Atlas ofFatigue Curves

Edited by

Howard E. BoyerSenior Technical EditorAmerican Society for Metals

The MaterialsInformation Society

ASM lnternatlonal"Materials Park, Ohio 44073-0002www.asminternational.org

PrefaceThis Atlas was developed to serve engineers who are looking for fatigue

data on a particular metal or alloy. In the past, the first step to locating thisdata was an expensive and time-consuming search through the technical liter-ature. Now, many ofthe important and frequently referenced curves are pre-sented together in this one volume. They are arranged by standard alloy des-ignationsand are accompanied by a textual explanation offatigue testing andinterpretation of test results. In each case, the individual curve is thoroughlyreferenced to the original source.

Having these important curves compiled in a single book will also facili-tate the computerization of these data. Plans are currently under way also tomake the data presented in this book available in ASCII files for analysis bycomputer programs.

The Atlas of Fatigue Curves is obviously not complete, in that manymore curves could be included. Persons wishing to contribute curves to thiscompilation for inclusion in future revisions should contact the Editors,Technical Books, American Society for Metals, Metals Park, Ohio 44073.

ContentsFatigue Testing 1

Introduction IFatigue Crack Initiation 4Fatigue Crack Propagation 12

SECTION 1: S-N Curves That Typify Effects of Major Variables 27I-I. S-NCurves Typical for Steel 271-2. S-NCurves Typical for Medium-Strength Steels 281-3. S-NDiagrams Comparing Endurance Limit for Seven Alloys 301-4. Steel: Effect of Microstructure 311-5. Steel: Influence of Derating Factors on Fatigue Characteristics 321-6. Steel: Correction Factors for Various Surface Conditions 331-7. Fatigue Behavior: Ferrous vs Nonferrous Metals 341-8. Comparison of Fatigue Characteristics: Mild Steel vs Aluminum Alloy 351-9. Carbon Steel: Effect of Lead as an Additive 36

1-10. Corrosion Fatigue: General Effect on Behavior 37I-II. Effect of Corrosion on Fatigue Characteristics of Several Steels 381-12. Steel: Effect of Hydrogen on Fatigue Crack Propagation 391-13. Relationship of Stress Amplitude and Cycles to Failure 401-14. Strain-Life and Stress-Life Curves 411-15. Fatigue Plot for Steel: Ultrasonic Attenuation vs Number of Cycles 42

SECTION 2: Low-Carbon Steels: Flat-Rolled, Weldments and Tubes 432-1. Typical S-N Curve for Low-Carbon Steel Under Axial Tension 432-2. AISI 1006: Effects of Biaxial Stretching and Cold Rolling 442-3. AISI 1006: Weldment; FCAW, TIG Dressed 452-4. AISI 1006: Weldment; Shear Joints 462-5. AISI 1006: Weldment; Lap-Shear Joints 472-6. AISI 1015: Effect of Cold Working 482-7. A533 Steel Plate: Fatigue Crack Growth Rate 492-8. A514F Steel Plate: Fatigue Crack Growth Rates 502-9. A514F and A633C: Variation in Fatigue Crack Growth Rate With Orientation 51

2-10. A514F: Scatterbands of Fatigue Crack Growth Rate 522-11. A633C Steel Plate: Scatterbands of Fatigue Crack Growth Rates 532-12. Low-Carbon Steel Weldment: Effects of Various Weld Defects 542-13. Low-Carbon Steel Weldment: Effect of Weld Reinforcement and Lack of

Inclusions 552-14. Low-Carbon Steel Weldment: Effect of Weld Reinforcement and Lack of

Penetration 562-15. Low-Carbon Steel Weldment: Computed Fatigue Strength; Weldment Contained

Lack of Fusion 572-16. Low-Carbon Steel Weldment: Effect of Reinforcement and Undercutting 582-17. Low-Carbon Steel: Transverse Butt Welds; Effect of Reinforcement 592-18. A36/E60S-3 Steel Plate: Butt Welds 602-19. A514F/EllO Steel: Bead on Plate Weldment 612-20. A36 and A514 Steel Plates: Butt Welded 622-21. A36 Plate Steel: Butt Welded 632-22. Low-Carbon Steel Tubes: Effect of Welding Technique 642-23. Low-Carbon Steel: Effect of Applied Anodic Currents in 3% NaCI 652-24. Low-Carbon Steel: Effect of pH in NaCI and NaOH 662-25. Low-Carbon Steel: Effect of Carburization and Decarburization 67

v

VI Contents

2-26. A514B Steel: Effect of Various Gaseous Environments on Fatigue CrackPropagation 68

2-27. Cast 1522 and 1541 Steels: Effect of Various Surface Conditions 692-28. Cast A216 (Grade WCC) Steel: Fatigue Crack Growth Rate 70

SECTION 3: Medium-Carbon Steels, Wrought and Cast 713-1. AISI 1030 (Cast) Compared With AISI 1020 (Wrought) 713-2. AISI 1035: Effect of Gas and Salt Bath Nitriding 723-3. AISI 1040: Cast vs Wrought 733-4. AISI 1045: Relationship of Hardness and Strain-Life Behavior 743-5. AISI 1141: Effect of Gas Nitriding 753-6. Medium-Carbon Steels: Interrelationship of Hardness, Strain Life and Fatigue

Life 763-7. Medium-Carbon Steel: Effect of Fillet Radii 773-8. Medium-Carbon Steel: Effect of Keyway Design 783-9. Medium-Carbon Steel: Effect of Residual Stresses 79

3-10. Medium-Carbon Cast Steel: Effect of Changes in Residual Stress 803-11. Medium-Carbon Cast Steel: S-NProjection (Effect of Applied Stress) 813-12. Medium-Carbon Cast Steel: Effect of Applied Stress (Shot Blasting) 82

SECTION 4: Alloy Steels: Low- to High-Carbon, Inclusive 834-1. Medium-Carbon Alloy Steels, Five Grades: Effect of Martensite Content 834-2. Medium-Carbon Alloy Steels, Six Grades: Hardness vs Endurance Limit 844-3. Medium-Carbon Alloy Steels: Effect of Specimen Orientation 854-4. 4027 Steel: Carburized vs Uncarburized 864-5. 4120 Steel: Effect of Surface Treatment in Hydrogen Environment 874-6. 4120 Steel: Effect of Surface Treatment in Hydrogen Environment 884-7. 4120 Steel: Effect of Various Surface Treatments on Fatigue Characteristics in Air

vs Hydrogen 894-8. 4130 Steel: Fatigue Crack Growth Rate vs Temperature in Hydrogen 904-9. 4135 and 4140 Steels: Cast vs Wrought 91

4-10. 4135 and 4140 Steels: Cast vs Wrought 924-11. 4140,4053 and 4063 Steels: Effect of Carbon Content and Hardness 934-12. 4140 Steel: Effect of Direction on Fatigue Crack Propagation 944-13. 4140 Steel: Effect of Cathodic Polarization 954-14. Cast 4330 Steel: Effects of Various Surface Conditions 964-15. 4340 Steel: Scatter of Fatigue Limit Data 974-16. 4340 Steel: Strength vs Fatigue Life 984-17. 4340 Steel: Total Strain vs Fatigue Life 994-18. 4340 Steel: Stress Amplitude vs Number of Reversals 1004-19. 4340 Steel: Effect of Periodic Overstrain 1014-20. 4340 Steel: Estimation of Constant Life 1024-21. 4340 Steel: Effect of Strength Level on Constant-Life Behavior 1034-22. 4340 Steel: Notched vs Unnotched Specimens 1044-23. 4340 Steel: Effect of Decarburization 1054-24. 4340H Steel: Effect of Inclusion Size 1064-25. 4340 Steel: Influence of Inclusion Size 1074-26. 4340 Steel: Effect of Hydrogenation; Static Fatigue 1084-27. 4340 Steel: Effect of Hydrogen 1094-28. 4340 Steel: Effect of Nitriding 1104-29. 4340 Steel: Effect of Nitriding and Shot Peening III4-30. 4340 Steel: Effect of Induction Hardening and Nitriding 1124-31. 4340 Steel: Effect of Surface Coatings 1134-32. 4340 Steel: Effect of Temperature on Constant-Lifetime Behavior 1144-33. 4520H Steel: Effect of Type of Quench 1154-34. 4520H Steel: Effect of Shot Peening 1164-35. 4620 Steel: Effect of Nitriding 1174-36. 4620 Steel: P/M-Forged 1184-37. 4620 Steel: P/M-Forged at Different Levels 119

Contents

4-38. 4625 Steel: P/M vs Ingot Forms 1204-39. 4640 Steel: P/M-Forged 1214-40. High-Carbon Steel (Eutectoid Carbon): Pearlite vs Spheroidite 1224-41. 52100 EF Steel: Surface Fatigue; Effect of Finish and Additives 1234-42. 52100 EF Steel: Surface Fatigue; Effect of Surface Finish and Speed 1244-43. 52100 EF Steel: Surface Fatigue; Effect of Lubricant Additives 1254-44. 52100 EF Steel: Surface Fatigue; Effect of Lubricant Viscosity, Slip Ratio and

Speed 1264-45. 52100 EF Steel: Rolling Ball Fatigue; Effect of Oil Additives 1274-46. 52100 Steel: Carburized vs Uncarburized 1284-47. 8620H Steel: Carburized; Results From Case and Core 1294-48. 8620H Steel: Effect of Variation in Carburizing Treatments 1304-49. 8620 Steel: Effect of Nitriding 1314-50. 8622 Steel: Effect of Grinding 1324-51. Cast 8630 Steel: Goodman Diagram for Bending Fatigue 1334-52. Cast 8630 Steel: Effect of Shrinkage 1344-53. Cast 8630 Steel: Effect of Shrinkage on Torsion Fatigue 1354-54. Cast 8630 Steel: Effect of Shrinkage on Torsion Fatigue 1364-55. Cast 8630 Steel: Effect of Shrinkage on Plate Bending 1374-56. Cast 8630 vs Wrought 8640 1384-57. 8630 and 8640 Steels: Effect of Notches on Cast and Wrought Specimens 1394-58. Nitralloy 135 Steel: Effect of Nitriding 1404-59. AMS 6475: Effects of Welding 1414-60. Medium-Carbon, ICr-Mo-V Steel Forging: Effect of Cycling Frequency 1424-61. EM 12 Steel: Effect of Temperature on Low-Cycle Fatigue 1434-62. Cast 0.5Cr-Mo-V Steel: Effects of Dwell Time in Elevated-Temperature

Testing 1444-63. Cast 0.5Cr-Mo-V Steel: Effect of Environment at 550C (1022 OF) 1454-64. Cast C-0.5Mo Steel: Effect of Temperature and Dwell Period on Cyclic Endurance

at Various Strain Amplitudes 146SECTION 5: HSLA Steels 147

5-1. HI-FORM 50 Steel vs 1006 1475-2. HI-FORM 50 Steel vs 1006: Stress Response 1485-3. HI-FORM 50 Steel Compared With 1006, DPI and DP2 1495-4. HSLA vs Mild Steel: Torsional Fatigue 1505-5. Proprietary HSLA Steel vs ASTM A440 1515-6. Comparison of HSLA Steel Grades BE, JF and KF for Plastic Strain Amplitude

vs Reversals to Failure 1525-7. Comparison of HSLA Steel Grades BE, JF and KF for Total Strain Amplitude

vs Reversals to Failure 1535-8. Comparison of a Dual-Phase HSLA Steel Grade With HI-FORM 50: Total Strain

Amplitude vs Reversals to Failure 1545-9. AISI 50 XF Steel: Effects of Cold Deformation 155

5-10. AISI 80 DF Steel: Effects of Cold Deformation 1565-11. Comparison of Three HSLA Steel Grades, Cb, Cb-V and Cb-V-Si: Strain Life

From Constant Amplitude 1575-12. Comparison of Stress Responses: DPI vs DP2 Dual-Phase HSLA Steels 1585-13. Dual-Phase HSLA Steel Grade: Stress Response for As-Received vs

Water-Quenched 1595-14. Dual-Phase HSLA Steel Grade: Stress Response for As-Received vs Gas-Jet-

Cooled 1605-15. S-N Comparison of Dual-Phase HSLA Steel Grades DPI and DP2 With

1006 1615-16. Comparison of Dual-Phase HSLA Steel DP2 With HI-FORM 50 1625-17. Comparison of Cyclic Strain Response Curves for Cb, Cb-V and Cb-V-Si Grades

of HSLA Steel 1635-18. Fatigue Crack Propagation Rate: Effect of Temperature for Two HSLA Steel

Grades 164

VII

172173

174

viii

5-19.

