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
rail car axles failed below Sy, brittle-like – and the static strength was not reduced!
fatigue begins at a crack
stress concentrations can play a big role in starting a crack

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 Stress-Life Strain-Life LEFM (Fracture Mechanics)
stress-based, for high-cycle fatigue, aims to prevent crack initiation
Strain-Life
useful when yielding begins (i.e., during crack initiation), for low-cycle fatigue
LEFM (Fracture Mechanics)
best model of crack propagation, for low-cycle fatigue

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

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
talk about each of these
pages 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. Uniaxial, Fully Reversed Strategy Loading & Stress Half
N (umber of cycles)
Fluctuating Load (Fa)
Tentative Design
Tentative Material Kt
a (nominal) Kf a
1, 2, 3 (principal)
´ (von Mises)

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

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

25. Uniaxial, Reversed ExampleB C D
(mm)
3mm fillets
6.8 kN
250
125 10 75
100 10 30 30 32 35 A B C D MB Mc
Mmax 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. Fluctuating Stress Failure Plot
constructed for a given number of cycles N Sy
Yield
Failure
Safety
Se or Sf
modified-Goodman
Soderberg
Gerber m Sy
Sut

30. The Data

31. “Augmented” Modified-Goodman PlotSy
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. Uniaxial Fluctuating Strategy Stress & Loading
N (umber of cycles)
Fluctuating Load (Fa)
Tentative Design
Tentative Material a
m (nom)
a (nom) m Kf Kt
Kfm
1a, 2a, 3a; 1m, 2m, 3m (principal)
´a, ´m (von Mises)

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

35. Uniaxial Fluctuating StrategyNf

36. Uniaxial, Fluctuating ExampleB
Fm=1 kN
Fa= 2 kN C D
(mm)
3mm fillets
250
125 10 75
100 10 30 30 32 35 A B C D MB Mc
Mmax 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 complex 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