23159.9 14155.9 -37315.8 29535.6 13442.6 -42978.1 268.7 20 0.150

106 297.00 23114.9 14006.9 -37121.9 29477.5 13297.5 -42775.0 266.7 20 0.150

107 299.00 23071.9 13857.9 -36929.9 29419.5 13153.5 -42572.9 264.8 20 0.150

108 301.00 23030.0 13709.0 -36738.9 29363.4 13010.4 -42373.8 262.8 20 0.150

109 303.00 22989.0 13560.0 -36549.0 29307.4 12866.3 -42173.7 260.9 20 0.150

110 305.00 22948.0 13412.0 -36360.0 29252.3 12724.3 -41976.6 258.9 20 0.150

111 307.00 22907.0 13266.0 -36173.1 29198.2 12581.2 -41779.5 257.0 20 0.150

112 309.00 22869.1 13118.1 -35987.1 29146.2 12439.2 -41585.4 255.0 20 0.150

113 311.00 22830.1 12972.1 -35802.1 29094.1 12298.1 -41392.2 253.0 20 0.150

114 313.00 22792.1 12826.1 -35618.2 29043.1 12157.1 -41200.2 251.1 20 0.150
C-19

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

115 315.00 22756.1 12681.1 -35437.2 28994.0 12016.0 -41010.1 249.1 20 0.150

116 317.00 22720.1 12535.1 -35255.3 28945.0 11874.9 -40819.9 247.2 20 0.150

117 319.00 22684.2 12391.2 -35075.3 28895.9 11734.9 -40630.8 245.2 20 0.150

118 321.00 22649.2 12247.2 -34896.4 28846.9 11595.9 -40442.7 243.2 20 0.150

119 323.00 22615.2 12103.2 -34718.4 28800.8 11456.8 -40257.6 241.3 20 0.150

120 325.00 22581.2 11960.2 -34541.5 28753.8 11318.7 -40072.5 239.3 20 0.150

121 327.00 22548.3 11817.3 -34365.5 28708.7 11179.7 -39888.4 237.3 20 0.150

122 329.00 22516.3 11675.3 -34191.6 28663.6 11042.6 -39706.3 235.4 20 0.150

123 331.00 22485.3 11533.3 -34018.6 28621.6 10904.6 -39526.2 233.4 20 0.150

124 333.00 22455.3 11391.3 -33846.7 28578.5 10768.5 -39347.1 231.4 20 0.150

125 335.00 22425.4 11250.4 -33675.8 28536.5 10631.5 -39168.0 229.4 20 0.150

126 337.00 22396.4 11110.4 -33506.8 28497.4 10495.4 -38992.8 227.5 20 0.150

127 339.00 22368.4 10970.4 -33338.9 28457.4 10360.4 -38817.7 225.5 20 0.150

128 341.00 22340.5 10830.5 -33170.9 28418.3 10225.3 -38643.6 223.5 20 0.150

129 343.00 22313.5 10691.5 -33005.0 28380.3 10090.3 -38470.5 221.5 20 0.150

130 345.00 22287.5 10553.5 -32841.1 28343.2 9956.2 -38299.4 219.6 20 0.150

131 347.00 22261.6 10414.6 -32676.1 28306.1 9822.1 -38128.3 217.6 20 0.150

132 349.00 22235.6 10276.6 -32512.2 28269.1 9689.1 -37958.2 215.6 20 0.150

133 351.00 22210.6 10139.6 -32350.3 28234.1 9556.0 -37790.1 213.6 20 0.150

134 353.00 22185.7 10002.7 -32188.3 28199.0 9423.0 -37622.0 211.7 20 0.150

135 355.00 22161.7 9865.7 -32027.4 28163.9 9289.9 -37453.9 209.7 20 0.150

136 357.00 22137.8 9728.7 -31866.5 28128.9 9158.9 -37287.8 207.7 20 0.150

137 359.00 22114.8 9593.8 -31708.6 28096.8 9026.8 -37123.7 205.7 20 0.150

138 361.00 22091.8 9457.8 -31549.7 28062.8 8895.8 -36958.5 203.7 20 0.150

139 363.00 22069.9 9321.9 -31391.7 28030.7 8764.7 -36795.5 201.8 20 0.150

140 365.00 22047.9 9187.9 -31235.8 27999.6 8633.7 -36633.3 199.8 20 0.150

141 367.00 22027.0 9053.0 -31079.9 27968.6 8503.6 -36472.2 197.8 20 0.150

142 369.00 22006.0 8919.0 -30925.0 27938.6 8374.5 -36313.1 195.8 20 0.150

143 371.00 21986.0 8786.0 -30772.1 27909.5 8244.5 -36154.0 193.9 20 0.150

144 373.00 21967.1 8653.1 -30620.2 27881.5 8116.4 -35997.9 191.9 20 0.150

145 375.00 21948.2 8520.2 -30468.3 27853.4 7988.4 -35841.8 189.9 20 0.150

146 377.00 21930.2 8387.2 -30317.4 27826.3 7859.4 -35685.7 187.9 20 0.150

147 379.00 21913.2 8255.2 -30168.5 27800.3 7732.3 -35532.6 185.9 20 0.150

148 381.00 21895.3 8125.3 -30020.6 27774.2 7605.2 -35379.5 184.0 20 0.150

149 383.00 21878.4 7993.4 -29871.7 27749.2 7477.2 -35226.4 182.0 20 0.150

150 385.00 21862.4 7862.4 -29724.8 27724.1 7351.1 -35075.3 180.0 20 0.150

151 387.00 21847.5 7732.5 -29579.9 27700.1 7225.1 -34925.2 178.0 20 0.150

152 389.00 21831.5 7603.5 -29435.0 27676.0 7099.0 -34775.0 176.1 20 0.150

153 391.00 21816.6 7473.6 -29290.2 27653.0 6974.0 -34627.0 174.1 20 0.150
C-20

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

154 393.00 21803.6 7344.6 -29148.3 27630.9 6848.9 -34479.8 172.1 20 0.150

155 395.00 21789.7 7215.7 -29005.4 27608.9 6723.9 -34332.7 170.1 20 0.150

156 397.00 21775.8 7087.8 -28863.5 27586.8 6599.8 -34186.6 168.1 20 0.150

157 399.00 21763.8 6959.8 -28723.7 27566.8 6476.8 -34043.5 166.1 20 0.150

158 401.00 21750.9 6832.9 -28583.8 27546.7 6352.7 -33899.4 164.2 20 0.150

159 403.00 21739.0 6706.0 -28444.9 27526.7 6229.7 -33756.3 162.2 20 0.150

160 405.00 21729.0 6579.0 -28308.1 27507.6 6107.6 -33615.2 160.2 20 0.150

161 407.00 21717.1 6454.1 -28171.2 27488.6 5985.6 -33474.1 158.2 20 0.150

162 409.00 21707.2 6327.2 -28034.4 27470.5 5863.5 -33334.0 156.2 20 0.150

163 411.00 21696.3 6203.3 -27899.5 27452.5 5742.5 -33194.9 154.3 20 0.150

164 413.00 21688.3 6077.3 -27765.7 27436.4 5620.4 -33056.8 152.3 20 0.150

165 415.00 21678.4 5953.4 -27631.8 27419.4 5500.4 -32919.7 150.3 20 0.150

166 417.00 21669.5 5829.5 -27499.0 27403.3 5380.3 -32783.6 148.3 20 0.150

167 419.00 21662.6 5705.6 -27368.2 27388.3 5259.3 -32647.5 146.3 20 0.150

168 421.00 21653.7 5582.7 -27236.3 27372.2 5140.2 -32512.4 144.3 20 0.150

169 423.00 21645.8 5459.8 -27105.5 27356.2 5021.2 -32377.3 142.3 20 0.150

170 425.00 21639.8 5336.8 -26976.7 27342.1 4902.1 -32244.2 140.3 20 0.150

171 427.00 21632.9 5214.9 -26847.9 27327.1 4785.1 -32112.1 138.4 20 0.150

172 429.00 21626.0 5094.0 -26720.0 27313.0 4667.0 -31980.0 136.4 20 0.150

173 431.00 21620.1 4973.1 -26593.2 27300.0 4549.0 -31848.9 134.4 20 0.150

174 433.00 21614.2 4852.2 -26466.4 27286.9 4431.9 -31718.8 132.4 20 0.150

175 435.00 21608.3 4731.3 -26339.6 27273.9 4314.8 -31588.7 130.4 20 0.150

176 437.00 21603.4 4611.4 -26214.8 27261.8 4197.8 -31459.6 128.4 20 0.150

177 439.00 21598.5 4490.5 -26089.0 27248.8 4081.8 -31330.5 126.4 20 0.150

178 441.00 21593.6 4370.6 -25964.2 27236.7 3965.7 -31202.4 124.4 20 0.150

179 443.00 21589.7 4250.7 -25840.5 27226.7 3848.6 -31075.3 122.4 20 0.150

180 445.00 21584.9 4131.9 -25716.7 27214.6 3733.6 -30948.2 120.4 20 0.150

181 447.00 21580.9 4012.9 -25593.9 27203.6 3618.6 -30822.2 118.4 20 0.150

182 449.00 21577.1 3895.1 -25472.1 27193.5 3503.5 -30697.0 116.4 20 0.150

183 450.00 21579.1 3836.1 -25415.3 27212.5 3446.5 -30659.0 115.6 20 0.150

184 451.00 21580.0 3804.0 -25384.0 27243.5 3416.5 -30660.0 114.8 20 0.150

185 454.00 21670.7 3722.7 -25393.3 27615.6 3339.5 -30955.1 113.6 20 0.150

186 459.00 22014.3 3631.3 -25645.6 28424.7 3253.7 -31678.4 112.6 20 0.150

187 467.00 22762.9 3581.9 -26344.8 29713.8 3201.9 -32915.7 111.6 20 0.150

188 477.00 23772.8 3644.8 -27417.6 31199.0 3252.9 -34451.9 110.6 20 0.150

189 478.00 23872.8 3655.8 -27528.5 31335.9 3264.0 -34599.9 110.5 20 0.150

190 488.00 24847.8 3823.8 -28671.7 32661.0 3418.0 -36079.0 109.8 20 0.150

191 492.00 25216.9 3910.9 -29127.8 33146.0 3498.0 -36644.0 109.5 20 0.150

192 502.00 26098.1 4160.1 -30258.2 34294.0 3731.0 -38025.1 108.9 20 0.150
C-21

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

193 509.00 26670.3 4355.3 -31025.5 35023.1 3915.0 -38938.1 108.5 20 0.150

194 519.00 27434.6 4657.6 -32092.2 35994.1 4200.0 -40194.1 108.0 20 0.150

195 529.00 28137.0 4974.0 -33111.0 36871.1 4500.1 -41371.2 107.5 20 0.150

196 539.00 28786.4 5302.4 -34088.8 37681.1 4811.1 -42492.2 107.0 20 0.150

197 549.00 29385.9 5634.9 -35020.8 38419.2 5127.1 -43546.3 106.6 20 0.150

198 553.00 29611.1 5769.1 -35380.2 38694.2 5255.1 -43949.3 106.4 20 0.150

199 563.00 30151.6 6103.6 -36255.3 39358.2 5574.2 -44932.3 106.1 20 0.150

200 573.00 30653.2 6437.2 -37090.4 39966.2 5892.2 -45858.4 105.7 20 0.150

201 582.00 31073.7 6734.7 -37808.5 40473.2 6176.3 -46649.5 105.4 20 0.150

202 592.00 31518.4 7062.4 -38580.7 41012.3 6488.3 -47500.6 105.1 20 0.150

203 602.00 31935.0 7386.0 -39321.1 41510.3 6798.3 -48308.7 104.8 20 0.150

204 612.00 32318.7 7702.7 -40021.4 41965.3 7100.4 -49065.7 104.5 20 0.150

205 617.00 32498.1 7858.1 -40356.1 42178.4 7248.4 -49426.8 104.4 20 0.150

206 627.00 32850.8 8161.8 -41012.6 42600.4 7539.4 -50139.8 104.2 20 0.150

207 637.00 33184.5 8459.5 -41644.0 42995.5 7823.5 -50819.0 103.9 20 0.150

208 647.00 33501.3 8750.3 -42251.6 43367.5 8101.5 -51469.0 103.7 20 0.150

209 657.00 33799.1 9033.1 -42832.1 43716.6 8371.6 -52088.1 103.5 20 0.150

210 661.00 33912.4 9144.4 -43056.8 43849.6 8477.6 -52327.2 103.4 20 0.150

211 671.00 34190.2 9417.2 -43607.3 44180.6 8737.6 -52918.3 103.2 20 0.150

212 681.00 34451.0 9683.0 -44134.0 44485.7 8991.7 -53477.4 103.1 20 0.150

213 691.00 34695.8 9939.8 -44635.7 44768.7 9237.7 -54006.5 102.9 20 0.150

214 701.00 34927.7 10191.7 -45119.4 45037.8 9477.8 -54515.6 102.7 20 0.150

215 721.00 35360.4 10675.4 -46035.8 45536.9 9938.9 -55475.8 102.4 20 0.150

216 731.00 35567.3 10908.3 -46475.6 45782.0 10161.0 -55942.9 102.3 20 0.150

217 741.00 35767.2 11137.2 -46904.4 46013.0 10380.0 -56393.1 102.2 20 0.150

218 751.00 35956.1 11360.1 -47316.3 46231.1 10592.1 -56823.2 102.1 20 0.150

219 761.00 36136.0 11578.0 -47714.1 46437.1 10800.1 -57237.3 102.0 20 0.150

220 781.00 36464.9 11994.9 -48459.8 46812.2 11196.3 -58008.5 101.7 20 0.150

221 801.00 36770.8 12391.8 -49162.6 47159.4 11575.4 -58734.7 101.5 20 0.150

222 815.00 36973.2 12664.2 -49637.3 47388.4 11834.4 -59222.9 101.4 20 0.150

223 825.00 37119.1 12855.1 -49974.2 47561.5 12016.5 -59578.0 101.3 20 0.150

224 835.00 37263.1 13044.1 -50307.2 47726.6 12196.6 -59923.2 101.3 20 0.150

225 845.00 37403.1 13232.1 -50635.2 47886.6 12374.6 -60261.3 101.2 20 0.150

226 855.00 37538.1 13416.1 -50954.1 48040.7 12549.7 -60590.4 101.2 20 0.150

227 875.00 37797.1 13776.1 -51573.1 48333.8 12891.8 -61225.6 101.1 20 0.150

228 895.00 38039.1 14124.1 -52163.2 48605.9 13223.9 -61829.9 101.0 20 0.150

229 915.00 38260.2 14456.2 -52716.3 48855.0 13539.0 -62394.1 100.9 20 0.150

230 955.00 38632.2 15058.2 -53690.3 49270.3 14111.3 -63381.6 100.7 20 0.150

231 995.00 38959.0 15602.0 -54561.0 49634.5 14627.5 -64262.0 100.6 20 0.150
C-22

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

232 1039.00 39281.1 16152.1 -55433.1 49992.7 15149.8 -65142.5 100.4 20 0.150

233 1049.00 39357.0 16272.0 -55628.9 50086.8 15263.8 -65350.6 100.4 20 0.150

234 1059.00 39432.9 16390.9 -55823.8 50174.8 15375.8 -65550.7 100.4 20 0.150

235 1069.00 39505.8 16508.8 -56014.6 50258.9 15487.9 -65746.8 100.5 20 0.150

236 1079.00 39576.7 16624.7 -56201.4 50340.0 15596.9 -65936.9 100.5 20 0.150

237 1099.00 39711.4 16848.4 -56559.9 50492.0 15809.1 -66301.1 100.6 20 0.150

238 1119.00 39835.1 17063.1 -56898.2 50630.1 16014.2 -66644.3 100.7 20 0.150

239 1139.00 39949.8 17268.8 -57218.6 50758.2 16208.2 -66966.5 100.8 20 0.150

240 1179.00 40151.9 17646.9 -57798.9 50983.4 16566.4 -67549.8 100.9 20 0.150

241 1219.00 40318.0 17985.0 -58302.9 51167.6 16887.6 -68055.1 101.1 20 0.150

242 1299.00 40594.3 18570.3 -59164.6 51472.9 17441.9 -68914.7 101.4 20 0.150

243 1379.00 40860.5 19134.5 -59995.0 51767.1 17977.1 -69744.3 101.7 20 0.150

244 1510.00 41284.2 20042.2 -61326.4 52234.6 18835.6 -71070.2 102.2 20 0.150

245 1512.00 41259.6 20143.6 -61403.3 52213.6 18938.6 -71152.3 102.2 20 0.150

246 1513.00 41289.9 20199.9 -61489.7 52432.7 18996.7 -71429.4 103.8 20 0.150

247 1514.00 41380.1 20266.1 -61646.3 52866.9 19063.8 -71930.7 105.5 20 0.150

248 1515.00 41505.4 20338.4 -61843.9 53291.0 19135.0 -72426.0 107.4 20 0.150

249 1516.00 41656.8 20416.8 -62073.6 53724.1 19212.1 -72936.3 109.3 20 0.150

250 1517.00 41830.2 20501.2 -62331.3 54160.3 19294.3 -73454.5 111.3 20 0.150

251 1518.00 42020.5 20590.5 -62611.1 54598.4 19381.4 -73979.8 113.3 20 0.150

252 1519.00 42227.0 20684.0 -62911.0 55036.5 19471.5 -74508.0 115.4 20 0.150

253 1520.00 42441.4 20783.4 -63224.8 55471.6 19566.6 -75038.3 117.4 20 0.150

254 1521.00 42664.9 20886.9 -63551.8 55903.8 19665.8 -75569.5 119.5 20 0.150

255 1522.00 42898.4 20993.4 -63891.8 56333.9 19768.9 -76102.8 121.7 20 0.150

256 1523.00 43137.9 21104.9 -64242.8 56759.0 19875.0 -76634.0 123.8 20 0.150

257 1524.00 43384.5 21221.5 -64606.0 57179.1 19986.1 -77165.2 126.0 20 0.150

258 1525.00 43635.0 21341.1 -64976.1 57596.2 20100.2 -77696.4 128.1 20 0.150

259 1526.00 43885.6 21465.6 -65351.2 58008.3 20218.3 -78226.6 130.3 20 0.150

260 1527.00 44140.2 21591.3 -65731.5 58418.4 20338.4 -78756.8 132.5 20 0.150

261 1528.00 44395.8 21720.8 -66116.6 58822.5 20462.5 -79285.0 134.7 20 0.150

262 1529.00 44653.4 21853.4 -66506.9 59224.6 20587.6 -79812.2 136.9 20 0.150

263 1530.00 44911.1 21990.1 -66901.3 59619.7 20718.7 -80338.4 139.1 20 0.150

264 1531.00 45171.8 22129.8 -67301.6 60011.8 20850.8 -80862.5 141.3 20 0.150

265 1532.00 45431.5 22272.5 -67704.0 60398.8 20985.9 -81384.7 143.5 20 0.150

266 1533.00 45692.2 22418.2 -68110.3 60781.9 21124.9 -81906.9 145.7 20 0.150

267 1534.00 45950.9 22565.9 -68516.8 61160.0 21265.0 -82425.0 147.9 20 0.150

268 1535.00 46209.6 22716.6 -68926.3 61536.1 21408.1 -82944.2 150.2 20 0.150

269 1536.00 46467.3 22868.3 -69335.7 61906.2 21553.2 -83459.4 152.4 20 0.150

270 1537.00 46725.1 23024.1 -69749.2 62273.2 21701.3 -83974.5 154.7 20 0.150
C-23

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

271 1538.00 46981.9 23180.9 -70162.8 62637.3 21850.3 -84487.6 156.9 20 0.150

272 1539.00 47236.7 23340.7 -70577.3 62996.4 22002.4 -84998.8 159.2 20 0.150

273 1540.00 47490.4 23503.4 -70993.9 63352.5 22156.5 -85508.9 161.4 20 0.150

274 1541.00 47744.2 23667.2 -71411.4 63703.5 22313.5 -86017.1 163.7 20 0.150

275 1542.00 47994.1 23834.0 -71828.1 64050.6 22471.6 -86522.2 165.9 20 0.150

276 1543.00 48243.9 24001.9 -72245.8 64395.7 22631.7 -87027.3 168.2 20 0.150

277 1544.00 48492.7 24170.7 -72663.3 64736.8 22792.7 -87529.5 170.5 20 0.150

278 1545.00 48737.5 24342.5 -73080.0 65072.8 22955.8 -88028.6 172.8 20 0.150

279 1546.00 48982.4 24514.4 -73496.7 65406.9 23119.9 -88526.8 175.0 20 0.150

280 1547.00 49225.2 24688.2 -73913.4 65737.9 23285.0 -89022.9 177.3 20 0.150

281 1548.00 49466.1 24863.1 -74329.2 66064.0 23452.0 -89516.0 179.6 20 0.150

282 1549.00 49704.9 25039.9 -74744.9 66387.1 23621.1 -90008.1 181.9 20 0.150

283 1550.00 49942.9 25217.9 -75160.7 66706.1 23791.1 -90497.3 184.2 20 0.150

284 1551.00 50177.7 25397.7 -75575.4 67021.2 23963.2 -90984.4 186.5 20 0.150

285 1552.00 50410.7 25579.6 -75990.3 67334.2 24135.3 -91469.5 188.8 20 0.150

286 1553.00 50642.5 25762.5 -76405.0 67643.3 24309.3 -91952.6 191.1 20 0.150

287 1554.00 50872.4 25946.4 -76818.9 67948.4 24485.4 -92433.7 193.4 20 0.150

288 1555.00 51099.4 26130.4 -77229.8 68249.4 24661.4 -92910.9 195.7 20 0.150

289 1556.00 51324.3 26317.2 -77641.5 68548.5 24838.5 -93387.0 198.0 20 0.150

290 1557.00 51548.2 26503.2 -78051.4 68844.5 25016.5 -93861.1 200.3 20 0.150

291 1558.00 51769.1 26690.1 -78459.2 69137.6 25194.6 -94332.2 202.6 20 0.150

292 1559.00 51989.1 26878.1 -78867.1 69426.7 25374.7 -94801.4 204.9 20 0.150

293 1560.00 52207.0 27066.0 -79273.0 69713.7 25554.7 -95268.5 207.2 20 0.150

294 1561.00 52423.0 27256.0 -79678.9 69996.8 25735.8 -95732.5 209.5 20 0.150

295 1562.00 52634.9 27445.9 -80080.8 70275.8 25916.8 -96192.7 211.8 20 0.150

296 1563.00 52846.9 27636.9 -80483.7 70552.9 26098.9 -96651.8 214.1 20 0.150

297 1564.00 53056.9 27827.9 -80884.8 70827.9 26281.0 -97108.9 216.4 20 0.150

298 1565.00 53264.8 28018.8 -81283.7 71099.0 26464.0 -97563.0 218.7 20 0.150

299 1566.00 53468.8 28211.8 -81680.6 71366.1 26648.1 -98014.2 221.0 20 0.150

300 1567.00 53672.7 28404.8 -82077.5 71632.1 26832.1 -98464.3 223.3 20 0.150

301 1568.00 53874.8 28598.8 -82473.5 71894.2 27018.2 -98912.4 225.6 20 0.150

302 1569.00 54074.7 28792.7 -82867.5 72154.2 27203.2 -99357.5 227.9 20 0.150

303 1570.00 54272.7 28986.7 -83259.4 72411.3 27389.3 -99800.6 230.2 20 0.150

304 1571.00 54467.7 29182.7 -83650.4 72664.4 27576.3 -100240.7 232.5 20 0.150

305 1572.00 54660.7 29379.7 -84040.4 72915.4 27763.4 -100678.8 234.9 20 0.150

306 1573.00 54852.7 29575.7 -84428.4 73163.4 27951.4 -101114.9 237.2 20 0.150

307 1574.00 55043.8 29770.7 -84814.5 73409.5 28139.5 -101549.0 239.5 20 0.150

308 1575.00 55230.7 29968.7 -85199.4 73652.6 28327.5 -101980.1 241.8 20 0.150
C-24

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

309 1576.00 55417.7 30164.8 -85582.5 73894.6 28515.6 -102410.2 244.1 20 0.150

310 1577.00 55602.7 30361.7 -85964.5 74133.7 28704.7 -102838.4 246.4 20 0.150

311 1578.00 55786.8 30558.8 -86345.5 74370.7 28892.8 -103263.5 248.8 20 0.150

312 1579.00 55968.8 30755.8 -86724.6 74604.8 29082.8 -103687.6 251.1 20 0.150

313 1580.00 56147.8 30953.8 -87101.6 74836.9 29270.9 -104107.7 253.4 20 0.150

314 1581.00 56326.8 31151.8 -87478.7 75067.9 29460.9 -104528.8 255.7 20 0.150

315 1582.00 56503.9 31349.9 -87853.8 75298.0 29648.9 -104946.9 258.1 20 0.150

316 1583.00 56679.9 31547.9 -88227.7 75525.0 29839.0 -105364.0 260.4 20 0.150

317 1584.00 56853.9 31745.9 -88599.8 75750.1 30029.1 -105779.1 262.7 20 0.150

318 1585.00 57027.0 31944.0 -88970.9 75973.1 30219.1 -106192.3 265.1 20 0.150

319 1586.00 57198.0 32143.0 -89341.0 76194.2 30409.2 -106603.4 267.4 20 0.150

320 1587.00 57368.1 32341.1 -89709.1 76413.2 30599.2 -107012.5 269.7 20 0.150

321 1588.00 57536.1 32540.0 -90076.1 76630.3 30789.3 -107419.6 272.1 20 0.150

322 1589.00 57702.1 32739.1 -90441.2 76843.4 30980.4 -107823.7 274.4 20 0.150

323 1590.00 57867.2 32938.2 -90805.3 77056.4 31170.4 -108226.8 276.7 20 0.150

324 1591.00 58030.2 33138.2 -91168.4 77266.5 31361.5 -108628.0 279.1 20 0.150

325 1592.00 58192.3 33337.3 -91529.5 77473.5 31553.5 -109027.0 281.4 20 0.150

326 1593.00 58352.3 33536.3 -91888.7 77678.6 31744.6 -109423.2 283.8 20 0.150

327 1594.00 58511.4 33736.4 -92247.8 77883.6 31934.6 -109818.3 286.1 20 0.150

328 1595.00 58669.5 33935.5 -92604.9 78085.7 32125.7 -110211.4 288.4 20 0.150

329 1596.00 58825.5 34134.5 -92960.1 78285.7 32317.8 -110603.5 290.8 20 0.150

330 1597.00 58980.6 34333.6 -93314.2 78484.8 32507.8 -110992.6 293.1 20 0.150

331 1598.00 59133.7 34532.7 -93666.3 78680.9 32698.9 -111379.8 295.5 20 0.150

332 1599.00 59286.7 34731.7 -94018.4 78875.9 32889.9 -111765.8 297.8 20 0.150

333 1600.00 59437.7 34930.7 -94368.5 79070.0 33079.9 -112149.9 300.2 20 0.150

334 1601.00 59587.8 35128.8 -94716.6 79261.0 33271.1 -112532.1 302.5 20 0.150

335 1602.00 59734.9 35328.9 -95063.8 79450.1 33461.1 -112911.2 304.9 20 0.150

336 1603.00 59882.0 35527.0 -95408.9 79638.1 33652.2 -113290.3 307.2 20 0.150

337 1604.00 60027.0 35726.0 -95753.0 79823.2 33842.2 -113665.4 309.5 20 0.150

338 1605.00 60171.1 35923.1 -96094.2 80007.2 34031.3 -114038.5 311.9 20 0.150

339 1606.00 60314.2 36120.2 -96434.4 80189.3 34221.3 -114410.7 314.2 20 0.150

340 1607.00 60454.3 36318.3 -96772.5 80368.4 34410.4 -114778.7 316.6 20 0.150

341 1608.00 60594.3 36515.3 -97109.7 80547.4 34599.4 -115146.9 318.9 20 0.150

342 1609.00 60732.4 36713.4 -97445.7 80723.5 34788.5 -115511.9 321.3 20 0.150

343 1610.00 60869.4 36910.5 -97779.9 80898.5 34977.6 -115876.1 323.7 20 0.150

344 1611.00 61004.5 37106.5 -98111.1 81070.6 35166.6 -116237.2 326.0 20 0.150

345 1612.00 61138.6 37304.6 -98443.2 81241.7 35355.7 -116597.3 328.4 20 0.150

346 1613.00 61272.7 37499.7 -98772.4 81411.7 35543.7 -116955.4 330.7 20 0.150

347 1614.00 61404.7 37696.7 -99101.5 81579.8 35732.8 -117312.5 333.1 20 0.150
C-25

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

348 1615.00 61533.8 37893.8 -99427.7 81744.8 35921.8 -117666.7 335.4 20 0.150

349 1616.00 61663.9 38089.9 -99753.8 81910.9 36108.9 -118019.8 337.8 20 0.150

350 1617.00 61793.0 38285.0 -100078.0 82074.9 36297.0 -118371.9 340.1 20 0.150

351 1618.00 61920.1 38481.1 -100401.2 82237.0 36485.0 -118722.0 342.5 20 0.150

352 1619.00 62047.1 38676.1 -100723.3 82398.0 36672.1 -119070.1 344.8 20 0.150

353 1620.00 62171.2 38871.2 -101042.5 82556.1 36860.1 -119416.2 347.2 20 0.150

354 1621.00 62295.3 39066.3 -101361.7 82714.1 37047.2 -119761.3 349.6 20 0.150

355 1622.00 62419.4 39260.4 -101679.8 82871.2 37234.2 -120105.5 351.9 20 0.150

356 1623.00 62540.5 39456.5 -101996.9 83026.3 37420.3 -120446.6 354.3 20 0.150

357 1624.00 62660.6 39649.6 -102310.1 83177.4 37607.3 -120784.7 356.6 20 0.150

358 1625.00 62779.7 39844.7 -102624.3 83328.4 37793.4 -121121.8 359.0 20 0.150

359 1626.00 62898.8 40036.8 -102935.5 83477.5 37979.5 -121456.9 361.3 20 0.150

360 1627.00 63014.8 40231.8 -103246.6 83624.5 38165.5 -121790.0 363.7 20 0.150

361 1628.00 63129.9 40423.9 -103553.8 83769.6 38350.5 -122120.1 366.0 20 0.150

362 1629.00 63244.0 40618.0 -103862.0 83914.6 38535.6 -122450.3 368.4 20 0.150

363 1630.00 63358.1 40809.1 -104167.1 84057.7 38720.7 -122778.4 370.8 20 0.150

364 1631.00 63470.2 41002.2 -104472.4 84198.7 38905.7 -123104.5 373.1 20 0.150

365 1632.00 63580.2 41194.2 -104774.5 84338.8 39089.8 -123428.6 375.5 20 0.150

366 1633.00 63689.3 41386.3 -105075.7 84476.9 39273.9 -123750.7 377.8 20 0.150

367 1634.00 63798.5 41578.4 -105376.9 84614.9 39457.9 -124072.8 380.2 20 0.150

368 1635.00 63906.5 41769.5 -105676.0 84751.0 39642.0 -124392.9 382.5 20 0.150

369 1636.00 64013.6 41959.6 -105973.2 84886.0 39826.0 -124712.1 384.9 20 0.150

370 1637.00 64118.7 42150.7 -106269.4 85020.1 40008.1 -125028.2 387.2 20 0.150

371 1638.00 64223.8 42340.8 -106564.6 85153.1 40191.1 -125344.3 389.6 20 0.150

372 1639.00 64327.9 42531.8 -106859.7 85285.2 40373.2 -125658.4 391.9 20 0.150