5-20.

5-21.5-22.5-23.5-24.

5-25.

5-26.5-27.5-28.

Contents

Effect of R-Ratio and Test Temperature on Crack Propagation of HSLA SteelGrade I 165

Effect of Test Temperature on Fatigue Crack Propagation Behavior for TwoHSLA Steel Grades 166

Stress-Cycle Curves for Weldments of Different HSLA Steel Grades 167Weldments (FCA W): SAE 980 X Steel vs 1006 168Weldments (TIG): DOMEX 640 XP Steel Welded Joints vs Parent Metal 169Weldments (FCAW Dressed by TIG): Fatigue Life Estimates Compared With

Experimental Data for SAE 980 X Steel 170SAE 980 X Steel Weldment (FCAW): Smooth Specimen vs TIG-Dressed vs

As-Welded 171SAE 980 X Steel Weldment (FCAW): Lap-Shear JointsMicroalloyed HSLA Steels: Properties of Fusion WeldsMicroalloyed HSLA Steels: Properties of Spot Welds

SECTION 6: High-Strength Alloy Steels 1766-1. HY-130 Steel: Effect of Notch Radii 1766-2. 300 M Steel: Effect of Notch Severity on Constant-Lifetime Behavior 1776-3. TRIP Steels Compared With Other High-Strength Grades 1786-4. Corrosion Fatigue: Special High-Strength Sucker-Rod Material 1796-5. Corrosion Fatigue Cracking of Sucker-Rod Material 1806-6. Hydrogenated Steel: Effect of Baking Time on Hydrogen Concentration 1816-7. Hydrogenated Steel: Effect of Notch Sharpness 182

SECTION 7: Heat-Resisting Steels 1837-1. 0.5%Mo Steel: Effect of Hold Time in Air and Vacuum at Different

Temperatures 1837-2. DIN 14 Steel (1.5 Cr, 0.90 Mo, 0.25 V): Effect of Liquid Nitriding 1847-3. 2.25Cr-1.0Mo Steel: Influence of Cyclic Strain Range on Endurance Limit in

Various Environments 1857-4. 2.25Cr-1.0Mo Steel: Effect of Elevated Temperature 1867-5. 2.25Cr-I.OMo Steel: Effect of Elevated Temperature and Strain Rate 1877-6. 2.25Cr-1.0Mo Steel: Effect of Temperature on Fatigue Crack Growth Rate 1887-7. 2.25Cr-1.0Mo Steel: Effect of Cyclic Frequency on Fatigue Crack Growth

Rate 1897-8. 2.25Cr-1.0Mo Steel: Fatigue Crack Growth Rates in Air and Hydrogen 1907-9. 2.25Cr-1.0Mo Steel: Effect of Holding Time 191

7-10. Cast 2.25Cr-1.0Mo Steel, Centrifugally Cast: Fatigue Properties at 540C(1000 OF) 192

7-11. HII Steel: Crack Growth Rate in Water and in Water Vapor 1937-12. 9.0Cr-1.0Mo Steel: Creep-Fatigue Characteristics 1947-13. 9.0Cr-1.0Mo Modified Steel: Stress Amplitudes Developed in Cycling 1957-14. 9.0Cr-1.0Mo Modified Steel: Effect of Deformation 196

SECTION 8: Stainless Steels 1978-1. Type 301 Stainless Steel: Scatter Band for Fatigue Crack Growth Rates 1978-2. Type 301 Stainless Steel: Effects of Temperature and Environment on Fatigue

Crack Growth Rate 1988-3. Type 304 Stainless Steel: Effect of Temperature on Frequency-Modified

Strains 1998-4. Type 304 Stainless Steel: Fatigue Crack Growth Rate-Annealed and Cold

Worked 2008-5. Type 304Stainless Steel: Effect of Humidity on Fatigue Crack Growth Rate 2018-6. Type 304 Stainless Steel: Effect of Aging on Fatigue Crack Growth Rate 2028-7. Type 304 Stainless Steel: Effect of Temperature on Fatigue Crack Growth

Rate 2038-8. Type 304 Stainless Steel: Damage Relation at 650C (1200 OF) 204

Contents

8-9. Type 304 Stainless Steel: Fatigue Crack Growth Rate at Room and SubzeroTemperatures 205

8-10. Types 304 and 304L Stainless Steel: Effect of Cryogenic Temperatures on FatigueCrack Growth Rate 206

8-11. Type 304 Stainless Steel: Fatigue Crack Growth Rate in Air With Variation inWaveforms 207

8-12. Type 304 Stainless Steel: Effect of Hold Time on Cycles to Failure 2088-13. Type 304 Stainless Steel: Effect of Hold Time and Continuous Cycling on Fatigue

Crack Growth Rates 2098-14. Type 304 Stainless Steel: Effect of Cyclic Frequency on Fatigue Crack Growth

Rate 2108-15. Type 304 Stainless Steel: Effect of Frequency on Fatigue Crack Growth

Behavior 2118-16. Type 304Stainless Steel Welded With Type 308:Fatigue Crack Growth Rates 2128-17. Types 304 and 310 Stainless Steel: Effect of Direction on S-N 2138-18. Types 304, 316, 321, and 348 Stainless Steel: Effects of Temperature on Fatigue

Crack Growth Rates 2148-19. Type 309S Stainless Steel: Effect of Grain Size on Fatigue Crack Growth

Rate 2158-20. Type 310S Stainless Steel: Effect of Temperature on Fatigue Crack Growth

Rate 2168-21. Type 316 Stainless Steel: Growth Rate of Fatigue Cracks in Weldments 2178-22. Type 316 Stainless Steel: Fatigue Crack Growth Rates-Aged vs Unaged 2188-23. Type 316 Stainless Steel: Fatigue Crack Growth Rates-Effect of Aging 2198-24. Type 316 Stainless Steel: Effect of Temperature on Fatigue Crack Growth

Rate 2208-25. Type 316 Stainless Steel: Effect of Cyclic Frequency on Fatigue Crack Growth

Rate 2218-26. Type 316 Stainless Steel: Fatigue Crack Growth Rate in the Annealed

Condition 2228-27. Type 316 Stainless Steel: Effect of Environment (Sodium, Helium, and Air) on

Cycles to Failure 2238-28. Types 316 and 321 Stainless Steel: Effects of Gaseous Environments on Fatigue

Crack Growth Rates 2248-29. Type 32I Stainless Steel: Effect of Hold Time on Fatigue Crack Growth Rates 2258-30. Type 403 Stainless Steel: Effect of Environment on Fatigue Crack Growth

Rate 2268-3I. Type 403 Modified Stainless Steel: Scatter of Fatigue Crack Growth Rates 2278-32. Type 422 Stainless Steel: Fatigue Crack Growth Rates in Precracked

Specimens 2288-33. Type 422 Stainless Steel: Fatigue Strength-Longitudinal vs Transverse 2298-34. Type 422 Stainless Steel: Effect of Temperature on Fatigue Strength 2308-35. Type 422 Stainless Steel: Effects of Delta Ferrite on Fatigue Strength 2318-36. 17-4PH Stainless Steel: Fatigue Crack Growth Rates in Airvs Salt Solution 2328-37. 15-5PH Stainless Steel: Fatigue Crack Growth Rates in Air vs Salt Solution 2338-38. PH 13-8 Mo Stainless Steel: Fatigue Crack Growth Rates at Room

Temperature 2348-39. PH 13-8 Mo Stainless Steel: Fatigue Crack Growth Rates in Air and Sump Tank

Water 2358-40. PH 13-8 Mo Stainless Steel: Fatigue Crack Growth Rates at Subzero

Temperatures 2368-41. PH 13-8 Mo Stainless Steel: Constant-Life Fatigue Diagram 2378-42. Types 600 and 329 Stainless Steel: S-NCurves for Two Processing Methods 2388-43. Grade 21-6-9 Stainless Steel: Effect of Temperature on Fatigue Crack Growth

Rates 2398-44. Kromarc 58Stainless Steel: Effect of Cryogenic Temperatures on Weldments 2408-45. Pyromet 538 Stainless Steel: Effects of Welding Methods on Fatigue Crack

Growth Rates 2418-46. Duplex Stainless Steel KCR 171: Corrosion Fatigue 242

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x Contents

SECTION 9: Maraging Steels 2439-1. Grades 200, 250, and 300 Maraging Steel: S-N Curves for Smooth and 'Notched

Specimens 2439-2. Grade 300 Maraging Steel: Fatigue Life in Terms of Total Strain 244

SECTION 10: Cast Irons 24510-1. Fatigue of Cast Irons as a Function of Structure-Sensitive Parameters 24510-2. Gray Iron: Fatigue Life, and Fatigue Limit as a Function of Temperature 24610-3. Gray Iron: S-N Curves for Unalloyed vs Alloyed 24710-4. Gray Iron: Effect of Environment 24810-5. Class 30 Gray Iron: Modified Goodman Diagram for Class 30 24910-6. Class 30 Gray Iron: Fatigue Crack Growth Rates for Class 30 25010-7. Gray Irons: Torsional Fatigue for Various Tensile Strength Values 25110-8. Gray Irons: Torsional Fatigue Data for Five Different Compositions 25210-9. Gray Irons: Thermal Fatigue-Effect of Aluminum Additions 253

10-10. Gray Irons: Thermal Fatigue-Effect of Chromium and MolybdenumAdditions 254

10-11. Gray Irons: Thermal Fatigue-Room Temperature and 540C (1000 OF) 25510-12. Gray Irons: Thermal Fatigue Properties-Comparisons With Ductile Cast Iron

and Carbon Steel 25610-13. Cast Irons: Thermal Fatigue Properties for Six Grades 25710-14. Ductile Iron: Effect of Microstructure on Endurance Ratio-Tensile Strength

Relationship 25810-15. Ductile Iron: Effect of Microstructure on Endurance Ratio-Tensile Strength

Relationship 25910-16. Ductile Iron: S-N Curves for Ferritic and Pearlitic Grades, Using V-Notched

Specimens 26010-17. Ductile Iron: S-N Curves for Ferritic and Pearlitic Grades, Using Unnotched

Specimens 26110-18. Ductile Iron: Fatigue Diagrams for Bending Stresses and Tension-Compression

Stresses 26210-19. Ductile Iron: Effect of Surface Conditions-As-Cast vs Polished Surface 26310-20. Ductile Iron: Fatigue Limit in Rotary Bending as Related to Hardness 26410-21. Ductile Iron: Effect of Rolling on Fatigue Characteristics 26510-22. Ductile Iron: Effect of Notches on a 65,800-psi-Tensile-Strength Grade 26610-23. Ductile Iron: Fatigue Crack Growth Rate Compared With That of

