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Over the Next Several Days

Over the Next Several Days. What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis Uniaxial Fully Reversed Uniaxial Fluctuating Multiaxial Crack Growth. Some History. Rail car axles The all-important microcrack

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Over the Next Several Days

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  1. Over the Next Several Days • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth

  2. Some History • Rail car axles • The all-important microcrack • Role of stress concentrations • Comet airplanes

  3. Three Stages of Fatigue Failure • Crack Initiation • Crack Propagation • oscillating stress… crack grows, stops growing, grows, stops growing… with crack growth due to tensile stresses • Fracture • sudden, brittle-like failure

  4. Identifying Fatigue Fractures beachmarks

  5. Three Theories

  6. ships, planes, vehicle chassis Low vs. High Cycle >103 cycles, high cycle fatigue car crank shaft – manufacturing equipment @ 100 rpm – ~2.5 E8 Rev/105 miles 1.25 E8 Rev/year <103 cycles, low cycle fatigue

  7. Types of Fatigue Loading Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

  8. Update • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth

  9. Testing Fatigue Properties • Rotating Beam – most data is from this type • Axial • lower or higher? Why? • Cantilever • Torsion

  10. Fully Reversed Empirical Data An S-N Curve (Stress-Life) Wrought Steel

  11. Fully Reversed Empirical Data Aluminum

  12. Endurance Limit A stress level below which a material can be cycled infinitely without failure Many materials have an endurance limit: low-strength carbon and alloy steels, some stainless steels, irons, molybdenum alloys, titanium alloys, and some polymers Many other materials DO NOT have an endurance limit: aluminum, magnesium, copper, nickel alloys, some stainless steels, high-strength carbon and alloy steels for these, we use a FATIGUE STRENGTH defined for a certain number of cycles (5E8 is typical)

  13. Update • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth

  14. Types of Fatigue Loading Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

  15. Getting Fatigue Data • Test a prototype • Test the exact material used • Published fatigue data • Use static data to estimate

  16. Estimating Se´ From Static Data see page 345 in your book… steels irons aluminums BUT, these are all for highly polished, circular rotating beams of a certain size

  17. Correction Factors pages 348-353 in your book

  18. Constructing Estimated S-N Curves The material strength at 103 cycles, Sm: Sm=0.9Sut for bending Sm=0.75Sut for axial loading The line from Sm to Se or Sf, Sn=aNb or logSn=loga + blogN

  19. Fatigue Stress Concentration Kf = 1+q(Kt-1) q = notch sensitivity function of material, Sut, Neuber constant, a notch radius, r

  20. Update • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth Uniaxial Multiaxial

  21. Types of Fatigue Loading Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

  22. Tentative Material Tentative Design a (nominal) Kt Kf a 1, 2, 3 (principal) ´ (von Mises) Uniaxial, Fully Reversed StrategyLoading & Stress Half N (umber of cycles) Fluctuating Load (Fa)

  23. Cload Csurf Csize Ctemp Creliab Se or Sf Estimated S-N Curve Uniaxial, Fully Reversed StrategyFatigue Half Se´ or Sf´

  24. Uniaxial Fully Reversed Strategy Nf = fatigue safety factor; Sn = Fatigue strength at n cycles;  ´= largest von Mises alternating stress

  25. Mmax MB Mc A B C D Uniaxial, Reversed Example A B C D (mm) 3mm fillets 6.8 kN 250 125 10 75 100 10 30 30 32 35 38 Sut=690 MPa Sy=580 Mpa

  26. Update • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth Uniaxial Multiaxial

  27. Types of Fatigue Loading Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

  28. Does Mean Stress Matter?

  29. Failure Yield modified-Goodman Gerber Soderberg Safety Fluctuating Stress Failure Plot a constructed for a given number of cycles N Sy Se or Sf m Sy Sut

  30. The Data

  31. “Augmented” Modified-Goodman Plot a Sy Se or Sf m Syc Sy Sut von Mises calculated for a and for m separately

  32. Factors of Safety • Four cases • a constant, m varies • a varies, m constant • a and m increase at constant ratio • a and m increase independently • If you know how the stress can vary, only use one of four cases • If stress can vary in any manner, Case 4 should be used (the most conservative)

  33. Tentative Material Tentative Design m (nom) Kt a (nom) Kf Kfm a m 1a, 2a, 3a; 1m, 2m, 3m (principal) ´a, ´m (von Mises) Uniaxial Fluctuating StrategyStress & Loading N (umber of cycles) Fluctuating Load (Fa)

  34. Cload Csurf Csize Ctemp Creliab Se or Sf Modified-Goodman Diagram Uniaxial Fluctuating Strategy Fatigue Aspects Se´ or Sf´

  35. Uniaxial Fluctuating Strategy Nf

  36. Mmax MB Mc A B C D Uniaxial, Fluctuating Example A B Fm=1 kN Fa= 2 kN C D (mm) 3mm fillets 250 125 10 75 100 10 30 30 32 35 38 Sut=690 MPa Sy=580 Mpa *NOT a rotating shaft*

  37. Strategy • Find ´a and ´m with appropriate stress concentration factors • Find Se • Plot modified-Goodman diagram • Find factor of safety

  38. Update • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth Uniaxial Multiaxial

  39. Types of Fatigue Loading Fully Reversed Repeated Fluctuating stress range amplitude ratio alternating component mean component stress ratio

  40. Multiaxial Fatigue • simple multiaxial stress • periodic, synchronous, in-phase • complex multiaxial stress • everything else • assuming synchronicity and being in-phase is usually conservative

  41. Fully Reversed Multiaxial • Find von Mises equivalent stress for alternating component • Cload implications

  42. Fluctuating Multiaxial • Sines Method • Von Mises Method modified-Goodman diagram

  43. Fatigue Recap • What is fatigue? • Types of Fatigue Loading • Empirical Data • Estimating Endurance/Fatigue Strength • Strategies for Analysis • Uniaxial Fully Reversed • Uniaxial Fluctuating • Multiaxial • Crack Growth Uniaxial Multiaxial

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