373 1640.00 64432.0 42721.0 -107152.9 85416.3 40555.2 -125971.5 394.3 20 0.150

374 1641.00 64533.0 42910.0 -107443.1 85545.3 40737.3 -126282.7 396.7 20 0.150

375 1642.00 64635.1 43099.1 -107734.3 85673.4 40919.4 -126592.8 399.0 20 0.150

376 1643.00 64736.2 43288.2 -108024.4 85801.4 41100.4 -126901.9 401.4 20 0.150

377 1644.00 64836.3 43476.3 -108312.7 85928.5 41281.5 -127210.0 403.7 20 0.150

378 1645.00 64934.4 43664.4 -108598.8 86054.6 41462.5 -127517.1 406.1 20 0.150

379 1646.00 65033.5 43852.5 -108886.0 86180.6 41643.6 -127824.2 408.5 20 0.150

380 1647.00 65131.6 44039.6 -109171.2 86306.6 41822.7 -128129.3 410.8 20 0.150

381 1648.00 65228.7 44227.7 -109456.4 86430.7 42003.7 -128434.5 413.2 20 0.150

382 1649.00 65324.8 44414.8 -109739.5 86553.8 42183.8 -128737.6 415.6 20 0.150

383 1650.00 65419.8 44601.9 -110021.7 86676.8 42362.8 -129039.7 418.0 20 0.150

384 1651.00 65516.0 44788.0 -110303.9 86798.9 42541.9 -129340.8 420.3 20 0.150

385 1652.00 65610.0 44974.0 -110584.1 86920.0 42719.9 -129639.9 422.7 20 0.150

386 1653.00 65702.1 45161.1 -110863.2 87038.0 42900.0 -129938.0 425.1 20 0.150
C-26

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

387 1654.00 65795.2 45346.2 -111141.5 87157.1 43078.1 -130235.1 427.4 20 0.150

388 1655.00 65887.3 45531.3 -111418.6 87275.1 43255.1 -130530.2 429.8 20 0.150

389 1656.00 65978.4 45716.4 -111694.8 87390.2 43434.2 -130824.4 432.2 20 0.150

390 1657.00 66068.5 45901.5 -111970.0 87506.2 43611.2 -131117.5 434.6 20 0.150

391 1658.00 66158.6 46085.6 -112244.2 87620.3 43789.3 -131409.6 436.9 20 0.150

392 1659.00 66246.7 46270.7 -112517.3 87734.4 43965.4 -131699.7 439.3 20 0.150

393 1660.00 66333.7 46454.8 -112788.5 87845.4 44142.4 -131987.9 441.7 20 0.150

394 1661.00 66421.9 46637.9 -113059.8 87956.5 44319.5 -132276.0 444.1 20 0.150

395 1662.00 66508.0 46820.9 -113328.9 88067.5 44494.5 -132562.1 446.5 20 0.150

396 1663.00 66594.0 47004.0 -113598.1 88176.6 44670.6 -132847.2 448.8 20 0.150

397 1664.00 66677.1 47187.1 -113864.2 88283.7 44846.7 -133130.3 451.2 20 0.150

398 1665.00 66761.2 47369.2 -114130.5 88390.7 45022.8 -133413.5 453.6 20 0.150

399 1666.00 66844.3 47552.3 -114396.7 88497.8 45196.8 -133694.6 456.0 20 0.150

400 1667.00 66927.4 47733.4 -114660.8 88602.9 45371.8 -133974.7 458.4 20 0.150

401 1668.00 67007.5 47915.5 -114923.0 88705.9 45546.9 -134252.8 460.7 20 0.150

402 1669.00 67088.6 48096.6 -115185.1 88809.0 45721.0 -134529.9 463.1 20 0.150

403 1670.00 67168.7 48276.7 -115445.3 88911.0 45895.0 -134806.0 465.5 20 0.150

404 1671.00 67246.7 48457.8 -115704.5 89011.1 46069.1 -135080.2 467.9 20 0.150

405 1672.00 67324.9 48638.9 -115963.8 89111.2 46242.1 -135353.3 470.3 20 0.150

406 1673.00 67402.0 48819.0 -116221.0 89210.2 46414.2 -135624.4 472.7 20 0.150

407 1674.00 67479.1 48998.1 -116477.1 89308.3 46587.2 -135895.5 475.1 20 0.150

408 1675.00 67554.2 49177.2 -116731.3 89405.3 46759.3 -136164.6 477.4 20 0.150

409 1676.00 67630.2 49355.3 -116985.5 89502.4 46930.4 -136432.8 479.8 20 0.150

410 1677.00 67705.3 49534.3 -117239.7 89598.4 47102.4 -136700.9 482.2 20 0.150

411 1678.00 67780.4 49711.4 -117491.9 89693.5 47274.5 -136968.0 484.6 20 0.150

412 1679.00 67853.5 49889.5 -117743.1 89787.6 47444.6 -137232.1 487.0 20 0.150

413 1680.00 67927.6 50066.6 -117994.2 89881.6 47615.6 -137497.3 489.4 20 0.150

414 1681.00 68000.7 50243.7 -118244.4 89975.7 47785.7 -137761.4 491.8 20 0.150

415 1682.00 68071.8 50421.8 -118493.6 90067.7 47955.8 -138023.5 494.2 20 0.150

416 1683.00 68143.8 50597.8 -118741.7 90160.8 48124.8 -138285.6 496.5 20 0.150

417 1684.00 68215.9 50773.9 -118989.9 90251.9 48295.9 -138547.8 498.9 20 0.150

418 1685.00 68287.0 50950.0 -119237.1 90342.9 48464.9 -138807.8 501.3 20 0.150

419 1686.00 68356.1 51126.1 -119482.2 90433.0 48633.0 -139066.0 503.7 20 0.150

420 1687.00 68426.2 51301.2 -119727.4 90521.0 48802.0 -139323.1 506.1 20 0.150

421 1688.00 68495.3 51476.3 -119971.6 90608.1 48970.1 -139578.2 508.5 20 0.150

422 1689.00 68562.4 51651.4 -120213.8 90693.2 49138.2 -139831.3 510.9 20 0.150

423 1690.00 68630.5 51825.5 -120455.9 90778.2 49306.2 -140084.5 513.2 20 0.150

424 1691.00 68697.6 51999.6 -120697.1 90863.3 49473.3 -140336.6 515.6 20 0.150

425 1692.00 68763.6 52173.6 -120937.2 90947.3 49640.3 -140587.7 518.0 20 0.150
C-27

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

426 1693.00 68828.7 52346.7 -121175.4 91029.4 49807.4 -140836.8 520.4 20 0.150

427 1694.00 68893.8 52519.8 -121413.6 91112.5 49973.5 -141085.9 522.8 20 0.150

428 1695.00 68958.9 52691.9 -121650.7 91194.5 50139.5 -141334.1 525.1 20 0.150

429 1696.00 69022.0 52865.0 -121886.9 91274.6 50305.6 -141580.2 527.5 20 0.150

430 1697.00 69085.1 53037.1 -122122.2 91355.6 50471.6 -141827.3 529.9 20 0.150

431 1698.00 69148.1 53209.1 -122357.2 91436.7 50635.7 -142072.4 532.3 20 0.150

432 1699.00 69210.2 53381.2 -122591.5 91515.8 50801.7 -142317.5 534.7 20 0.150

433 1700.00 69271.3 53551.3 -122822.6 91594.8 50964.8 -142559.7 537.0 20 0.150

434 1701.00 69333.4 53721.4 -123054.8 91672.9 51129.9 -142802.8 539.4 20 0.150

435 1702.00 69394.4 53892.5 -123286.9 91751.0 51294.0 -143044.9 541.8 20 0.150

436 1703.00 69453.5 54062.6 -123516.1 91828.0 51457.0 -143285.0 544.2 20 0.150

437 1704.00 69513.6 54232.6 -123746.2 91904.1 51621.1 -143525.2 546.6 20 0.150

438 1705.00 69572.7 54401.7 -123974.3 91981.1 51783.1 -143764.3 549.0 20 0.150

439 1706.00 69631.8 54570.8 -124202.5 92056.2 51946.2 -144002.4 551.3 20 0.150

440 1707.00 69689.8 54739.8 -124429.7 92131.2 52108.2 -144239.5 553.7 20 0.150

441 1708.00 69747.9 54907.9 -124655.8 92207.3 52271.3 -144478.6 556.1 20 0.150

442 1709.00 69806.0 55076.0 -124882.0 92283.4 52433.4 -144716.7 558.5 20 0.150

443 1710.00 69862.0 55245.0 -125107.1 92358.4 52594.4 -144952.8 560.9 20 0.150

444 1711.00 69914.7 55365.7 -125280.4 92335.4 52707.4 -145042.8 562.5 20 0.150

445 1712.00 69926.3 55479.3 -125405.7 92153.4 52815.4 -144968.8 563.7 20 0.150

446 1714.00 69845.4 55689.5 -125534.9 91603.3 53012.3 -144615.6 565.4 20 0.150

447 1716.00 69666.5 55876.5 -125542.9 90974.2 53190.2 -144164.4 566.6 20 0.150

448 1719.00 69272.9 56118.9 -125391.8 89974.0 53422.0 -143396.0 568.0 20 0.150

449 1722.00 68784.2 56320.2 -125104.3 88968.9 53615.9 -142584.8 569.2 20 0.150

450 1726.00 68049.7 56529.7 -124579.4 87653.7 53821.7 -141475.4 570.5 20 0.150

451 1730.00 67269.1 56682.1 -123951.1 86381.6 53973.6 -140355.2 571.6 20 0.150

452 1735.00 66266.5 56801.6 -123068.1 84861.5 54095.5 -138957.1 572.8 20 0.150

453 1740.00 65265.8 56853.8 -122119.7 83417.5 54153.5 -137571.0 573.9 20 0.150

454 1746.00 64091.2 56845.2 -120936.4 81779.5 54154.5 -135933.9 575.0 20 0.150

455 1752.00 62958.4 56770.4 -119728.7 80241.5 54091.5 -134333.0 576.1 20 0.150

456 1759.00 61707.4 56618.5 -118325.9 78575.6 53954.5 -132530.1 577.2 20 0.150

457 1766.00 60527.3 56418.3 -116945.6 77026.6 53770.6 -130797.2 578.3 20 0.150

458 1774.00 59270.1 56136.1 -115406.3 75397.7 53507.7 -128905.4 579.4 20 0.150

459 1782.00 58098.7 55819.7 -113918.5 73893.8 53210.8 -127104.6 580.4 20 0.150

460 1791.00 56877.2 55428.2 -112305.3 72340.9 52841.9 -125182.8 581.5 20 0.150

461 1800.00 55746.4 55011.5 -110757.9 70915.0 52447.0 -123361.9 582.5 20 0.150

462 1810.00 54585.5 54528.5 -109114.1 69462.1 51990.1 -121452.2 583.6 20 0.150

463 1820.00 53516.4 54030.4 -107546.7 68133.2 51516.2 -119649.3 584.6 20 0.150

464 1830.00 52524.1 53524.1 -106048.2 66907.2 51034.2 -117941.5 585.6 20 0.150
C-28

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

465 1831.00 52429.1 53474.1 -105903.1 66791.2 50985.3 -117776.5 585.6 20 0.150

466 1841.00 51509.6 52960.5 -104470.1 65663.3 50496.3 -116159.7 586.5 20 0.150

467 1843.00 51334.4 52858.4 -104192.9 65449.3 50399.3 -115848.7 586.7 20 0.150

468 1853.00 50493.8 52350.8 -102844.6 64423.4 49914.4 -114337.8 587.5 20 0.150

469 1856.00 50254.6 52199.6 -102454.2 64132.4 49770.4 -113902.8 587.8 20 0.150

470 1866.00 49496.8 51702.8 -101199.5 63213.5 49295.5 -112508.9 588.5 20 0.150

471 1870.00 49213.4 51505.4 -100718.8 62872.5 49107.5 -111980.0 588.8 20 0.150

472 1880.00 48536.4 51023.4 -99559.8 62055.5 48646.5 -110702.0 589.5 20 0.150

473 1885.00 48212.9 50785.9 -98998.8 61668.5 48419.5 -110088.0 589.8 20 0.150

474 1895.00 47586.8 50317.8 -97904.7 60915.6 47972.6 -108888.1 590.4 20 0.150

475 1902.00 47169.0 49995.0 -97164.0 60418.5 47663.6 -108082.1 590.9 20 0.150

476 1912.00 46596.8 49540.8 -96137.7 59732.5 47230.6 -106963.1 591.4 20 0.150

477 1921.00 46110.6 49140.6 -95251.3 59156.6 46847.6 -106004.1 591.9 20 0.150

478 1931.00 45598.3 48703.3 -94301.7 58545.5 46430.6 -104976.1 592.4 20 0.150

479 1941.00 45118.9 48276.9 -93395.8 57981.5 46022.5 -104004.1 592.9 20 0.150

480 1942.00 45072.8 48234.8 -93307.5 57927.5 45982.5 -103910.0 593.0 20 0.150

481 1952.00 44626.3 47818.3 -92444.6 57399.5 45585.5 -102985.0 593.4 20 0.150

482 1962.00 44200.8 47418.8 -91619.7 56900.5 45204.5 -102104.9 593.8 20 0.150

483 1966.00 44035.3 47261.3 -91296.6 56707.4 45053.4 -101760.9 594.0 20 0.150

484 1976.00 43628.8 46871.8 -90500.6 56227.4 44681.4 -100908.8 594.3 20 0.150

485 1986.00 43236.3 46488.3 -89724.7 55770.4 44315.4 -100085.8 594.7 20 0.150

486 1994.00 42936.1 46186.1 -89122.3 55421.3 44027.4 -99448.7 595.0 20 0.150

487 2004.00 42567.6 45814.6 -88382.2 54988.3 43672.3 -98660.6 595.3 20 0.150

488 2014.00 42215.1 45450.1 -87665.2 54578.2 43324.2 -97902.5 595.6 20 0.150

489 2024.00 41889.5 45096.5 -86986.1 54202.2 42988.2 -97190.4 595.9 20 0.150

490 2028.00 41765.9 44959.9 -86725.8 54061.2 42856.2 -96917.3 596.0 20 0.150

491 2038.00 41467.3 44628.3 -86095.7 53711.1 42541.1 -96252.2 596.2 20 0.150

492 2048.00 41181.8 44305.8 -85487.6 53382.0 42233.0 -95615.0 596.4 20 0.150

493 2058.00 40907.2 43990.2 -84897.4 53066.9 41932.9 -94999.9 596.7 20 0.150

494 2068.00 40645.7 43681.7 -84327.4 52766.9 41638.9 -94405.8 596.9 20 0.150

495 2072.00 40542.1 43561.1 -84103.2 52648.8 41523.8 -94172.7 597.0 20 0.150

496 2082.00 40288.6 43260.6 -83549.3 52351.8 41238.8 -93590.5 597.2 20 0.150

497 2092.00 40041.1 42968.1 -83009.2 52066.7 40959.7 -93026.4 597.3 20 0.150

498 2102.00 39804.7 42679.7 -82484.3 51795.6 40686.6 -92482.2 597.5 20 0.150

499 2112.00 39578.2 42400.2 -81978.4 51537.5 40419.5 -91957.1 597.6 20 0.150

500 2132.00 39153.4 41861.4 -81014.7 51055.4 39906.4 -90961.7 598.0 20 0.150

501 2134.00 39114.0 41808.1 -80922.1 51010.4 39855.4 -90865.7 598.0 20 0.150

502 2144.00 38912.7 41549.7 -80462.4 50774.3 39610.3 -90384.5 598.1 20 0.150

503 2154.00 38717.3 41297.3 -80014.7 50551.2 39369.2 -89920.4 598.2 20 0.150
C-29

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

504 2164.00 38531.0 41051.0 -79581.9 50339.1 39135.1 -89474.1 598.3 20 0.150

505 2174.00 38356.6 40811.6 -79168.2 50141.0 38907.0 -89048.0 598.4 20 0.150

506 2194.00 38033.0 40355.1 -78388.1 49776.8 38472.8 -88249.6 598.6 20 0.150

507 2214.00 37744.5 39925.5 -77670.1 49452.6 38064.6 -87517.2 598.8 20 0.150

508 2234.00 37463.2 39505.2 -76968.3 49135.4 37666.4 -86801.9 599.0 20 0.150

509 2239.00 37393.5 39401.5 -76795.1 49057.4 37567.4 -86624.8 599.0 20 0.150

510 2249.00 37246.4 39192.4 -76438.8 48883.3 37368.3 -86251.6 599.0 20 0.150

511 2259.00 37098.2 38982.2 -76080.5 48713.2 37168.2 -85881.4 599.0 20 0.150

512 2269.00 36951.1 38771.1 -75722.2 48546.1 36967.1 -85513.3 599.0 20 0.150

513 2279.00 36807.0 38559.9 -75366.9 48382.0 36766.0 -85148.1 599.0 20 0.150

514 2299.00 36520.7 38138.7 -74659.4 48058.8 36365.8 -84424.7 599.1 20 0.150

515 2319.00 36247.5 37721.5 -73968.9 47750.7 35970.7 -83721.3 599.1 20 0.150

516 2339.00 36002.4 37330.4 -73332.7 47476.5 35597.5 -83074.0 599.1 20 0.150

517 2379.00 35574.6 36617.6 -72192.2 46997.1 34920.1 -81917.2 599.1 20 0.150

518 2419.00 35224.4 36002.4 -71226.8 46606.8 34334.8 -80941.6 599.2 20 0.150

519 2499.00 34744.6 35060.5 -69805.1 46073.2 33439.2 -79512.4 599.3 20 0.150

520 2579.00 34401.2 34352.2 -68753.4 45689.8 32766.8 -78456.6 599.4 20 0.150

521 2739.00 33740.6 33000.6 -66741.1 44955.0 31477.0 -76432.0 599.5 20 0.150

522 2899.00 33104.1 31683.1 -64787.2 44244.2 30222.2 -74466.5 599.7 20 0.150

523 3210.00 32518.4 30204.4 -62722.8 43589.3 28808.3 -72397.6 600.0 20 0.150

524 3210.00 36431.2 25862.2 -62293.4 47466.4 24528.4 -71994.8 500.0 50 0.550

525 3220.00 36424.2 25861.2 -62285.4 47449.4 24527.4 -71976.8 499.9 50 0.550

526 3230.00 36414.2 25858.2 -62272.4 47435.4 24524.4 -71959.8 499.8 50 0.550

527 3240.00 36405.2 25854.2 -62259.4 47422.4 24520.4 -71942.8 499.8 50 0.550

528 3250.00 36396.2 25850.2 -62246.4 47411.4 24516.4 -71927.8 499.7 50 0.550

529 3270.00 36381.2 25841.2 -62222.3 47392.4 24507.4 -71899.8 499.5 50 0.550

530 3290.00 36369.2 25831.2 -62200.3 47376.4 24498.4 -71874.8 499.4 50 0.550

531 3310.00 36359.2 25821.2 -62180.3 47364.4 24488.4 -71852.8 499.2 50 0.550

532 3311.00 36318.3 25804.3 -62122.6 47322.4 24473.4 -71795.7 499.2 50 0.550

533 3312.00 36245.5 25784.5 -62029.9 47102.3 24452.3 -71554.5 498.0 50 0.550

534 3313.00 36122.6 25754.6 -61877.2 46695.1 24424.1 -71119.2 496.5 50 0.550

535 3314.00 35964.7 25720.7 -61685.4 46267.0 24391.0 -70658.0 494.8 50 0.550

536 3315.00 35780.8 25679.8 -61460.7 45817.8 24352.8 -70170.7 493.0 50 0.550

537 3316.00 35572.9 25634.0 -61206.9 45356.7 24309.7 -69666.4 491.2 50 0.550

538 3317.00 35347.1 25583.0 -60930.1 44888.5 24262.5 -69151.1 489.2 50 0.550

539 3318.00 35104.1 25527.1 -60631.3 44416.4 24210.4 -68626.8 487.3 50 0.550

540 3319.00 34851.3 25465.3 -60316.5 43943.2 24155.2 -68098.5 485.3 50 0.550

541 3320.00 34587.3 25401.3 -59988.7 43471.1 24095.1 -67566.2 483.2 50 0.550

542 3321.00 34315.4 25331.4 -59646.9 43001.0 24030.0 -67031.0 481.2 50 0.550
C-30

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

543 3322.00 34034.5 25258.5 -59293.0 42532.8 23962.8 -66495.7 479.1 50 0.550

544 3323.00 33745.6 25180.6 -58926.2 42067.7 23890.7 -65958.4 477.0 50 0.550

545 3324.00 33452.6 25098.6 -58551.3 41604.6 23815.6 -65420.1 474.9 50 0.550

546 3325.00 33156.7 25013.7 -58170.4 41144.5 23737.5 -64881.9 472.7 50 0.550

547 3326.00 32857.8 24924.8 -57782.5 40688.3 23655.3 -64343.7 470.6 50 0.550

548 3327.00 32556.8 24833.8 -57390.7 40235.2 23571.3 -63806.5 468.4 50 0.550

549 3328.00 32252.9 24737.9 -56990.8 39785.1 23482.1 -63267.3 466.2 50 0.550

550 3329.00 31947.9 24639.9 -56587.9 39339.0 23392.0 -62731.0 464.1 50 0.550

551 3330.00 31641.0 24538.0 -56179.0 38895.9 23297.9 -62193.8 461.9 50 0.550

552 3331.00 31333.0 24434.0 -55767.1 38457.8 23201.8 -61659.6 459.7 50 0.550

553 3332.00 31025.1 24326.1 -55351.2 38023.7 23101.7 -61125.4 457.5 50 0.550

554 3333.00 30717.1 24215.1 -54932.2 37592.6 22998.6 -60591.2 455.3 50 0.550

555 3334.00 30409.2 24103.2 -54512.3 37165.5 22894.5 -60060.0 453.1 50 0.550

556 3335.00 30101.2 23988.2 -54089.4 36741.4 22787.4 -59528.9 450.8 50 0.550

557 3336.00 29795.2 23870.2 -53665.5 36322.3 22678.3 -59000.7 448.6 50 0.550

558 3337.00 29489.3 23750.3 -53239.5 35906.2 22566.2 -58472.5 446.4 50 0.550

559 3338.00 29183.3 23627.3 -52810.6 35493.2 22453.2 -57946.3 444.1 50 0.550

560 3339.00 28879.3 23502.3 -52381.6 35085.1 22337.1 -57422.1 441.9 50 0.550

561 3340.00 28575.3 23375.3 -51950.7 34680.0 22218.0 -56897.9 439.6 50 0.550

562 3341.00 28273.4 23247.4 -51520.7 34278.9 22097.9 -56376.8 437.4 50 0.550

563 3342.00 27972.4 23116.4 -51088.8 33880.8 21975.8 -55856.6 435.1 50 0.550

564 3343.00 27673.4 22984.4 -50657.8 33486.7 21852.7 -55339.5 432.8 50 0.550

565 3344.00 27375.4 22850.4 -50225.8 33094.6 21727.6 -54822.3 430.6 50 0.550

566 3345.00 27079.4 22714.4 -49793.9 32707.6 21600.6 -54308.1 428.3 50 0.550

567 3346.00 26784.5 22577.5 -49361.9 32322.5 21472.5 -53795.0 426.0 50 0.550

568 3347.00 26492.5 22438.5 -48930.9 31941.4 21343.4 -53284.8 423.7 50 0.550

569 3348.00 26200.5 22298.5 -48499.0 31563.3 21212.3 -52775.7 421.4 50 0.550

570 3349.00 25911.5 22156.5 -48068.0 31189.3 21080.3 -52269.5 419.2 50 0.550

571 3350.00 25623.5 22013.5 -47637.0 30818.2 20945.2 -51763.3 416.9 50 0.550

572 3351.00 25336.5 21869.5 -47206.0 30450.1 20810.1 -51260.2 414.6 50 0.550

573 3352.00 25053.5 21722.5 -46776.0 30087.0 20673.0 -50760.1 412.3 50 0.550

574 3353.00 24770.5 21574.5 -46345.0 29726.0 20534.0 -50259.9 410.0 50 0.550

575 3354.00 24490.5 21426.5 -45917.0 29368.9 20394.9 -49763.8 407.7 50 0.550

576 3355.00 24211.5 21277.5 -45489.0 29013.8 20254.8 -49268.6 405.4 50 0.550

577 3356.00 23935.5 21126.5 -45062.0 28662.7 20113.7 -48776.5 403.1 50 0.550

578 3357.00 23660.5 20975.5 -44636.0 28312.7 19971.7 -48284.3 400.7 50 0.550

579 3358.00 23386.5 20823.5 -44210.0 27966.6 19828.6 -47795.2 398.4 50 0.550

580 3359.00 23115.5 20670.5 -43786.0 27623.5 19685.5 -47309.0 396.1 50 0.550

581 3360.00 22845.5 20517.5 -43362.9 27281.4 19541.5 -46822.9 393.8 50 0.550
C-31

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

582 3361.00 22577.5 20363.5 -42940.9 26942.4 19397.4 -46339.8 391.5 50 0.550

583 3362.00 22311.5 20207.4 -42518.9 26606.3 19250.3 -45856.6 389.1 50 0.550

584 3363.00 22045.4 20052.4 -42097.9 26272.2 19104.3 -45376.5 386.8 50 0.550

585 3364.00 21783.4 19895.4 -41678.9 25941.2 18957.2 -44898.4 384.5 50 0.550

586 3365.00 21521.4 19738.4 -41259.8 25612.1 18810.1 -44422.2 382.1 50 0.550

587 3366.00 21263.4 19580.4 -40843.8 25287.0 18661.0 -43948.1 379.8 50 0.550

588 3367.00 21005.4 19421.4 -40426.8 24964.0 18512.0 -43475.9 377.5 50 0.550

589 3368.00 20748.4 19262.4 -40010.7 24643.9 18360.9 -43004.8 375.1 50 0.550

590 3369.00 20495.3 19102.3 -39597.7 24326.8 18210.8 -42537.7 372.8 50 0.550

591 3370.00 20242.3 18942.3 -39184.7 24011.8 18059.8 -42071.5 370.4 50 0.550

592 3371.00 19992.3 18781.3 -38773.6 23700.7 17907.7 -41608.4 368.1 50 0.550

593 3372.00 19743.3 18619.3 -38362.6 23390.6 17755.6 -41146.2 365.7 50 0.550

594 3373.00 19496.3 18457.3 -37953.6 23083.5 17602.6 -40686.1 363.4 50 0.550

595 3374.00 19251.2 18295.2 -37546.5 22779.5 17449.5 -40228.9 361.0 50 0.550

596 3375.00 19007.2 18132.2 -37139.4 22476.4 17296.4 -39772.8 358.6 50 0.550

597 3376.00 18764.2 17969.2 -36733.4 22175.3 17143.3 -39318.7 356.3 50 0.550

598 3377.00 18524.2 17806.2 -36330.4 21877.3 16990.3 -38867.5 353.9 50 0.550

599 3378.00 18285.1 17642.2 -35927.3 21581.2 16835.2 -38416.4 351.6 50 0.550

600 3379.00 18048.1 17479.1 -35527.3 21288.1 16681.1 -37969.2 349.2 50 0.550

601 3380.00 17811.1 17315.1 -35126.2 20996.0 16527.0 -37523.1 346.8 50 0.550

602 3381.00 17577.1 17150.1 -34727.1 20707.0 16372.0 -37079.0 344.5 50 0.550

603 3382.00 17345.1 16986.1 -34331.1 20421.9 16216.9 -36638.8 342.1 50 0.550

604 3383.00 17113.0 16822.0 -33935.1 20137.8 16061.9 -36199.7 339.7 50 0.550

605 3384.00 16885.0 16657.0 -33542.0 19856.8 15906.8 -35763.5 337.4 50 0.550

606 3385.00 16657.0 16492.0 -33149.0 19577.7 15750.7 -35328.4 335.0 50 0.550

607 3386.00 16429.9 16327.9 -32757.9 19300.6 15594.6 -34895.3 332.7 50 0.550

608 3387.00 16206.9 16161.9 -32368.8 19026.5 15438.5 -34465.1 330.3 50 0.550

609 3388.00 15983.9 15996.9 -31980.7 18753.5 15282.5 -34036.0 327.9 50 0.550

610 3389.00 15761.9 15831.9 -31593.7 18483.4 15126.4 -33609.8 325.5 50 0.550

611 3390.00 15542.8 15665.8 -31208.6 18216.3 14969.3 -33185.7 323.2 50 0.550

612 3391.00 15324.8 15499.8 -30824.6 17950.3 14812.3 -32762.5 320.8 50 0.550

613 3392.00 15108.8 15332.8 -30441.5 17686.2 14655.2 -32341.4 318.4 50 0.550

614 3393.00 14893.7 15167.7 -30061.4 17424.1 14499.1 -31923.3 316.0 50 0.550

615 3394.00 14679.7 15001.7 -29681.4 17164.1 14342.1 -31506.1 313.7 50 0.550

616 3395.00 14468.7 14835.6 -29304.3 16906.0 14186.0 -31092.0 311.3 50 0.550

617 3396.00 14257.6 14669.6 -28927.3 16648.9 14028.9 -30677.8 308.9 50 0.550

618 3397.00 14047.6 14503.6 -28551.2 16393.9 13872.9 -30266.7 306.5 50 0.550

619 3398.00 13839.5 14338.5 -28178.1 16141.8 13715.8 -29857.5 304.2 50 0.550

620 3399.00 13632.5 14172.5 -27805.0 15889.7 13558.7 -29448.4 301.8 50 0.550
C-32

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

621 3400.00 13426.5 14006.5 -27433.0 15639.6 13402.6 -29042.3 299.4 50 0.550

622 3401.00 13222.5 13841.5 -27063.9 15392.6 13245.6 -28638.1 297.0 50 0.550

623 3402.00 13019.4 13675.4 -26694.8 15146.5 13088.5 -28235.0 294.6 50 0.550

624 3403.00 12818.4 13510.4 -26328.7 14902.4 12932.4 -27834.8 292.2 50 0.550

625 3404.00 12618.4 13344.4 -25962.7 14660.3 12775.3 -27435.7 289.8 50 0.550

626 3405.00 12419.3 13178.3 -25597.6 14419.3 12619.3 -27038.6 287.5 50 0.550

627 3406.00 12222.3 13013.3 -25235.5 14180.2 12463.2 -26643.4 285.1 50 0.550

628 3407.00 12025.2 12848.2 -24873.5 13943.1 12307.1 -26250.3 282.7 50 0.550

629 3408.00 11830.2 12683.2 -24513.4 13707.1 12151.1 -25858.1 280.3 50 0.550

630 3409.00 11637.2 12518.2 -24155.3 13474.0 11994.0 -25468.0 277.9 50 0.550

631 3410.00 11444.1 12353.1 -23797.2 13241.9 11837.9 -25079.8 275.5 50 0.550

632 3411.00 11254.1 12188.1 -23442.2 13012.8 11681.8 -24694.7 273.1 50 0.550

633 3412.00 11064.0 12023.0 -23087.1 12783.8 11525.8 -24309.6 270.7 50 0.550

634 3413.00 10875.0 11858.0 -22733.0 12555.7 11369.7 -23925.4 268.3 50 0.550

635 3414.00 10688.0 11694.0 -22381.9 12330.6 11214.6 -23545.3 265.9 50 0.550