Steel 26710-24. Malleable Iron: S-N Curve Comparisons of Four Grades 26810-25. Pearlitic Malleable Iron: Effect of Surface Conditions on S-N Curves 26910-26. Pearlitic Malleable Iron: Effect of Nitriding 27010-27. Ferritic Malleable Iron: Effect of Notch Radius and Depth 271

SECTION 11: Heat-Resisting Alloys 272II-I. A286: Effect of Environment 27211-2. A286: Effect of Frequency on Life at 593C (1095 OF) 27311-3. A286: Fatigue Crack Growth Rates at Room and Elevated Temperatures 27411-4. Astroloy: S-N Curves for Powder vs Conventional Forgings 27511-5. Astroloy: Powder vs Conventional Forgings Tested at 705C (1300 OF) 27611-6. FSX-430: Effect of Grain Size on Cycles to Cracking 27711-7. FSX-430: Effect of Grain Size on Fatigue Crack Propagation Rate 27811-8. HS-31: Effect of Testing Temperature 27911-9. IN 738 LC Casting Alloy: Standard vs HIP'd Material 280

11-10. IN 738 LC: Effect of Grain Size on Cycles to Failure 281II-II. IN 738 LC: Effect of Grain Size on Cycles to Cracking 28211-12. IN 738 LC: Effect of Grain Size on Fatigue Crack Propagation Rate 28311-13. IN 738 LC: Fatigue Crack Growth Rate at 850C (1560 OF) 28411-14. Inconel 550: Axial Tensile Fatigue Properties in Air and Vacuum at 1090 K 285

Contents

11-15. Inconel625: Effect of Temperature on Cycles to Failure 286I 1-16. Inconel 706: Effect of Temperature on Fatigue Crack Growth Rate 28711-17. Inconel "7I3C": Effect of Elevated Temperatures on Fatigue Characteristics 288II-18. Inconel "7I3C" and As-Cast HS-31: Comparison of Two Alloys for Number of

Cycles in Thermal Fatigue to Initiate Cracks 28911-19. Inconel 718: Effect of Frequency on Fatigue Crack Propagation Rate 2901I-20. Inconel 718: Relationship of Fatigue Crack Propagation Rate With Stress

Intensity 29II1-21. Inconel 718: Relationship of Fatigue Crack Growth Rate With Load/Time Wave-

forms 2921I-22. Inconel 718: Fatigue Crack Growth Rate in Air vs Helium 29311-23. Inconel 718: Effect of Environment on Fatigue Crack Growth Rate 29411-24. Inconel 718: Fatigue Crack Growth Rate in Air Plus 5% Sulfur Dioxide 295I1-25. lnconel 7I8: Fatigue Crack Growth Rate in Air at Room Temperature 29611-26. Inconel 718: Fatigue Crack Growth Rate in Air at 316C (600 OF) 29711-27. Inconel 718: Fatigue Crack Growth Rate in Air at 427C (800 OF) 29811-28. Inconel 718: Fatigue Crack Growth Rate in Air at 538C (1000 OF) 299II-29. Inconel 718: Fatigue Crack Growth Rate in Air at 649C (1200 OF) 30011-30. Inconel 718: Fatigue Crack Growth Rates at Cryogenic Temperatures 3011I-31. Inconel 718 and X-750: Fatigue Crack Growth Rates at Cryogenic

Temperatures 302I1-32. Inconel X-750: Effect of Temperature on Fatigue Crack Growth Rates 303I1-33. Jethete M I52: Interrelationship of Tempering Treatment, Alloy Class, and Testing

Temperature With Fatigue Characteristics 30411-34. Lapelloy: Interrelationship of Hardness and Strength With Fatigue

Characteristics 30511-35. MAR-M200: Effect of Atmosphere on Cycles to Failure 30611-36. MAR-M509: Correlation of Initial Crack Propagation and Dendrite Arm

Spacing 30711-37. MAR-M509: Correlation Between Number of Cycles Required to Initiate a Crack

and Dendrite Arm Spacing 3081I-38. MERL 76, P/M: Axial Low-Cycle Fatigue Life of As-HIP'd Alloy at 540C

(1000 OF) 30911-39. Nickel-Base Alloys: Effect of Solidification Conditions on Cycles to Onset

of Cracking 31011-40. Rene 95 (As-HIP): Cyclic Crack Growth Behavior Under Continuous and Hold-

Time Conditions 3I I11-41. Rene 95: Effect of Temperature on Fatigue Crack Growth Rate 312I 1-42. S-8 I6: Effect of Notches on Cycles to Failure at 900C (1650 F) 31311-43. Udimet 700: Fatigue Crack Growth Rates at 850C (1560 OF) 31411-44. U-700 and MAR-M200: Comparison of Fatigue Properties 3151I-45. Waspaloy: Stress-Response Curves 316I1-46. X-40: Effect of Grain Size and Temperature on Fatigue Characteristics 31711-47. Cast Heat-Resisting Alloys: Ranking for Resistance to Thermal Fatigue 318

SECTION 12: Aluminum Alloys 31912-1. Corrosion-Fatigue Properties of Aluminum Alloys Compared With Those of

Other Alloys 31912-2. Comparisons of Aluminum Alloys With Magnesium and Steel: Tensile Strength

vs Endurance Limit 32012-3. Aluminum Alloys (General): Yield Strength vs Fatigue Strength 32112-4. Comparison of Aluminum Alloy Grades for Crack Propagation Rate 32212-5. Alloy 1100: Relationship of Fatigue Cycles and Hardness for HO and H14

Tempers 32312-6. Alloy 1100: Interrelationship of Fatigue Cycles, Acoustic Harmonic Generation

and Hardness 32412-7. Alloy 2014-T6: Notched vs Unnotched Specimens; Effect on Cycles to Failure 32512-8. Alloy 2024-T3: Effect of Air vs Vacuum Environments on Cycles to Failure 32612-9. Alloy 2024-T4 Alclad Sheet: Effect of Bending on Cycles to Failure 327

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12-13.12-14.

12-15.

12-16.12-17.12-18.

12-19.12-20.

12-21.

12-22.12-23.

12-24.

12-25.

12-26.12-27.

12-28.12-29.

12-30.

12-31.

12-32.

12-33.12-34.

12-35.12-36.

12-37.12-38.12-39.

12-40.12-41.12-42.12-43.12-44.

12-45.12-46.12-47.

12-48.12-49.

12-50.

Contents

Alloy 2024-T4: High-Cycle vs Low-Cycle Fatigue 328Alloy 2024-T4: Relationship of Stress and Fatigue Cycles 329Alloy 2024-T4: Dependence of the Average Rocking Curve Halfwidth 7J on Dis-

tance From the Surface 330Alloys 2024 and X2024: Effect of Alloy Purity on Cycles to Failure 331Alloys 2024 and 2124: Relationship of Particle Size and Fatigue

Characteristics 332Alloys 2024-T4 and 2124-T4: Comparison of Resistance to Fatigue Crack

Initiation 333Alloys 2024-TJ and 7075-T6: Summary of Fatigue Crack Growth Rates 334Alloys 2024-T4 and 7075-T6: Effect of Product Form and Notches 335Alloys 2024-T351 and 7075-T73XXX: Comparison of P / M Extrusions and

Rod 336Alloy 2048-T851: Longitudinal vs Transverse for Axial Fatigue 337Alloy 2048-T851: Notched vs Unnotched Specimens at Room and Elevated

Temperatures 338Alloy 2048-T851: Fatigue Crack Propagation Rates in LT and TL

Orientations 339Alloy 2048-T85I: Modified Goodman Diagram for Axial Fatigue 340Alloy 2219-T851: Dependence of Relaxation Behavior on the Cyclic Hardening

Parameter 341Alloy 2219-T851: Effect of Strain Amplitude on the Relaxation of ResidualSurface Stress With Fatigue 342Alloy 2219-T851: Relationship of Fatigue Cycles to Different Depth Distributions

of Surface Stress 343Alloy 2219-T851: Probability of Fatigue Failure 344Alloys 3003-0, 5154-H34 and 6061-T6: Effect of Alloy on Fatigue Characteristics

of Weldments 345Alloy 5083-0 Plate: Effect of Orientation on Fatigue Crack Growth Rates 346Alloy 5083-0 Plate: Effect of Temperature and Humidity on Fatigue Crack Growth

Rates 347Alloys 5086-H34, 5086-H36, 6061-T6, 7075-T73 and 2024-T3: Comparative

Resistance to Axial-Stress Fatigue 348Alloys 5083-0/5183: Fatigue Life Predictions and Experimental Data Results for

Double V-Butt Welds 349Alloys 5083-0/5183: Predicted Effect of Stress Relief and Stress Ratio on Fatigue

Life of Butt Welds 3507XXX Alloys: Cyclic Strain vs Crack Initiation Life 351Alloy 7050: Influence of Alloy Composition and Dispersoid Effect on Mean

Calculated Fatigue Life 352Alloy 7050: Effect of Grain Shape on Cycles to Failure 353Alloy 7075 (TMP, T6 and T651): Effect of Thermomechanical Processing on Cycles

to Failure 354Alloys 7075 and 7475: Effect of Inclusion Density on Cycles to Failure 355Alloy 7075: Effect of TMT on Cycles to Failure 356Alloys 7075 and 7050: Relative Ranking for Constant Amplitude and Periodic

Overload 357Alloy 7075: Effect of Environment and Mode of Loading 358Alloy 7075-T6: Effects of Corrosion and Pre-Corrosion 359Alloy 7075-T73: Effect of a 3.5% NaCl Environment on Cycles to Failure 360Alloy 7075: Effect of Cathodic Polarization on Fatigue Behavior 361Alloy 7075-T6: Effect of Surface Treatments and Notch Designs on Number of

Cycles to Failure 362Alloy 7075-T6: Effect of R-Ratio on Fatigue Crack Propagation 364Alloy 7075: Effect of Predeformation on Fatigue Crack Propagation Rates 365Alloys 7075 and 2024-T3: Comparative Fatigue Crack Growth Rates for Two

Alloys in Varying Humidity 366Alloy 7075-T65I: Fatigue Life as Related to Harmonic Generation 367Alloys 7075-T6 and 7475-T73: Effect of Laser-Shock Treatment on Fatigue

Properties 368Alloy 7075-T6: Effect of Laser-Shock Treatment on Hi-Lok Joints 369

Contents

12-51. Alloy 7075 (High Purity): Effect of Iron and Silicon on Cycles to Failure 37012-52. Alloy X-7075: Effect of Grain Size on Cycles to Failure 37112-53. Alloy X-7075: Effect of Grain Size on Stress-Life Behavior 37212-54. Alloy X-7075: Effect of Environment; Air vs Vacuum 37314-55. Alloy X-7075: Effect of Environment on Two Different Grain Sizes 37412-56. Alloy X-7075: Effect of Grain-Boundary Ledges on Cycles to Failure 37512-57. Alloys X-7075 and 7075: Effects of Chromium Inclusions on Fatigue Crack

Propagation 37612-58. Alloy 7475-T6: S-N Diagram for a Superplastic Fine-Grain Alloy 37712-59. Alloy 7475: Effect of Alignment of Grain Boundaries on Cycles to Failure 37812-60. Alloy 7475-T6: Superplastic vs Nonsuperplastic, as Related to Fatigue Crack

Growth 37912-61. Alloys X-7075 and 7075: Effect of Chromium-Containing Inclusions on Cycles to