636 3415.00 10500.9 11529.9 -22030.9 12106.6 11058.6 -23165.1 263.5 50 0.550

637 3416.00 10315.9 11364.9 -21680.8 11883.5 10902.5 -22785.9 261.1 50 0.550

638 3417.00 10131.9 11200.9 -21332.7 11662.4 10747.4 -22409.8 258.7 50 0.550

639 3418.00 9948.8 11036.8 -20985.6 11442.3 10592.3 -22034.7 256.3 50 0.550

640 3419.00 9767.8 10872.8 -20640.5 11224.3 10437.3 -21661.5 253.9 50 0.550

641 3420.00 9585.7 10709.7 -20295.5 11006.2 10283.2 -21289.3 251.5 50 0.550

642 3421.00 9405.7 10546.7 -19952.4 10790.1 10129.1 -20919.2 249.1 50 0.550

643 3422.00 9227.7 10382.7 -19610.3 10577.0 9973.0 -20550.1 246.7 50 0.550

644 3423.00 9049.6 10219.6 -19269.2 10362.0 9820.0 -20181.9 244.3 50 0.550

645 3424.00 8873.6 10056.6 -18930.2 10149.9 9664.9 -19814.7 241.9 50 0.550

646 3425.00 8696.5 9894.5 -18591.1 9936.8 9510.8 -19447.6 239.4 50 0.550

647 3426.00 8521.5 9731.5 -18253.0 9724.7 9357.7 -19082.5 237.0 50 0.550

648 3427.00 8347.5 9569.5 -17916.9 9515.7 9203.7 -18719.3 234.6 50 0.550

649 3428.00 8173.4 9407.4 -17580.8 9306.6 9049.6 -18356.1 232.2 50 0.550

650 3429.00 8000.4 9245.4 -17245.7 9099.5 8895.5 -17995.0 229.7 50 0.550

651 3430.00 7830.3 9082.3 -16912.7 8893.4 8743.4 -17636.9 227.3 50 0.550

652 3431.00 7659.3 8921.3 -16580.6 8688.4 8590.4 -17278.7 224.9 50 0.550

653 3432.00 7490.2 8759.2 -16249.5 8486.3 8437.3 -16923.6 222.5 50 0.550

654 3433.00 7321.2 8598.2 -15919.4 8284.2 8284.2 -16568.4 220.0 50 0.550

655 3434.00 7153.2 8437.2 -15590.3 8083.1 8131.1 -16214.2 217.6 50 0.550

656 3435.00 6987.1 8276.1 -15263.2 7884.1 7979.1 -15863.1 215.2 50 0.550

657 3436.00 6821.1 8115.1 -14936.1 7685.0 7827.0 -15512.0 212.7 50 0.550

658 3437.00 6656.0 7955.0 -14611.1 7487.9 7674.9 -15162.8 210.3 50 0.550

659 3438.00 6492.0 7794.0 -14286.0 7290.8 7523.8 -14814.6 207.9 50 0.550
C-33

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

660 3439.00 6328.0 7634.0 -13961.9 7095.7 7371.7 -14467.5 205.4 50 0.550

661 3440.00 6165.9 7474.9 -13640.8 6901.7 7220.7 -14122.3 203.0 50 0.550

662 3441.00 6003.9 7314.9 -13318.8 6708.6 7069.6 -13778.2 200.6 50 0.550

663 3442.00 5842.8 7155.8 -12998.6 6517.5 6917.5 -13435.0 198.1 50 0.550

664 3443.00 5682.8 6996.8 -12679.6 6326.4 6767.4 -13093.9 195.7 50 0.550

665 3444.00 5523.7 6837.7 -12361.5 6138.3 6617.3 -12755.7 193.3 50 0.550

666 3445.00 5365.7 6679.7 -12045.4 5952.3 6467.3 -12419.5 190.8 50 0.550

667 3446.00 5208.7 6521.7 -11730.3 5766.2 6318.2 -12084.4 188.4 50 0.550

668 3447.00 5053.6 6363.6 -11417.2 5583.1 6168.1 -11751.2 186.0 50 0.550

669 3448.00 4898.6 6205.6 -11104.2 5400.0 6019.1 -11419.1 183.5 50 0.550

670 3449.00 4744.5 6047.5 -10792.1 5219.0 5869.0 -11088.0 181.1 50 0.550

671 3450.00 4592.5 5890.5 -10483.0 5038.9 5719.9 -10758.8 178.7 50 0.550

672 3451.00 4439.5 5734.5 -10173.9 4858.8 5571.8 -10430.7 176.2 50 0.550

673 3452.00 4289.4 5577.4 -9866.9 4681.8 5423.8 -10105.5 173.8 50 0.550

674 3453.00 4138.4 5421.4 -9559.8 4503.7 5275.7 -9779.4 171.4 50 0.550

675 3454.00 3989.4 5265.4 -9254.7 4327.6 5127.6 -9455.2 168.9 50 0.550

676 3455.00 3841.3 5109.3 -8950.6 4153.5 4980.5 -9134.1 166.5 50 0.550

677 3456.00 3693.3 4954.3 -8647.5 3978.4 4833.4 -8811.9 164.1 50 0.550

678 3457.00 3547.2 4799.2 -8346.4 3806.4 4686.4 -8492.7 161.6 50 0.550

679 3458.00 3401.2 4644.2 -8045.4 3634.3 4539.3 -8173.6 159.2 50 0.550

680 3459.00 3256.2 4489.2 -7745.3 3463.2 4393.2 -7856.4 156.8 50 0.550

681 3460.00 3112.1 4335.1 -7447.2 3294.1 4247.1 -7541.3 154.3 50 0.550

682 3461.00 2969.1 4181.1 -7150.2 3125.1 4101.1 -7226.1 151.9 50 0.550

683 3462.00 2827.0 4027.0 -6854.1 2958.0 3956.0 -6914.0 149.5 50 0.550

684 3463.00 2685.0 3874.0 -6559.0 2790.9 3809.9 -6600.8 147.0 50 0.550

685 3464.00 2544.0 3721.0 -6264.9 2623.8 3664.8 -6288.7 144.6 50 0.550

686 3465.00 2403.9 3567.9 -5971.8 2457.8 3519.8 -5977.5 142.1 50 0.550

687 3466.00 2263.9 3414.9 -5678.8 2291.7 3374.7 -5666.4 139.7 50 0.550

688 3467.00 2124.8 3263.8 -5388.7 2126.6 3230.6 -5357.3 137.2 50 0.550

689 3468.00 1986.8 3110.8 -5097.6 1961.6 3087.6 -5049.1 134.7 50 0.550

690 3469.00 1848.8 2958.8 -4807.5 1798.5 2942.5 -4741.0 132.3 50 0.550

691 3470.00 1711.7 2806.7 -4518.4 1636.4 2799.4 -4435.8 129.8 50 0.550

692 3471.00 1636.4 2674.4 -4310.8 1636.4 2674.4 -4310.8 128.2 50 0.550

693 3471.20 1636.4 2674.4 -4310.8 1636.4 2674.4 -4310.8 128.2 5 0.100

694 3471.40 0.0 0.0 0.0 0.0 0.0 0.0 128.2 5 0.100

695 3471.60 3272.8 5348.8 -8621.6 3272.8 5348.8 -8621.6 128.2 5 0.100

696 3471.80 1636.4 2674.4 -4310.8 1636.4 2674.4 -4310.8 128.2 5 0.100

697 3472.00 1605.2 2549.2 -4154.4 1808.4 2555.4 -4363.9 127.0 50 0.550

698 3474.00 1655.0 2318.0 -3973.0 2351.6 2337.6 -4689.1 125.5 50 0.550
C-34

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

699 3476.00 1809.1 2111.1 -3920.2 2976.7 2140.7 -5117.4 124.4 50 0.550

700 3479.00 2175.5 1842.5 -4018.0 3971.9 1881.9 -5853.8 123.2 50 0.550

701 3483.00 2810.2 1552.2 -4362.3 5293.1 1598.1 -6891.2 121.9 50 0.550

702 3487.00 3528.7 1326.7 -4855.5 6575.3 1374.3 -7949.5 120.9 50 0.550

703 3492.00 4479.2 1126.2 -5605.4 8103.4 1172.4 -9275.8 119.8 50 0.550

704 3498.00 5631.4 985.4 -6616.9 9825.5 1024.5 -10850.0 118.8 50 0.550

705 3505.00 6945.4 930.4 -7875.8 11686.6 958.5 -12645.1 117.7 50 0.550

706 3513.00 8371.2 980.2 -9351.4 13634.6 994.6 -14629.2 116.6 50 0.550

707 3522.00 9866.8 1139.8 -11006.7 15627.6 1135.6 -16763.2 115.6 50 0.550

708 3532.00 11393.4 1413.4 -12806.8 17626.6 1384.6 -19011.2 114.5 50 0.550

709 3542.00 12793.0 1754.0 -14547.0 19432.6 1702.6 -21135.2 113.6 50 0.550

710 3543.00 12927.0 1790.0 -14716.9 19602.6 1737.6 -21340.2 113.5 50 0.550

711 3553.00 14199.6 2184.6 -16384.3 21226.6 2106.6 -23333.3 112.7 50 0.550

712 3555.00 14439.6 2266.6 -16706.2 21528.6 2185.6 -23714.3 112.5 50 0.550

713 3565.00 15578.3 2692.3 -18270.7 22966.7 2586.6 -25553.3 111.8 50 0.550

714 3569.00 16004.2 2867.2 -18871.5 23497.7 2753.7 -26251.3 111.5 50 0.550

715 3579.00 17003.1 3313.1 -20316.2 24746.7 3177.7 -27924.4 110.8 50 0.550

716 3584.00 17470.0 3539.1 -21009.1 25324.7 3391.7 -28716.4 110.4 50 0.550

717 3594.00 18349.0 3992.0 -22341.0 26412.7 3823.7 -30236.4 109.8 50 0.550

718 3601.00 18921.0 4310.0 -23231.0 27113.8 4126.7 -31240.5 109.4 50 0.550

719 3611.00 19694.1 4761.1 -24455.1 28063.8 4556.8 -32620.6 108.9 50 0.550

720 3620.00 20340.2 5165.2 -25505.3 28848.8 4943.8 -33792.6 108.4 50 0.550

721 3630.00 21009.4 5610.3 -26619.7 29661.9 5369.9 -35031.7 107.9 50 0.550

722 3640.00 21629.6 6050.6 -27680.2 30407.9 5790.9 -36198.8 107.4 50 0.550

723 3641.00 21689.6 6094.6 -27784.2 30479.9 5832.9 -36312.8 107.4 50 0.550

724 3651.00 22275.9 6522.9 -28798.8 31187.9 6242.9 -37430.9 107.0 50 0.550

725 3661.00 22827.2 6942.2 -29769.5 31847.0 6645.0 -38492.0 106.6 50 0.550

726 3666.00 23088.4 7147.4 -30235.8 32159.0 6841.0 -39000.0 106.4 50 0.550

727 3676.00 23590.8 7549.8 -31140.6 32763.1 7225.0 -39988.1 106.0 50 0.550

728 3686.00 24060.3 7940.3 -32000.5 33320.1 7599.1 -40919.2 105.7 50 0.550

729 3695.00 24451.7 8280.7 -32732.4 33782.1 7925.2 -41707.3 105.3 50 0.550

730 3705.00 24858.2 8647.2 -33505.5 34265.2 8277.2 -42542.4 105.1 50 0.550

731 3715.00 25234.8 9003.8 -34238.6 34708.2 8617.2 -43325.5 104.8 50 0.550

732 3725.00 25596.4 9349.4 -34945.8 35131.3 8948.3 -44079.6 104.5 50 0.550

733 3730.00 25770.7 9519.7 -35290.4 35334.3 9112.3 -44446.6 104.3 50 0.550

734 3740.00 26113.4 9855.4 -35968.8 35740.4 9432.4 -45172.8 104.1 50 0.550

735 3750.00 26442.1 10185.1 -36627.1 36124.4 9747.4 -45871.9 103.9 50 0.550

736 3760.00 26753.8 10506.8 -37260.6 36487.5 10055.5 -46543.0 103.7 50 0.550

737 3770.00 27050.6 10821.6 -37872.1 36831.6 10355.6 -47187.1 103.4 50 0.550
C-35

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

738 3775.00 27193.9 10975.9 -38169.8 36996.6 10503.6 -47500.2 103.3 50 0.550

739 3785.00 27471.7 11279.7 -38751.5 37323.6 10793.6 -48117.3 103.2 50 0.550

740 3795.00 27736.6 11574.6 -39311.2 37630.7 11074.7 -48705.4 103.0 50 0.550

741 3805.00 27992.4 11862.4 -39854.9 37924.8 11350.8 -49275.5 102.8 50 0.550

742 3815.00 28240.3 12150.3 -40390.6 38210.8 11624.8 -49835.6 102.7 50 0.550

743 3835.00 28705.2 12703.2 -41408.4 38741.9 12153.9 -50895.9 102.3 50 0.550

744 3836.00 28727.3 12730.3 -41457.6 38767.0 12180.0 -50946.9 102.3 50 0.550

745 3846.00 28948.3 12998.2 -41946.5 39027.0 12434.0 -51461.0 102.2 50 0.550

746 3856.00 29164.2 13259.2 -42423.5 39275.1 12683.1 -51958.2 102.1 50 0.550

747 3866.00 29370.2 13514.2 -42884.5 39511.1 12926.1 -52437.3 102.0 50 0.550

748 3876.00 29566.2 13762.2 -43328.5 39735.2 13162.2 -52897.4 101.9 50 0.550

749 3896.00 29932.3 14236.3 -44168.6 40150.3 13615.3 -53765.7 101.7 50 0.550

750 3916.00 30260.4 14682.4 -44942.8 40523.4 14039.5 -54562.9 101.5 50 0.550

751 3933.00 30512.2 15039.2 -45551.3 40806.6 14378.6 -55185.1 101.3 50 0.550

752 3943.00 30655.2 15239.2 -45894.4 40973.6 14569.6 -55543.2 101.3 50 0.550

753 3953.00 30789.3 15434.3 -46223.6 41127.7 14754.7 -55882.4 101.2 50 0.550

754 3963.00 30915.4 15621.3 -46536.7 41270.7 14932.8 -56203.5 101.2 50 0.550

755 3973.00 31034.4 15803.4 -46837.8 41404.8 15104.8 -56509.6 101.2 50 0.550

756 3993.00 31273.5 16162.5 -47436.0 41673.9 15446.9 -57120.9 101.1 50 0.550

757 4013.00 31507.7 16520.7 -48028.3 41937.1 15787.1 -57724.1 101.0 50 0.550

758 4033.00 31736.9 16876.9 -48613.8 42194.2 16126.2 -58320.4 100.9 50 0.550

759 4073.00 32189.5 17585.5 -49774.9 42701.4 16798.4 -59499.9 100.7 50 0.550

760 4113.00 32633.2 18288.2 -50921.5 43196.7 17466.7 -60663.4 100.6 50 0.550

761 4178.00 33196.8 19276.8 -52473.6 43822.1 18404.1 -62226.2 100.3 50 0.550

762 4188.00 33272.9 19408.9 -52681.8 43916.1 18529.1 -62445.3 100.4 50 0.550

763 4198.00 33347.9 19535.9 -52883.8 44002.2 18650.2 -62652.4 100.4 50 0.550

764 4208.00 33418.9 19657.9 -53076.9 44082.2 18766.3 -62848.5 100.4 50 0.550

765 4218.00 33483.0 19775.0 -53257.9 44155.3 18876.3 -63031.6 100.5 50 0.550

766 4238.00 33596.8 19989.8 -53586.6 44283.4 19080.4 -63363.8 100.5 50 0.550

767 4258.00 33689.6 20182.6 -53872.2 44387.5 19262.5 -63650.0 100.6 50 0.550

768 4278.00 33769.2 20354.2 -54123.4 44475.6 19424.6 -63900.1 100.7 50 0.550

769 4318.00 33939.1 20692.1 -54631.3 44664.7 19744.7 -64409.4 100.8 50 0.550

770 4358.00 34102.1 21025.1 -55127.2 44845.9 20059.9 -64905.7 101.0 50 0.550

771 4438.00 34414.2 21675.2 -56089.4 45190.2 20677.2 -65867.3 101.3 50 0.550

772 4500.00 34647.9 22171.9 -56819.8 45448.4 21147.4 -66595.8 101.5 50 0.550

773 4503.00 34705.3 22242.3 -56947.5 45510.4 21216.5 -66726.9 101.5 50 0.550

774 4505.00 34807.3 22297.3 -57104.5 45846.5 21273.6 -67120.1 103.0 50 0.550

775 4507.00 34971.2 22364.3 -57335.5 46249.7 21337.7 -67587.4 104.6 50 0.550

776 4509.00 35168.3 22441.3 -57609.7 46653.8 21411.8 -68065.6 106.2 50 0.550
C-36

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

777 4511.00 35388.4 22525.4 -57913.8 47054.9 21491.9 -68546.8 107.9 50 0.550

778 4513.00 35620.6 22616.6 -58237.1 47450.0 21579.0 -69029.1 109.6 50 0.550

779 4515.00 35865.7 22714.7 -58580.5 47839.1 21672.2 -69511.3 111.3 50 0.550

780 4517.00 36116.0 22819.0 -58935.0 48221.2 21771.2 -69992.5 113.1 50 0.550

781 4519.00 36368.2 22928.2 -59296.4 48596.3 21875.4 -70471.7 114.8 50 0.550

782 4521.00 36623.5 23042.5 -59666.0 48965.5 21983.4 -70948.9 116.6 50 0.550

783 4523.00 36879.8 23161.8 -60041.7 49325.6 22097.5 -71423.1 118.4 50 0.550

784 4525.00 37136.1 23286.1 -60422.3 49680.6 22214.6 -71895.3 120.2 50 0.550

785 4527.00 37391.5 23413.5 -60805.1 50028.7 22335.7 -72364.4 122.0 50 0.550

786 4529.00 37644.9 23545.9 -61190.8 50370.8 22460.8 -72831.6 123.8 50 0.550

787 4531.00 37896.3 23680.3 -61576.6 50704.9 22588.9 -73293.8 125.6 50 0.550

788 4533.00 38145.7 23819.7 -61965.4 51033.0 22720.9 -73753.9 127.4 50 0.550

789 4535.00 38392.2 23961.2 -62353.4 51356.1 22855.0 -74211.1 129.2 50 0.550

790 4537.00 38636.7 24104.7 -62741.3 51673.1 22992.1 -74665.2 131.1 50 0.550

791 4539.00 38877.2 24251.2 -63128.3 51985.2 23130.2 -75115.4 132.9 50 0.550

792 4541.00 39114.7 24399.7 -63514.3 52290.3 23271.3 -75561.6 134.7 50 0.550

793 4543.00 39349.2 24550.2 -63899.3 52589.4 23415.4 -76004.7 136.6 50 0.550

794 4545.00 39581.7 24702.7 -64284.4 52883.4 23561.4 -76444.8 138.4 50 0.550

795 4547.00 39810.3 24857.2 -64667.5 53173.5 23707.5 -76881.0 140.3 50 0.550

796 4549.00 40034.8 25013.8 -65048.6 53457.6 23855.6 -77313.1 142.1 50 0.550

797 4551.00 40257.4 25170.4 -65427.7 53737.6 24004.7 -77742.3 144.0 50 0.550

798 4553.00 40476.0 25329.0 -65804.9 54011.7 24155.7 -78167.4 145.8 50 0.550

799 4555.00 40692.5 25487.5 -66180.0 54282.8 24306.8 -78589.6 147.7 50 0.550

800 4557.00 40906.1 25647.1 -66553.2 54548.9 24458.9 -79007.7 149.5 50 0.550

801 4559.00 41115.7 25808.8 -66924.5 54809.9 24612.9 -79422.9 151.4 50 0.550

802 4561.00 41323.4 25970.4 -67293.7 55068.0 24767.0 -79835.0 153.3 50 0.550

803 4563.00 41527.0 26134.0 -67661.0 55320.1 24923.1 -80243.1 155.1 50 0.550

804 4565.00 41728.6 26297.6 -68026.3 55569.1 25079.1 -80648.3 157.0 50 0.550

805 4567.00 41926.3 26461.3 -68387.6 55814.2 25234.2 -81048.4 158.9 50 0.550

806 4569.00 42123.0 26625.0 -68748.0 56055.3 25391.3 -81446.6 160.7 50 0.550

807 4571.00 42316.6 26789.6 -69106.3 56293.3 25548.4 -81841.7 162.6 50 0.550

808 4573.00 42507.3 26954.3 -69461.6 56528.4 25705.4 -82233.9 164.5 50 0.550

809 4575.00 42696.0 27119.9 -69815.9 56759.5 25862.5 -82622.0 166.4 50 0.550

810 4577.00 42882.7 27284.7 -70167.4 56986.6 26021.6 -83008.1 168.3 50 0.550

811 4579.00 43065.4 27450.3 -70515.7 57210.6 26178.7 -83389.3 170.1 50 0.550

812 4581.00 43246.0 27616.0 -70862.1 57430.7 26337.7 -83768.4 172.0 50 0.550

813 4583.00 43423.8 27781.8 -71205.5 57646.8 26495.8 -84142.6 173.9 50 0.550

814 4585.00 43599.5 27948.5 -71547.9 57860.9 26653.9 -84514.7 175.8 50 0.550

815 4587.00 43773.2 28114.2 -71887.4 58071.9 26811.9 -84883.9 177.7 50 0.550
C-37

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

816 4589.00 43944.9 28279.9 -72224.8 58280.0 26971.0 -85251.0 179.6 50 0.550

817 4591.00 44114.6 28445.6 -72560.2 58485.1 27129.1 -85614.2 181.5 50 0.550

818 4593.00 44281.4 28611.4 -72892.7 58687.1 27287.1 -85974.3 183.3 50 0.550

819 4595.00 44447.1 28776.1 -73223.2 58886.2 27446.2 -86332.4 185.2 50 0.550

820 4597.00 44608.8 28941.8 -73550.7 59082.3 27603.3 -86685.6 187.1 50 0.550

821 4599.00 44769.6 29107.6 -73877.1 59275.4 27762.4 -87037.7 189.0 50 0.550

822 4601.00 44928.3 29272.3 -74200.7 59466.4 27919.4 -87385.9 190.9 50 0.550

823 4603.00 45085.1 29437.1 -74522.1 59654.5 28077.5 -87732.0 192.8 50 0.550

824 4605.00 45239.8 29601.8 -74841.6 59840.6 28234.6 -88075.2 194.7 50 0.550

825 4607.00 45392.6 29766.6 -75159.1 60023.7 28391.7 -88415.3 196.6 50 0.550

826 4609.00 45544.3 29930.3 -75474.6 60204.7 28548.7 -88753.5 198.5 50 0.550

827 4611.00 45693.1 30094.1 -75787.2 60383.8 28704.8 -89088.6 200.4 50 0.550

828 4613.00 45839.9 30257.8 -76097.7 60558.9 28860.9 -89419.8 202.3 50 0.550

829 4615.00 45985.6 30420.6 -76406.3 60732.9 29016.0 -89748.9 204.2 50 0.550

830 4617.00 46129.4 30583.4 -76712.8 60904.0 29172.0 -90076.0 206.1 50 0.550

831 4619.00 46272.2 30745.1 -77017.3 61072.1 29328.1 -90400.2 208.0 50 0.550

832 4621.00 46412.0 30907.0 -77318.9 61239.2 29482.2 -90721.3 209.9 50 0.550

833 4623.00 46550.7 31068.7 -77619.4 61403.2 29637.2 -91040.5 211.8 50 0.550

834 4625.00 46687.5 31229.5 -77917.0 61565.3 29791.3 -91356.6 213.7 50 0.550

835 4627.00 46821.3 31391.3 -78212.6 61725.4 29944.4 -91669.8 215.6 50 0.550

836 4629.00 46956.1 31550.1 -78506.1 61883.5 30098.5 -91981.9 217.5 50 0.550

837 4631.00 47087.8 31710.8 -78798.7 62040.5 30250.5 -92291.1 219.4 50 0.550

838 4633.00 47219.7 31869.7 -79089.3 62195.6 30403.6 -92599.2 221.4 50 0.550

839 4635.00 47349.4 32028.4 -79377.9 62348.7 30555.7 -92904.4 223.3 50 0.550

840 4637.00 47477.2 32187.2 -79664.4 62500.8 30706.8 -93207.5 225.2 50 0.550

841 4639.00 47605.0 32345.0 -79950.0 62650.8 30858.8 -93509.7 227.1 50 0.550

842 4641.00 47729.8 32502.8 -80232.6 62798.9 31008.9 -93807.8 229.0 50 0.550

843 4643.00 47853.6 32659.6 -80513.2 62945.0 31159.0 -94104.0 230.9 50 0.550

844 4645.00 47977.4 32815.4 -80792.8 63090.1 31309.1 -94399.1 232.8 50 0.550

845 4647.00 48099.2 32972.2 -81071.4 63233.1 31459.1 -94692.3 234.7 50 0.550

846 4649.00 48219.0 33128.0 -81347.0 63375.2 31607.2 -94982.4 236.6 50 0.550

847 4651.00 48338.8 33282.8 -81621.6 63515.3 31756.3 -95271.6 238.5 50 0.550

848 4653.00 48455.6 33437.6 -81893.2 63652.3 31904.3 -95556.7 240.5 50 0.550

849 4655.00 48571.4 33592.4 -82163.8 63789.4 32051.4 -95840.8 242.4 50 0.550

850 4657.00 48687.2 33745.2 -82432.4 63924.5 32198.5 -96123.0 244.3 50 0.550

851 4659.00 48800.0 33900.0 -82700.0 64057.6 32345.6 -96403.1 246.2 50 0.550

852 4661.00 48912.8 34051.8 -82964.7 64188.6 32492.7 -96681.3 248.1 50 0.550

853 4663.00 49023.6 34204.6 -83228.3 64318.7 32637.7 -96956.5 250.0 50 0.550

854 4665.00 49133.5 34356.5 -83489.9 64447.8 32782.8 -97230.6 252.0 50 0.550
C-38

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

855 4667.00 49242.3 34506.3 -83748.5 64574.9 32926.9 -97501.8 253.9 50 0.550

856 4669.00 49350.1 34658.1 -84008.2 64702.0 33071.0 -97772.9 255.8 50 0.550

857 4671.00 49457.9 34807.9 -84265.8 64828.0 33215.1 -98043.1 257.7 50 0.550

858 4673.00 49565.7 34956.7 -84522.5 64954.1 33358.1 -98312.2 259.7 50 0.550

859 4675.00 49671.5 35106.5 -84778.0 65078.2 33501.2 -98579.4 261.6 50 0.550

860 4677.00 49776.3 35255.3 -85031.7 65200.3 33644.3 -98844.5 263.5 50 0.550

861 4679.00 49881.2 35403.2 -85284.3 65323.3 33785.4 -99108.7 265.4 50 0.550

862 4681.00 49985.0 35552.0 -85537.0 65444.4 33927.4 -99371.8 267.4 50 0.550

863 4683.00 50087.8 35699.8 -85787.5 65565.5 34068.5 -99634.0 269.3 50 0.550

864 4685.00 50190.6 35846.6 -86037.2 65684.6 34209.6 -99894.1 271.2 50 0.550

865 4687.00 50292.4 35992.4 -86284.9 65803.6 34349.6 -100153.3 273.2 50 0.550

866 4689.00 50392.2 36139.2 -86531.5 65919.7 34489.7 -100409.5 275.1 50 0.550

867 4691.00 50492.1 36285.1 -86777.1 66036.8 34628.8 -100665.6 277.0 50 0.550

868 4693.00 50591.9 36429.9 -87021.8 66152.9 34767.9 -100920.8 279.0 50 0.550

869 4695.00 50690.7 36574.7 -87265.4 66267.0 34907.0 -101174.0 280.9 50 0.550

870 4697.00 50788.5 36718.5 -87507.1 66381.0 35045.0 -101426.1 282.8 50 0.550

871 4699.00 50884.3 36862.3 -87746.7 66493.1 35182.1 -101675.2 284.8 50 0.550

872 4701.00 50981.2 37005.2 -87986.4 66605.2 35320.2 -101925.4 286.7 50 0.550

873 4703.00 51076.0 37149.0 -88225.0 66716.3 35456.3 -102172.6 288.6 50 0.550

874 4705.00 51170.8 37291.8 -88462.7 66826.4 35593.3 -102419.7 290.6 50 0.550

875 4707.00 51264.6 37433.6 -88698.3 66935.4 35729.4 -102664.9 292.5 50 0.550

876 4709.00 51358.4 37574.4 -88932.9 67043.5 35864.5 -102908.0 294.4 50 0.550

877 4711.00 51449.3 37716.3 -89165.6 67150.6 35998.6 -103149.2 296.4 50 0.550

878 4713.00 51541.1 37857.1 -89398.2 67256.7 36133.7 -103390.3 298.3 50 0.550

879 4715.00 51631.9 37996.9 -89628.8 67361.8 36268.7 -103630.5 300.3 50 0.550

880 4717.00 51722.8 38136.8 -89859.5 67466.8 36401.8 -103868.7 302.2 50 0.550

881 4719.00 51811.6 38275.6 -90087.2 67569.9 36534.9 -104104.8 304.1 50 0.550

882 4721.00 51899.4 38414.4 -90313.8 67672.0 36667.0 -104338.9 306.1 50 0.550

883 4723.00 51987.2 38552.2 -90539.4 67773.1 36800.1 -104573.1 308.0 50 0.550

884 4725.00 52074.0 38691.0 -90765.1 67874.1 36932.1 -104806.2 310.0 50 0.550

885 4727.00 52160.9 38827.9 -90988.7 67973.2 37064.2 -105037.4 311.9 50 0.550

886 4729.00 52245.7 38964.7 -91210.4 68072.3 37194.3 -105266.6 313.9 50 0.550

887 4731.00 52329.6 39101.5 -91431.1 68169.4 37324.4 -105493.7 315.8 50 0.550

888 4733.00 52413.4 39237.4 -91650.8 68265.5 37455.4 -105720.9 317.7 50 0.550

889 4735.00 52497.2 39372.2 -91869.4 68361.5 37585.5 -105947.1 319.7 50 0.550

890 4737.00 52579.0 39507.0 -92086.1 68456.6 37714.6 -106171.2 321.6 50 0.550

891 4739.00 52660.9 39641.9 -92302.7 68550.7 37842.7 -106393.4 323.6 50 0.550

892 4741.00 52740.7 39775.6 -92516.3 68642.8 37971.8 -106614.6 325.5 50 0.550

893 4743.00 52820.5 39909.5 -92730.0 68734.9 38098.9 -106833.7 327.5 50 0.550
C-39

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

894 4745.00 52900.3 40043.3 -92943.6 68827.9 38225.9 -107053.9 329.4 50 0.550

895 4747.00 52980.1 40175.2 -93155.3 68919.0 38353.0 -107272.0 331.4 50 0.550

896 4749.00 53059.0 40307.0 -93366.0 69009.1 38480.1 -107489.2 333.3 50 0.550

897 4750.00 53093.9 40372.9 -93466.8 69031.1 38542.1 -107573.3 334.1 50 0.550

898 4751.00 53108.1 40421.1 -93529.2 69018.1 38588.1 -107606.2 335.0 50 0.550

899 4754.00 53061.8 40553.8 -93615.5 68708.1 38712.1 -107420.2 336.1 50 0.550

900 4759.00 52798.7 40727.7 -93526.4 68005.0 38878.0 -106883.0 337.1 50 0.550

901 4767.00 52178.8 40912.8 -93091.7 66874.9 39058.9 -105933.8 338.2 50 0.550

902 4777.00 51324.0 41021.0 -92345.0 65574.8 39169.8 -104744.7 339.2 50 0.550

903 4778.00 51239.1 41026.1 -92265.1 65455.8 39173.8 -104629.7 339.2 50 0.550

904 4788.00 50409.9 41026.9 -91436.8 64299.9 39181.9 -103481.7 340.0 50 0.550

905 4792.00 50095.2 41008.2 -91103.5 63880.9 39164.9 -103045.8 340.3 50 0.550