Failure 38012-62. Aluminum Forging Alloys: Stress Amplitude vs Reversals to Failure 38112-63. AI-5Mg-0.5Ag: Effect of Condition on Fatigue Characteristics 38212-64. AI-Zn-Mg and AI-Zn-Mg-Zr: Effect of Grain Size on Strain-Life Behavior 38312-65. AI-Zn-Mg: Strain-Life Curves of a Large-Grained Alloy 38412-66. Aluminum With a Copper Overlay: Stress Amplitude vs Cycles to Failure 38512-67. P/M Alloys 7090 and 7091 vs Extruded 2024 38612-68. P / M Alloys 7090 and 709I vs 1/ M 7050 and 7075 Products 38712-69. P/M Aluminum Alloys: Typical Fatigue Behavior 38812-70. P / M Aluminum Alloys: Comparison With Specimens Made by Ingot

Metallurgy 38912-71. P/M Aluminum Alloys: Comparison With Forged 7175 for Cycles to

Failure 39012-72. Various Aluminum Alloys: Comparison of Grades for Corrosion-Fatigue Crack

Growth Rates; Air vs Salt Water 39112-73. Various Aluminum Alloys: Comparison of Grades for Corrosion-Fatigue Crack

Growth Rates in Salt Water 39212-74. Various Aluminum Alloys: Wrought vs Cast, and Influence of Casting Method on

Fatigue Life 39312-75. Aluminum Casting Alloy AL-195: Interrelationship of Fatigue Properties With

Degree of Porosity 39412-76. Aluminum Casting Alloy LM25-T6: Squeeze Formed vs Chill Cast; Effect on

Reversals to Failure 395

SECTION 13: Copper Alloys 39613-1. Copper: Effect of Air and Water Vapor on Cycles to Failure 39613-2. Copper: Applied Plastic-Strain Amplitude vs Fatigue Life 39713-3. Copper Alloy CI 1000 (ETP Wire): Effect of Temperature on Fatigue

Strength 39813-4. Copper Alloy C26000 (Cartridge Brass): Influence of Grain Size and Cold Work on

Cycles to Failure 39913-5. Copper Alloy C83600 (Leaded Red Brass): S-N Curves; Scatter Band 40013-6. Copper Alloy C86500 (Manganese Bronze): S-N Curves; Scatter Band 40113-7. Copper Alloys C87500 and C87800 (Silicon Brasses): S-N Curves; Scatter

Band 40213-8. Copper Alloy C92200 (Navy "M" Bronze): S-N Curves; Scatter Band 40313-9. Copper Alloy C93700 (High-Leaded Tin Bronze): S-NCurves; Scatter Band 404

13-10. Copper Alloy No. 192: Effect of Salt Spray on Tubes 40513-1 I. Copper Alloy 955: Goodman-Type Diagram 406

SECTION 14: Magnesium Alloys 40714-1. Magnesium Casting Alloy QE22A-T6: Effects of Notches and Testing

Temperature 40714-2. Magnesium Casting Alloy QH2 IA-T6: S-N Curves; Effects of Notches and Testing

Temperature 40814-3. Mg-AI-Zn Casting Alloys: Effects of Surface Conditions on Fatigue

Properties 409

xiii

xiv

SECTION 15: Molybdenum

Contents

41015-1. Molybdenum: Fatigue Limit Ratio vs Temperature 410

SECTION 16: Tin Alloys 41116-1. Tin-Lead Soldering Alloy: S-N Data for Soldered Joints 41116-2. Babbitt: Variation of Bearing Life With Babbitt Thickness 41216-3. SAEI2 Bearing Alloy: Effect of Temperature on Fatigue Life 413

SECTION 17: Titanium and Titanium Alloys 41417-1. Unalloyed Titanium, Grade 3: S-N Curves for Annealed vs Cold Rolled 41417-2. Unalloyed Titanium, Grade 4: S-N Curves for Three Testing

Temperatures 41517-3. Ti-24V and Ti-32V: Stress Amplitude vs Cycles to Failure 41617-4. Ti-5AI-2.5Sn: Effects of Notches and Types of Surface Finish 41717-5. Ti-5AI-2.5Sn and Ti-6AI-4V: Fatigue Crack Growth Rates 41817-6. Ti-6AI-6V-2Sn: Effects of Machining and Grinding 41917-7. Ti-6AI-6V-2Sn (HIP): S-N Curves for Titanium Alloy Powder Consolidated

by HIP 42017-8. Ti-6AI-6V-2Sn (HIP): S-N Curves for Annealed Plate vs HIP 42117-9. Ti-6AI-2Sn-4Zr-2Mo: Bar Chart Presentation on Effects of Machining and

Grinding 42217-10. Ti-6AI-2Sn-4Zr-2Mo: Constant-Life Fatigue Diagram 42317-11. Ti-6AI-2Sn-4Zr-6Mo: Low-Cycle Axial Fatigue Curves 42417-12. Ti-8Mo-2Fe-3AI: S-NCurves; 'Solution Treated and Aged Condition 42517-13. Ti-IOV-2Fe-3AI: S-N Curves; Notched vs Unnotched Specimens in Axial

Fatigue 42617-14. Ti-IOV-2Fe-3AI and Ti-6AI-4V: Comparison of Fatigue Crack Growth

Rates 42717-15. Ti-IOV-2Fe-3AI: S-N Curve; Notched Bar Fatigue Life for a Series of Forgings

Compared With Ti-6AI-4V Plate 42817-16. Ti-I3V-IICr-3AI: Constant-Life Fatigue Diagrams 42917-17. Ti-6AI-4V: Effect of Condition and Notches on Fatigue Characteristics 43017-18. Ti-6AI-4V: Effect of Direction on Endurance 43117-19. Ti-6AI-4V: Effect of Isothermally Rolled vs Extruded Material on Cycles to

Failure 43217-20. Ti-6AI-4V: Comparison of Wrought vs Isostatically Pressed Material for Cycles

to Failure 43317-21. Ti-6AI-4V: Effect of Fretting and Temperature on Cycles to Failure 43417-22. Ti-6AI-4V (Beta Rolled): Effect of Finishing Operations on Cycles to

Failure 43517-23. Ti-6AI-4V: Effect of Yield Strength on Stress-Life Behavior 43617-24. Ti-6AI-4V: Effect of Stress Relief on Cycles to Failure 43717-25. Ti-6AI-4V: Interrelationship of Machining Practice and Cutting Fluids on Cycles to

Failure 43817-26. Ti-6AI-4V: Relative Effects of Machining and Grinding Operations on Endurance

Limit 43917-27. Ti-6AI-4V: Effects of Various Metal Removal Operations on Endurance

Limit 44017-28. Ti-6AI-4V: Effect of Texture on Fatigue Strength 44117-29. Ti-6AI-4V: Effect of Complex Texture on Cycles to Failure 42217-30. Ti-6AI-4V: Effect of Texture and Environment on Cycles to Failure 44317-31. Ti-6AI-4V: Fatigue Crack Growth Rates 44417-32. Ti-6AI-4V: Fatigue Crack Growth Rates for ISR Tee, and Extrusions 44517-33. Ti-6AI-4V: Fatigue Crack Growth Rates 44617-34. Ti-6AI-4V: Effect of Final Cooling on Fatigue Crack Growth Rates 44717-35. Ti-6AI-4V: Effect of Dwell Time on Fatigue Crack Growth Rates 44817-36. Ti-6AI-4V: Fatigue Crack Growth Data 44917-37. Ti-6AI-4V P/ M: Comparison of HIP'd Material With Alpha-Beta Forgings for

Cycles to Failure 450

Contents

17-38. Ti-6AI-4V PIM: Comparisons of HIP'd Material With Annealed Plate for Cyclesto Failure 45 I

17-39. Ti-6AI-4V P/M: Effect of Powder Mesh Size on Fatigue Properties 45217-40. Ti-6AI-4V P/M: Comparison of Blended Elemental, Prealloyed and Wrought

Material for Effect on Cycles to Failure 45317-41. Ti-6AI-4V: P/M Compacts vs 11M Specimens: Cycles to Failure 45417-42. Ti-6AI-4V: Comparison of Specimens Processed by Various Fabrication Processes

for Cycles to Failure 45517-43. Ti-6AI-4V: Comparison of Fatigue Crack Growth Rate, PIM vs II M 45617-44. Ti-6AI-4V: Base Metal vs SSEB-Welded Material for Cycles to Failure 45717-45. Ti-6AI-4V: Base Metal vs SSEB-Welded Material for Cycles to Failure 45817-46. Ti-6AI-4V EB Weldments: Base Metal Compared With Flawless Weldments 45917-47. Ti-6AI-4V EB Weldments: Effects of Porosity on Cycles to Failure 46017-48. Ti-6AI-4V Gas Metal-Arc Weldments: Effects of Porosity on Cycles to

Failure 46117-49. Ti-6AI-4V: Unwelded vs Electron Beam Welded Material for Cycles to

Failure 46217-50. Ti-6AI-4V: S-N Diagram for Laser-Welded Sheet 46317-51. Ti-6AI-4V (Cast): S-N Diagram for Notched Specimens 464

SECTION 18: Zirconium 46518-1. Zirconium 702: Effects of Notches and Testing Temperature on Cycles to

Failure 465SECTION 19: Steel Castings 466

(For other data on steel castings see Sections 3,4 and 5, on carbon andalloy steels.)

19-1. Steel Castings (General): Effect of Design and Welding Practice on FatigueCharacteristics 466

19-2. Steel Castings (General): Effects of Discontinuities on FatigueCharacteristics 467

SECTION 20: Closed-Die Forgings 468(See also under specific grades of alloys.)

20-1. Closed-Die Steel Forgings: Effect of Surface Condition on Fatigue Limit 468SECTION 21: Powder Metallurgy Parts 469

(See also under specific alloys.)21-1. P/M: Relation of Density to Fatigue Limit and Fatigue Ratio 46921-2. PIM: Relation of Fatigue Limit to Tensile Strength for Sintered Steels 47021-3. PIM (Nickel Steels): As-Sintered vs Quenched and Tempered for Cycles to

Failure 4712I-4. PIM (Nickel Steels): Relation Between Fatigue Limit and Tensile Strength for

Sintered Steels 47221-5. P/M (Nickel Steels): Effect of Notches on Cycles to Failure for the As-Sintered

Condition 47321-6. PIM (Nickel Steels): Effect of Notches on Cycles to Failure for the Quenched and

Tempered Condition 47421-7. P/M (Low-Carbon, 1-5%Cu): Effects of Notches and Nitriding on Cycles to

Failure 4752 I-8. PIM (Sintered Iron, Low-Carbon, No Copper): Effect of Density and Nitriding on

Cycles to Failure 47621-9. P/M: Effect of Nitriding on Ductile Iron and Sintered Iron (3%Cu) for Cycles to

Failure 477SECTION 22: Composites 478

22-1. Brass/ Mild Steel Composite: Comparison of Brass-Clad Mild Steel With Brass andMild Steel for Cycles to Failure 478

22-2. Stainless Steell Mild Steel Composite: Comparison of Stainless-Clad Mild SteelWith Stainless Steel and Mild Steel for Cycles to Failure 479

xv

xvi Contents

SECTION 23: Effects of Surface Treatments 48023-1. Carbon and Alloy Steels (Seven Grades): Effects of Nitrocarburizing on Fatigue

Strength 48023-2. Carbon and Alloy Steels (Seven Grades): Effects of Tufftriding on Fatigue

Characteristics 48123-3. Carbon and Alloy Steels (Six Grades): Effects of Nitriding on Fatigue

Strength 48223-4. Carbon-Manganese Steel: Effects of Nickel Coating on Fatigue Strength 483

SECTION 24: Test Results for Component Parts 48424-1. Coil Springs, Music Wire (Six Sizes): Data Presented by Means of a Goodman

Diagram 48424-2. Coil Springs: S-N Data for Oil-Tempered and Music Wire Grades 48524-3. Coil Springs: Effects of Shot Peening on Cycles to Failure 48624-4. Coil Springs, 8650 and 8660 Steels: Relation of Design Stresses and Probability of

Failure 487 .24-5. Coil Springs, HSLA Steels: Effects of Corrosion on Cycles to Failure 48824-6. Leaf Springs, 5160 Steel: Maximum Applied Stress vs Cycles to Failure 48924-7. Front Suspension Torsion Bar Springs, 5160H Steel: Distribution of Fatigue

Results for Simulated Service Testing 49024-8. Gears, Carburized Low-Carbon Steel: Relation of Life Factor to Required

Life 49124-9. Gears, Carburized Low-Carbon Steel: Bending Stress vs Cycles to Failure 492

24-10. Gears, Carburized Low-Carbon Steel: Effect of Shot Peening on Cycles toFailure 493

24-11. Gears, Carburized Low-Carbon Steel: Probability-Stress-Life Design Curves 49424-12. Gears, 8620H Carburized: Bending or Contact Stress vs Cycles to Fracture or

Pitting 49524-13. Gears, 8620H Carburized: A Weibull Analysis of Bending Fatigue Data 49624-14. Gears, 8620H Carburized: T-N Curves for Six-Pinion, Four-Square Tests 49724-15. Hypoid Gears, 8620H Carburized: Minimum Confidence Level; Stress vs Cycles to

Rupture 49824-16. Hypoid, Zero I and Spiral Bevel Gears, 8620H Carburized: S-NScatter Band and

Minimum Confidence Level 49924-17. Spiral Bevel and Zero I Bevel Gears, 8620H Carburized: S-N Scatter Band and

Minimum Confidence Level 50024-18. Gears, 8620H Case Hardened: Relation of Life Factor to Cycles to Rupture 50124-19. Bevel Gears, Low-Carbon Steel Case Hardened: Relation of Life Factor to Cycles

to Rupture for Various Confidence Levels 50224-20. Gears, AMS 6265: S-N Data for Cut vs Forged 50324-21. Spur Gears, 8620H: S-N Data for Cut vs Forged 50424-22. Gears and Pinions: PIM 4600V vs 4615; Weibull Distributions 50524-23. Gears and Pinions: PIM Grades 4600V and 2000 vs 4615; Percent Failure vs

Time 50624-24. Gear Steel AMS 6265: Parent Metal vs Electron Beam Welded 50724-25. Gears, 42 CrMo4 (German Specification): S-N Curves for Various Profiles 50824-26. Gears, 42 CrMo4 (German Specification): Endurance Test Results in the Weibull

Distribution Diagram 50924-27. Bolts, 1040 and 4037 Steels: Maximum Bending Stress vs Number of Stress

Cycles 51024-28. Bolts: S-N Data for Roll Threading Before and After Heat Treatment 51124-29. Power Shafts, AMS 6382 and AMS 6260: Electron Beam Welded vs Silver Brazed

Joints 51224-30. Axle Shafts, 1046, 1541 and 50B54 Steels: S-N Data for Induction Hardening vs

Through Hardening 51324-31. Steel Rollers, 8620H Carburized: Effects of Carburizing Temperature and

Quenching Practice on Surface Fatigue 514

Contents

24-32. Steel Rollers, 8620H Carburized: Effects of Carburizing Temperature andQuenching Practice on Surface Fatigue 515

24-33. Linkage Arm, Cast Low-Carbon Steel: Starting Crack Size vs Cycles toFailure 516

24-34. Notched Links, Hot Rolled Low-Carbon Steel: S-N Data for Component TestModel 517

24-35. Fuselage Brace, Ti-6AI-6V-2Sn: Fatigue Endurance of HIP-ConsolidatedPowder 518

xvii

Fatigue Testing

1

IntroductionFatigue is the progressive, localized, perma-

nent structural change that occurs in materialssubjected to fluctuating stresses and strains thatmay result in cracks or fracture after a sufficientnumber of fluctuations. Fatigue fractures arecaused by the simultaneous action of cyclicstress, tensile stress and plastic strain. If anyoneof these three is not present, fatigue cracking willnot initiate and propagate. The cyclic stressstarts the crack; the tensile stress produces crackgrowth (propagation). Although compressivestress will not cause fatigue, compression loadmay do so.

The process of fatigue consists of three stages: Initial fatigue damage leading to crack nu-

cleation and crack initiation Progressive cyclic growth of a crack (crack

propagation) until the remaining un crackedcross section of a part becomes too weak tosustain the loads imposed

Final, sudden fracture of the remainingcross section

Fatigue cracking normally results from cyclicstresses that are well below the static yieldstrength of the material. (In low-cycle fatigue,however, or if the material has an appreciablework-hardening rate, the stresses also may beabove the static yield strength.)

Fatigue cracks initiate and propagate in re-gions where the strain is most severe. Becausemost engineering materials contain defects andthus regions of stress concentration that intensifystrain, most fatigue cracks initiate and growfrom structural defects. Under the action of cy-clic loading, a plastic zone (or region of deforma-tion) develops at the defect tip. This zone of highdeformation becomes an initiation site for a fa-tigue crack. The crack propagates under the ap-plied stress through the material until completefracture results. On the microscopic scale, themost important feature of the fatigue process isnucleation of one or more cracks under the influ-

ence of reversed stresses that exceed the flowstress, followed by development of cracks at per-sistent slip bands or at grain boundaries.

Prediction of Fatigue LifeThe fatigue life of any specimen or structure is

the number of stress (strain) cycles required tocause failure. This number is a function of manyvariables, including stress level, stress state, cy-clic wave form, fatigue environment, and themetallurgical condition of the material. Smallchanges in the specimen or test conditions cansignificantly affect fatigue behavior, making ana-lytical prediction of fatigue life difficult. There-fore, the designer may rely on experience withsimilar components in service rather than onlaboratory evaluation of mechanical test speci-mens. Laboratory tests, however, are essential inunderstanding fatigue behavior, and currentstudies with fracture mechanics test specimensare beginning to provide satisfactory designcriteria.

Laboratory fatigue tests can be classified ascrack initiation or crack propagation. In crackinitiation testing, specimens or parts are sub-jected to the number of stress cycles required fora fatigue crack to initiate and to subsequentlygrow large enough to produce failure.

Incrack propagation testing, fracture mechan-ics methods are used to determine the crackgrowth rates of preexisting cracks under cyclicloading. Fatigue crack propagation may becaused by cyclic stresses in a benign environ-ment, or by the combined effects of cyclic stressesand an aggressive environment (corrosion fa-tigue).

Fatigue Crack InitiationMost laboratory fatigue testing is done either

with axial loading, or in bending, thus producingonly tensile and compressive stresses. The stressusually is cycled either between a maximum anda minimum tensile stress, or between a maximumtensile stress and a maximum compressive stress.

2 Fatigue Testing

Number of cycles to fracture, N

Fig. 2 Typical S-N curves for constantamplitude and sinusoidal loading

150

125'iii.:.!.

100

Introduction 3

403020J.K. MPa\ m

10

10 103 105

Cycles to failure

Fig.3 Typical plot of strain range versuscycles-to-failure for low-cycle fatigue

10- 3Q)

10- 2 U>-~c::

10-4 is the ratio of thefatigue strength of a smooth (unnotched) speci-men to the fatigue strength of a notched speci-men at the same number of cycles.

Fatigue notch sensitivity, q, for a material isdetermined by comparing the fatigue notch fac-tor, KJ, and the stress-concentration factor, K"for a specimen of a given size containing a stressconcentrator of a given shape and size. A com-mon definition of fatigue notch sensitivity is q =(KJ - l)f(K, - 1), in which q may vary betweenzero (where KJ= 1) and 1 (where KJ= K,). Thisvalue may be stated as percentage.

Fatigue Crack PropagationIn large structural components, the existence

of a crack does not necessarily imply imminentfailure of the part. Significant structural life mayremain in the cyclic growth of the crack to a sizeat which a critical failure occurs. The objective offatigue crack propagation testing is to determinethe rates at which subcritical cracks grow undercyclic loadings prior to reaching a size critical forfracture.

The growth or extension of a fatigue crackunder cyclic loading is principally controlled bymaximum load and stress ratio. However, as incrack initiation, there are a number of additionalfactors that may exert a strong influence, includ-ing environment, frequency, temperature, andgrain direction. Fatigue crack propagation test-ing usually involves constant-load-amplitude cy-

LIVE GRAPHClick here to view

4 Fatigue Testing

Fatigue Crack InitiationCrack initiation tests are procedures in which

a specimen or part is subjected to cyclic loadingto failure. A large portion of the total number ofcycles in these tests is spent initiating the crack.Although crack initiation tests conducted onsmall specimens do not precisely establish the fa-tigue life of a large part, such tests do providedata on the intrinsic fatigue crack initiation be-havior of a metal or alloy. As a result, such datacan be utilized to develop criteria to prevent fa-tigue failures in engineering design. Examples ofthe use of small-specimen fatigue test data can befound in the basis of the fatigue design codes forboilers and pressure vessels, complex welded, riv-eted, or bolted structures, and automotive andaerospace components.

Fatigue CrackingFatigue cracks normally result from cyclic

stresses that are below the yield strength of themetal. In low-cycle fatigue, however, the cyclicstress may be above the static yield strength, es-pecially in a material with an appreciable work-hardening rate. Generally, a fatigue crack is in-itiated at a highly stressed region of a componentsubjected to cyclic loading of sufficient magni-tude. The crack then propagates in progressivecyclic growth through the cross section of thepart until the maximum load cannot be carried,and complete fracture results.

Crack Nucleation. A variety of crystallo-graphic features have been observed to nucleatefatigue cracks. In pure metals, tubular holes thatdevelop in persistent slip bands, slip band extru-sion-intrusion pairs at free surfaces, and twinboundaries are common nucleation sites. Grainboundaries in polycrystalline metals, even in theabsence of inherent grain boundary weakness,are crack nucleation sites. At high strain rates,this appears to be the preferred site. Nucleationat grain boundaries appears to be a geometricaleffect, whereas nucleation at twin boundaries isassociated with active slip on crystallographicplanes immediately adjacent and parallel to thetwin boundary.

The foregoing processes also occur in alloysand heterogeneous materials. However, alloyingand commercial production practices introducesegregation, inclusions, second-phase particles,and other features that disturb the structure. All

of these phenomena have a significant influenceon the crack nucleation process. In general, al-loying that (1) enhances cross slip, (2) enhancestwinning, or (3) increases the rate of work hard-ening will stimulate crack nucleation. On theother hand, alloying usually raises the flow stressof a metal, thus offsetting its potentially detri-mental effect on fatigue crack nucleation.

Crack Initiation. Fatigue cracks initiate atpoints of maximum local stress and minimumlocal strength. The local stress pattern is deter-mined by the shape of the part and by the typeand magnitude of the loading. In addition to thegeometric features of a part, features such as sur-face and metallurgical imperfections can act toconcentrate stress locally. Surface imperfectionssuch as scratches, dents, burrs, cuts, and othermanufacturing flaws are the most obvious sitesat which fatigue cracks initiate. Except for in-stances where internal defects or special surface-hardening treatments are involved, fatigue cracksinitiate at the surface.