906 4802.00 49349.8 40922.8 -90272.7 62888.9 39090.0 -101978.9 340.9 50 0.550

907 4809.00 48865.2 40842.2 -89707.4 62262.0 39015.0 -101277.0 341.3 50 0.550

908 4819.00 48211.5 40684.5 -88896.1 61418.1 38868.0 -100286.1 341.8 50 0.550

909 4829.00 47604.7 40495.7 -88100.4 60652.1 38689.1 -99341.3 342.4 50 0.550

910 4839.00 47043.8 40291.8 -87335.6 59944.2 38496.2 -98440.4 342.8 50 0.550

911 4849.00 46529.7 40076.8 -86606.5 59305.2 38292.2 -97597.5 343.2 50 0.550

912 4852.00 46384.7 40010.7 -86395.4 59126.3 38230.3 -97356.5 343.4 50 0.550

913 4862.00 45921.6 39789.6 -85711.1 58551.3 38019.3 -96570.6 343.7 50 0.550

914 4872.00 45493.4 39564.4 -85057.8 58027.3 37804.3 -95831.7 344.1 50 0.550

915 4879.00 45214.2 39406.2 -84620.4 57688.3 37653.3 -95341.7 344.4 50 0.550

916 4889.00 44833.9 39178.9 -84012.8 57221.4 37437.4 -94658.8 344.7 50 0.550

917 4899.00 44479.6 38951.6 -83431.1 56793.4 37221.4 -94014.8 345.0 50 0.550

918 4909.00 44151.1 38726.1 -82877.2 56401.4 37004.4 -93405.8 345.3 50 0.550

919 4912.00 44058.0 38659.0 -82717.0 56290.4 36940.4 -93230.8 345.4 50 0.550

920 4922.00 43753.5 38434.5 -82188.1 55922.4 36725.4 -92647.8 345.6 50 0.550

921 4932.00 43462.0 38210.0 -81672.0 55575.4 36511.4 -92086.8 345.9 50 0.550

922 4942.00 43183.5 37986.5 -81169.9 55244.4 36298.4 -91542.8 346.1 50 0.550

923 4952.00 42918.9 37763.9 -80682.7 54933.4 36085.4 -91018.8 346.4 50 0.550

924 4953.00 42892.8 37741.8 -80634.6 54902.4 36065.4 -90967.8 346.4 50 0.550

925 4963.00 42636.2 37519.2 -80155.4 54594.4 35852.4 -90446.8 346.6 50 0.550

926 4973.00 42392.5 37301.5 -79694.1 54307.4 35645.4 -89952.7 346.8 50 0.550

927 4983.00 42176.0 37106.0 -79282.0 54054.3 35457.3 -89511.7 347.0 50 0.550

928 4993.00 41975.4 36917.4 -78892.9 53820.3 35277.3 -89097.7 347.2 50 0.550

929 5007.00 41707.7 36659.7 -78367.4 53509.3 35031.3 -88540.6 347.4 50 0.550

930 5017.00 41524.1 36481.1 -78005.2 53289.3 34861.3 -88150.6 347.6 50 0.550

931 5027.00 41347.5 36308.5 -77656.1 53083.2 34695.2 -87778.5 347.7 50 0.550
C-40

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

932 5037.00 41182.0 36140.0 -77321.9 52891.2 34534.2 -87425.5 347.8 50 0.550

933 5047.00 41025.4 35976.4 -77001.9 52709.2 34379.2 -87088.4 347.9 50 0.550

934 5067.00 40742.3 35668.3 -76410.6 52384.1 34085.1 -86469.3 348.2 50 0.550

935 5087.00 40494.3 35384.2 -75878.5 52100.1 33814.1 -85914.1 348.4 50 0.550

936 5097.00 40372.7 35246.7 -75619.4 51954.1 33683.0 -85637.1 348.5 50 0.550

937 5107.00 40252.2 35110.2 -75362.3 51814.0 33553.0 -85367.0 348.6 50 0.550

938 5117.00 40135.7 34977.6 -75113.3 51681.0 33426.0 -85107.0 348.6 50 0.550

939 5127.00 40025.1 34846.1 -74871.2 51552.9 33300.9 -84853.9 348.7 50 0.550

940 5147.00 39815.1 34591.1 -74406.2 51312.9 33058.9 -84371.7 348.8 50 0.550

941 5167.00 39621.1 34349.1 -73970.2 51091.8 32827.8 -83919.6 348.9 50 0.550

942 5187.00 39443.1 34119.1 -73562.2 50890.7 32608.7 -83499.4 349.0 50 0.550

943 5227.00 39132.3 33692.3 -72824.6 50540.5 32201.5 -82742.1 349.3 50 0.550

944 5251.00 38972.2 33460.2 -72432.5 50361.5 31980.5 -82341.9 349.4 50 0.550

945 5261.00 38902.8 33364.8 -72267.7 50277.4 31890.4 -82167.8 349.4 50 0.550

946 5271.00 38832.4 33269.4 -72101.8 50194.4 31800.4 -81994.8 349.4 50 0.550

947 5281.00 38762.0 33173.0 -71934.9 50114.3 31708.3 -81822.7 349.4 50 0.550

948 5291.00 38691.5 33077.6 -71769.1 50034.3 31616.3 -81650.6 349.5 50 0.550

949 5311.00 38558.7 32886.7 -71445.5 49883.2 31436.2 -81319.4 349.5 50 0.550

950 5331.00 38437.9 32706.9 -71144.8 49748.1 31263.1 -81011.2 349.5 50 0.550

951 5351.00 38326.2 32535.2 -70861.3 49621.0 31101.0 -80722.1 349.5 50 0.550

952 5391.00 38127.8 32222.8 -70350.6 49398.9 30803.9 -80202.9 349.5 50 0.550

953 5431.00 37963.6 31948.6 -69912.2 49214.8 30543.8 -79758.6 349.5 50 0.550

954 5511.00 37723.7 31520.7 -69244.4 48947.6 30135.6 -79083.1 349.6 50 0.550

955 5591.00 37575.4 31224.4 -68799.8 48782.4 29854.4 -78636.8 349.6 50 0.550

956 5751.00 37296.2 30686.2 -67982.4 48471.1 29342.1 -77813.1 349.7 50 0.550

957 5911.00 37029.2 30166.2 -67195.4 48174.8 28845.8 -77020.6 349.7 50 0.550

958 6231.00 36851.6 29750.7 -66602.3 47976.5 28449.5 -76426.1 349.9 50 0.550

959 6450.00 36709.4 29379.4 -66088.8 47818.3 28094.3 -75912.6 350.0 50 0.550

960 6450.00 37709.4 24757.4 -62466.7 48508.8 23348.4 -71857.3 299.5 20 0.050

961 6452.00 37934.9 24819.7 -62754.6 49589.4 23397.6 -72987.0 304.2 20 0.050

962 6453.00 38192.5 24886.6 -63079.0 50514.4 23450.2 -73964.7 308.1 20 0.050

963 6454.00 38522.3 24971.4 -63493.7 51524.1 23517.9 -75042.0 312.4 20 0.050

964 6455.00 38905.6 25071.6 -63977.2 52575.9 23599.1 -76175.1 316.9 20 0.050

965 6456.00 39331.8 25185.6 -64517.3 53651.2 23693.3 -77344.5 321.6 20 0.050

966 6457.00 39797.6 25313.0 -65110.7 54746.4 23799.9 -78546.3 326.5 20 0.050

967 6458.00 40293.4 25452.8 -65746.2 55850.1 23918.3 -79768.4 331.4 20 0.050

968 6459.00 40817.6 25604.6 -66422.2 56960.9 24048.3 -81009.2 336.5 20 0.050

969 6460.00 41359.4 25767.0 -67126.4 58070.8 24188.8 -82259.6 341.7 20 0.050

970 6461.00 41915.6 25939.4 -67855.0 59177.7 24339.3 -83517.0 346.9 20 0.050
C-41

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

971 6462.00 42486.3 26122.0 -68608.3 60281.4 24499.9 -84781.4 352.1 20 0.050

972 6463.00 43071.6 26314.7 -69386.3 61382.1 24670.7 -86052.8 357.5 20 0.050

973 6464.00 43670.7 26517.6 -70188.3 62479.4 24851.2 -87330.7 362.9 20 0.050

974 6465.00 44277.8 26729.3 -71007.0 63570.3 25040.9 -88611.2 368.3 20 0.050

975 6466.00 44891.1 26949.6 -71840.8 64654.3 25239.0 -89893.3 373.8 20 0.050

976 6467.00 45510.8 27178.6 -72689.4 65731.2 25445.9 -91177.1 379.3 20 0.050

977 6468.00 46136.9 27416.2 -73553.1 66801.1 25661.2 -92462.2 384.9 20 0.050

978 6469.00 46768.7 27662.3 -74431.0 67863.8 25885.0 -93748.7 390.5 20 0.050

979 6470.00 47401.2 27915.0 -75316.2 68918.1 26115.3 -95033.4 396.1 20 0.050

980 6471.00 48033.4 28173.7 -76207.1 69964.1 26351.5 -96315.6 401.7 20 0.050

981 6472.00 48665.1 28438.6 -77103.7 71001.3 26593.9 -97595.2 407.4 20 0.050

982 6473.00 49296.4 28709.5 -78006.0 72030.1 26842.3 -98872.4 413.1 20 0.050

983 6474.00 49927.4 28986.6 -78914.0 73050.4 27096.6 -100147.0 418.8 20 0.050

984 6475.00 50557.9 29269.9 -79827.7 74062.1 27357.1 -101419.2 424.5 20 0.050

985 6476.00 51187.9 29559.2 -80747.1 75065.3 27623.6 -102688.9 430.3 20 0.050

986 6477.00 51817.6 29854.7 -81672.3 76059.9 27896.1 -103956.1 436.1 20 0.050

987 6478.00 52446.9 30156.2 -82603.0 77046.1 28174.6 -105220.7 441.9 20 0.050

988 6479.00 53075.7 30463.9 -83539.6 78023.5 28459.3 -106482.9 447.7 20 0.050

989 6480.00 53703.6 30777.3 -84480.9 78992.7 28749.4 -107742.1 453.6 20 0.050

990 6481.00 54328.9 31094.9 -85423.7 79953.5 29043.9 -108997.4 459.4 20 0.050

991 6482.00 54951.2 31416.8 -86368.0 80906.1 29342.3 -110248.4 465.3 20 0.050

992 6483.00 55570.6 31742.8 -87313.4 81850.5 29644.7 -111495.2 471.2 20 0.050

993 6484.00 56187.1 32072.9 -88260.0 82786.6 29951.2 -112737.8 477.1 20 0.050

994 6485.00 56800.7 32407.2 -89207.9 83714.4 30261.9 -113976.3 483.1 20 0.050

995 6486.00 57411.4 32745.6 -90157.0 84634.1 30576.4 -115210.6 489.0 20 0.050

996 6487.00 58019.1 33088.1 -91107.2 85545.4 30895.2 -116440.6 494.9 20 0.050

997 6488.00 58623.9 33434.8 -92058.7 86448.6 31217.9 -117666.6 500.9 20 0.050

998 6489.00 59225.8 33785.7 -93011.4 87343.6 31544.7 -118888.3 506.9 20 0.050

999 6490.00 59824.8 34140.6 -93965.4 88230.3 31875.6 -120105.8 512.9 20 0.050

1000 6491.00 60420.5 34498.7 -94919.3 89109.3 32209.6 -121318.9 518.9 20 0.050

1001 6492.00 61012.8 34858.6 -95871.3 89981.9 32545.1 -122527.0 524.9 20 0.050

1002 6493.00 61601.5 35220.0 -96821.5 90847.9 32882.1 -123730.0 531.0 20 0.050

1003 6494.00 62186.7 35583.2 -97769.8 91707.4 33220.8 -124928.2 537.0 20 0.050

1004 6495.00 62768.2 35947.9 -98716.1 92560.3 33561.0 -126121.4 543.0 20 0.050

1005 6496.00 63346.1 36314.4 -99660.5 93406.9 33902.6 -127309.5 549.1 20 0.050

1006 6497.00 63920.6 36682.2 -100602.9 94246.8 34245.9 -128492.7 555.2 20 0.050

1007 6498.00 64491.4 37051.9 -101543.3 95080.1 34590.9 -129671.0 561.2 20 0.050

1008 6499.00 65058.7 37423.1 -102481.8 95907.1 34937.2 -130844.3 567.3 20 0.050

1009 6500.00 65622.3 37795.9 -103418.2 96727.5 35285.2 -132012.7 573.4 20 0.050
C-42

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1010 6501.00 66123.3 38152.8 -104276.0 97218.6 35621.3 -132840.0 578.1 20 0.050

1011 6502.00 66510.5 38481.5 -104992.0 97268.0 35936.4 -133204.4 580.9 20 0.050

1012 6503.00 66802.9 38789.3 -105592.2 97143.6 36236.2 -133379.8 583.1 20 0.050

1013 6504.00 67018.5 39079.7 -106098.2 96928.0 36522.4 -133450.4 585.0 20 0.050

1014 6506.00 67286.8 39618.9 -106905.8 96369.6 37059.7 -133429.3 588.0 20 0.050

1015 6508.00 67386.1 40109.1 -107495.2 95713.4 37553.5 -133266.9 590.5 20 0.050

1016 6510.00 67365.0 40556.9 -107921.9 95009.3 38007.8 -133017.1 592.6 20 0.050

1017 6512.00 67267.1 40969.0 -108236.1 94289.1 38428.0 -132717.1 594.5 20 0.050

1018 6514.00 67096.5 41346.0 -108442.4 93555.6 38814.0 -132369.6 596.2 20 0.050

1019 6516.00 66874.8 41692.0 -108566.8 92819.1 39169.9 -131989.0 597.8 20 0.050

1020 6518.00 66614.0 42006.5 -108620.5 92088.4 39494.2 -131582.6 599.2 20 0.050

1021 6520.00 66321.8 42289.9 -108611.7 91367.1 39787.8 -131154.8 600.4 20 0.050

1022 6522.00 66017.6 42549.9 -108567.5 90659.3 40057.9 -130717.2 601.6 20 0.050

1023 6524.00 65702.5 42787.1 -108489.6 89965.4 40305.1 -130270.5 602.8 20 0.050

1024 6526.00 65376.7 43001.2 -108377.9 89285.4 40529.1 -129814.5 603.9 20 0.050

1025 6528.00 65040.0 43192.5 -108232.5 88619.2 40730.2 -129349.4 604.9 20 0.050

1026 6530.00 64693.1 43361.1 -108054.2 87966.9 40908.6 -128875.5 605.8 20 0.050

1027 6532.00 64343.0 43512.9 -107856.0 87327.5 41070.0 -128397.5 606.7 20 0.050

1028 6534.00 63992.2 43649.8 -107642.0 86700.8 41216.4 -127917.1 607.5 20 0.050

1029 6536.00 63640.7 43771.8 -107412.5 86086.7 41347.7 -127434.3 608.4 20 0.050

1030 6538.00 63288.5 43878.7 -107167.2 85485.3 41463.8 -126949.1 609.2 20 0.050

1031 6540.00 62935.6 43970.8 -106906.3 84896.5 41564.9 -126461.4 609.9 20 0.050

1032 6542.00 62583.2 44051.8 -106635.0 84317.9 41655.0 -125972.9 610.6 20 0.050

1033 6544.00 62236.0 44125.3 -106361.3 83751.0 41737.2 -125488.2 611.3 20 0.050

1034 6546.00 61894.9 44190.2 -106085.1 83197.4 41811.0 -125008.4 612.0 20 0.050

1035 6548.00 61559.7 44246.9 -105806.6 82657.1 41876.1 -124533.2 612.7 20 0.050

1036 6550.00 61230.5 44295.3 -105525.9 82130.1 41932.8 -124062.9 613.3 20 0.050

1037 6552.00 60907.4 44335.2 -105242.6 81616.3 41980.9 -123597.2 613.9 20 0.050

1038 6554.00 60590.2 44366.9 -104957.1 81115.8 42020.5 -123136.3 614.5 20 0.050

1039 6556.00 60279.1 44390.2 -104669.3 80628.5 42051.6 -122680.2 615.1 20 0.050

1040 6558.00 59974.0 44405.1 -104379.1 80154.6 42074.2 -122228.8 615.6 20 0.050

1041 6560.00 59674.8 44411.8 -104086.5 79693.9 42088.2 -121782.1 616.2 20 0.050

1042 6562.00 59381.7 44410.0 -103791.7 79246.4 42093.8 -121340.2 616.7 20 0.050

1043 6564.00 59094.7 44399.9 -103494.5 78812.3 42090.7 -120903.0 617.1 20 0.050

1044 6566.00 58813.5 44381.5 -103195.0 78391.3 42079.4 -120470.6 617.6 20 0.050

1045 6568.00 58537.4 44358.0 -102895.4 77979.9 42062.6 -120042.6 618.1 20 0.050

1046 6570.00 58265.4 44331.1 -102596.5 77576.1 42042.4 -119618.5 618.5 20 0.050

1047 6572.00 57997.7 44300.8 -102298.5 77179.8 42018.7 -119198.5 618.9 20 0.050

1048 6574.00 57734.2 44267.4 -102001.6 76790.9 41991.6 -118782.5 619.3 20 0.050
C-43

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1049 6576.00 57474.9 44230.7 -101705.6 76409.4 41961.3 -118370.7 619.7 20 0.050

1050 6578.00 57219.9 44190.5 -101410.4 76035.6 41927.4 -117963.0 620.1 20 0.050

1051 6580.00 56969.2 44147.0 -101116.2 75669.2 41890.0 -117559.2 620.5 20 0.050

1052 6582.00 56722.6 44100.4 -100823.0 75310.3 41849.3 -117159.5 620.9 20 0.050

1053 6584.00 56480.3 44050.3 -100530.6 74958.8 41805.1 -116763.9 621.3 20 0.050

1054 6586.00 56242.2 43997.0 -100239.2 74614.9 41757.6 -116372.5 621.6 20 0.050

1055 6588.00 56008.4 43940.3 -99948.7 74278.3 41706.6 -115985.0 622.0 20 0.050

1056 6590.00 55778.8 43880.3 -99659.1 73949.4 41652.1 -115601.5 622.3 20 0.050

1057 6593.00 55440.9 43785.4 -99226.2 73467.2 41565.4 -115032.6 622.8 20 0.050

1058 6596.00 55103.8 43689.8 -98793.5 72986.6 41477.9 -114464.5 623.3 20 0.050

1059 6599.00 54766.7 43594.3 -98361.1 72506.0 41390.3 -113896.3 623.8 20 0.050

1060 6602.00 54432.5 43498.1 -97930.6 72029.7 41302.1 -113331.8 624.2 20 0.050

1061 6605.00 54104.7 43400.4 -97505.1 71563.1 41212.1 -112775.2 624.7 20 0.050

1062 6608.00 53783.2 43301.0 -97084.2 71106.3 41120.4 -112226.6 625.2 20 0.050

1063 6611.00 53468.1 43200.2 -96668.3 70659.3 41026.9 -111686.2 625.6 20 0.050

1064 6614.00 53159.4 43097.7 -96257.0 70222.2 40931.6 -111153.7 626.0 20 0.050

1065 6617.00 52857.0 42993.7 -95850.7 69794.7 40834.6 -110629.3 626.5 20 0.050

1066 6620.00 52561.0 42888.0 -95449.1 69377.1 40735.8 -110112.9 626.9 20 0.050

1067 6623.00 52271.4 42780.9 -95052.2 68969.2 40635.4 -109604.6 627.3 20 0.050

1068 6626.00 51988.1 42672.2 -94660.3 68571.1 40533.1 -109104.2 627.7 20 0.050

1069 6629.00 51711.2 42561.8 -94273.0 68182.8 40429.2 -108611.9 628.0 20 0.050

1070 6632.00 51440.6 42449.9 -93890.6 67804.2 40323.4 -108127.6 628.4 20 0.050

1071 6635.00 51176.5 42336.5 -93513.0 67435.5 40215.9 -107651.4 628.8 20 0.050

1072 6638.00 50918.6 42221.5 -93140.1 67076.5 40106.7 -107183.2 629.1 20 0.050

1073 6641.00 50667.2 42104.9 -92772.1 66727.3 39995.7 -106723.0 629.4 20 0.050

1074 6644.00 50422.1 41986.8 -92408.8 66387.9 39883.0 -106270.9 629.7 20 0.050

1075 6647.00 50183.3 41866.9 -92050.2 66058.2 39768.6 -105826.8 630.0 20 0.050

1076 6650.00 49950.7 41745.7 -91696.4 65738.0 39652.4 -105390.4 630.3 20 0.050

1077 6653.00 49719.8 41624.1 -91343.8 65420.3 39535.9 -104956.2 630.6 20 0.050

1078 6656.00 49488.9 41502.4 -90991.3 65102.6 39419.2 -104521.9 630.9 20 0.050

1079 6659.00 49259.3 41381.1 -90640.4 64786.8 39302.9 -104089.7 631.2 20 0.050

1080 6662.00 49035.5 41260.9 -90296.4 64479.3 39187.4 -103666.6 631.5 20 0.050

1081 6665.00 48817.9 41141.7 -89959.6 64180.5 39072.9 -103253.4 631.8 20 0.050

1082 6669.00 48537.4 40984.6 -89522.0 63796.0 38921.7 -102717.7 632.1 20 0.050

1083 6673.00 48267.9 40829.4 -89097.3 63427.1 38772.2 -102199.4 632.5 20 0.050

1084 6677.00 48009.3 40676.3 -88685.6 63074.0 38624.6 -101698.5 632.8 20 0.050

1085 6681.00 47761.7 40525.1 -88286.8 62736.6 38478.5 -101215.1 633.1 20 0.050

1086 6685.00 47525.1 40375.9 -87901.0 62414.9 38334.3 -100749.2 633.4 20 0.050

1087 6689.00 47299.4 40228.7 -87528.1 62108.9 38191.8 -100300.7 633.6 20 0.050
C-44

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1088 6693.00 47084.7 40083.5 -87168.2 61818.6 38051.0 -99869.5 633.9 20 0.050

1089 6698.00 46831.7 39904.7 -86736.4 61477.8 37877.4 -99355.2 634.2 20 0.050

1090 6701.00 46603.9 39774.0 -86377.9 60824.2 37755.5 -98579.7 632.3 20 0.050

1091 6702.00 46316.5 39672.0 -85988.5 59679.0 37670.2 -97349.2 627.7 20 0.050

1092 6703.00 45899.6 39538.3 -85437.9 58296.1 37560.9 -95857.0 622.2 20 0.050

1093 6704.00 45379.4 39378.4 -84757.7 56793.2 37430.3 -94223.5 616.1 20 0.050

1094 6705.00 44782.7 39196.1 -83978.9 55231.2 37280.3 -92511.5 609.7 20 0.050

1095 6706.00 44125.2 38993.7 -83119.0 53636.6 37112.2 -90748.9 603.0 20 0.050

1096 6707.00 43411.4 38772.0 -82183.4 52014.7 36926.2 -88940.9 596.1 20 0.050

1097 6708.00 42655.0 38532.6 -81187.6 50381.1 36723.5 -87104.6 589.1 20 0.050

1098 6709.00 41858.1 38276.0 -80134.1 48737.4 36504.2 -85241.6 581.9 20 0.050

1099 6710.00 41036.3 38004.5 -79040.8 47094.9 36270.1 -83365.0 574.6 20 0.050

1100 6711.00 40194.2 37718.9 -77913.1 45457.0 36021.5 -81478.5 567.2 20 0.050

1101 6712.00 39331.7 37419.3 -76750.9 43823.4 35758.7 -79582.0 559.7 20 0.050

1102 6713.00 38448.9 37105.6 -75554.5 42194.3 35481.4 -77675.7 552.1 20 0.050

1103 6714.00 37546.9 36778.1 -74325.0 40570.0 35189.9 -75759.9 544.5 20 0.050

1104 6715.00 36634.3 36438.6 -73073.0 38954.8 34885.8 -73840.6 536.8 20 0.050

1105 6716.00 35713.6 36087.7 -71801.3 37349.6 34569.4 -71919.0 529.0 20 0.050

1106 6717.00 34784.7 35725.3 -70510.1 35754.5 34240.7 -69995.3 521.1 20 0.050

1107 6718.00 33847.8 35351.7 -69199.5 34169.6 33899.7 -68069.3 513.3 20 0.050

1108 6719.00 32903.9 34967.0 -67870.9 32594.9 33546.8 -66141.8 505.3 20 0.050

1109 6720.00 31960.1 34574.3 -66534.4 31032.1 33184.8 -64216.9 497.3 20 0.050

1110 6721.00 31018.1 34174.2 -65192.3 29481.5 32814.0 -62295.5 489.3 20 0.050

1111 6722.00 30078.2 33766.8 -63845.0 27943.2 32434.7 -60378.0 481.2 20 0.050

1112 6723.00 29140.5 33352.0 -62492.5 26417.1 32046.9 -58464.0 473.2 20 0.050

1113 6724.00 28204.8 32930.2 -61135.0 24903.3 31650.4 -56553.8 465.0 20 0.050

1114 6725.00 27271.5 32501.4 -59772.9 23401.7 31245.5 -54647.2 456.9 20 0.050

1115 6726.00 26424.0 32089.6 -58513.6 22373.1 30850.9 -53224.1 450.7 20 0.050

1116 6727.00 25733.8 31711.5 -57445.3 21978.7 30479.7 -52458.4 447.2 20 0.050

1117 6728.00 25174.6 31356.3 -56530.9 21835.1 30123.8 -51958.9 444.5 20 0.050

1118 6729.00 24720.2 31019.1 -55739.3 21824.4 29780.9 -51605.4 442.4 20 0.050

1119 6730.00 24344.3 30696.3 -55040.6 21886.1 29449.2 -51335.4 440.6 20 0.050

1120 6731.00 24034.0 30387.8 -54421.8 21993.1 29129.9 -51123.0 438.9 20 0.050

1121 6732.00 23784.9 30092.9 -53877.7 22140.4 28822.5 -50962.9 437.5 20 0.050

1122 6733.00 23583.0 29809.8 -53392.8 22311.4 28526.5 -50837.9 436.2 20 0.050

1123 6734.00 23425.9 29538.2 -52964.1 22504.4 28241.1 -50745.4 435.1 20 0.050

1124 6736.00 23195.2 29021.8 -52217.0 22918.7 27697.1 -50615.9 433.0 20 0.050

1125 6738.00 23063.5 28539.3 -51602.8 23362.5 27187.6 -50550.0 431.2 20 0.050

1126 6740.00 23019.4 28088.2 -51107.5 23830.2 26710.4 -50540.5 429.7 20 0.050
C-45

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1127 6743.00 23056.6 27472.0 -50528.6 24536.0 26058.7 -50594.6 427.7 20 0.050

1128 6746.00 23188.5 26931.0 -50119.5 25228.8 25486.9 -50715.7 426.0 20 0.050

1129 6749.00 23358.9 26444.5 -49803.4 25896.0 24973.4 -50869.4 424.5 20 0.050

1130 6752.00 23566.0 26011.6 -49577.6 26537.2 24517.4 -51054.6 423.2 20 0.050

1131 6755.00 23808.7 25631.7 -49440.4 27152.4 24118.6 -51271.0 422.1 20 0.050

1132 6758.00 24067.0 25289.0 -49356.1 27744.4 23759.7 -51504.2 421.0 20 0.050

1133 6761.00 24331.4 24976.4 -49307.8 28314.2 23433.0 -51747.2 420.1 20 0.050

1134 6764.00 24602.0 24693.7 -49295.6 28861.9 23138.4 -52000.4 419.2 20 0.050

1135 6767.00 24876.7 24436.6 -49313.3 29390.1 22871.2 -52261.3 418.5 20 0.050

1136 6770.00 25146.7 24194.6 -49341.2 29901.1 22620.2 -52521.3 417.7 20 0.050

1137 6773.00 25410.3 23968.2 -49378.4 30393.4 22385.6 -52779.0 417.0 20 0.050

1138 6776.00 25667.5 23757.4 -49424.9 30867.2 22167.3 -53034.5 416.3 20 0.050

1139 6779.00 25919.3 23562.7 -49482.1 31324.0 21965.8 -53289.8 415.7 20 0.050

1140 6782.00 26167.8 23384.8 -49552.5 31766.3 21782.3 -53548.6 415.1 20 0.050

1141 6785.00 26412.8 23223.6 -49636.4 32194.3 21616.5 -53810.8 414.5 20 0.050

1142 6789.00 26734.1 23035.1 -49769.2 32742.7 21423.1 -54165.8 413.8 20 0.050

1143 6793.00 27048.9 22873.9 -49922.8 33267.0 21258.5 -54525.4 413.1 20 0.050

1144 6797.00 27347.7 22733.4 -50081.1 33759.9 21115.4 -54875.3 412.5 20 0.050

1145 6801.00 27627.6 22614.2 -50241.8 34217.7 20994.4 -55212.1 411.9 20 0.050

1146 6805.00 27888.5 22516.3 -50404.8 34640.2 20895.4 -55535.6 411.4 20 0.050

1147 6810.00 28188.1 22423.9 -50612.0 35118.8 20802.8 -55921.6 410.8 20 0.050

1148 6815.00 28458.0 22364.8 -50822.7 35542.2 20744.8 -56286.9 410.4 20 0.050

1149 6820.00 28708.7 22331.0 -51039.7 35929.0 20712.7 -56641.7 409.9 20 0.050

1150 6825.00 28966.5 22301.9 -51268.4 36325.4 20685.5 -57010.9 409.5 20 0.050

1151 6830.00 29230.5 22275.5 -51506.0 36730.5 20661.5 -57391.9 409.0 20 0.050

1152 6835.00 29494.9 22249.5 -51744.4 37136.2 20637.4 -57773.6 408.6 20 0.050

1153 6840.00 29759.4 22223.6 -51983.0 37541.8 20613.3 -58155.1 408.2 20 0.050

1154 6845.00 30024.0 22197.8 -52221.8 37947.4 20589.3 -58536.8 407.7 20 0.050

1155 6850.00 30288.4 22172.2 -52460.6 38352.6 20565.4 -58918.0 407.3 20 0.050

1156 6853.00 30491.5 22172.0 -52663.5 38800.0 20563.9 -59363.9 407.9 20 0.050

1157 6855.00 30663.5 22183.2 -52846.7 39168.1 20572.9 -59741.0 408.7 20 0.050

1158 6857.00 30850.3 22201.5 -53051.8 39541.7 20588.6 -60130.3 409.6 20 0.050

1159 6859.00 31046.7 22225.8 -53272.6 39913.8 20610.4 -60524.3 410.5 20 0.050

1160 6861.00 31247.3 22255.7 -53502.9 40280.0 20638.0 -60918.0 411.5 20 0.050

1161 6863.00 31449.9 22290.8 -53740.7 40638.6 20670.9 -61309.6 412.5 20 0.050

1162 6865.00 31653.8 22331.0 -53984.8 40989.3 20709.1 -61698.4 413.5 20 0.050

1163 6867.00 31856.4 22376.0 -54232.3 41330.8 20752.3 -62083.1 414.6 20 0.050

1164 6869.00 32057.6 22425.4 -54483.0 41663.1 20800.0 -62463.2 415.7 20 0.050

1165 6872.00 32352.7 22506.8 -54859.5 42143.4 20879.2 -63022.7 417.3 20 0.050
C-46

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1166 6875.00 32638.6 22596.3 -55234.8 42601.9 20966.8 -63568.7 419.0 20 0.050