Relation to Environment. Corrosion fatiguedescribes the degradation of the fatigue strengthof a metal by the initiation and growth of cracksunder the combined action of cyclic loading anda corrosive environment. Because it is a synergis-tic effect of fatigue and corrosion, corrosion fa-tigue can produce a far greater degradation instrength than either effect acting alone or by su-perposition of the singular effects. An unlimitednumber of gaseous and liquid mediums may af-fect fatigue crack initiation in a given material.Fretting corrosion, which occurs from relativemotion between joints, may also accelerate fa-tigue crack initiation.

Fatigue Testing RegimesThe magnitude of the nominal stress on a cy-

clically loaded component frequently is mea-sured by the amount of overstress-that is, theamount by which the nominal stress exceeds thefatigue limit or the long-life fatigue strength ofthe material used in the component. The numberof load cycles that a component under low over-stress can endure is high; thus, the term high-cycle fatigue is often applied.

As the magnitude of the nominal stress in-creases, initiation of multiple cracks is morelikely. Also, spacing between fatigue striations,which indicate the progressive growth of thecrack front, is increased, and the region of finalfast fracture is increased in size.

Fatigue Crack Initiation 5

Low-cycle fatigue is the regime characterizedby high overstress. The arbitrary, but commonlyaccepted, dividing line between high-cycle andlow-cycle fatigue is considered to be about 104 to105 cycles. In practice, this distinction is made bydetermining whether the dominant componentof the strain imposed during cyclic loading iselastic (high cycle) or plastic (low cycle), which inturn depends on the properties of the metal aswell as the magnitude of the nominal stress.

Presentation of Fatigue Data. High-cycle fa-tigue data are presented graphically as stress (S)versus cycles-to-failure (N) in S-N diagrams orS-N curves. These are described in the Introduc-tion to this Section along with the symbols andnomenclature commonly applied in fatigue test-ing. Because the stress in high-cycle fatigue testsis usually within the elastic range, the calculationof stress amplitude, stress range, or maximumstress on the S-axis is made using simple equa-tions from mechanics ofmaterials; i.e., stress cal-culated using the specimen dimensions and thecontrolled load or deflection applied axially, inflexure, or in torsion.

Figure 5 illustrates a stress-strain loop undercontrolled constant-strain cycling in a low-cyclefatigue test. During initial loading, the stress-strain curve is O-A-B. Upon unloading, yieldingbegins in compression at a lower stress C due to

Fig. 5 Stress-strain loop for constant-strain cycling

the Bauschinger effect. In reloading in tension, ahysteresis loop develops. The dimensions of thisloop are described by its width df (the totalstrain range) and its height da (the stress range).The total strain range df consists of an elasticstrain component dfe= dalE and a plastic straincomponent dfp

The width of the hysteresis loop depends onthe level of cyclic strain. When the level of cyclicstrain is small, the hysteresis loop becomes verynarrow. For tests conducted under constant df,the stress range da usually changes with an in-creasing number of cycles.

The common method of presenting low-cyclefatigue data is to plot either the plastic strainrange, df p' or the total strain range, df, versus N.When plotted using log-log coordinates, a straightline can befit to the dfp-Nplot. The slope of thisline in the region where plastic strain dominateshas shown little variation for the large number ofmetals and alloys tested in low-cycle fatigue, theaverage value being Y2. This power-law relation-ship between dfpand Nis known as the Coffin-Manson relationship. Figure 6 is an example ofthe typical presentation of low-cycle fatigue testresults.

Classification of FatigueTesting Machines

Fatigue test specimens are primarily describedby the mode of loading:

Direct (axial) stress Plane bending Rotating beam Alternating torsion Combined stressTesting machines, however, may be universal-

type machines that are capable of conducting allof the above modes ofloading, depending on thefixturing used.

Fatigue Testing Machine ComponentsWhether simple or complex, all fatigue testing

machines consist of the same basic components:a load train, controllers, and monitors. The loadtrain consists of the load frame, gripping devices,test specimen, and drive (loading) system. Typi-cal load train components in an electrohydraulicaxial fatigue machine are shown in Fig. 7.

The load frame is the structure of the machinethat reacts to the forces applied to the specimenby the drive system.

6 Fatigue Testing

Q.'""1

Fatigue Crack Initiation 7

{a} {bl {e} {dl lei Ifl (g)

(a) Standard grip body for wedge-type grips. (b) V-grips for rounds for use in standard grip body. (c) Flat grips forspecimens for use in standard grip body. (d)Universal open-front holders. (e)Adapters for special samples (screws,bolts, studs, etc.) for use with universal open-front holders. (f) Holders for threaded samples. (g)Snubber-type wiregrips for flexible wire or cable.

Fig. 8 Grip designs used for axial fatigue testing

Grips. Proper gripping is not simply the at-tachment of the test specimen in the load train.Grip failure sometimes occurs prior to specimenfailure. Frequently, satisfactory gripping evolvesafter specimen design development. Care mustbe taken in grip design and specimen installationin the grips to prevent misalignment. The gripsshown in Fig. 8 are typical of those used for axialfatigue tests.

Axial (Direct-Stress)Fatigue Testing Machines

The direct-stress fatigue testing machine sub-jects a test specimen to a uniform stress or strainthrough its cross section. For the same cross sec-tion, an axial fatigue testing machine must beable to apply a greater force than a static bendingmachine to achieve the same stress.

Electromechanical systems have been devel-oped for axial fatigue studies. Generally, theseare open-loop systems, but often have partialclosed-loop features to continuously correctmean load.

In crank and lever machines, a cyclic load isapplied to one end of the test specimen through adeflection-calibrated lever that is driven by avariable-throw crank. The load is transmitted tothe specimen through a flexure system, whichprovides straight-line motion to the specimen.The other end of the specimen is connected to ahydraulic piston that is part of an electrohydraul-ically controlled load-maintaining system thatsenses specimen yielding. This system automati-cally and steplessly restores the preset loadthrough the hydraulic piston.

Servohydraulic closed-loop systems offer op-timum control, monitoring, and versatility in fa-tigue testing systems. These can be obtained as

component systems and can be upgraded as re-quired. A hydraulic actuator typically is used toapply the load in axial fatigue testing.

Electromagnetic or magnetostrictive excita-tion is used for axial fatigue testing machinedrive systems, particularly when low-load ampli-tudes and high-cycle fatigue lives are desired inshort test durations. The high cyclicfrequency ofoperation of these types of machines enables test-ing to long fatigue lives (>108 cycles) withinweeks.

Bending Fatigue MachinesThe most common types of fatigue machines

are small bending fatigue machines, In general,these simple, inexpensive systems allow labora-tories to conduct extensive test programs with alow equipment investment.

Cantilever beam machines, in which the testspecimen has a tapered width, thickness, or di-ameter, result in a portion ofthe test area havinguniform stress with smaller load requirementsthan required for uniform bending or axial fa-tigue of the same section size.

Rotating Beam Machines. Typical rotatingbeam machine types are shown in Fig. 9. TheR.R. Moore-type machines (Fig. 9a) can operateup to 10000 rpm. In all bending-type tests, onlythe material near the surface is subjected to themaximum stress; therefore, in a small-diameterspecimen, only a very small volume of material isunder test.

Torsional Fatigue Testing MachinesTorsional fatigue tests can be performed on

axial-type machines using the proper fixtures ifthe maximum twist required is small. Specially

8 Fatigue Testing

~Load

A

(a) (b)

(a) Four-point loading R.R. Moore testing machine. (b) Single-end rotating cantilever testing machine.Fig. 9 Schematic of rotating beam fatigue testing machines

Program

Specimen

.,.,C:::}:;;:;;;:;;;:;:l:::;~~,.Rota ry actu ato r

----- Torque feedback -----IIIIII

Displacementtransducer

L----IAngular Idisplay feedback ...-----i----r--....,

Hydraulicservice

manifold

Hydraulicpowersupply

Fig. 10 Schematic of a servohydraulic torsional fatigue testing machine

designed torsional fatigue testing machines con-sist of electromechanical machines, in which lin-ear motion is changed to rotational motion bythe use of cranks, and servo hydraulic machines,in which rotary actuators are incorporated in aclosed-loop testing system (Fig. 10).Special-Purpose FatigueTesting Machines

To perform fatigue testing of components thatare prone to fatigue failure (gears, bearings, wire,etc.), special devices have been used, sometimesas modifications to an existing fatigue machine.Wire testers are a modification of rotating beammachines, in which a length of the test wire is

used as the beam and is deflected (buckled) aknown amount and rotated.

Rolling contact fatigue testers usually areconstant-load machines in which a Hertzian con-tact stress between two rotating bearings is ap-plied until occurrence of fatigue failure by pittingor spalling is indicated by a vibration or noiselevel in the system. Rolling contact fatigue of balland roller bearings under controlled lubricationconditions is a specialized field of fatigue testing.

Multiaxial Fatigue Testing MachinesMany special fatigue testing machines have

been designed to apply two or more modes ofloading, in or out of phase, to specimens to de-

Fatigue Crack Initiation 9

termine the properties of metals under biaxial ortriaxial stresses.

Fatigue Test SpecimensA typical fatigue test specimen has three areas:

the test section and the two grip ends. The gripends are designed to transfer load from the testmachine grips to the test section and may beidentical, particularly for axial fatigue tests. Thetransition from the grip ends to the test area isdesigned with large, smoothly blended radii toeliminate any stress concentrations in the tran-sition.

The design and type of specimen used dependon the fatigue testing machine used and the ob-jective of the fatigue study. The test section in thespecimen is reduced in cross section to preventfailure in the grip ends and should be propor-tioned to use the upper ranges of the load capac-ity ofthe fatigue machine; i.e., avoiding very lowload amplitudes where sensitivity and responseof the system are decreased. Several types of fa-tigue test specimens are illustrated in Fig. 11.

Effect of Stress ConcentrationFatigue strength is reduced significantly by the

introduction of a stress raiser such as a notch orhole. Because actual machine elements invari-ably contain stress raisers such as fillets, key-ways, screw threads, press fits, and holes, fatiguecracks in structural parts usually initiate at suchgeometrical irregularities.

An optimum way of minimizing fatigue failureis the reduction of avoidable stress raisersthrough careful design and the prevention of ac-cidental stress raisers by careful machining andfabrication. Stress concentration can also arisefrom surface roughness and metallurgical stressraisers such as porosity, inclusions, local over-heating in grinding, and decarburization.

The effect of stress raisers on fatigue is gener-ally studied by testing specimens containing anotch, usually a V-notch or a U-notch. The pres-ence ofa notch in a specimen under uniaxial loadintroduces three effects: (1) there is an increase orconcentration of stress at the root of the notch,(2) a stress gradient is set up from the root of thenotch toward the center of the specimen, and (3)a triaxial state of stress is produced at the notchroot.

The ratio of the maximum stress in the regionof the notch (or other stress concentration) to thecorresponding nominal stress is the stress-con-

D

( ~=====-t-$4.8 mm (3116 in.) ~ RD, selected on basis of ultimate strengthof material R, 12.7 mm (0.50 in.)

(a)

30 mm (13/16 in.)"] k 50 ~m_1-$-O~2m.) :cDTapered D, 12.7 mm (0.50 in.)

Ib)

I'" 90 mm (3:6i~ 19 mml(% in.)

~~--R~ ~ '\ I12 mm (0.48 in.)

D, 5 to 10 mm (0.20 to 0.40 in.) selected onbasis of ultimate strength of materialR, 90 to 250 mm (3.5 to 10 in.)

[c]

.25 mm (1.0 in.) D 38 mm (1V2 in.)

~---~ ~3--~ . ~ 5"43'38 mm (1'12 in.)

(d)

D, selected on basis of ultimate strength of materialR, 75 to 250 mm (3 to 10 in.)