1167 6878.00 32921.6 22692.0 -55613.5 43048.6 21060.7 -64109.3 420.8 20 0.050

1168 6881.00 33203.6 22793.1 -55996.7 43487.1 21160.2 -64647.2 422.5 20 0.050

1169 6884.00 33482.9 22898.3 -56381.2 43917.5 21263.8 -65181.3 424.3 20 0.050

1170 6887.00 33759.2 23007.4 -56766.6 44340.1 21371.3 -65711.4 426.1 20 0.050

1171 6890.00 34032.6 23120.4 -57153.0 44754.7 21482.6 -66237.3 427.9 20 0.050

1172 6893.00 34303.0 23236.1 -57539.1 45162.1 21596.7 -66758.8 429.7 20 0.050

1173 6896.00 34569.9 23353.6 -57923.5 45563.2 21712.5 -67275.7 431.5 20 0.050

1174 6899.00 34834.6 23473.5 -58308.0 45959.7 21830.6 -67790.3 433.3 20 0.050

1175 6902.00 35097.9 23596.5 -58694.4 46352.8 21951.8 -68304.6 435.1 20 0.050

1176 6905.00 35360.0 23722.8 -59082.8 46742.6 22076.1 -68818.7 437.0 20 0.050

1177 6908.00 35620.4 23852.1 -59472.5 47128.3 22203.5 -69331.8 438.8 20 0.050

1178 6911.00 35872.9 23983.7 -59856.5 47501.1 22333.0 -69834.1 440.6 20 0.050

1179 6914.00 36115.5 24116.9 -60232.5 47857.9 22464.2 -70322.1 442.5 20 0.050

1180 6917.00 36348.3 24252.0 -60600.2 48198.9 22596.9 -70795.9 444.4 20 0.050

1181 6920.00 36571.5 24387.7 -60959.2 48525.1 22730.4 -71255.5 446.3 20 0.050

1182 6923.00 36785.3 24524.0 -61309.3 48836.6 22864.5 -71701.1 448.2 20 0.050

1183 6926.00 36989.6 24661.0 -61650.5 49133.6 22999.0 -72132.6 450.2 20 0.050

1184 6929.00 37184.4 24798.4 -61982.8 49416.0 23134.0 -72550.0 452.1 20 0.050

1185 6933.00 37429.7 24982.6 -62412.3 49770.4 23314.9 -73085.3 454.8 20 0.050

1186 6937.00 37669.0 25169.5 -62838.5 50114.7 23498.4 -73613.2 457.4 20 0.050

1187 6941.00 37906.6 25359.9 -63266.5 50455.5 23685.3 -74140.9 460.1 20 0.050

1188 6945.00 38143.5 25553.0 -63696.5 50794.2 23875.0 -74669.2 462.7 20 0.050

1189 6949.00 38379.3 25747.3 -64126.7 51131.0 24065.6 -75196.6 465.4 20 0.050

1190 6953.00 38611.6 25940.8 -64552.5 51462.4 24255.2 -75717.6 468.0 20 0.050

1191 6957.00 38840.3 26133.5 -64973.8 51788.3 24443.9 -76232.2 470.7 20 0.050

1192 6961.00 39065.4 26325.2 -65390.6 52108.7 24631.6 -76740.3 473.4 20 0.050

1193 6965.00 39286.7 26516.1 -65802.8 52423.6 24818.3 -77241.9 476.1 20 0.050

1194 6969.00 39504.5 26706.0 -66210.5 52733.0 25003.9 -77737.0 478.8 20 0.050

1195 6973.00 39718.6 26895.1 -66613.7 53037.0 25188.6 -78225.6 481.4 20 0.050

1196 6977.00 39929.0 27083.2 -67012.3 53335.4 25372.3 -78707.7 484.1 20 0.050

1197 6981.00 40135.8 27270.5 -67406.3 53628.4 25555.0 -79183.3 486.8 20 0.050

1198 6985.00 40338.9 27456.9 -67795.7 53915.8 25736.7 -79652.5 489.6 20 0.050

1199 6989.00 40538.2 27642.3 -68180.5 54197.8 25917.4 -80115.2 492.3 20 0.050

1200 6993.00 40734.0 27826.8 -68560.7 54474.3 26097.0 -80571.3 495.0 20 0.050

1201 6997.00 40926.0 28010.3 -68936.3 54745.2 26275.8 -81021.0 497.7 20 0.050

1202 7001.00 41114.4 28192.9 -69307.3 55010.9 26453.5 -81464.4 500.4 20 0.050

1203 7005.00 41300.1 28374.3 -69674.4 55272.7 26629.8 -81902.5 503.2 20 0.050

1204 7009.00 41483.4 28554.4 -70037.8 55530.9 26804.8 -82335.7 505.9 20 0.050
C-47

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1205 7014.00 41708.9 28777.7 -70486.6 55848.5 27021.8 -82870.3 509.3 20 0.050

1206 7019.00 41930.4 28999.1 -70929.5 56160.4 27236.6 -83397.0 512.8 20 0.050

1207 7024.00 42148.1 29218.4 -71366.5 56466.7 27449.4 -83916.1 516.2 20 0.050

1208 7029.00 42360.1 29435.0 -71795.2 56765.1 27659.4 -84424.4 519.6 20 0.050

1209 7034.00 42557.7 29644.6 -72202.3 57043.0 27862.3 -84905.3 523.1 20 0.050

1210 7039.00 42739.1 29846.5 -72585.6 57298.5 28057.6 -85356.1 526.6 20 0.050

1211 7045.00 42935.7 30078.6 -73014.3 57575.4 28281.8 -85857.2 530.8 20 0.050

1212 7053.00 43110.4 30356.8 -73467.2 57680.2 28552.8 -86233.0 535.5 20 0.050

1213 7059.00 42983.8 30490.9 -73474.7 57209.4 28693.2 -85902.6 536.7 20 0.050

1214 7064.00 42804.1 30567.0 -73371.1 56797.4 28775.5 -85572.9 537.5 20 0.050

1215 7069.00 42596.5 30616.9 -73213.4 56396.7 28831.3 -85228.0 538.1 20 0.050

1216 7074.00 42380.8 30646.6 -73027.4 56014.1 28866.2 -84880.4 538.6 20 0.050

1217 7079.00 42164.8 30658.9 -72823.7 55651.4 28883.3 -84534.7 539.0 20 0.050

1218 7085.00 41909.3 30654.0 -72563.3 55241.8 28883.4 -84125.2 539.5 20 0.050

1219 7091.00 41662.9 30631.6 -72294.4 54859.6 28865.4 -83725.0 540.0 20 0.050

1220 7097.00 41426.8 30597.5 -72024.3 54500.6 28835.3 -83335.9 540.4 20 0.050

1221 7103.00 41201.9 30555.2 -71757.1 54162.3 28796.7 -82959.0 540.7 20 0.050

1222 7110.00 40956.1 30497.9 -71454.0 53797.1 28743.2 -82540.3 541.1 20 0.050

1223 7117.00 40731.1 30434.8 -71165.9 53467.3 28683.5 -82150.8 541.5 20 0.050

1224 7125.00 40497.3 30361.2 -70858.5 53127.5 28613.2 -81740.7 541.8 20 0.050

1225 7134.00 40262.9 30279.5 -70542.4 52788.7 28534.9 -81323.6 542.2 20 0.050

1226 7144.00 40037.5 30190.3 -70227.9 52465.7 28448.8 -80914.5 542.5 20 0.050

1227 7152.00 39839.5 30110.6 -69950.1 52074.9 28373.4 -80448.2 542.0 20 0.050

1228 7154.00 39713.2 30069.5 -69782.7 51738.6 28337.6 -80076.1 540.9 20 0.050

1229 7156.00 39554.4 30018.5 -69572.9 51374.0 28293.0 -79666.9 539.7 20 0.050

1230 7158.00 39373.1 29958.9 -69331.9 50998.2 28240.1 -79238.3 538.3 20 0.050

1231 7160.00 39176.2 29891.5 -69067.7 50618.3 28179.8 -78798.1 536.9 20 0.050

1232 7162.00 38969.9 29817.4 -68787.3 50238.8 28112.6 -78351.4 535.5 20 0.050

1233 7164.00 38754.8 29736.6 -68491.4 49860.3 28038.6 -77898.9 534.0 20 0.050

1234 7166.00 38533.9 29649.8 -68183.7 49484.0 27958.3 -77442.3 532.5 20 0.050

1235 7168.00 38308.9 29557.1 -67866.0 49110.8 27872.0 -76982.8 531.0 20 0.050

1236 7170.00 38080.7 29459.1 -67539.7 48740.9 27780.1 -76521.0 529.5 20 0.050

1237 7172.00 37852.2 29356.8 -67209.0 48375.2 27683.9 -76059.0 527.9 20 0.050

1238 7174.00 37624.6 29251.2 -66875.8 48015.0 27584.0 -75599.0 526.3 20 0.050

1239 7176.00 37398.2 29142.3 -66540.5 47660.7 27480.6 -75141.3 524.8 20 0.050

1240 7178.00 37172.9 29030.2 -66203.0 47312.2 27373.8 -74686.0 523.2 20 0.050

1241 7180.00 36948.8 28914.9 -65863.7 46969.6 27263.6 -74233.2 521.6 20 0.050

1242 7182.00 36727.2 28797.2 -65524.3 46632.8 27151.0 -73783.8 519.9 20 0.050

1243 7184.00 36508.0 28677.5 -65185.5 46302.0 27035.9 -73337.9 518.3 20 0.050
C-48

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1244 7186.00 36291.5 28555.6 -64847.2 45976.8 26918.7 -72895.5 516.7 20 0.050

1245 7188.00 36077.7 28431.7 -64509.4 45657.5 26799.1 -72456.6 515.0 20 0.050

1246 7190.00 35866.4 28305.7 -64172.1 45343.9 26677.3 -72021.3 513.4 20 0.050

1247 7192.00 35657.9 28178.1 -63836.1 45035.8 26553.8 -71589.6 511.7 20 0.050

1248 7194.00 35452.5 28049.8 -63502.3 44732.4 26429.5 -71161.9 510.0 20 0.050

1249 7196.00 35249.9 27920.8 -63170.7 44433.9 26304.2 -70738.1 508.3 20 0.050

1250 7198.00 35050.3 27791.1 -62841.4 44140.2 26178.2 -70318.4 506.7 20 0.050

1251 7200.00 34853.6 27660.7 -62514.3 43851.2 26051.3 -69902.5 505.0 20 0.050

1252 7202.00 34659.6 27529.6 -62189.2 43566.7 25923.6 -69490.3 503.3 20 0.050

1253 7205.00 34373.5 27331.8 -61705.4 43148.1 25730.6 -68878.7 500.7 20 0.050

1254 7208.00 34093.4 27132.6 -61226.0 42739.3 25535.9 -68275.2 498.1 20 0.050

1255 7211.00 33819.3 26931.9 -60751.2 42340.3 25339.5 -67679.8 495.6 20 0.050

1256 7214.00 33551.2 26729.7 -60280.9 41951.1 25141.3 -67092.3 493.0 20 0.050

1257 7217.00 33288.9 26526.3 -59815.2 41571.4 24941.4 -66512.9 490.4 20 0.050

1258 7220.00 33032.1 26322.8 -59354.9 41200.0 24741.4 -65941.4 487.8 20 0.050

1259 7223.00 32780.7 26119.3 -58900.0 40836.5 24541.2 -65377.7 485.1 20 0.050

1260 7226.00 32534.6 25916.0 -58450.6 40481.0 24340.9 -64821.9 482.5 20 0.050

1261 7229.00 32293.9 25712.8 -58006.7 40133.4 24140.5 -64273.9 479.9 20 0.050

1262 7232.00 32058.4 25509.9 -57568.3 39793.7 23939.9 -63733.7 477.2 20 0.050

1263 7235.00 31828.4 25306.9 -57135.3 39461.9 23739.4 -63201.3 474.5 20 0.050

1264 7238.00 31603.6 25104.2 -56707.8 39138.1 23538.7 -62676.8 471.9 20 0.050

1265 7241.00 31384.2 24901.6 -56285.7 38822.2 23338.0 -62160.1 469.2 20 0.050

1266 7244.00 31169.6 24699.4 -55869.0 38513.2 23137.4 -61650.7 466.5 20 0.050

1267 7247.00 30958.8 24498.6 -55457.5 38209.8 22938.1 -61147.9 463.8 20 0.050

1268 7250.00 30752.2 24298.9 -55051.1 37911.8 22739.7 -60651.5 461.1 20 0.050

1269 7253.00 30549.4 24100.3 -54649.8 37619.5 22542.3 -60161.8 458.4 20 0.050

1270 7256.00 30350.7 23902.9 -54253.6 37332.6 22346.0 -59678.5 455.7 20 0.050

1271 7259.00 30155.7 23706.8 -53862.5 37051.1 22150.4 -59201.5 453.0 20 0.050

1272 7262.00 29964.0 23511.7 -53475.7 36774.2 21955.9 -58730.1 450.3 20 0.050

1273 7265.00 29775.8 23317.5 -53093.3 36501.9 21762.3 -58264.2 447.6 20 0.050

1274 7268.00 29590.8 23124.5 -52715.3 36234.1 21569.7 -57803.8 444.8 20 0.050

1275 7271.00 29409.1 22932.6 -52341.7 35971.0 21377.9 -57348.8 442.1 20 0.050

1276 7274.00 29230.7 22741.7 -51972.4 35712.3 21187.0 -56899.3 439.4 20 0.050

1277 7277.00 29055.7 22551.9 -51607.6 35458.3 20997.1 -56455.3 436.6 20 0.050

1278 7280.00 28883.9 22363.1 -51246.9 35208.8 20807.9 -56016.8 433.9 20 0.050

1279 7284.00 28659.9 22113.1 -50773.0 34883.4 20557.2 -55440.5 430.2 20 0.050

1280 7288.00 28441.8 21864.9 -50306.7 34566.0 20308.1 -54874.1 426.6 20 0.050

1281 7292.00 28229.6 21618.6 -49848.1 34256.8 20060.6 -54317.3 422.9 20 0.050

1282 7296.00 28023.2 21374.0 -49397.2 33955.6 19814.7 -53770.4 419.2 20 0.050
C-49

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1283 7300.00 27822.8 21131.5 -48954.3 33662.9 19570.6 -53233.5 415.5 20 0.050

1284 7304.00 27627.6 20891.5 -48519.1 33377.1 19328.8 -52705.9 411.8 20 0.050

1285 7308.00 27436.9 20653.9 -48090.9 33097.7 19089.1 -52186.8 408.1 20 0.050

1286 7312.00 27250.9 20419.1 -47670.0 32824.4 18852.0 -51676.3 404.4 20 0.050

1287 7316.00 27070.2 20187.5 -47257.7 32558.1 18618.1 -51176.2 400.6 20 0.050

1288 7320.00 26895.0 19959.6 -46854.5 32299.4 18387.4 -50686.8 396.9 20 0.050

1289 7324.00 26725.3 19735.0 -46460.3 32048.0 18160.4 -50208.3 393.2 20 0.050

1290 7328.00 26561.0 19514.1 -46075.1 31804.0 17936.6 -49740.6 389.4 20 0.050

1291 7332.00 26402.2 19296.8 -45699.0 31567.4 17716.5 -49283.9 385.7 20 0.050

1292 7336.00 26248.8 19083.0 -45331.8 31338.3 17499.7 -48838.0 381.9 20 0.050

1293 7341.00 26064.6 18820.6 -44885.2 31062.2 17233.6 -48295.8 377.2 20 0.050

1294 7346.00 25889.0 18563.7 -44452.7 30797.8 16972.9 -47770.7 372.5 20 0.050

1295 7351.00 25729.8 18314.4 -44044.2 30590.9 16719.5 -47310.5 368.0 20 0.050

1296 7356.00 25787.7 18120.5 -43908.2 31037.2 16516.1 -47553.2 366.2 20 0.050

1297 7360.00 25944.0 17998.7 -43942.8 31479.1 16387.6 -47866.8 365.3 20 0.050

1298 7364.00 26139.4 17899.0 -44038.3 31921.0 16283.4 -48204.4 364.5 20 0.050

1299 7368.00 26355.0 17817.9 -44172.9 32351.0 16199.9 -48550.8 363.9 20 0.050

1300 7372.00 26578.0 17752.3 -44330.4 32764.3 16133.4 -48897.7 363.3 20 0.050

1301 7376.00 26799.5 17699.1 -44498.6 33158.7 16080.4 -49239.1 362.8 20 0.050

1302 7380.00 27019.0 17658.2 -44677.2 33534.1 16040.9 -49575.0 362.3 20 0.050

1303 7385.00 27287.8 17623.3 -44911.1 33980.2 16008.5 -49988.7 361.8 20 0.050

1304 7390.00 27548.6 17604.7 -45153.3 34401.9 15993.5 -50395.4 361.3 20 0.050

1305 7395.00 27800.7 17598.6 -45399.3 34801.9 15991.5 -50793.4 360.8 20 0.050

1306 7400.00 28043.1 17600.8 -45643.8 35183.6 15998.0 -51181.6 360.4 20 0.050

1307 7405.00 28276.0 17611.1 -45887.0 35546.9 16012.9 -51559.8 360.0 20 0.050

1308 7410.00 28499.2 17629.7 -46128.9 35891.9 16036.2 -51928.2 359.6 20 0.050

1309 7416.00 28754.5 17662.9 -46417.4 36281.7 16075.2 -52356.9 359.2 20 0.050

1310 7422.00 28997.4 17704.5 -46701.9 36649.0 16122.8 -52771.8 358.8 20 0.050

1311 7428.00 29229.0 17751.8 -46980.7 36997.4 16176.0 -53173.4 358.5 20 0.050

1312 7434.00 29449.3 17804.7 -47254.0 37326.8 16234.6 -53561.4 358.2 20 0.050

1313 7441.00 29692.1 17873.6 -47565.7 37687.1 16310.1 -53997.1 357.8 20 0.050

1314 7448.00 29922.9 17947.5 -47870.4 38027.5 16390.3 -54417.8 357.5 20 0.050

1315 7454.00 30143.1 18019.2 -48162.2 38416.7 16466.4 -54883.1 357.7 20 0.050

1316 7458.00 30329.6 18079.1 -48408.6 38753.7 16528.0 -55281.7 358.2 20 0.050

1317 7462.00 30528.0 18145.9 -48673.9 39090.4 16596.5 -55686.9 358.8 20 0.050

1318 7466.00 30731.1 18218.5 -48949.6 39420.6 16671.4 -56092.0 359.4 20 0.050

1319 7470.00 30935.0 18296.2 -49231.2 39742.9 16751.5 -56494.4 360.0 20 0.050

1320 7474.00 31136.8 18378.1 -49514.9 40056.3 16835.7 -56892.1 360.7 20 0.050

1321 7479.00 31384.3 18485.9 -49870.3 40435.0 16946.7 -57381.8 361.5 20 0.050
C-50

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1322 7484.00 31625.3 18598.7 -50224.0 40798.4 17062.6 -57861.0 362.4 20 0.050

1323 7489.00 31858.3 18715.3 -50573.6 41146.2 17182.4 -58328.5 363.3 20 0.050

1324 7494.00 32083.0 18835.3 -50918.3 41478.8 17305.2 -58784.0 364.2 20 0.050

1325 7499.00 32299.3 18956.9 -51256.2 41797.2 17429.8 -59227.0 365.1 20 0.050

1326 7504.00 32507.5 19079.6 -51587.2 42102.7 17555.1 -59657.8 366.1 20 0.050

1327 7509.00 32709.4 19203.1 -51912.5 42397.4 17681.1 -60078.4 367.0 20 0.050

1328 7514.00 32904.8 19327.6 -52232.4 42681.4 17807.8 -60489.2 368.0 20 0.050

1329 7520.00 33131.1 19477.6 -52608.7 43008.8 17960.3 -60969.1 369.2 20 0.050

1330 7526.00 33349.5 19628.7 -52978.2 43323.7 18113.6 -61437.3 370.4 20 0.050

1331 7532.00 33560.5 19781.0 -53341.4 43626.7 18268.0 -61894.7 371.6 20 0.050

1332 7538.00 33764.0 19934.5 -53698.5 43917.9 18423.3 -62341.2 372.8 20 0.050

1333 7544.00 33960.1 20089.2 -54049.3 44197.5 18579.4 -62776.9 374.0 20 0.050

1334 7550.00 34149.9 20244.2 -54394.0 44467.1 18735.8 -63202.9 375.3 20 0.050

1335 7557.00 34363.6 20425.1 -54788.7 44769.7 18918.2 -63687.9 376.7 20 0.050

1336 7564.00 34570.6 20606.3 -55176.9 45062.2 19100.3 -64162.5 378.2 20 0.050

1337 7571.00 34770.6 20784.2 -55554.8 45344.1 19279.0 -64623.1 379.7 20 0.050

1338 7578.00 34961.5 20956.5 -55918.0 45613.1 19451.8 -65064.9 381.2 20 0.050

1339 7586.00 35168.1 21146.1 -56314.2 45904.3 19641.6 -65545.8 382.9 20 0.050

1340 7594.00 35365.1 21330.7 -56695.8 46181.2 19826.2 -66007.4 384.7 20 0.050

1341 7602.00 35554.4 21513.0 -57067.5 46446.9 20008.2 -66455.1 386.4 20 0.050

1342 7610.00 35735.8 21691.6 -57427.4 46701.0 20186.4 -66887.5 388.2 20 0.050

1343 7619.00 35930.5 21888.0 -57818.5 46973.7 20381.9 -67355.6 390.2 20 0.050

1344 7628.00 36115.5 22079.3 -58194.8 47232.3 20572.1 -67804.4 392.2 20 0.050

1345 7638.00 36309.6 22286.0 -58595.6 47503.1 20777.5 -68280.6 394.4 20 0.050

1346 7648.00 36491.5 22486.6 -58978.1 47756.6 20976.4 -68733.0 396.7 20 0.050

1347 7689.00 36366.2 22934.3 -59300.5 47251.0 21436.0 -68687.0 398.7 20 0.050

1348 7738.00 36108.9 23096.6 -59205.5 46820.0 21602.6 -68422.7 399.2 20 0.050

1349 7753.00 35949.2 23097.3 -59046.5 46272.3 21609.9 -67882.1 397.3 20 0.050

1350 7755.00 35776.3 23058.5 -58834.7 45777.5 21579.1 -67356.5 395.2 20 0.050

1351 7757.00 35561.6 23006.8 -58568.4 45257.2 21536.2 -66793.4 393.0 20 0.050

1352 7759.00 35317.3 22943.6 -58260.9 44726.8 21482.1 -66208.9 390.7 20 0.050

1353 7761.00 35055.1 22870.7 -57925.8 44196.2 21417.9 -65614.0 388.2 20 0.050

1354 7763.00 34780.0 22788.8 -57568.8 43668.7 21344.4 -65013.0 385.7 20 0.050

1355 7765.00 34493.7 22698.2 -57191.9 43145.2 21261.6 -64406.9 383.2 20 0.050

1356 7767.00 34201.7 22599.9 -56801.6 42628.5 21170.8 -63799.3 380.6 20 0.050

1357 7769.00 33904.7 22494.2 -56398.9 42118.8 21071.9 -63190.6 378.0 20 0.050

1358 7771.00 33606.6 22382.3 -55989.0 41616.6 20966.6 -62583.2 375.3 20 0.050

1359 7773.00 33309.4 22265.0 -55574.5 41122.6 20855.1 -61977.7 372.7 20 0.050

1360 7775.00 33013.1 22142.4 -55155.4 40636.6 20737.9 -61374.5 370.0 20 0.050
C-51

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1361 7777.00 32717.7 22014.2 -54731.9 40158.7 20614.7 -60773.4 367.3 20 0.050

1362 7779.00 32423.3 21880.4 -54303.7 39688.8 20485.5 -60174.3 364.5 20 0.050

1363 7781.00 32130.4 21741.9 -53872.3 39226.8 20351.0 -59577.8 361.8 20 0.050

1364 7783.00 31840.8 21599.6 -53440.4 38772.6 20212.4 -58984.9 359.0 20 0.050

1365 7785.00 31554.4 21453.3 -53007.7 38326.1 20069.4 -58395.6 356.2 20 0.050

1366 7787.00 31271.1 21303.7 -52574.8 37887.4 19922.5 -57809.9 353.4 20 0.050

1367 7789.00 30991.1 21150.1 -52141.2 37456.4 19771.5 -57227.9 350.6 20 0.050

1368 7791.00 30714.3 20993.1 -51707.4 37033.0 19616.5 -56649.5 347.8 20 0.050

1369 7793.00 30441.2 20834.3 -51275.5 36616.0 19459.3 -56075.3 345.0 20 0.050

1370 7795.00 30171.7 20674.1 -50845.8 36205.1 19300.4 -55505.5 342.1 20 0.050

1371 7797.00 29906.3 20512.7 -50419.0 35800.6 19140.1 -54940.7 339.3 20 0.050

1372 7799.00 29644.7 20350.2 -49995.0 35402.8 18978.2 -54381.0 336.4 20 0.050

1373 7801.00 29387.3 20186.6 -49573.9 35011.3 18815.0 -53826.2 333.6 20 0.050

1374 7803.00 29133.7 20022.0 -49155.7 34626.3 18650.3 -53276.6 330.7 20 0.050

1375 7805.00 28884.1 19856.2 -48740.4 34247.6 18484.4 -52732.0 327.8 20 0.050

1376 7807.00 28638.4 19689.3 -48327.7 33875.2 18316.9 -52192.1 324.9 20 0.050

1377 7809.00 28396.6 19521.3 -47917.9 33509.2 18147.9 -51657.1 322.0 20 0.050

1378 7811.00 28158.7 19352.2 -47510.9 33149.4 17977.6 -51126.9 319.1 20 0.050

1379 7813.00 27924.6 19182.0 -47106.6 32795.9 17805.7 -50601.7 316.2 20 0.050

1380 7815.00 27694.5 19010.7 -46705.2 32448.8 17632.5 -50081.3 313.3 20 0.050

1381 7817.00 27468.1 18838.7 -46306.7 32107.7 17458.0 -49565.7 310.3 20 0.050

1382 7819.00 27245.3 18666.4 -45911.6 31771.6 17283.1 -49054.8 307.4 20 0.050

1383 7821.00 27025.8 18494.3 -45520.0 31440.5 17108.1 -48548.6 304.4 20 0.050

1384 7823.00 26809.8 18322.2 -45132.0 31114.2 16932.9 -48047.2 301.5 20 0.050

1385 7825.00 26597.3 18150.1 -44747.4 30793.0 16757.3 -47550.3 298.5 20 0.050

1386 7827.00 26388.1 17978.2 -44366.3 30476.7 16581.5 -47058.2 295.6 20 0.050

1387 7829.00 26182.5 17806.2 -43988.7 30165.4 16405.5 -46570.8 292.6 20 0.050

1388 7831.00 25980.4 17634.3 -43614.6 29858.9 16229.3 -46088.2 289.6 20 0.050

1389 7833.00 25781.5 17462.5 -43244.0 29557.4 16052.7 -45610.1 286.7 20 0.050

1390 7835.00 25586.2 17290.6 -42876.8 29260.9 15875.9 -45136.8 283.7 20 0.050

1391 7837.00 25394.4 17118.9 -42513.3 28969.4 15698.8 -44668.2 280.7 20 0.050

1392 7839.00 25206.0 16947.2 -42153.2 28682.8 15521.5 -44204.3 277.7 20 0.050

1393 7841.00 25021.0 16775.5 -41796.6 28401.1 15344.0 -43745.1 274.7 20 0.050

1394 7843.00 24839.2 16604.2 -41443.5 28123.7 15166.5 -43290.2 271.7 20 0.050

1395 7845.00 24659.8 16433.9 -41093.6 27849.5 14989.6 -42839.0 268.7 20 0.050

1396 7847.00 24482.9 16264.1 -40747.0 27578.5 14813.2 -42391.7 265.7 20 0.050

1397 7849.00 24308.4 16095.4 -40403.8 27310.7 14637.3 -41948.0 262.7 20 0.050

1398 7851.00 24136.4 15927.5 -40063.9 27046.0 14462.2 -41508.1 259.6 20 0.050

1399 7853.00 23966.9 15760.4 -39727.2 26784.6 14287.4 -41072.0 256.6 20 0.050
C-52

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1400 7855.00 23799.7 15594.2 -39393.9 26526.3 14113.3 -40639.6 253.6 20 0.050

1401 7857.00 23635.1 15428.7 -39063.8 26271.2 13939.8 -40210.9 250.6 20 0.050

1402 7860.00 23392.6 15182.3 -38574.9 25894.3 13680.4 -39574.7 246.0 20 0.050

1403 7863.00 23155.5 14937.6 -38093.1 25524.3 13422.2 -38946.6 241.5 20 0.050

1404 7866.00 22923.7 14694.8 -37618.5 25161.2 13165.4 -38326.6 236.9 20 0.050

1405 7869.00 22697.3 14453.8 -37151.2 24804.9 12909.7 -37714.6 232.3 20 0.050

1406 7872.00 22476.2 14214.9 -36691.0 24455.3 12655.3 -37110.6 227.8 20 0.050

1407 7875.00 22260.5 13977.6 -36238.1 24112.7 12402.1 -36514.8 223.2 20 0.050

1408 7878.00 22050.0 13742.4 -35792.4 23777.0 12150.1 -35927.0 218.6 20 0.050

1409 7881.00 21845.0 13508.9 -35353.9 23448.0 11899.3 -35347.3 214.0 20 0.050

1410 7884.00 21645.2 13277.4 -34922.6 23125.9 11649.8 -34775.7 209.4 20 0.050

1411 7887.00 21450.8 13047.9 -34498.6 22810.6 11401.5 -34212.2 204.8 20 0.050

1412 7890.00 21261.7 12820.1 -34081.8 22502.3 11154.3 -33656.7 200.2 20 0.050

1413 7893.00 21077.9 12594.1 -33672.1 22200.7 10908.6 -33109.3 195.6 20 0.050

1414 7896.00 20899.5 12370.1 -33269.6 21906.0 10663.9 -32569.9 190.9 20 0.050

1415 7899.00 20726.4 12148.0 -32874.4 21618.2 10420.5 -32038.7 186.3 20 0.050

1416 7902.00 20558.1 11927.8 -32485.9 21336.3 10178.6 -31514.9 181.6 20 0.050

1417 7905.00 20393.7 11710.2 -32103.9 21059.1 9938.4 -30997.5 177.0 20 0.050

1418 7908.00 20233.3 11494.9 -31728.3 20786.4 9699.9 -30486.4 172.3 20 0.050

1419 7911.00 20077.0 11281.9 -31358.9 20518.5 9463.0 -29981.5 167.7 20 0.050

1420 7914.00 19924.5 11071.3 -30995.8 20255.2 9227.9 -29483.1 163.0 20 0.050

1421 7917.00 19776.0 10862.9 -30638.9 19996.4 8994.4 -28990.8 158.4 20 0.050

1422 7920.00 19631.4 10656.9 -30288.2 19742.2 8762.5 -28504.8 153.7 20 0.050

1423 7923.00 19490.7 10453.1 -29943.8 19492.6 8532.4 -28025.0 149.0 20 0.050

1424 7926.00 19353.9 10251.8 -29605.7 19247.7 8303.8 -27551.5 144.4 20 0.050

1425 7929.00 19221.1 10052.8 -29273.8 19007.4 8077.0 -27084.4 139.7 20 0.050

1426 7932.00 19092.1 9856.0 -28948.1 18771.6 7851.8 -26623.4 135.0 20 0.050

1427 7935.00 18967.2 9661.5 -28628.7 18540.5 7628.3 -26168.9 130.3 20 0.050

1428 7938.00 18846.1 9469.7 -28315.8 18314.2 7406.7 -25720.9 125.6 20 0.050

1429 7942.00 18691.0 9217.5 -27908.5 18019.8 7114.1 -25133.9 119.3 20 0.050

1430 7946.00 18542.9 8969.6 -27512.5 17733.9 6824.8 -24558.7 113.1 20 0.050

1431 7950.00 18401.8 8726.2 -27128.0 17456.4 6538.9 -23995.3 106.8 20 0.050

1432 7955.00 18482.6 8467.2 -26949.8 18078.2 6243.2 -24321.4 103.0 20 0.050

1433 7958.00 18671.8 8338.2 -27010.0 18653.6 6107.5 -24761.1 101.7 20 0.050

1434 7960.00 18826.6 8261.3 -27087.9 19047.7 6031.7 -25079.4 101.0 20 0.050

1435 7962.00 18993.3 8191.4 -27184.8 19440.8 5966.0 -25406.8 100.3 20 0.050

1436 7964.00 19171.1 8128.7 -27299.9 19832.0 5910.6 -25742.6 99.7 20 0.050

1437 7966.00 19355.9 8072.7 -27428.6 20219.1 5864.4 -26083.5 99.1 20 0.050

1438 7968.00 19545.2 8023.5 -27568.7 20600.6 5827.1 -26427.7 98.6 20 0.050
C-53

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1439 7970.00 19738.0 7980.7 -27718.7 20976.3 5798.1 -26774.5 98.1 20 0.050

1440 7972.00 19930.5 7943.4 -27873.9 21345.3 5775.5 -27120.8 97.6 20 0.050

1441 7974.00 20122.6 7911.7 -28034.3 21707.4 5759.5 -27466.9 97.1 20 0.050

1442 7977.00 20409.8 7874.5 -28284.2 22237.7 5747.3 -27985.0 96.4 20 0.050

1443 7980.00 20695.8 7849.7 -28545.4 22752.1 5749.2 -28501.4 95.8 20 0.050

1444 7983.00 20978.0 7835.1 -28813.1 23251.2 5762.2 -29013.4 95.2 20 0.050

1445 7986.00 21255.0 7830.0 -29085.0 23734.9 5785.0 -29520.0 94.7 20 0.050

1446 7989.00 21527.0 7834.2 -29361.2 24203.3 5817.4 -30020.7 94.2 20 0.050

1447 7992.00 21793.7 7847.0 -29640.7 24656.9 5858.3 -30515.2 93.7 20 0.050

1448 7995.00 22055.1 7865.1 -29920.1 25098.5 5903.9 -31002.4 93.2 20 0.050

1449 7998.00 22310.8 7888.2 -30199.1 25528.3 5953.8 -31482.1 92.7 20 0.050

1450 8001.00 22561.1 7916.3 -30477.4 25946.4 6008.0 -31954.4 92.3 20 0.050

1451 8004.00 22805.8 7949.5 -30755.3 26352.8 6066.7 -32419.6 91.8 20 0.050

1452 8007.00 23045.2 7988.1 -31033.2 26748.0 6130.2 -32878.1 91.4 20 0.050

1453 8010.00 23279.3 8031.9 -31311.2 27131.8 6198.4 -33330.3 91.0 20 0.050

1454 8013.00 23508.1 8081.1 -31589.1 27504.4 6271.6 -33776.0 90.7 20 0.050

1455 8016.00 23731.4 8135.5 -31866.9 27865.6 6349.5 -34215.1 90.3 20 0.050

1456 8019.00 23950.0 8193.7 -32143.7 28217.3 6430.4 -34647.7 89.9 20 0.050

1457 8022.00 24164.2 8254.8 -32419.1 28560.7 6513.4 -35074.1 89.6 20 0.050

1458 8025.00 24374.2 8318.5 -32692.8 28895.9 6598.3 -35494.2 89.3 20 0.050

1459 8028.00 24579.9 8384.8 -32964.7 29222.7 6685.5 -35908.2 89.0 20 0.050

1460 8031.00 24781.1 8454.0 -33235.1 29541.2 6774.6 -36315.8 88.6 20 0.050

1461 8034.00 24978.0 8525.7 -33503.7 29851.4 6865.7 -36717.1 88.3 20 0.050

1462 8038.00 25233.6 8625.3 -33858.9 30252.2 6990.3 -37242.5 88.0 20 0.050

1463 8042.00 25481.3 8729.5 -34210.9 30638.3 7118.4 -37756.8 87.6 20 0.050

1464 8046.00 25723.7 8836.1 -34559.8 31014.4 7248.1 -38262.5 87.2 20 0.050

1465 8050.00 25961.9 8944.3 -34906.2 31382.7 7378.1 -38760.8 86.9 20 0.050

1466 8053.00 26175.7 9034.5 -35210.2 31818.5 7484.2 -39302.7 87.4 20 0.050

1467 8055.00 26347.3 9101.8 -35449.1 32166.1 7561.6 -39727.7 87.9 20 0.050

1468 8057.00 26531.8 9173.0 -35704.8 32520.8 7643.3 -40164.1 88.5 20 0.050

1469 8059.00 26725.1 9248.2 -35973.3 32877.0 7729.2 -40606.2 89.2 20 0.050

1470 8061.00 26923.5 9326.7 -36250.2 33231.7 7818.5 -41050.2 89.9 20 0.050

1471 8063.00 27125.1 9408.6 -36533.7 33583.4 7911.2 -41494.6 90.6 20 0.050

1472 8065.00 27329.5 9493.8 -36823.3 33931.8 8007.3 -41939.1 91.3 20 0.050

1473 8067.00 27535.0 9581.8 -37116.8 34276.0 8106.2 -42382.3 92.1 20 0.050

1474 8069.00 27741.3 9672.8 -37414.1 34616.0 8208.1 -42824.1 92.9 20 0.050

1475 8071.00 27946.9 9766.4 -37713.3 34951.5 8312.3 -43263.7 93.6 20 0.050

1476 8073.00 28151.4 9862.2 -38013.5 35282.1 8418.6 -43700.8 94.4 20 0.050

1477 8075.00 28354.6 9960.3 -38314.9 35608.1 8527.0 -44135.1 95.2 20 0.050
C-54

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1478 8077.00 28556.6 10060.6 -38617.2 35929.3 8637.5 -44566.8 96.0 20 0.050

1479 8079.00 28757.2 10163.1 -38920.3 36245.4 8749.9 -44995.3 96.8 20 0.050

1480 8081.00 28956.0 10267.7 -39223.6 36556.5 8864.1 -45420.5 97.7 20 0.050

1481 8083.00 29152.6 10373.7 -39526.2 36862.4 8979.4 -45841.9 98.5 20 0.050

1482 8085.00 29346.8 10481.4 -39828.2 37163.3 9096.2 -46259.5 99.3 20 0.050

1483 8087.00 29538.9 10590.4 -40129.2 37459.1 9214.1 -46673.2 100.2 20 0.050

1484 8089.00 29728.5 10701.2 -40429.7 37749.9 9333.3 -47083.2 101.0 20 0.050

1485 8092.00 30008.7 10869.8 -40878.4 38176.6 9514.2 -47690.9 102.3 20 0.050

1486 8095.00 30283.3 11040.3 -41323.6 38593.2 9696.3 -48289.5 103.6 20 0.050

1487 8098.00 30552.4 11212.4 -41764.8 38999.7 9879.3 -48879.0 105.0 20 0.050

1488 8101.00 30816.0 11386.2 -42202.1 39396.2 10063.3 -49459.6 106.3 20 0.050

1489 8104.00 31075.2 11561.1 -42636.3 39784.7 10247.8 -50032.5 107.6 20 0.050

1490 8107.00 31330.2 11737.0 -43067.3 40165.2 10432.9 -50598.1 109.0 20 0.050

1491 8110.00 31580.9 11914.2 -43495.1 40538.0 10618.5 -51156.5 110.3 20 0.050

1492 8113.00 31827.4 12092.3 -43919.7 40902.6 10804.9 -51707.5 111.7 20 0.050

1493 8116.00 32069.4 12271.7 -44341.1 41259.5 10991.7 -52251.2 113.1 20 0.050

1494 8119.00 32307.3 12451.5 -44758.8 41609.1 11178.6 -52787.6 114.5 20 0.050

1495 8122.00 32541.1 12631.4 -45172.5 41951.8 11365.0 -53316.8 115.9 20 0.050

1496 8125.00 32770.8 12811.4 -45582.2 42287.7 11551.0 -53838.7 117.3 20 0.050

1497 8128.00 32996.6 12991.3 -45987.9 42616.6 11736.8 -54353.4 118.7 20 0.050

1498 8131.00 33218.1 13171.4 -46389.5 42938.8 11922.0 -54860.8 120.1 20 0.050

1499 8134.00 33435.5 13351.5 -46787.0 43254.0 12107.0 -55361.0 121.5 20 0.050

1500 8137.00 33648.7 13531.5 -47180.2 43562.4 12291.4 -55853.8 122.9 20 0.050

1501 8140.00 33857.8 13711.6 -47569.4 43864.1 12475.5 -56339.6 124.4 20 0.050

1502 8143.00 34062.9 13891.4 -47954.3 44159.0 12659.2 -56818.3 125.8 20 0.050

1503 8146.00 34264.4 14070.8 -48335.2 44448.4 12842.1 -57290.4 127.3 20 0.050

1504 8149.00 34462.6 14249.6 -48712.2 44732.4 13023.9 -57756.3 128.7 20 0.050

1505 8152.00 34657.4 14427.7 -49085.1 45011.0 13204.9 -58215.9 130.2 20 0.050

1506 8155.00 34848.6 14605.3 -49453.9 45284.1 13385.0 -58669.1 131.7 20 0.050

1507 8158.00 35036.6 14782.2 -49818.8 45552.0 13564.0 -59116.1 133.1 20 0.050

1508 8161.00 35222.2 14958.6 -50180.8 45816.1 13742.4 -59558.5 134.6 20 0.050

1509 8164.00 35405.6 15134.6 -50540.2 46076.8 13920.1 -59996.8 136.1 20 0.050

1510 8167.00 35587.1 15310.0 -50897.1 46334.1 14097.1 -60431.2 137.6 20 0.050

1511 8170.00 35766.5 15485.0 -51251.5 46588.2 14273.3 -60861.5 139.1 20 0.050

1512 8174.00 36002.3 15717.5 -51719.9 46921.8 14507.2 -61429.0 141.0 20 0.050

1513 8178.00 36234.4 15949.3 -52183.7 47249.4 14739.9 -61989.4 143.0 20 0.050

1514 8182.00 36462.8 16180.0 -52642.8 47571.1 14971.4 -62542.5 145.0 20 0.050

1515 8186.00 36687.4 16409.7 -53097.1 47886.9 15201.4 -63088.3 147.0 20 0.050

1516 8190.00 36907.9 16638.2 -53546.1 48196.4 15429.8 -63626.2 149.1 20 0.050
C-55

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1517 8196.00 37147.9 16791.1 -53938.9 48540.5 15584.7 -64125.2 152.2 20 0.050

1518 8200.00 37361.6 17024.4 -54386.0 48839.0 15817.4 -64656.4 154.2 20 0.050

1519 8204.00 37570.9 17255.5 -54826.3 49130.8 16047.5 -65178.2 156.2 20 0.050

1520 8208.00 37775.9 17483.8 -55259.7 49416.4 16274.7 -65691.0 158.2 20 0.050

1521 8212.00 37976.9 17709.7 -55686.6 49695.9 16499.2 -66195.1 160.3 20 0.050

1522 8216.00 38173.9 17933.7 -56107.6 49969.8 16721.5 -66691.3 162.3 20 0.050

1523 8220.00 38367.2 18155.8 -56522.9 50237.9 16941.7 -67179.6 164.4 20 0.050

1524 8224.00 38556.5 18375.7 -56932.2 50500.4 17159.5 -67659.9 166.4 20 0.050

1525 8228.00 38741.9 18593.6 -57335.5 50757.1 17375.1 -68132.2 168.5 20 0.050

1526 8232.00 38923.3 18809.4 -57732.7 51008.1 17588.4 -68596.5 170.6 20 0.050

1527 8236.00 39100.8 19023.0 -58123.9 51253.3 17799.5 -69052.7 172.6 20 0.050

1528 8240.00 39274.4 19234.6 -58509.0 51492.8 18008.2 -69500.9 174.7 20 0.050

1529 8245.00 39485.7 19496.0 -58981.6 51784.0 18265.9 -70049.9 177.3 20 0.050

1530 8250.00 39690.8 19754.1 -59444.9 52066.3 18520.1 -70586.3 179.9 20 0.050

1531 8255.00 39889.6 20008.8 -59898.4 52339.6 18770.6 -71110.2 182.5 20 0.050

1532 8260.00 40082.4 20260.2 -60342.5 52604.2 19017.7 -71621.9 185.1 20 0.050

1533 8265.00 40270.2 20508.3 -60778.5 52861.7 19261.4 -72123.1 187.8 20 0.050

1534 8270.00 40453.0 20753.4 -61206.4 53112.2 19501.8 -72614.0 190.4 20 0.050

1535 8275.00 40630.9 20995.1 -61626.1 53355.8 19738.8 -73094.6 193.0 20 0.050

1536 8280.00 40804.4 21234.0 -62038.4 53593.1 19972.7 -73565.8 195.7 20 0.050

1537 8285.00 40974.8 21470.5 -62445.3 53826.1 20204.2 -74030.3 198.3 20 0.050

1538 8290.00 41142.2 21704.6 -62846.9 54054.8 20433.2 -74488.1 201.0 20 0.050

1539 8295.00 41306.7 21936.5 -63243.2 54279.4 20659.9 -74939.3 203.7 20 0.050

1540 8301.00 41500.0 22211.7 -63711.7 54543.4 20928.6 -75472.0 206.9 20 0.050

1541 8307.00 41689.0 22483.5 -64172.5 54801.3 21193.9 -75995.2 210.1 20 0.050

1542 8313.00 41873.5 22751.8 -64625.3 55053.0 21455.5 -76508.5 213.3 20 0.050

1543 8319.00 42053.6 23016.6 -65070.3 55298.5 21713.6 -77012.1 216.5 20 0.050

1544 8325.00 42229.3 23278.0 -65507.3 55537.9 21968.2 -77506.1 219.7 20 0.050

1545 8331.00 42400.5 23536.0 -65936.5 55771.1 22219.2 -77990.2 222.9 20 0.050

1546 8337.00 42567.1 23790.4 -66357.5 55998.1 22466.5 -78464.6 226.1 20 0.050

1547 8343.00 42729.3 24041.2 -66770.5 56218.9 22710.3 -78929.2 229.4 20 0.050

1548 8349.00 42886.9 24288.6 -67175.5 56433.6 22950.4 -79383.9 232.6 20 0.050

1549 8356.00 43065.2 24572.7 -67637.9 56676.1 23226.2 -79902.3 236.4 20 0.050

1550 8363.00 43237.3 24852.1 -68089.3 56910.3 23497.1 -80407.4 240.2 20 0.050

1551 8370.00 43403.2 25126.5 -68529.8 57136.1 23763.1 -80899.2 243.9 20 0.050

1552 8377.00 43563.0 25396.3 -68959.2 57353.5 24024.2 -81377.7 247.7 20 0.050

1553 8384.00 43717.3 25661.5 -69378.8 57563.6 24280.8 -81844.4 251.6 20 0.050

1554 8391.00 43866.9 25922.6 -69789.5 57767.2 24533.2 -82300.4 255.4 20 0.050

1555 8399.00 44031.9 26215.6 -70247.5 57992.0 24816.3 -82808.3 259.7 20 0.050
C-56

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1556 8407.00 44193.0 26504.2 -70697.2 58211.5 25095.1 -83306.5 264.1 20 0.050

1557 8415.00 44349.5 26787.9 -71137.3 58424.8 25368.8 -83793.6 268.5 20 0.050

1558 8419.00 44498.4 27087.9 -71586.3 58620.7 25659.7 -84280.4 270.6 20 0.050

1559 8428.00 44659.6 27383.5 -72043.0 58841.5 25944.4 -84785.9 275.5 20 0.050

1560 8437.00 44815.4 27673.6 -72489.0 59055.2 26223.8 -85279.1 280.5 20 0.050

1561 8446.00 44965.9 27958.3 -72924.2 59261.8 26497.8 -85759.6 285.4 20 0.050

1562 8461.00 44857.1 28321.6 -73178.7 58713.7 26860.7 -85574.4 289.8 20 0.050

1563 8467.00 44651.9 28399.4 -73051.2 58301.1 26943.3 -85244.4 290.4 20 0.050

1564 8473.00 44429.2 28451.4 -72880.6 57906.2 26999.7 -84906.0 290.9 20 0.050

1565 8479.00 44205.6 28483.4 -72689.0 57533.2 27035.6 -84568.9 291.4 20 0.050

1566 8486.00 43948.5 28499.4 -72448.0 57125.5 27055.4 -84180.9 291.9 20 0.050

1567 8493.00 43701.2 28497.2 -72198.4 56746.0 27056.5 -83802.5 292.3 20 0.050

1568 8500.00 43465.3 28484.2 -71949.5 56389.9 27046.4 -83436.3 292.7 20 0.050

1569 8508.00 43211.3 28459.0 -71670.3 56011.1 27024.0 -83035.1 293.1 20 0.050

1570 8516.00 42973.9 28422.7 -71396.5 55662.7 26990.1 -82652.7 293.4 20 0.050

1571 8525.00 42724.9 28372.8 -71097.8 55301.6 26942.5 -82244.1 293.8 20 0.050

1572 8534.00 42493.9 28317.2 -70811.1 54969.3 26888.7 -81858.0 294.1 20 0.050

1573 8544.00 42257.8 28248.8 -70506.6 54632.9 26822.0 -81454.9 294.5 20 0.050

1574 8555.00 42016.1 28170.9 -70187.0 54290.3 26745.7 -81036.0 294.8 20 0.050

1575 8566.00 41790.5 28092.5 -69882.9 53971.9 26668.6 -80640.4 295.1 20 0.050

1576 8578.00 41562.8 28006.2 -69569.0 53651.9 26583.4 -80235.3 295.4 20 0.050

1577 8591.00 41337.8 27912.0 -69249.8 53337.6 26490.1 -79827.7 295.7 20 0.050

1578 8605.00 41119.7 27809.9 -68929.6 53035.3 26388.6 -79424.0 295.9 20 0.050

1579 8621.00 40894.2 27698.1 -68592.3 52724.0 26277.3 -79001.3 296.2 20 0.050

1580 8638.00 40679.8 27585.5 -68265.3 52429.3 26164.9 -78594.2 296.5 20 0.050

1581 8658.00 40460.9 27461.0 -67921.9 52130.3 26040.4 -78170.7 296.7 20 0.050

1582 8680.00 40247.7 27333.2 -67580.9 51840.6 25912.3 -77752.9 296.9 20 0.050

1583 8704.00 40035.1 27202.8 -67237.9 51552.3 25781.5 -77333.9 297.2 20 0.050

1584 8731.00 39824.2 27070.7 -66894.9 51267.3 25648.8 -76916.1 297.4 20 0.050

1585 8761.00 39618.8 26924.6 -66543.4 50991.7 25502.3 -76494.0 297.6 20 0.050

1586 8803.00 39407.8 26794.4 -66202.3 50709.6 25370.4 -76080.0 297.8 20 0.050

1587 8854.00 39197.5 26660.4 -65857.9 50429.9 25234.4 -75664.3 298.1 20 0.050

1588 8926.00 38986.2 26522.5 -65508.7 50151.5 25094.2 -75245.6 298.3 20 0.050

1589 9012.00 38780.3 26372.3 -65152.6 49882.2 24942.2 -74824.4 298.5 20 0.050

1590 9114.00 38585.3 26191.0 -64776.3 49629.6 24760.5 -74390.1 298.6 20 0.050

1591 9223.00 38406.7 25975.1 -64381.8 49400.1 24546.2 -73946.3 298.8 20 0.050

1592 9377.00 38233.1 25747.8 -63980.9 49178.1 24321.2 -73499.3 299.0 20 0.050

1593 9668.00 38063.5 25510.6 -63574.1 48962.3 24087.0 -73049.2 299.1 20 0.050

1594 9796.00 37922.9 25219.4 -63142.2 48782.4 23801.4 -72583.8 299.3 20 0.050
C-57

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1595 9969.00 37784.9 24923.6 -62708.5 48605.8 23511.4 -72117.1 299.4 20 0.050

1596 9971.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1597 9973.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1598 9974.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1599 9976.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1600 9979.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1601 9983.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1602 9986.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1603 9989.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1604 9993.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1605 9996.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1606 9999.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1607 10003.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1608 10006.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1609 10009.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1610 10013.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1611 10016.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1612 10018.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1613 10021.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1614 10023.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1615 10024.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1616 10026.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1617 10029.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1618 10033.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1619 10036.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1620 10039.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1621 10043.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1622 10046.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1623 10049.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1624 10053.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1625 10056.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1626 10059.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1627 10063.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1628 10066.33 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1629 10068.67 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1630 10071.00 48988.8 27018.6 -76007.5 60187.0 25621.8 -85808.9 70.0 100 0.550

1631 10119.00 49078.2 27061.5 -76139.7 60322.2 25661.0 -85983.2 71.1 100 0.549

1632 10159.00 49140.3 27107.2 -76247.5 60404.9 25703.4 -86108.3 72.1 100 0.547

1633 10199.00 49186.1 27152.1 -76338.2 60463.9 25745.2 -86209.1 73.1 100 0.546
C-58

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1634 10239.00 49219.0 27192.5 -76411.5 60506.2 25782.8 -86288.9 74.2 100 0.545

1635 10279.00 49242.0 27227.4 -76469.5 60536.2 25814.9 -86351.0 75.3 100 0.544

1636 10319.00 49257.4 27256.9 -76514.3 60556.9 25841.8 -86398.8 76.3 100 0.543

1637 10359.00 49266.9 27281.2 -76548.1 60570.6 25863.9 -86434.4 77.4 100 0.541

1638 10399.00 49271.5 27301.0 -76572.5 60578.6 25881.6 -86460.2 78.5 100 0.540

1639 10439.00 49272.2 27316.8 -76589.0 60582.2 25895.3 -86477.5 79.6 100 0.539

1640 10479.00 49269.8 27328.9 -76598.7 60582.0 25905.7 -86487.7 80.7 100 0.538

1641 10519.00 49264.6 27337.8 -76602.5 60578.9 25912.9 -86491.8 81.8 100 0.537

1642 10559.00 49257.3 27344.1 -76601.3 60573.3 25917.4 -86490.7 82.9 100 0.535

1643 10599.00 49248.0 27347.7 -76595.7 60565.5 25919.6 -86485.1 84.0 100 0.534

1644 10639.00 49237.2 27349.2 -76586.3 60555.9 25919.7 -86475.5 85.1 100 0.533

1645 10679.00 49224.9 27348.6 -76573.5 60544.6 25917.9 -86462.5 86.2 100 0.532

1646 10719.00 49211.4 27346.4 -76557.8 60532.1 25914.3 -86446.4 87.3 100 0.531

1647 10759.00 49196.9 27342.4 -76539.3 60518.4 25909.2 -86427.6 88.4 100 0.529

1648 10799.00 49181.4 27337.1 -76518.5 60503.7 25902.7 -86406.4 89.5 100 0.528

1649 10839.00 49165.2 27330.4 -76495.6 60488.1 25895.0 -86383.1 90.6 100 0.527

1650 10879.00 49148.2 27322.6 -76470.8 60471.6 25886.2 -86357.8 91.7 100 0.526

1651 10919.00 49130.7 27313.6 -76444.3 60454.5 25876.3 -86330.8 92.8 100 0.525

1652 10959.00 49112.5 27303.8 -76416.3 60436.7 25865.6 -86302.3 93.9 100 0.523

1653 10999.00 49093.9 27293.0 -76386.8 60418.4 25853.9 -86272.4 95.0 100 0.522

1654 11039.00 49074.8 27281.3 -76356.1 60399.6 25841.5 -86241.2 96.1 100 0.521

1655 11079.00 49055.3 27269.0 -76324.3 60380.4 25828.4 -86208.8 97.2 100 0.520

1656 11119.00 49035.5 27256.0 -76291.5 60360.8 25814.6 -86175.4 98.3 100 0.519

1657 11159.00 49015.3 27242.4 -76257.7 60340.8 25800.3 -86141.1 99.4 100 0.517

1658 11199.00 48994.7 27228.2 -76222.9 60319.6 25785.5 -86105.1 100.5 100 0.516

1659 11235.00 48975.3 27215.2 -76190.5 60299.5 25771.9 -86071.4 101.5 100 0.515

1660 11271.00 48955.1 27201.9 -76157.0 60279.2 25758.0 -86037.2 102.5 100 0.514

1661 11319.00 48927.7 27183.6 -76111.2 60252.2 25738.9 -85991.1 103.9 100 0.513

1662 11359.00 48904.9 27167.3 -76072.2 60229.5 25722.2 -85951.6 105.0 100 0.511

1663 11399.00 48882.1 27150.3 -76032.5 60206.7 25704.7 -85911.3 106.1 100 0.510

1664 11439.00 48859.3 27132.8 -75992.1 60183.7 25686.7 -85870.4 107.2 100 0.509

1665 11479.00 48836.3 27114.8 -75951.1 60160.6 25668.2 -85828.8 108.3 100 0.508

1666 11519.00 48813.3 27096.4 -75909.7 60137.5 25649.3 -85786.8 109.4 100 0.507

1667 11559.00 48790.2 27077.6 -75867.8 60114.3 25630.0 -85744.3 110.5 100 0.505

1668 11599.00 48767.0 27058.5 -75825.5 60091.0 25610.4 -85701.3 111.6 100 0.504

1669 11639.00 48743.8 27039.1 -75782.9 60067.5 25590.6 -85658.1 112.7 100 0.503

1670 11679.00 48720.4 27019.6 -75740.0 60044.0 25570.7 -85614.7 113.8 100 0.502

1671 11719.00 48696.9 27000.3 -75697.1 60020.3 25550.9 -85571.2 114.9 100 0.501

1672 11759.00 48673.1 26980.9 -75654.0 59996.3 25531.1 -85527.5 116.1 100 0.499
C-59

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1673 11799.00 48649.3 26961.3 -75610.6 59972.3 25511.1 -85483.4 117.2 100 0.498

1674 11839.00 48625.4 26941.5 -75567.0 59948.2 25490.9 -85439.1 118.3 100 0.497

1675 11879.00 48601.4 26921.7 -75523.1 59924.0 25470.6 -85394.6 119.4 100 0.496

1676 11919.00 48577.3 26901.6 -75479.0 59899.7 25450.1 -85349.9 120.5 100 0.495

1677 11959.00 48553.2 26881.5 -75434.7 59875.3 25429.6 -85304.9 121.6 100 0.493

1678 11999.00 48529.0 26861.2 -75390.1 59850.9 25408.9 -85259.8 122.7 100 0.492

1679 12039.00 48504.6 26840.8 -75345.5 59826.3 25388.2 -85214.5 123.8 100 0.491

1680 12079.00 48480.3 26820.3 -75300.6 59801.7 25367.2 -85169.0 124.9 100 0.490

1681 12119.00 48455.9 26799.8 -75255.6 59777.1 25346.3 -85123.4 126.0 100 0.489

1682 12159.00 48431.4 26779.0 -75210.4 59752.3 25325.2 -85077.6 127.2 100 0.487

1683 12199.00 48406.8 26758.3 -75165.1 59727.5 25304.1 -85031.6 128.3 100 0.486

1684 12239.00 48382.2 26737.5 -75119.7 59702.7 25282.8 -84985.5 129.4 100 0.485

1685 12279.00 48357.6 26716.5 -75074.1 59677.8 25261.6 -84939.3 130.5 100 0.484

1686 12319.00 48332.9 26695.5 -75028.4 59652.8 25240.2 -84893.0 131.6 100 0.483

1687 12359.00 48308.2 26674.5 -74982.7 59627.8 25218.8 -84846.6 132.7 100 0.481

1688 12399.00 48283.3 26653.4 -74936.8 59602.7 25197.4 -84800.1 133.8 100 0.480

1689 12435.00 48261.0 26634.4 -74895.4 59580.1 25178.0 -84758.1 134.8 100 0.479

1690 12471.00 48238.6 26615.3 -74854.0 59557.5 25158.6 -84716.1 135.8 100 0.478

1691 12519.00 48208.7 26589.8 -74798.5 59527.3 25132.6 -84659.9 137.2 100 0.477

1692 12559.00 48183.8 26568.5 -74752.3 59502.0 25111.0 -84613.0 138.3 100 0.475

1693 12599.00 48158.8 26547.1 -74705.9 59476.8 25089.3 -84566.1 139.4 100 0.474

1694 12639.00 48133.7 26525.7 -74659.5 59451.5 25067.5 -84518.9 140.5 100 0.473

1695 12679.00 48108.7 26504.3 -74613.0 59426.1 25045.8 -84471.8 141.6 100 0.472

1696 12719.00 48083.6 26482.9 -74566.4 59400.7 25023.9 -84424.6 142.7 100 0.471

1697 12759.00 48058.4 26461.4 -74519.8 59375.3 25002.1 -84377.3 143.8 100 0.469

1698 12799.00 48033.2 26439.8 -74473.1 59349.8 24980.1 -84329.9 144.9 100 0.468

1699 12839.00 48008.0 26418.3 -74426.3 59324.3 24958.2 -84282.5 146.0 100 0.467

1700 12879.00 47982.8 26396.7 -74379.4 59298.8 24936.3 -84235.0 147.1 100 0.466

1701 12919.00 47957.5 26375.0 -74332.5 59273.2 24914.3 -84187.5 148.3 100 0.465

1702 12959.00 47932.2 26353.4 -74285.6 59247.6 24892.3 -84139.9 149.4 100 0.463

1703 12999.00 47906.9 26331.6 -74238.5 59222.0 24870.1 -84092.1 150.5 100 0.462

1704 13039.00 47881.8 26309.5 -74191.3 59196.5 24847.7 -84044.2 151.6 100 0.461

1705 13079.00 47856.8 26287.1 -74144.0 59171.3 24824.9 -83996.2 152.7 100 0.460

1706 13119.00 47832.3 26264.8 -74097.1 59146.4 24802.2 -83948.6 153.8 100 0.459

1707 13159.00 47808.1 26243.2 -74051.3 59121.9 24780.3 -83902.2 154.9 100 0.457

1708 13199.00 47783.9 26222.1 -74006.0 59097.5 24758.8 -83856.3 156.0 100 0.456

1709 13239.00 47759.7 26200.9 -73960.6 59073.0 24737.3 -83810.3 157.1 100 0.455

1710 13279.00 47735.5 26179.7 -73915.2 59048.5 24715.8 -83764.3 158.3 100 0.454

1711 13319.00 47711.3 26158.5 -73869.8 59024.1 24694.2 -83718.3 159.4 100 0.453
C-60

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1712 13359.00 47687.1 26137.2 -73824.4 58999.6 24672.7 -83672.3 160.5 100 0.451