Ie)(a)Torsional specimen. (bl Rotating cantilever beam spec-imen. (c) Rotating beam specimen. (d) Plate specimen forcantilever reverse bending. Ie) Axial loading specimen.

Fig. 11 Typical fatigue test specimens

10 Fatigue Testing

Effect of Mean Stress

Table 1 Effect of specimen size on the fatiguelimit of normalized plain carbon steel inreversed bending

A series of fatigue tests can be conducted atvarious mean stresses, and the results can beplotted as a series of S-N curves. A description ofapplied stresses and S-N curves can be found inthe Introduction to this Section. For design pur-poses, it is more useful to know how the meanstress affects the permissible alternating stressamplitude for a given life (number of cycles).This usually is accomplished by plotting the al-lowable stress amplitude for a specific number ofcycles as a function of the associated mean stress.

At zero mean stress, the allowable stress am-plitude is the effective fatigue limit for a specifiednumber of cycles. As the mean stress increases,the permissible amplitudes steadily decrease. Ata mean stress equal to the ultimate tensilestrength of the material, the permissible ampli-tude is zero.

The two straight lines and the curve shown in

Surface Effects and FatigueGenerally, fatigue properties are very sensitive

to surface conditions. Except in special caseswhere internal defects or case hardening is in-volved, all fatigue cracks initiate at the surface.Factors that affect the surface of a fatigue speci-men can be divided into three categories: (1) sur-face roughness or stress raisers at the surface, (2)changes in the properties of the surface metal,and (3) changes in the residual stress condition ofthe surface. Additionally, the surface may besubjected to oxidation and corrosion.

Surface Roughness. In general, fatigue life in-creases as the magnitude of surface roughnessdecreases. Decreasing surface roughness mini-mizes local stress raisers. Therefore, special at-tention must be given to the surface preparationof fatigue test specimens. Typically, a metallo-graphic finish, free of machining grooves andgrinding scratches, is necessary. Figure 12 illus-trates the effects that various surface conditionshave on the fatigue properties of steel.

362921

Fatigue limitMPa ksi

0.30 248l.50 2006.00 144

Specimen diametermm in.

7.638152

cent ration factor, K,(see the Introduction to thisSection). In some situations, values of K,can becalculated using the theory of elasticity, or can bemeasured using photoelastic plastic models.

The effect of notches on fatigue strength is de-termined by comparing the S-N curves of notchedand unnotched specimens. The data for notchedspecimens usually are plotted in terms of nomi-nal stress based on the net cross section of thespecimen. The effectiveness of the notch in de-creasing the fatigue limit is expressed by thefatigue-notch factor, Kp This factor is the ratioof the fatigue limit of unnotched specimens to thefatigue limit of notched specimens.

For materials that do not exhibit a fatiguelimit, the fatigue-notch factor is based on the fa-tigue strength at a specified number of cycles.Values of KJhave been found to vary with (1)severity of the notch, (2) type of notch, (3) mate-rial, (4) type of loading, and (5) stress level.

Effect of Test Specimen SizeIt is not possible to predict directly the fatigue

performance oflarge machine members from theresults oflaboratory tests on small specimens. Inmost cases, a size effect exists; i.e., the fatiguestrength of large members is lower than that ofsmall specimens. Precise determination of thisphenomenon is difficult. It is extremely difficultto prepare geometrically similar specimens of in-creasing diameter that have the same metallurgi-cal structure and residual stress distributionthroughout the cross section. The problems in fa-tigue testing of large specimens are considerable,and few fatigue machines can accommodatespecimens with a wide range of cross sections.

Changing the size of a fatigue specimen usu-ally results in variations oftwo factors. First, in-creasing the diameter increases the volume orsurface area of the specimen. The change inamount of surface is significant, because fatiguefailures usually initiate at the surface. Secondly,for plain or notched specimens loaded in bendingor torsion, an increase in diameter usually de-creases the stress gradient across the diameterand increases the volume of material that ishighly stressed.

Experimental data on the size effect in fatiguetypically show that the fatigue limit decreaseswith increasing specimen diameter. Horger'sdata for steel shafts tested in reversed bending(Table 1) show that the fatigue limit can be ap-preciably reduced in large section sizes.

Fatigue Crack Initiation 11

30200 I----t----+---+---+-----+---+---+--~.,___f-----~

1000 ,...---,....----,----r---,-------r-----r------,-----,...-----,

900~~;;::~~;;;;t;;~==~===~~=~===t===~==~800ra..ro 700 100 'iii

90 -""~ 600 ~--_t_---~2.......,_1_--~~=_---="""" .......=_-_+--_1_----_t_-__l vi~ W ~~ 500 70 U;

~ ~~ 60 ~~ 400 Q)

~ >> 50 ~~ >

Qi~ 300 t-----t-----t---+----+----+--"""""~--~""""""----+--___I 40 Qj~ ~~ EE 0o uu

2 5 10 20 50 100 200 500Life, 1000 cycles

Fig. 12 Effect of surface conditions on the fatigue properties of steel (302 to 321 HB)

Tensilestrength, Su

Fig. 13 represent the three most widely used em-pirical relationships for describing the effect ofmean stress on fatigue strength. The straight linejoining the alternating fatigue strength to thetensile strength is the modified Goodman law.Goodman's original law included the assump-tion that the fatigue limit was equal to one thirdof the tensile strength; this has since been gener-alized to the relation shown in Fig. 13, using thefatigue strength as determined experimentally.

Stress Amplitude. Because stress amplitudevaries widely under actual loading conditions, itis necessary to predict fatigue life under variousstress amplitudes. The most widely used methodof estimating fatigue under complex loading isprovided by the linear damage law. This is a hy-pothesis first suggested by Palmgren and re-stated by Miner, and is sometimes known asMiner's rule.

The assumption is made that the applicationof n.cycles at a stress amplitude S;, for which theaverage number of cycles to failure is N;, causesan amount of fatigue damage that is measured bythe cumulative cycles ratio n;/N;, and that fail-ure will occur when "'i.(n;/ N;) = 1.

This method is not applicable in all cases, andnumerous alternative theories of cumulative lin-ear damage have been suggested. Some consid-erations of redistribution of stresses have beenclarified, but there is as yet no satisfactory ap-proach for all situations.

Fatigue strength, S

CI)" / Gerber's parabola

vi /~ Modified Goodman line~OJC

Mean stress, SmAs shown by the modified Goodman line. Gerber's parab-ola. and Soderberg line. See text for discussion.

Fig. 13 Effect of mean stress on the al-ternating stress amplitude

The effect of varying the stress amplitude (lin-ear damage) can be evaluated experimentally bymeans of a test in which a given number of stresscycles are applied to a test piece at one stress am-plitude. The test is then continued to fracture at adifferent amplitude. Alternatively, the stress canbe changed from one stress amplitude to anotherat regular intervals; such tests are known asblock, or interval, tests. These tests do not simu-late service conditions, but may serve a usefulpurpose for assessing the linear damage law andindicating its limitations.

12 Fatigue Testing

Stress-intensity factor range UK). ksi\. fil.Corrosion Fatigue10 20 50 100

Suess-tntensnv teeter range UK), MPa \ m

where C and n are constants for a given materialand stress ratio.

30 40 50 60 80 100208 10

, qII

a ~~] 6~

i .9'r;~Region 1: I ~~o Islow crack I I

I- growth Ida ~ C(~KlnI~ 1. dN

i dO Region 3: I:

rapid r--W unstablet---- sx; crack I

I Ie? '0 growlh ! r--5 II if II'I Region 2: power-taw behavior 1

6 I,c

1;1I,j>I

I

Yield strength of 470 MPa (70 ksi). Test conditions: R =0.10; ambient room air, 24C (75 OF).

Fig. 14 Fatigue crack growth behaviorof ASTM A533 B1 steel

data on five specimens of ASTM A533 HI steeltested at 24 0 C (75 0 F). A plot of similar shape isanticipated with most structural alloys; the abso-lute values of da/dNand I:!..K, however, are de-pendent on the material.

Results of fatigue crack growth rate tests fornearly all metallic structural materials haveshown that the da/ dN versus I:!..K curves havethree distinct regions. The behavior in Region I(Fig. 14)exhibits a fatigue crack growth thresh-old, I:!..K"" which corresponds to the stress-intensity factor range below which cracks do notpropagate.

At intermediate values of I:!..K (Region II inFig. 14), a straight line usually is obtained on alog-log plot of I:!..K versus da/ dN. This is de-scribed by the power-law relationship:

dadN = C(I:!..K)"

Corrosion fatigue is the combined action ofrepeated or fluctuating stress and a corrosive en-vironment to produce progressive cracking. Us-ually, environmental effects are deleterious to fa-tigue life, producing cracks in fewer cycles thanwould be required in a more inert environment.Once fatigue cracks have formed, the corrosiveaspect also may accelerate the rate of crackgrowth.

In corrosion fatigue, the magnitude of cyclicstress and the number of times it is applied arenot the only critical loading parameters. Time-dependent environmental effects also are ofprime importance. When failure occurs by cor-rosion fatigue, stress-cycle frequency, stress-wave shape, and stress ratio all affect the crack-ing processes.

Fatigue failure of structural and equipmentcomponents due to cyclic loading has long been amajor design problem and the subject ofnumer-ous investigations. Although considerable fa-tigue data are available; the majority has beenconcerned with the nominal stress required tocause failure in a given number of cycles-namely, S-N curves. Usually, such data are ob-tained by testing smooth or notched specimens.With this type of testing, however, it is difficult todistinguish between fatigue crack initiation lifeand fatigue crack propagation life.

Preexisting flaws or crack-like defects within amaterial reduce or may eliminate the crack initia-tion portion of the fatigue life of the component.Fracture mechanics methodology enhances theunderstanding of the initiation and propagationof fatigue cracks and assists in solving the prob-lem of designing to prevent fatigue failures.

Fatigue CrackPropagation

Fatigue CrackPropagation Test Methods

The general nature of fatigue crack propaga-tion using fracture mechanics techniques issummarized in Fig. 14. A logarithmic plot of thecrack growth per cycle, da/ dN, versus the stress-intensity factor range, I:!..K, corresponding to theload cycle applied to a specimen is illustrated.The da/ dN versus I:!..K plot was constructed of

Fatigue Crack Propagation 13

50 100 20010 205

10- 2o 12 Ni steelo 10 Ni steel

Ql HY-80 steel Ql"0

HY-130 steel 10- 4 "0> >~ ~E c::E 10- 3......:

14 Fatigue Testing

6.a~ 0.04 Wfor 0.25 ~!!.- ~ 0.40W

6.a~ 0.02 W for 0.40 ~ !!.-~ 0.60W

a6.a~ 0.01 Wfor -;;::: 0.60W

For center-cracked tension specimens:

6.a~ 0.03 Wfor 2a < 0.60W

6.a~ 0.02 W for~> 0.60W

Fatigue crack growth rate data can be calcu-lated by several methods. The most commonlyused methods, however, are the secant and in-cremental polynomial methods. The secant meth-od consists of the slope of the straight line con-necting two adjacent data points. This method,although simpler, results in more scatter in mea-sured crack growth rate.

The incremental polynomial method fits asecon~-order ,Polynomial expression (parabola)to typically five to seven adjacent data points,and the slope of this expression is the growthrate. The incremental polynomial method elimi-nates some of the scatter in growth rate that isinherent in fatigue testing.

Numerous relationships have been generatedto correlate crack growth rate and stress-intensitydata. The most widely accepted relationship isthat proposed by Paris. This is a linear relation-ship when plotted on log-log coordinates andgenerally yields a reasonable fit to the data inRegion II (see Fig. 14) of the crack growthregime.