1713 13399.00 47662.9 26116.0 -73778.9 58975.1 24651.1 -83626.2 161.6 100 0.450

1714 13439.00 47638.7 26094.8 -73733.5 58950.7 24629.5 -83580.2 162.7 100 0.449

1715 13479.00 47614.6 26073.5 -73688.1 58926.3 24607.9 -83534.1 163.8 100 0.448

1716 13519.00 47590.4 26052.2 -73642.6 58901.8 24586.3 -83488.1 164.9 100 0.447

1717 13559.00 47566.3 26030.9 -73597.2 58877.4 24564.7 -83442.1 166.0 100 0.445

1718 13599.00 47542.1 26009.6 -73551.8 58853.0 24543.1 -83396.1 167.1 100 0.444

1719 13635.00 47520.4 25990.5 -73510.9 58831.0 24523.6 -83354.7 168.1 100 0.443

1720 13671.00 47498.7 25971.4 -73470.0 58809.1 24504.2 -83313.3 169.1 100 0.442

1721 13707.00 47477.0 25952.2 -73429.2 58787.1 24484.8 -83271.9 170.1 100 0.441

1722 13737.00 47458.9 25936.3 -73395.2 58768.9 24468.5 -83237.4 171.0 100 0.440

1723 13767.00 47440.8 25920.3 -73361.2 58750.6 24452.4 -83203.0 171.8 100 0.439

1724 13797.00 47422.8 25904.4 -73327.2 58732.3 24436.1 -83168.5 172.6 100 0.438

1725 13827.00 47404.7 25888.5 -73293.2 58714.1 24420.0 -83134.0 173.5 100 0.437

1726 13857.00 47386.6 25872.5 -73259.2 58695.8 24403.8 -83099.6 174.3 100 0.436

1727 13887.00 47368.6 25856.6 -73225.2 58677.5 24387.7 -83065.2 175.1 100 0.436

1728 13917.00 47350.5 25840.7 -73191.2 58659.3 24371.5 -83030.8 176.0 100 0.435

1729 13947.00 47332.5 25824.8 -73157.3 58641.1 24355.3 -82996.3 176.8 100 0.434

1730 13977.00 47314.5 25808.8 -73123.3 58622.8 24339.2 -82962.0 177.6 100 0.433

1731 14007.00 47296.4 25792.9 -73089.3 58604.6 24322.9 -82927.5 178.5 100 0.432

1732 14037.00 47278.4 25777.0 -73055.4 58586.3 24306.8 -82893.1 179.3 100 0.431

1733 14067.00 47260.4 25761.1 -73021.5 58568.1 24290.6 -82858.7 180.1 100 0.430

1734 14097.00 47242.3 25745.2 -72987.5 58549.8 24274.6 -82824.4 181.0 100 0.429

1735 14127.00 47224.3 25729.3 -72953.6 58531.6 24258.4 -82790.0 181.8 100 0.428

1736 14157.00 47206.3 25713.4 -72919.7 58513.4 24242.2 -82755.6 182.6 100 0.427

1737 14187.00 47188.3 25697.5 -72885.8 58495.2 24226.0 -82721.3 183.5 100 0.427

1738 14217.00 47170.3 25681.6 -72851.9 58477.0 24209.9 -82686.9 184.3 100 0.426

1739 14247.00 47152.3 25665.7 -72818.0 58458.8 24193.7 -82652.6 185.1 100 0.425

1740 14277.00 47134.3 25649.8 -72784.1 58440.6 24177.6 -82618.2 186.0 100 0.424

1741 14307.00 47116.3 25633.9 -72750.2 58422.5 24161.5 -82583.9 186.8 100 0.423

1742 14337.00 47098.3 25618.0 -72716.3 58404.2 24145.3 -82549.6 187.6 100 0.422

1743 14367.00 47080.3 25602.2 -72682.5 58386.1 24129.2 -82515.3 188.5 100 0.421

1744 14397.00 47062.4 25586.2 -72648.6 58367.9 24113.1 -82481.0 189.3 100 0.420

1745 14427.00 47044.3 25570.4 -72614.7 58349.7 24097.0 -82446.7 190.1 100 0.419

1746 14457.00 47026.3 25554.5 -72580.9 58331.6 24080.8 -82412.3 191.0 100 0.418

1747 14487.00 47008.4 25538.6 -72547.0 58313.4 24064.7 -82378.1 191.8 100 0.418

1748 14517.00 46990.5 25522.7 -72513.2 58295.2 24048.6 -82343.8 192.6 100 0.417

1749 14544.00 46974.3 25508.5 -72482.8 58278.9 24034.0 -82313.0 193.4 100 0.416

1750 14571.00 46958.1 25494.2 -72452.3 58262.5 24019.6 -82282.1 194.1 100 0.415
C-61

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1751 14607.00 46936.5 25475.2 -72411.7 58240.8 24000.3 -82241.0 195.1 100 0.414

1752 14637.00 46918.6 25459.3 -72377.9 58222.7 23984.0 -82206.7 196.0 100 0.413

1753 14667.00 46900.7 25443.3 -72344.1 58204.5 23968.0 -82172.5 196.8 100 0.412

1754 14697.00 46882.8 25427.5 -72310.3 58186.4 23951.9 -82138.2 197.6 100 0.411

1755 14727.00 46864.9 25411.7 -72276.5 58168.3 23935.8 -82104.0 198.5 100 0.410

1756 14757.00 46846.9 25395.9 -72242.8 58150.1 23919.7 -82069.8 199.3 100 0.409

1757 14787.00 46828.9 25380.0 -72209.0 58132.0 23903.6 -82035.6 200.1 100 0.409

1758 14817.00 46810.8 25364.6 -72175.4 58113.6 23888.0 -82001.6 201.0 100 0.408

1759 14847.00 46792.6 25349.2 -72141.8 58095.2 23872.4 -81967.6 201.8 100 0.407

1760 14877.00 46774.1 25334.2 -72108.3 58076.5 23857.1 -81933.6 202.6 100 0.406

1761 14907.00 46755.1 25319.2 -72074.3 58057.4 23841.9 -81899.3 203.5 100 0.405

1762 14937.00 46735.8 25303.5 -72039.3 58037.8 23826.0 -81863.8 204.3 100 0.404

1763 14967.00 46716.3 25287.0 -72003.3 58018.1 23809.2 -81827.3 205.1 100 0.403

1764 14997.00 46696.7 25270.5 -71967.2 57998.4 23792.3 -81790.7 206.0 100 0.402

1765 15027.00 46677.3 25253.9 -71931.1 57978.7 23775.4 -81754.1 206.8 100 0.401

1766 15057.00 46657.8 25237.2 -71895.0 57958.9 23758.6 -81717.5 207.6 100 0.400

1767 15087.00 46638.2 25220.6 -71858.9 57939.2 23741.6 -81680.8 208.4 100 0.400

1768 15117.00 46618.7 25204.0 -71822.7 57919.4 23724.7 -81644.2 209.3 100 0.399

1769 15147.00 46599.2 25187.3 -71786.5 57899.6 23707.9 -81607.5 210.1 100 0.398

1770 15177.00 46579.5 25170.8 -71750.3 57879.8 23691.0 -81570.8 210.9 100 0.397

1771 15207.00 46560.0 25154.1 -71714.1 57860.0 23674.1 -81534.1 211.8 100 0.396

1772 15237.00 46540.4 25137.5 -71677.9 57840.2 23657.1 -81497.3 212.6 100 0.395

1773 15267.00 46520.9 25120.8 -71641.6 57820.4 23640.2 -81460.6 213.4 100 0.394

1774 15297.00 46501.2 25104.2 -71605.5 57800.5 23623.3 -81423.8 214.3 100 0.393

1775 15327.00 46481.5 25087.7 -71569.2 57780.6 23606.5 -81387.1 215.1 100 0.392

1776 15357.00 46461.9 25070.9 -71532.8 57760.8 23589.4 -81350.2 215.9 100 0.391

1777 15387.00 46442.2 25054.3 -71496.5 57740.8 23572.6 -81313.4 216.8 100 0.391

1778 15417.00 46422.5 25037.6 -71460.1 57720.9 23555.5 -81276.4 217.6 100 0.390

1779 15444.00 46404.8 25022.6 -71427.4 57702.9 23540.3 -81243.2 218.4 100 0.389

1780 15471.00 46387.0 25007.7 -71394.7 57685.0 23525.1 -81210.1 219.1 100 0.388

1781 15507.00 46363.3 24987.6 -71350.9 57661.0 23504.8 -81165.8 220.1 100 0.387

1782 15537.00 46343.6 24970.9 -71314.4 57641.0 23487.8 -81128.8 220.9 100 0.386

1783 15567.00 46323.8 24954.2 -71278.0 57621.0 23470.7 -81091.7 221.8 100 0.385

1784 15597.00 46304.0 24937.5 -71241.5 57601.0 23453.7 -81054.7 222.6 100 0.384

1785 15627.00 46284.2 24920.7 -71204.9 57581.0 23436.7 -81017.6 223.4 100 0.383

1786 15657.00 46264.4 24903.9 -71168.3 57560.9 23419.7 -80980.6 224.3 100 0.382

1787 15687.00 46244.5 24887.2 -71131.7 57540.8 23402.7 -80943.5 225.1 100 0.382

1788 15717.00 46224.7 24870.4 -71095.1 57520.7 23385.7 -80906.3 225.9 100 0.381

1789 15747.00 46204.9 24853.6 -71058.5 57500.6 23368.6 -80869.1 226.8 100 0.380
C-62

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1790 15777.00 46184.9 24836.9 -71021.8 57480.4 23351.5 -80832.0 227.6 100 0.379

1791 15807.00 46165.0 24820.1 -70985.1 57460.3 23334.4 -80794.8 228.4 100 0.378

1792 15837.00 46145.2 24803.2 -70948.4 57440.1 23317.4 -80757.5 229.3 100 0.377

1793 15867.00 46125.2 24786.4 -70911.7 57419.9 23300.4 -80720.3 230.1 100 0.376

1794 15897.00 46105.2 24769.7 -70874.9 57399.7 23283.2 -80683.0 230.9 100 0.375

1795 15927.00 46085.3 24752.8 -70838.0 57379.5 23266.1 -80645.6 231.8 100 0.374

1796 15957.00 46065.3 24735.9 -70801.3 57359.3 23249.0 -80608.3 232.6 100 0.373

1797 15987.00 46045.3 24719.2 -70764.5 57339.1 23231.8 -80571.0 233.4 100 0.373

1798 16017.00 46025.3 24702.3 -70727.6 57318.8 23214.7 -80533.5 234.3 100 0.372

1799 16047.00 46005.2 24685.5 -70690.7 57298.6 23197.5 -80496.1 235.1 100 0.371

1800 16077.00 45985.2 24668.6 -70653.8 57278.3 23180.3 -80458.6 235.9 100 0.370

1801 16107.00 45965.2 24651.6 -70616.8 57258.0 23163.2 -80421.2 236.8 100 0.369

1802 16137.00 45945.1 24634.8 -70579.9 57237.7 23145.9 -80383.7 237.6 100 0.368

1803 16167.00 45925.0 24617.9 -70542.9 57217.4 23128.8 -80346.3 238.4 100 0.367

1804 16197.00 45905.0 24601.0 -70505.9 57197.0 23111.7 -80308.7 239.3 100 0.366

1805 16227.00 45884.8 24584.0 -70468.9 57176.7 23094.3 -80271.1 240.1 100 0.365

1806 16257.00 45864.7 24567.1 -70431.9 57156.3 23077.2 -80233.5 240.9 100 0.364

1807 16287.00 45844.6 24550.2 -70394.8 57135.9 23060.0 -80195.9 241.8 100 0.364

1808 16317.00 45824.3 24533.3 -70357.7 57115.5 23042.8 -80158.3 242.6 100 0.363

1809 16344.00 45806.2 24518.0 -70324.2 57097.1 23027.2 -80124.4 243.4 100 0.362

1810 16371.00 45788.0 24502.8 -70290.8 57078.7 23011.8 -80090.5 244.1 100 0.361

1811 16407.00 45763.8 24482.4 -70246.2 57054.2 22991.1 -80045.3 245.1 100 0.360

1812 16437.00 45743.6 24465.4 -70209.0 57033.7 22973.8 -80007.5 245.9 100 0.359

1813 16467.00 45723.4 24448.4 -70171.8 57013.2 22956.5 -79969.7 246.8 100 0.358

1814 16497.00 45703.1 24431.4 -70134.5 56992.7 22939.3 -79932.0 247.6 100 0.357

1815 16527.00 45682.8 24414.5 -70097.3 56972.2 22922.0 -79894.2 248.4 100 0.356

1816 16557.00 45662.6 24397.4 -70060.0 56951.7 22904.7 -79856.3 249.3 100 0.355

1817 16587.00 45642.3 24380.3 -70022.6 56931.1 22887.3 -79818.5 250.1 100 0.355

1818 16617.00 45622.2 24362.8 -69985.0 56910.9 22869.5 -79780.3 250.9 100 0.354

1819 16647.00 45602.4 24345.0 -69947.4 56890.6 22851.4 -79742.0 251.8 100 0.353

1820 16677.00 45582.9 24326.9 -69909.7 56870.9 22832.9 -79703.8 252.6 100 0.352

1821 16707.00 45563.8 24308.8 -69872.6 56851.6 22814.5 -79666.1 253.4 100 0.351

1822 16737.00 45545.4 24291.5 -69836.9 56832.9 22797.0 -79629.9 254.3 100 0.350

1823 16767.00 45527.1 24275.4 -69802.5 56814.4 22780.6 -79594.9 255.1 100 0.349

1824 16797.00 45508.8 24259.5 -69768.3 56795.9 22764.3 -79560.2 255.9 100 0.348

1825 16827.00 45490.5 24243.4 -69733.9 56777.4 22748.0 -79525.4 256.8 100 0.347

1826 16857.00 45472.2 24227.5 -69699.6 56758.8 22731.8 -79490.6 257.6 100 0.346

1827 16887.00 45453.8 24211.5 -69665.4 56740.3 22715.7 -79455.9 258.4 100 0.346

1828 16917.00 45435.5 24195.5 -69631.0 56721.8 22699.3 -79421.1 259.3 100 0.345
C-63

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1829 16947.00 45417.2 24179.5 -69596.7 56703.3 22683.1 -79386.4 260.1 100 0.344

1830 16977.00 45399.0 24163.4 -69562.4 56684.8 22666.8 -79351.6 260.9 100 0.343

1831 17007.00 45380.7 24147.4 -69528.1 56666.3 22650.5 -79316.8 261.8 100 0.342

1832 17037.00 45362.4 24131.4 -69493.8 56647.8 22634.2 -79282.0 262.6 100 0.341

1833 17067.00 45344.0 24115.4 -69459.4 56629.3 22617.9 -79247.3 263.4 100 0.340

1834 17097.00 45325.8 24099.3 -69425.2 56610.8 22601.6 -79212.5 264.3 100 0.339

1835 17127.00 45307.5 24083.4 -69390.9 56592.3 22585.4 -79177.7 265.1 100 0.338

1836 17157.00 45289.3 24067.2 -69356.5 56573.8 22569.1 -79142.9 265.9 100 0.337

1837 17187.00 45271.0 24051.3 -69322.2 56555.3 22552.9 -79108.2 266.8 100 0.337

1838 17217.00 45252.8 24035.2 -69288.0 56536.8 22536.5 -79073.4 267.6 100 0.336

1839 17244.00 45236.2 24020.8 -69257.0 56520.3 22521.9 -79042.2 268.3 100 0.335

1840 17271.00 45219.8 24006.3 -69226.2 56503.6 22507.3 -79010.9 269.1 100 0.334

1841 17283.96 45200.3 24006.5 -69206.8 56484.0 22507.2 -78991.3 269.5 100 0.334

1842 17296.92 45180.7 24006.6 -69187.3 56464.4 22507.3 -78971.6 269.8 100 0.333

1843 17316.58 45151.0 24006.9 -69157.9 56434.5 22507.4 -78941.9 270.4 100 0.333

1844 17336.25 45121.3 24007.1 -69128.5 56404.7 22507.4 -78912.1 270.9 100 0.332

1845 17355.93 45091.6 24007.4 -69099.0 56374.9 22507.5 -78882.4 271.4 100 0.331

1846 17375.61 45062.0 24007.6 -69069.6 56345.0 22507.6 -78852.6 272.0 100 0.331

1847 17395.30 45032.3 24007.9 -69040.1 56315.2 22507.7 -78822.9 272.5 100 0.330

1848 17414.99 45002.5 24008.2 -69010.7 56285.3 22507.9 -78793.2 273.1 100 0.330

1849 17434.69 44972.8 24008.4 -68981.2 56255.5 22507.9 -78763.3 273.6 100 0.329

1850 17454.39 44943.1 24008.7 -68951.8 56225.6 22508.0 -78733.6 274.2 100 0.328

1851 17474.09 44913.3 24009.0 -68922.3 56195.7 22508.1 -78703.8 274.7 100 0.328

1852 17493.80 44883.6 24009.2 -68892.8 56165.9 22508.2 -78674.0 275.3 100 0.327

1853 17513.52 44853.8 24009.5 -68863.3 56135.9 22508.2 -78644.2 275.8 100 0.327

1854 17533.24 44824.0 24009.7 -68833.8 56106.1 22508.3 -78614.4 276.4 100 0.326

1855 17552.96 44794.3 24010.0 -68804.3 56076.1 22508.5 -78584.7 276.9 100 0.326

1856 17572.70 44764.5 24010.2 -68774.8 56046.3 22508.5 -78554.8 277.5 100 0.325

1857 17583.85 44747.7 24010.3 -68758.1 56029.3 22508.6 -78537.9 277.8 100 0.325

1858 17595.00 44730.9 24010.6 -68741.5 56012.5 22508.7 -78521.1 278.1 100 0.324

1859 17607.96 44711.3 24010.7 -68722.0 55992.8 22508.7 -78501.5 278.4 100 0.324

1860 17620.92 44691.8 24010.9 -68702.7 55973.1 22508.8 -78481.9 278.8 100 0.324

1861 17640.67 44662.1 24011.1 -68673.1 55943.3 22508.9 -78452.2 279.4 100 0.323

1862 17660.42 44632.3 24011.4 -68643.6 55913.4 22508.9 -78422.3 279.9 100 0.322

1863 17680.18 44602.5 24011.6 -68614.1 55883.4 22509.1 -78392.5 280.5 100 0.322

1864 17699.94 44572.6 24011.9 -68584.6 55853.5 22509.1 -78362.6 281.0 100 0.321

1865 17719.71 44542.8 24012.2 -68555.0 55823.5 22509.3 -78332.8 281.5 100 0.321

1866 17739.48 44513.0 24012.4 -68525.4 55793.6 22509.3 -78302.9 282.1 100 0.320

1867 17759.26 44483.2 24012.7 -68495.9 55763.6 22509.5 -78273.1 282.6 100 0.319
C-64

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1868 17779.04 44453.4 24013.0 -68466.4 55733.7 22509.6 -78243.2 283.2 100 0.319

1869 17798.82 44423.5 24013.3 -68436.8 55703.7 22509.6 -78213.3 283.7 100 0.318

1870 17818.62 44393.7 24013.5 -68407.2 55673.7 22509.7 -78183.5 284.3 100 0.318

1871 17838.41 44363.8 24013.8 -68377.6 55643.7 22509.8 -78153.5 284.8 100 0.317

1872 17858.21 44334.0 24014.1 -68348.1 55613.8 22509.9 -78123.7 285.4 100 0.316

1873 17878.02 44304.1 24014.4 -68318.5 55583.7 22510.1 -78093.8 285.9 100 0.316

1874 17897.83 44274.3 24014.6 -68288.9 55553.7 22510.2 -78063.8 286.5 100 0.315

1875 17908.42 44258.3 24014.7 -68273.1 55537.8 22510.2 -78048.0 286.8 100 0.315

1876 17919.00 44242.3 24015.0 -68257.3 55521.7 22510.3 -78032.0 287.1 100 0.315

1877 17931.96 44222.8 24015.1 -68237.9 55502.1 22510.3 -78012.4 287.4 100 0.314

1878 17944.92 44203.3 24015.3 -68218.5 55482.4 22510.5 -77992.9 287.8 100 0.314

1879 17964.75 44173.4 24015.6 -68189.0 55452.4 22510.5 -77963.0 288.4 100 0.313

1880 17984.58 44143.5 24015.9 -68159.4 55422.4 22510.7 -77933.0 288.9 100 0.313

1881 18004.42 44113.6 24016.1 -68129.7 55392.4 22510.8 -77903.1 289.5 100 0.312

1882 18024.26 44083.7 24016.4 -68100.1 55362.3 22510.9 -77873.2 290.0 100 0.311

1883 18044.11 44053.8 24016.7 -68070.5 55332.3 22510.9 -77843.2 290.6 100 0.311

1884 18063.96 44023.9 24016.9 -68040.8 55302.2 22511.1 -77813.4 291.1 100 0.310

1885 18083.82 43994.0 24017.2 -68011.2 55272.1 22511.3 -77783.4 291.7 100 0.310

1886 18103.68 43964.1 24017.5 -67981.6 55242.1 22511.3 -77753.4 292.2 100 0.309

1887 18123.55 43934.1 24017.7 -67951.9 55212.0 22511.5 -77723.5 292.8 100 0.308

1888 18143.42 43904.2 24018.1 -67922.3 55182.0 22511.5 -77693.5 293.3 100 0.308

1889 18163.30 43874.2 24018.5 -67892.6 55151.9 22511.6 -77663.5 293.9 100 0.307

1890 18183.18 43844.2 24018.7 -67862.9 55121.8 22511.8 -77633.5 294.4 100 0.307

1891 18203.07 43814.3 24019.0 -67833.3 55091.7 22511.9 -77603.6 295.0 100 0.306

1892 18222.96 43784.3 24019.2 -67803.5 55061.6 22512.1 -77573.6 295.5 100 0.305

1893 18243.00 43754.2 24019.4 -67773.7 55031.3 22512.1 -77543.4 296.1 100 0.305

1894 18279.00 43699.9 24020.1 -67720.0 54976.8 22512.4 -77489.2 297.1 100 0.304

1895 18309.00 43654.8 24020.5 -67675.2 54931.5 22512.6 -77444.0 297.9 100 0.303

1896 18339.00 43609.6 24020.9 -67630.5 54886.0 22512.7 -77398.8 298.7 100 0.302

1897 18369.00 43564.4 24021.4 -67585.8 54840.7 22512.9 -77353.6 299.6 100 0.301

1898 18399.00 43519.2 24022.0 -67541.2 54795.3 22513.3 -77308.5 300.4 100 0.300

1899 18429.00 43473.6 24023.3 -67496.9 54749.5 22514.4 -77263.9 301.2 100 0.299

1900 18459.00 43427.7 24024.8 -67452.5 54703.5 22515.8 -77219.3 302.1 100 0.298

1901 18489.00 43381.5 24026.6 -67408.1 54657.2 22517.4 -77174.6 302.9 100 0.297

1902 18519.00 43334.4 24028.0 -67362.4 54609.9 22518.6 -77128.5 303.7 100 0.297

1903 18549.00 43286.7 24028.0 -67314.7 54561.9 22518.3 -77080.2 304.6 100 0.296

1904 18579.00 43239.0 24027.1 -67266.0 54514.0 22517.2 -77031.2 305.4 100 0.295

1905 18609.00 43191.3 24026.1 -67217.4 54466.0 22516.0 -76982.0 306.2 100 0.294

1906 18639.00 43143.6 24025.2 -67168.8 54418.1 22514.7 -76932.8 307.1 100 0.293
C-65

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1907 18669.00 43096.0 24024.2 -67120.2 54370.2 22513.5 -76883.7 307.9 100 0.292

1908 18699.00 43048.2 24023.4 -67071.5 54322.1 22512.3 -76834.4 308.7 100 0.291

1909 18729.00 43000.5 24022.4 -67022.9 54274.2 22511.1 -76785.2 309.6 100 0.290

1910 18759.00 42952.7 24021.5 -66974.2 54226.2 22509.9 -76736.1 310.4 100 0.289

1911 18789.00 42905.1 24020.5 -66925.6 54178.2 22508.6 -76686.8 311.2 100 0.288

1912 18819.00 42857.3 24019.6 -66876.8 54130.1 22507.4 -76637.5 312.1 100 0.288

1913 18849.00 42809.5 24018.7 -66828.2 54082.1 22506.2 -76588.3 312.9 100 0.287

1914 18879.00 42761.7 24017.8 -66779.5 54034.0 22505.0 -76539.0 313.7 100 0.286

1915 18909.00 42713.9 24016.9 -66730.8 53986.0 22503.7 -76489.7 314.6 100 0.285

1916 18939.00 42666.1 24016.0 -66682.0 53937.8 22502.6 -76440.5 315.4 100 0.284

1917 18969.00 42618.2 24015.0 -66633.2 53889.8 22501.3 -76391.1 316.2 100 0.283

1918 18999.00 42570.3 24014.2 -66584.5 53841.6 22500.2 -76341.8 317.1 100 0.282

1919 19029.00 42522.5 24013.1 -66535.6 53793.5 22499.0 -76292.5 317.9 100 0.281

1920 19059.00 42474.7 24012.2 -66486.8 53745.4 22497.8 -76243.1 318.7 100 0.280

1921 19089.00 42426.7 24011.3 -66438.0 53697.2 22496.5 -76193.6 319.6 100 0.279

1922 19116.00 42383.6 24010.4 -66394.1 53653.9 22495.3 -76149.2 320.3 100 0.279

1923 19143.00 42340.5 24009.6 -66350.1 53610.6 22494.1 -76104.7 321.1 100 0.278

1924 19179.00 42282.9 24008.5 -66291.4 53552.7 22492.7 -76045.3 322.1 100 0.277

1925 19209.00 42235.0 24007.5 -66242.5 53504.4 22491.5 -75995.9 322.9 100 0.276

1926 19239.00 42187.1 24006.5 -66193.6 53456.3 22490.1 -75946.4 323.7 100 0.275

1927 19269.00 42139.1 24005.5 -66144.6 53408.0 22488.9 -75896.9 324.6 100 0.274

1928 19299.00 42091.1 24004.6 -66095.7 53359.8 22487.6 -75847.4 325.4 100 0.273

1929 19329.00 42043.1 24003.6 -66046.7 53311.5 22486.3 -75797.8 326.2 100 0.272

1930 19359.00 41995.1 24002.6 -65997.6 53263.2 22485.1 -75748.2 327.1 100 0.271

1931 19389.00 41947.1 24001.5 -65948.6 53214.9 22483.7 -75698.7 327.9 100 0.270

1932 19419.00 41899.0 24000.6 -65899.6 53166.6 22482.4 -75649.0 328.7 100 0.270

1933 19449.00 41850.9 23999.6 -65850.5 53118.2 22481.2 -75599.4 329.6 100 0.269

1934 19479.00 41803.0 23998.5 -65801.4 53070.0 22479.8 -75549.8 330.4 100 0.268

1935 19509.00 41754.9 23997.4 -65752.3 53021.6 22478.5 -75500.1 331.2 100 0.267

1936 19539.00 41706.7 23996.6 -65703.3 52973.3 22477.0 -75450.3 332.1 100 0.266

1937 19569.00 41658.6 23995.4 -65654.0 52924.8 22475.8 -75400.7 332.9 100 0.265

1938 19599.00 41610.5 23994.4 -65604.9 52876.5 22474.4 -75350.9 333.7 100 0.264

1939 19629.00 41562.4 23993.4 -65555.8 52828.0 22473.2 -75301.2 334.6 100 0.263

1940 19659.00 41514.3 23992.2 -65506.5 52779.7 22471.7 -75251.3 335.4 100 0.262

1941 19689.00 41466.1 23991.2 -65457.3 52731.2 22470.3 -75201.6 336.2 100 0.261

1942 19719.00 41417.9 23990.2 -65408.1 52682.8 22469.0 -75151.8 337.1 100 0.261

1943 19749.00 41369.8 23989.0 -65358.8 52634.3 22467.6 -75101.9 337.9 100 0.260

1944 19779.00 41321.6 23988.0 -65309.5 52585.9 22466.2 -75052.1 338.7 100 0.259

1945 19809.00 41273.4 23986.8 -65260.2 52537.4 22464.8 -75002.2 339.6 100 0.258
C-66

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1946 19839.00 41225.1 23985.8 -65210.9 52488.9 22463.5 -74952.3 340.4 100 0.257