Other relationships based on the Paris equa-tion, such as the commonly used Forman equa-tl?n, are used to represent the variation of da/ dNwith other key variables, including load ratio, Rand the critical K value, K" at which rapid frac~ture of the specimen occurs (Region III in Fig.14). The Forman equation is:

da = C(6.K)"dN (1 - R)(K,. - 6.K)

where Cand n are material constants of the sametypes as those in the Paris equation, but of differ-ent values. An advantage of the Forman equa-tion is that it describes the type of acceleratedda/dNbehavior that is often observed at highvalues of 6.K, which is not described by the Parisequation.

Additionally, the Forman equation describesthe frequently observed increase in da/ dN asso-

! II

Two holes W/3 diam

! I !I

-rW

~----+-----J_l

2an i.sthe machined notch; a is the crack length; B is thespecimen thickness.

Fig. 16 Standard center-cracked ten-sion specimen for fatigue crack propaga-tion testing when the width (WI of thespecimen ';;;;75 mm (3 in.)

R= 0.1 is commonly used for developing data forcomparative purposes.

Testing often is performed in laboratory air atroom temperature; however, any gaseous or liq-uid environment and temperature of interestmay be used to determine the effect of tempera-ture, corrosion, or other chemical reaction oncyclic loading.

Data Analysis. For constant-amplitude load-ing, a set of crack-length versus elapsed-cycledata (a versus N) is generated, with the specimenloading, Pmax and Pmin' generally held constant.Figure 18illustrates a typical a versus N plot. Theminimum crack-length interval, 6.a, betweendata points (see Fig. 18)should be 0.25 mm (0.01in.) or ten times the crack-length measurementprecision, which is defined as the standard devia-tion on the mean value of crack length deter-mined for a set of replicate measurements. Thisprevents the measurement of erroneous growthrates from a group of data points that are spacedtoo closely relative to the precision of data mea-surement and relative to the scatter of data.

Crack measurement intervals are recom-mended in ASTM E 647 according to specimentype. For compact-type specimens:

Fatigue Crack Propagation 15

Two holes0.25Wdiam

r0.6W

1t

0.275W

tt

0.275W

t r0.6W~~_1_

1+--- a----;~Allowable thickness: W/20 s B s W/4Minimum dimensions: W = 25 mm (1.0 in.)

an = 0.20W)(1-+------w-------;~I

~------1.25W-------:;~I

Fig. 17 Standard compact-type specimen for fatigue crack propagation testing (see Fig.16 for explanation of symbols)

2.2

2.0

1.8 C

1.6 or the effect of R on da / dN, theForman equation can be used to represent theda/dNbehavior. When only ~Kin Region II isinvolved, the less complex Paris equation may beused.

16 Fatigue Testing

Short cracks that becomenon propagating cracks

Short cracksthat join longcrack behaviorq/;/"// / \

/ Short cracks that behave\', / as long cracks\ ./\---\\

Stress-intensity factor range

Fig. 19 Typical short crack behavior

sity expressions are valid only over a range of theratio of crack length to specimen width (a/W).For example, the expression given in Table 2 forthe compact-type specimen is valid for a / W >0.2; the expression for the center-cracked tensionspecimen is valid for 2a/W< 0.95. The use ofstress-intensity expressions outside their appli-cable crack-length region can produce signifi-cant errors in data.

The size of the specimen must also be appro-priate. To follow the rules of linear elastic frac-ture mechanics, the specimen must be predomi-nantly elastic. However, unlike the requirementsfor plane-strain fracture toughness testing, thestresses at the crack tip do not have to be main-tained in a plane-strain state. The stress state isconsidered to be a controlled test variable. Thematerial characteristics, specimen size, cracklength, and applied load will dictate whether thespecimen is predominantly elastic. Because theloading mode of different specimens varies sig-nificantly, each specimen geometry must be con-sidered separately.

Notch Preparation. The method by which anotch is machined depends on the specimen

Recently, it has been well documented thatshort cracks may behave differently from largecracks when plotted in the standard form of cy-clic crack growth rate versus stress intensity.

A short crack is difficult to define. It may besmall compared to the microstructure of thematerial to be studied (I to 50 /.Lm) when the con-cepts of continuum mechanics are of interest. Itcan also be small compared to the plastic zonesize (10 to 1000 /.Lm). In this situation, linear elas-tic fracture mechanics might be replaced withelastic-plastic fracture mechanics. The crackmay also be physically small (500 to 1000 /.Lm)when crack closure, crack tip shape, environ-ment, and growth mechanisms are of concern.Figure 19 schematically illustrates the possiblebehavior of short cracks.

The most accurate definition would be the stress-intensity value below which fatigue crack growthwill not occur. It is extremely expensive to obtaina true definition of IJ.K,h, and in some materials atrue threshold may be nonexistent. Generally,designers are more interested in the near-thresh-old regime, such as the IJ.Kthat corres~onds to afatigue crack growth rate of 10-8 to 10- 0 tn] cycle(3.9 X 10-7 to 10-9 in.j cycle). Because the dura-tion of the tests increases greatly for each addi-tional decade of near-threshold data (10-8 to 10-9to 10-10, etc., m/cycle), the precise design re-quirements should be determined in advance ofthe test.

Selection of Test SpecimensSelection of a fatigue crack growth test speci-

men is usually based on the availability of thematerial and the types of test systems and crack-monitoring devices to be used. The two mostwidely used types of specimens are the center-cracked tension specimen and the compact-typespecimen (see Fig. 16 and 17). However, anyspecimen configuration with a known stress-intensity factor solution can be used in fatiguecrack growth testing, assuming that the appro-priate equipment is available for controlling thetest and measuring the crack dimensions. Stress-intensity factor solutions for center-cracked ten-sion and compact-type specimens are given inTable 2.

Consideration of the range of application ofthe stress-intensity solution of a specimen con-figuration is very important. Many stress-inten-

Behavior of Short Cracks

Fatigue Crack Propagation

Table 2 Stress-intensity factor solutions for standardized (ASTM E 647)fatigue crack growth specimen geometriesCenter-cracked tension specimens (Fig. 16)

sr ~ traI:!.K= Ii V 2Wsec2

2a . 1'" 2awhere a = -; expression va id 10r-< 0.95W W

Compact-type specimens (Fig. 17)_ I:!.P(2 + a) 2 3 4

I:!.K - ru; 3/2 (0.886 +4.64a - 13.32a + 14.Tl - 5.6a )By W(l-a)

a . li f awhere a = -; expression va Id or- 0.2W W

17

material and the desired notch root radius (p).Sawcutting is the easiest method, but is generallyacceptable only for aluminum alloys. For anotch root radius of p ~ 0.25 mm (0.010 in.) inaluminum alloys, milling or broaching is re-quired. A similar notch root radius in low- andmedium-strength steels can be produced bygrinding. For high-strength steel alloys, nickel-base superalloys, and titanium alloys, electricaldischarge machining may be necessary to pro-duce a notch root radius of p ~ 0.25 mm (0.010in.).

Precracking of a specimen prior to testing isconducted at stress intensities sufficient to causea crack to initiate from the starter notch andpropagate to a length that will eliminate the ef-fect of the notch. To decrease the amount of timeneeded for precracking to occur, common prac-tice is to initiate the pre cracking at a load abovethat which will be used during testing and to sub-sequently reduce the load.

Load generally is reduced uniformly to avoidtransient effects. Crack growth can be arrestedabove the threshold stress-intensity value due toformation of the increased plastic zone ahead ofthe tip of the advancing crack. Therefore, thestep size of the load during precracking shouldbe minimized. Reduction in the maximum loadshould not be greater than 20% of the previousload condition. As the crack approaches the finaldesired size, this percentage may be decreased.

Gripping of the specimen must be done in amanner that does not violate the stress-intensitysolution requirements. For example, in a single-edge notched specimen, it is possible to producea grip that permits rotation in the loading of thespecimen, or it is possible to produce a rigid grip.

Each of these requires a different stress-intensitysolution. In grips that are permitted to rotate,such as the compact-type specimen grip, the pinand the hole clearances must be designed to min-imize friction. It is also advisable to consider lat-eral movement above and below the grips.

Gripping arrangements for compact-type andcenter-cracked tension specimens are describedin ASTM E 647. For a center-cracked tensionspecimen less than 75 mm (3 in.) in width, a singlepin grip is generally suitable. Wider specimensgenerally require additional pins, friction grip-ping, or some other method to provide sufficientstrength in the specimen and grip to prohibitfailure at undesirable locations, such as in thegrips. Grips designed for compact-type speci-mens are illustrated in Fig. 20.

Crack-LengthMeasurement Techniques

Several different techniques have been devel-oped to monitor the initiation, growth, and in-stability of cracks, including optical (visual andphotographic), electrical (eddy current and re-sistance), compliance, ultrasonic, and acousticemission monitoring techniques.

Optical Crack Measurement TechniquesMonitoring of fatigue crack length as a func-

tion of cycles is most commonly conducted visu-ally by observing the crack at the specimen sur-faces with a traveling low-power microscope at amagnification of 20 to 50X. Crack-length mea-surements are made at intervals such that anearly even distribution of da] dN versus ~K isachieved. The minimum amount of extension be-

18 Fatigue Testing

(a) C(aD) = 0D/P, (b) C(a1) = 01/PFig. 21 Schematic of the relationshipbetween compliance and crack length

ure 21 illustrates that the more deeply a specimenis cracked, the greater the amount of 0 measuredfor a specific value of tensile load. Compliancecan also be defined for shear and torsional loadsapplied to cracked specimens, and crack exten-sion under these loading modes can be similarlydetermined.

Specimen load is simultaneously measured byan electronic load cell and conditioner / amplifiersystem, and the output is directed to the samedata-acquisition system. A generalized schematicof the circuits involved is shown in Fig. 22.

t

p

p

~--al~p

(a)

(b)

Fig. 20 Grips designed for fatigue crackpropagation testing of compact-typespecimens (courtesy of MTS SystemsCorp.)

tween readings is commonly about 0.25 mm(0.10 in.).

The optical technique is straightforward and,if the specimen is carefully polished and does notoxidize during the test, produces accurate re-sults. However, the process is time consuming,subjective, and can be automated only withcomplicated and expensive video-digitizingequipment. In addition, many fatigue crackgrowth rate tests are conducted in simulated-service environments that obscure direct obser-vation of the crack.

Compliance Method ofCrack Extension Measurement

The compliance of an elastically strained spec-imen containing a crack of length a measuredfrom the load line to the crack tip is usually ex-pressed as the quotient of the displacement, 0,and the tensile load, P, with the displacementmeasured along, or parallel to, the load line. Fig-

x-v recorder

Loadt a, a1 a2 a/P'~

I

Fatigue Crack Propagation

SpecimenDisplacementgage ....-+----... )'Lr

J=1Gage

condition

Loadcell

10 V dcLoad cellcondition

19

10 V dc

Fig. 22 Components of a compliance measurement system

The required sensitivity of the systems de-pends on specimen geometry and size; in general,noise-free, amplified output on the order of I Vdc per I mm (0.04 in.) of deflection is satisfac-tory. Similarly, for the load range applied to thespecimen, an approximately I V de change insignal from the load cell is required for accuratecalculation of the compliance.

Electric PotentialCrack Monitoring Technique

The electrical potential, or potential drop,technique has gained increasingly wide accep-tance in fracture research as one of the most ac-curate and efficient methods for monitoring theinitiation and propagation of cracks. This meth-od relies on the fact that there will be a distur-bance in the electrical potential field about anydisconti