1947 19869.00 41176.9 23984.6 -65161.5 52440.4 22461.9 -74902.4 341.2 100 0.256

1948 19899.00 41128.6 23983.6 -65112.2 52391.9 22460.6 -74852.5 342.1 100 0.255

1949 19929.00 41080.4 23982.4 -65062.8 52343.3 22459.2 -74802.5 342.9 100 0.254

1950 19959.00 41032.2 23981.3 -65013.5 52294.8 22457.8 -74752.6 343.7 100 0.253

1951 19989.00 40983.9 23980.1 -64964.0 52246.2 22456.3 -74702.5 344.6 100 0.252

1952 20016.00 40940.4 23979.1 -64919.5 52202.5 22455.0 -74657.5 345.3 100 0.252

1953 20043.00 40896.9 23978.1 -64875.0 52158.8 22453.8 -74612.5 346.1 100 0.251

1954 20079.00 40839.0 23976.7 -64815.6 52100.5 22451.9 -74552.4 347.1 100 0.250

1955 20109.00 40790.6 23975.5 -64766.1 52051.8 22450.5 -74502.3 347.9 100 0.249

1956 20139.00 40742.2 23974.4 -64716.6 52003.3 22449.0 -74452.3 348.7 100 0.248

1957 20169.00 40693.9 23973.1 -64667.0 51954.6 22447.4 -74402.1 349.6 100 0.247

1958 20199.00 40645.6 23971.7 -64617.3 51906.1 22445.7 -74351.8 350.4 100 0.246

1959 20229.00 40597.8 23969.5 -64567.3 51857.9 22443.2 -74301.2 351.2 100 0.245

1960 20259.00 40550.3 23966.9 -64517.2 51810.1 22440.3 -74250.4 352.1 100 0.244

1961 20289.00 40503.3 23964.1 -64467.4 51762.9 22437.0 -74199.8 352.9 100 0.243

1962 20319.00 40457.3 23961.7 -64418.9 51716.5 22434.2 -74150.8 353.7 100 0.243

1963 20349.00 40412.0 23961.3 -64373.3 51671.1 22433.4 -74104.5 354.6 100 0.242

1964 20379.00 40366.7 23961.6 -64328.3 51625.6 22433.6 -74059.2 355.4 100 0.241

1965 20409.00 40321.5 23962.0 -64283.5 51580.1 22433.7 -74013.8 356.2 100 0.240

1966 20439.00 40276.2 23962.3 -64238.6 51534.7 22433.8 -73968.5 357.1 100 0.239

1967 20469.00 40231.0 23962.7 -64193.7 51489.2 22433.9 -73923.1 357.9 100 0.238

1968 20499.00 40185.7 23963.0 -64148.8 51443.8 22433.9 -73877.8 358.7 100 0.237

1969 20529.00 40140.6 23963.3 -64103.9 51398.4 22434.1 -73832.5 359.6 100 0.236

1970 20559.00 40095.3 23963.8 -64059.1 51352.9 22434.2 -73787.2 360.4 100 0.235

1971 20589.00 40050.1 23964.1 -64014.2 51307.5 22434.3 -73741.8 361.2 100 0.234

1972 20619.00 40004.8 23964.6 -63969.4 51262.1 22434.5 -73696.5 362.1 100 0.234

1973 20649.00 39959.6 23964.8 -63924.5 51216.6 22434.7 -73651.3 362.9 100 0.233

1974 20679.00 39914.4 23965.3 -63879.7 51171.2 22434.7 -73605.9 363.7 100 0.232

1975 20709.00 39869.2 23965.7 -63834.9 51125.8 22434.9 -73560.7 364.6 100 0.231

1976 20739.00 39824.0 23966.1 -63790.1 51080.3 22435.1 -73515.4 365.4 100 0.230

1977 20769.00 39778.7 23966.6 -63745.3 51035.0 22435.2 -73470.2 366.2 100 0.229

1978 20799.00 39733.6 23967.0 -63700.5 50989.6 22435.4 -73424.9 367.1 100 0.228

1979 20829.00 39688.3 23967.4 -63655.7 50944.1 22435.5 -73379.7 367.9 100 0.227

1980 20859.00 39643.1 23967.8 -63610.9 50898.8 22435.6 -73334.4 368.7 100 0.226

1981 20889.00 39598.0 23968.1 -63566.1 50853.4 22435.8 -73289.2 369.5 100 0.225

1982 20916.00 39557.3 23968.5 -63525.8 50812.6 22435.9 -73248.5 370.3 100 0.225

1983 20943.00 39516.6 23969.0 -63485.6 50771.8 22436.1 -73207.8 371.0 100 0.224

1984 20979.00 39462.4 23969.4 -63431.8 50717.3 22436.2 -73153.5 372.0 100 0.223
C-67

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

1985 21009.00 39417.3 23969.9 -63387.1 50671.8 22436.5 -73108.3 372.9 100 0.222

1986 21039.00 39372.0 23970.3 -63342.3 50626.5 22436.7 -73063.2 373.7 100 0.221

1987 21069.00 39326.9 23970.8 -63297.6 50581.2 22436.8 -73017.9 374.5 100 0.220

1988 21099.00 39281.7 23971.1 -63252.8 50535.7 22437.1 -72972.8 375.4 100 0.219

1989 21129.00 39236.6 23971.6 -63208.2 50490.4 22437.2 -72927.6 376.2 100 0.218

1990 21159.00 39191.4 23972.0 -63163.4 50445.1 22437.3 -72882.4 377.0 100 0.217

1991 21189.00 39146.2 23972.5 -63118.8 50399.7 22437.5 -72837.2 377.9 100 0.216

1992 21219.00 39101.2 23972.9 -63074.1 50354.4 22437.7 -72792.1 378.7 100 0.216

1993 21249.00 39056.0 23973.4 -63029.4 50309.1 22437.9 -72746.9 379.5 100 0.215

1994 21279.00 39010.9 23973.8 -62984.7 50263.7 22438.0 -72701.8 380.4 100 0.214

1995 21309.00 38965.7 23974.3 -62940.0 50218.4 22438.3 -72656.6 381.2 100 0.213

1996 21339.00 38920.6 23974.7 -62895.3 50173.0 22438.5 -72611.6 382.0 100 0.212

1997 21369.00 38875.5 23975.1 -62850.6 50127.7 22438.7 -72566.4 382.9 100 0.211

1998 21399.00 38830.4 23975.6 -62805.9 50082.4 22438.9 -72521.3 383.7 100 0.210

1999 21429.00 38785.3 23976.0 -62761.3 50037.0 22439.2 -72476.2 384.5 100 0.209

2000 21459.00 38740.1 23976.5 -62716.6 49991.8 22439.2 -72431.0 385.4 100 0.208

2001 21489.00 38695.1 23976.9 -62672.0 49946.5 22439.5 -72386.0 386.2 100 0.207

2002 21519.00 38649.9 23977.4 -62627.3 49901.1 22439.7 -72340.8 387.0 100 0.207

2003 21549.00 38604.9 23977.8 -62582.7 49855.9 22439.9 -72295.8 387.9 100 0.206

2004 21579.00 38559.7 23978.3 -62538.0 49810.6 22440.2 -72250.7 388.7 100 0.205

2005 21609.00 38514.7 23978.8 -62493.4 49765.3 22440.2 -72205.6 389.5 100 0.204

2006 21639.00 38469.6 23979.2 -62448.8 49720.0 22440.5 -72160.5 390.4 100 0.203

2007 21669.00 38424.6 23979.7 -62404.2 49674.8 22440.7 -72115.5 391.2 100 0.202

2008 21699.00 38379.4 23980.2 -62359.6 49629.5 22440.9 -72070.4 392.0 100 0.201

2009 21729.00 38334.4 23980.7 -62315.1 49584.2 22441.2 -72025.4 392.9 100 0.200

2010 21759.00 38289.3 23981.2 -62270.5 49539.0 22441.4 -71980.4 393.7 100 0.199

2011 21789.00 38244.2 23981.6 -62225.9 49493.7 22441.6 -71935.4 394.5 100 0.198

2012 21816.00 38203.7 23982.0 -62185.8 49453.0 22441.8 -71894.8 395.3 100 0.198

2013 21843.00 38163.2 23982.5 -62145.7 49412.3 22442.0 -71854.3 396.0 100 0.197

2014 21879.00 38109.1 23983.1 -62092.2 49358.0 22442.3 -71800.3 397.0 100 0.196

2015 21909.00 38064.0 23983.6 -62047.6 49312.8 22442.5 -71755.3 397.9 100 0.195

2016 21939.00 38019.1 23984.0 -62003.1 49267.6 22442.8 -71710.3 398.7 100 0.194

2017 21969.00 37974.0 23984.5 -61958.5 49222.3 22443.0 -71665.4 399.5 100 0.193

2018 21999.00 37929.0 23985.1 -61914.0 49177.1 22443.2 -71620.3 400.4 100 0.192

2019 22029.00 37883.9 23985.6 -61869.5 49131.9 22443.5 -71575.4 401.2 100 0.191

2020 22059.00 37839.0 23986.0 -61824.9 49086.6 22443.8 -71530.4 402.0 100 0.190

2021 22089.00 37793.9 23986.5 -61780.4 49041.4 22444.0 -71485.4 402.9 100 0.189

2022 22119.00 37748.8 23987.1 -61735.9 48996.2 22444.2 -71440.4 403.7 100 0.189

2023 22149.00 37703.8 23987.7 -61691.5 48950.9 22444.5 -71395.4 404.5 100 0.188
C-68

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

2024 22179.00 37658.7 23988.2 -61646.9 48905.7 22444.8 -71350.5 405.4 100 0.187

2025 22209.00 37613.7 23988.8 -61602.5 48860.4 22445.3 -71305.6 406.2 100 0.186

2026 22239.00 37568.6 23989.3 -61558.0 48815.1 22445.5 -71260.7 407.0 100 0.185

2027 22269.00 37523.6 23989.9 -61513.5 48769.9 22445.8 -71215.7 407.9 100 0.184

2028 22299.00 37478.5 23990.5 -61469.0 48724.7 22446.2 -71170.9 408.7 100 0.183

2029 22329.00 37433.6 23990.9 -61424.5 48679.5 22446.4 -71125.9 409.5 100 0.182

2030 22359.00 37388.5 23991.6 -61380.1 48634.3 22446.8 -71081.1 410.4 100 0.181

2031 22389.00 37343.5 23992.1 -61335.6 48589.1 22447.0 -71036.1 411.2 100 0.180

2032 22419.00 37298.5 23992.7 -61291.2 48543.8 22447.5 -70991.3 412.0 100 0.180

2033 22449.00 37253.4 23993.2 -61246.7 48498.7 22447.7 -70946.4 412.9 100 0.179

2034 22479.00 37208.4 23993.9 -61202.3 48453.5 22448.0 -70901.5 413.7 100 0.178

2035 22509.00 37163.4 23994.5 -61157.9 48408.2 22448.4 -70856.6 414.5 100 0.177

2036 22539.00 37118.5 23994.9 -61113.4 48363.1 22448.6 -70811.7 415.4 100 0.176

2037 22569.00 37073.4 23995.6 -61069.0 48318.0 22448.9 -70766.9 416.2 100 0.175

2038 22599.00 37028.5 23996.2 -61024.6 48272.7 22449.3 -70722.0 417.0 100 0.174

2039 22629.00 36983.5 23996.7 -60980.2 48227.6 22449.6 -70677.2 417.9 100 0.173

2040 22659.00 36938.6 23997.3 -60935.8 48182.4 22450.0 -70632.4 418.7 100 0.172

2041 22689.00 36893.6 23997.8 -60891.4 48137.3 22450.3 -70587.6 419.5 100 0.171

2042 22716.00 36853.1 23998.5 -60851.5 48096.6 22450.6 -70547.2 420.3 100 0.171

2043 22743.00 36812.6 23999.0 -60811.6 48056.0 22450.9 -70506.9 421.0 100 0.170

2044 22779.00 36758.7 23999.6 -60758.4 48001.8 22451.4 -70453.2 422.0 100 0.169

2045 22809.00 36713.8 24000.3 -60714.1 47956.8 22451.6 -70408.4 422.9 100 0.168

2046 22839.00 36668.8 24000.9 -60669.7 47911.7 22452.0 -70363.6 423.7 100 0.167

2047 22869.00 36623.9 24001.5 -60625.4 47866.5 22452.3 -70318.9 424.5 100 0.166

2048 22899.00 36579.0 24002.1 -60581.1 47821.4 22452.7 -70274.1 425.4 100 0.165

2049 22929.00 36534.1 24002.7 -60536.8 47776.3 22453.1 -70229.4 426.2 100 0.164

2050 22959.00 36489.1 24003.4 -60492.5 47731.2 22453.5 -70184.7 427.0 100 0.163

2051 22989.00 36444.3 24003.9 -60448.2 47686.1 22453.8 -70139.9 427.9 100 0.162

2052 23019.00 36399.3 24004.6 -60403.9 47640.9 22454.3 -70095.2 428.7 100 0.162

2053 23049.00 36354.5 24005.2 -60359.6 47595.9 22454.6 -70050.6 429.5 100 0.161

2054 23079.00 36309.5 24005.8 -60315.3 47550.8 22455.0 -70005.8 430.4 100 0.160

2055 23109.00 36264.6 24006.5 -60271.1 47505.8 22455.4 -69961.1 431.2 100 0.159

2056 23139.00 36219.8 24007.0 -60226.8 47460.7 22455.8 -69916.5 432.0 100 0.158

2057 23169.00 36174.8 24007.8 -60182.6 47415.6 22456.1 -69871.7 432.9 100 0.157

2058 23199.00 36130.0 24008.4 -60138.4 47370.6 22456.5 -69827.1 433.7 100 0.156

2059 23229.00 36085.1 24009.0 -60094.1 47325.5 22456.9 -69782.4 434.5 100 0.155

2060 23259.00 36040.3 24009.7 -60050.0 47280.5 22457.3 -69737.8 435.4 100 0.154

2061 23289.00 35995.4 24010.3 -60005.8 47235.5 22457.7 -69693.1 436.2 100 0.153

2062 23319.00 35950.6 24011.0 -59961.6 47190.4 22458.2 -69648.6 437.0 100 0.153
C-69

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

2063 23349.00 35905.7 24011.7 -59917.4 47145.3 22458.6 -69603.9 437.9 100 0.152

2064 23379.00 35860.9 24012.3 -59873.2 47100.4 22458.9 -69559.3 438.7 100 0.151

2065 23409.00 35816.0 24013.0 -59829.0 47055.3 22459.4 -69514.7 439.5 100 0.150

2066 23439.00 35771.2 24013.6 -59784.8 47010.3 22459.8 -69470.1 440.4 100 0.149

2067 23469.00 35726.3 24014.4 -59740.7 46965.3 22460.3 -69425.5 441.2 100 0.148

2068 23499.00 35681.4 24015.1 -59696.5 46920.2 22460.7 -69381.0 442.0 100 0.147

2069 23529.00 35636.6 24015.7 -59652.3 46875.2 22461.1 -69336.3 442.9 100 0.146

2070 23559.00 35591.8 24016.4 -59608.2 46830.3 22461.5 -69291.8 443.7 100 0.145

2071 23589.00 35547.0 24017.2 -59564.1 46785.2 22462.0 -69247.2 444.5 100 0.144

2072 23616.00 35506.6 24017.7 -59524.3 46744.7 22462.4 -69207.2 445.3 100 0.144

2073 23643.00 35466.3 24018.3 -59484.6 46704.2 22462.8 -69167.0 446.0 100 0.143

2074 23691.00 35394.6 24019.5 -59414.1 46632.2 22463.5 -69095.7 447.4 100 0.146

2075 23731.00 35334.9 24020.4 -59355.2 46572.2 22464.1 -69036.3 448.5 100 0.148

2076 23771.00 35275.1 24021.4 -59296.5 46512.3 22464.7 -68977.0 449.6 100 0.150

2077 23811.00 35215.4 24022.2 -59237.6 46452.3 22465.3 -68917.6 450.7 100 0.152

2078 23851.00 35155.7 24023.2 -59178.9 46392.4 22465.9 -68858.3 451.8 100 0.155

2079 23891.00 35096.0 24024.1 -59120.1 46332.5 22466.5 -68799.0 452.9 100 0.157

2080 23931.00 35036.3 24025.1 -59061.4 46272.6 22467.2 -68739.7 454.0 100 0.159

2081 23971.00 34976.7 24025.9 -59002.6 46212.7 22467.7 -68680.4 455.1 100 0.162

2082 24011.00 34917.0 24026.8 -58943.9 46152.8 22468.2 -68621.1 456.2 100 0.164

2083 24051.00 34857.4 24027.7 -58885.1 46092.9 22468.9 -68561.8 457.3 100 0.166

2084 24091.00 34797.7 24028.6 -58826.3 46033.1 22469.4 -68502.5 458.5 100 0.168

2085 24131.00 34738.1 24029.6 -58767.7 45973.3 22469.9 -68443.2 459.6 100 0.171

2086 24171.00 34678.6 24030.4 -58708.9 45913.5 22470.4 -68383.9 460.7 100 0.173

2087 24211.00 34618.9 24031.3 -58650.3 45853.7 22471.0 -68324.7 461.8 100 0.175

2088 24251.00 34559.4 24032.2 -58591.6 45793.9 22471.6 -68265.5 462.9 100 0.178

2089 24291.00 34499.8 24033.2 -58533.0 45734.1 22472.2 -68206.3 464.0 100 0.180

2090 24331.00 34440.2 24034.2 -58474.4 45674.3 22472.8 -68147.1 465.1 100 0.182

2091 24371.00 34380.7 24035.1 -58415.8 45614.4 22473.5 -68088.0 466.2 100 0.184

2092 24411.00 34321.1 24036.1 -58357.2 45554.6 22474.2 -68028.9 467.3 100 0.187

2093 24451.00 34261.5 24037.1 -58298.7 45494.8 22474.9 -67969.7 468.5 100 0.189

2094 24491.00 34202.0 24038.1 -58240.1 45435.0 22475.6 -67910.6 469.6 100 0.191

2095 24531.00 34142.4 24039.3 -58181.7 45375.2 22476.3 -67851.6 470.7 100 0.194

2096 24571.00 34082.8 24040.3 -58123.1 45315.5 22477.0 -67792.5 471.8 100 0.196

2097 24611.00 34023.3 24041.4 -58064.6 45255.7 22477.7 -67733.4 472.9 100 0.198

2098 24651.00 33963.8 24042.3 -58006.1 45195.9 22478.5 -67674.4 474.0 100 0.200

2099 24691.00 33904.2 24043.4 -57947.7 45136.2 22479.1 -67615.3 475.1 100 0.203

2100 24731.00 33844.7 24044.5 -57889.2 45076.4 22479.9 -67556.3 476.2 100 0.205

2101 24771.00 33785.1 24045.6 -57830.7 45016.7 22480.6 -67497.3 477.3 100 0.207
C-70

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

2102 24807.00 33731.6 24046.4 -57778.1 44962.9 22481.3 -67444.2 478.3 100 0.209

2103 24843.00 33678.0 24047.5 -57725.5 44909.1 22481.9 -67391.0 479.3 100 0.211

2104 24891.00 33606.6 24048.7 -57655.4 44837.4 22482.8 -67320.2 480.7 100 0.214

2105 24931.00 33547.1 24049.8 -57596.9 44777.7 22483.5 -67261.3 481.8 100 0.216

2106 24971.00 33487.7 24050.9 -57538.6 44718.0 22484.3 -67202.4 482.9 100 0.219

2107 25011.00 33428.2 24052.0 -57480.2 44658.3 22485.1 -67143.4 484.0 100 0.221

2108 25051.00 33368.7 24053.1 -57421.8 44598.6 22485.9 -67084.5 485.1 100 0.223

2109 25091.00 33309.3 24054.2 -57363.4 44539.0 22486.5 -67025.4 486.2 100 0.226

2110 25131.00 33249.8 24055.2 -57305.1 44479.3 22487.3 -66966.6 487.3 100 0.228

2111 25171.00 33190.4 24056.3 -57246.7 44419.6 22488.1 -66907.7 488.5 100 0.230

2112 25211.00 33131.0 24057.4 -57188.4 44360.0 22488.8 -66848.8 489.6 100 0.232

2113 25251.00 33071.5 24058.6 -57130.1 44300.2 22489.6 -66789.9 490.7 100 0.235

2114 25291.00 33012.1 24059.7 -57071.8 44240.6 22490.4 -66731.1 491.8 100 0.237

2115 25331.00 32952.7 24060.7 -57013.4 44181.0 22491.1 -66672.1 492.9 100 0.239

2116 25371.00 32893.2 24061.9 -56955.2 44121.3 22492.0 -66613.4 494.0 100 0.242

2117 25411.00 32833.9 24063.0 -56896.9 44061.7 22492.8 -66554.5 495.1 100 0.244

2118 25451.00 32774.5 24064.2 -56838.7 44002.1 22493.5 -66495.6 496.2 100 0.246

2119 25491.00 32715.0 24065.4 -56780.4 43942.5 22494.4 -66436.9 497.3 100 0.248

2120 25531.00 32655.7 24066.5 -56722.2 43882.9 22495.2 -66378.0 498.4 100 0.251

2121 25571.00 32596.4 24067.6 -56663.9 43823.3 22496.0 -66319.2 499.6 100 0.253

2122 25611.00 32534.2 24069.3 -56603.5 43742.9 22497.4 -66240.3 500.7 100 0.255

2123 25651.00 32459.3 24073.8 -56533.2 43650.2 22501.8 -66151.9 501.8 100 0.257

2124 25691.00 32374.4 24079.5 -56454.0 43560.9 22507.6 -66068.6 502.9 100 0.260

2125 25731.00 32286.5 24087.6 -56374.2 43478.9 22514.7 -65993.6 504.0 100 0.262

2126 25771.00 32200.7 24093.8 -56294.5 43401.1 22518.0 -65919.1 505.1 100 0.264

2127 25811.00 32124.2 24089.1 -56213.4 43325.5 22515.9 -65841.5 506.2 100 0.267

2128 25851.00 32050.2 24081.4 -56131.6 43251.9 22509.5 -65761.4 507.3 100 0.269

2129 25891.00 31978.4 24070.7 -56049.1 43180.0 22499.7 -65679.7 508.4 100 0.271

2130 25931.00 31908.4 24058.1 -55966.5 43109.7 22487.3 -65597.0 509.6 100 0.273

2131 25971.00 31840.0 24043.6 -55883.6 43041.0 22472.9 -65513.9 510.7 100 0.276

2132 26007.00 31779.7 24029.3 -55809.0 42980.3 22458.7 -65439.0 511.7 100 0.278

2133 26043.00 31720.5 24014.0 -55734.6 42920.8 22443.4 -65364.2 512.7 100 0.280

2134 26091.00 31643.0 23992.8 -55635.8 42842.7 22422.2 -65264.9 514.0 100 0.283

2135 26131.00 31579.5 23974.8 -55554.3 42778.8 22404.2 -65183.1 515.1 100 0.285

2136 26171.00 31516.6 23957.4 -55474.0 42715.7 22386.8 -65102.5 516.2 100 0.287

2137 26211.00 31454.2 23941.7 -55395.9 42652.9 22371.2 -65024.1 517.3 100 0.289

2138 26251.00 31390.8 23931.2 -55322.1 42589.3 22360.5 -64949.8 518.4 100 0.292

2139 26291.00 31325.2 23927.1 -55252.4 42523.1 22356.2 -64879.3 519.5 100 0.294

2140 26331.00 31259.1 23924.4 -55183.5 42456.5 22353.0 -64809.5 520.7 100 0.296
C-71

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

2141 26371.00 31192.9 23921.7 -55114.5 42389.7 22349.8 -64739.6 521.8 100 0.299

2142 26411.00 31126.6 23918.9 -55045.5 42323.0 22346.6 -64669.6 522.9 100 0.301

2143 26451.00 31060.4 23916.0 -54976.4 42256.3 22343.5 -64599.7 524.0 100 0.303

2144 26491.00 30994.1 23913.3 -54907.3 42189.4 22340.4 -64529.8 525.1 100 0.305

2145 26531.00 30927.8 23910.4 -54838.2 42122.7 22337.1 -64459.8 526.2 100 0.308

2146 26571.00 30861.5 23907.6 -54769.1 42055.8 22333.9 -64389.7 527.3 100 0.310

2147 26611.00 30795.1 23904.8 -54699.9 41989.0 22330.7 -64319.7 528.4 100 0.312

2148 26651.00 30728.8 23901.9 -54630.7 41922.2 22327.4 -64249.6 529.5 100 0.315

2149 26691.00 30662.4 23899.0 -54561.5 41855.2 22324.2 -64179.4 530.7 100 0.317

2150 26731.00 30596.1 23896.1 -54492.1 41788.4 22320.8 -64109.2 531.8 100 0.319

2151 26771.00 30529.7 23893.3 -54422.9 41721.4 22317.6 -64039.0 532.9 100 0.321

2152 26811.00 30463.3 23890.3 -54353.6 41654.5 22314.3 -63968.8 534.0 100 0.324

2153 26851.00 30396.8 23887.4 -54284.2 41587.6 22311.0 -63898.6 535.1 100 0.326

2154 26891.00 30330.3 23884.5 -54214.8 41520.6 22307.6 -63828.3 536.2 100 0.328

2155 26931.00 30263.8 23881.6 -54145.4 41453.6 22304.4 -63757.9 537.3 100 0.331

2156 26971.00 30197.3 23878.6 -54075.9 41386.5 22301.1 -63687.6 538.4 100 0.333

2157 27011.00 30130.8 23875.6 -54006.4 41319.5 22297.7 -63617.2 539.5 100 0.335

2158 27051.00 30064.2 23872.7 -53936.9 41252.4 22294.3 -63546.7 540.7 100 0.337

2159 27091.00 29997.7 23869.7 -53867.4 41185.4 22290.9 -63476.3 541.8 100 0.340

2160 27131.00 29931.1 23866.7 -53797.8 41118.3 22287.6 -63405.9 542.9 100 0.342

2161 27171.00 29864.5 23863.7 -53728.2 41051.1 22284.2 -63335.3 544.0 100 0.344

2162 27207.00 29804.6 23860.9 -53665.5 40990.7 22281.2 -63271.9 545.0 100 0.346

2163 27243.00 29744.6 23858.2 -53602.9 40930.3 22278.0 -63208.3 546.0 100 0.348

2164 27259.56 29696.7 23835.0 -53531.7 40853.4 22255.3 -63108.7 546.1 100 0.342

2165 27276.12 29643.4 23805.1 -53448.5 40779.9 22226.4 -63006.4 546.2 100 0.335

2166 27303.72 29561.3 23748.7 -53309.9 40676.1 22171.9 -62848.0 546.3 100 0.324

2167 27331.32 29489.0 23690.2 -53179.2 40588.0 22115.0 -62703.0 546.4 100 0.312

2168 27358.92 29425.7 23632.0 -53057.8 40512.5 22059.4 -62572.0 546.4 100 0.301

2169 27386.52 29370.0 23576.4 -52946.4 40447.1 22005.9 -62452.9 546.5 100 0.290

2170 27414.12 29320.4 23523.5 -52844.0 40389.6 21954.3 -62343.9 546.5 100 0.278

2171 27441.72 29276.1 23472.5 -52748.6 40338.7 21905.3 -62244.0 546.6 100 0.267

2172 27469.32 29236.0 23424.2 -52660.2 40293.0 21859.0 -62152.0 546.6 100 0.256

2173 27496.92 29199.6 23378.3 -52577.8 40251.9 21814.1 -62066.0 546.6 100 0.245

2174 27524.52 29166.2 23334.2 -52500.4 40214.4 21772.6 -61987.0 546.6 100 0.233

2175 27552.12 29135.5 23292.6 -52428.1 40180.2 21731.9 -61912.0 546.7 100 0.222

2176 27579.72 29107.1 23252.7 -52359.8 40148.5 21693.5 -61842.1 546.7 100 0.211

2177 27607.32 29080.6 23214.8 -52295.5 40119.3 21656.8 -61776.1 546.7 100 0.200

2178 27634.92 29055.8 23178.3 -52234.2 40092.1 21622.0 -61714.1 546.7 100 0.188

2179 27657.00 29037.0 23149.9 -52186.9 40071.4 21594.8 -61666.2 546.7 100 0.179
C-72

Point No. Time

(sec.)

Membrane + Bending Stresses Total Stresses Metal

Temp.

(°F)

No. of

Cycles

DO

(ppm) S’12

(psi)

S’23

(psi)

S’31

(psi)

S’12

(psi)

S’23

(psi)

S’31

(psi)

2180 27673.56 29023.4 23129.4 -52152.8 40056.5 21574.7 -61631.2 546.7 100 0.172

2181 27690.12 29010.3 23109.3 -52119.6 40042.2 21555.1 -61597.2 546.7 100 0.166

2182 27717.72 28989.6 23076.8 -52066.3 40019.7 21524.6 -61544.3 546.8 100 0.154

2183 27745.32 28969.9 23046.2 -52016.1 39998.4 21494.0 -61492.3 546.8 100 0.143

2184 27772.92 28951.3 23015.6 -51966.9 39978.2 21465.2 -61443.4 546.8 100 0.132

2185 27800.52 28933.5 22987.1 -51920.7 39959.0 21437.5 -61396.5 546.8 100 0.121

2186 27828.12 28916.5 22958.9 -51875.5 39940.5 21410.0 -61350.5 546.8 100 0.109

2187 27855.72 28900.2 22931.1 -51831.3 39923.1 21383.6 -61306.6 546.8 100 0.098

2188 27883.32 28884.6 22904.5 -51789.1 39906.3 21358.4 -61264.7 546.8 100 0.087

2189 27910.92 28869.6 22879.4 -51748.9 39890.2 21333.6 -61223.8 546.8 100 0.075

2190 27938.52 28855.1 22854.7 -51709.8 39874.7 21309.1 -61183.8 546.8 100 0.064

2191 27966.12 28841.1 22830.6 -51671.6 39859.7 21285.2 -61144.9 546.8 100 0.053

2192 27993.72 28827.6 22806.9 -51634.5 39845.3 21262.7 -61108.0 546.9 100 0.042

2193 28021.32 28814.6 22783.8 -51598.4 39831.4 21240.7 -61072.1 546.9 100 0.030

2194 28048.92 28801.9 22761.4 -51563.3 39818.0 21219.1 -61037.2 546.9 100 0.019

2195 28071.00 28792.1 22744.1 -51536.2 39807.6 21201.6 -61009.2 546.9 100 0.010

2196 28387.00 28745.0 22648.4 -51393.4 39755.2 21111.7 -60866.9 546.9 100 0.010

2197 28681.03 28716.7 22589.5 -51306.3 39724.0 21054.7 -60778.7 546.9 100 0.010

2198 28975.06 28698.5 22549.0 -51247.5 39703.7 21016.9 -60720.6 547.0 100 0.010

2199 29269.59 28686.5 22522.4 -51209.0 39690.4 20991.1 -60681.5 547.0 100 0.010

2200 29564.22 28678.7 22504.0 -51182.6 39681.6 20973.8 -60655.4 547.0 100 0.010

2201 29858.93 28673.4 22492.0 -51165.4 39675.9 20962.5 -60638.4 547.0 100 0.010

2202 30153.68 28670.0 22484.2 -51154.2 39672.1 20955.3 -60627.4 547.0 100 0.010

2203 30448.45 28667.8 22478.3 -51146.1 39669.6 20949.8 -60619.3 547.0 100 0.010

2204 30743.24 28666.2 22474.8 -51141.1 39667.9 20946.4 -60614.3 547.0 100 0.010

2205 31038.05 28665.2 22472.8 -51138.0 39666.8 20944.6 -60611.3 547.0 100 0.010

2206 31332.86 28664.6 22471.4 -51136.0 39666.1 20942.2 -60608.3 547.0 100 0.010

2207 31859.52 28664.0 22470.0 -51134.0 39665.4 20941.0 -60606.3 547.0 100 0.010

2208 32386.19 28663.6 22468.4 -51132.0 39664.9 20940.4 -60605.3 547.0 100 0.010

2209 32912.86 28663.5 22468.5 -51131.9 39664.8 20939.5 -60604.3 547.0 100 0.010

2210 33439.52 28663.4 22468.6 -51131.9 39664.6 20939.7 -60604.3 547.0 100 0.010

2211 33966.19 28663.3 22467.7 -51130.9 39664.5 20939.8 -60604.3 547.0 100 0.010

2212 34492.86 28663.3 22467.7 -51130.9 39664.5 20939.8 -60604.3 547.0 100 0.010

2213 35019.52 28663.3 22467.7 -51130.9 39664.5 20939.8 -60604.3 547.0 100 0.010

2214 35546.19 28663.3 22467.7 -51130.9 39664.5 20939.8 -60604.3 547.0 100 0.010

2215 35971.00 28663.3 22467.7 -51130.9 39664.5 20939.8 -60604.3 547.0 100 0.010
C-73

C5 References

C-1. EPRI Report No. 1025823, “Guidelines for Addressing Environmental Effects in Fatigue Usage 

Calculations,” Electric Power Research Institute, Palo Alto, CA, December 2012.

C-2. ASME Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Facility 

Components, “Division 1 - Subsection NB, Class 1 Components,” American Society of 

Mechanical Engineers, New York, NY, July 1, 2013 (2013 Edition).




UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

------------------

OFFICIAL BUSINESS
NUREG/CR-6909

Revision 1, Draft

Effect of LWR Coolant Environments on the Fatigue Life of Reactor Materials