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Fatigue Basics

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Fatigue Basics Chris Wilson Last updated March 26, 2007 Fatigue (Progressive Failure) Types of Loading Static (no cycling) Working load (cyclic as a function of ... – PowerPoint PPT presentation

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Title: Fatigue Basics


1
Fatigue Basics
  • Chris Wilson
  • Last updated March 26, 2007

2
Fatigue (Progressive Failure)
  • Types of Loading
  • Static (no cycling)
  • Working load (cyclic as a function of
    performance)
  • Vibration (secondary loading)
  • Impact loads
  • Accidental loads
  • Fatigue Damage/failure mechanism caused by
    cyclic loading

3
History and Implications
  • 1800s railroad car axles (Wöhler, Germany)
  • Failure in USA cost 150 billion per year
  • 80 of failures caused by cyclic loading, 50
    unnecessary

4
Accumulation of Fatigue Cycles
  • Airplanes 10 takeoff/landings per day or 3600
    per year
  • Electric generator 60 Hz (cycles/s) or 2.16?105
    cycles/hr or 5.2?106 cycles/day or 1.9?109
    cycles/year

5
Stages of Fatigue
  • Crack nucleation localized shear bands develop
    and a microcrack forms (often takes a short time)
  • Crack propagation microcrack opens with tensile
    load, closes with compression (usually takes a
    long time)
  • Sudden fracture due to unstable crack growth
    (short time)

6
Fatigue Approaches
  • Stress-Life (S-N) Approach Can use for lives
    greater than 1000 cycles
  • Strain-Life (e-N) Approach Must use for less
    than 1000 cycles, can use for greater
  • Fatigue Crack Growth (FCG) Use fracture mechanics

Focus for ME 4010
7
Cyclic Stress Terms
8
Examples
9
Examples
10
Examples
11
Waveform Examples
  • Periodic
  • Sinusoidal
  • Triangular
  • Square
  • Random
  • Constant Amplitude vs. Variable Amplitude

12
Fatigue Testing
  • Typical Test
  • 0.3 in dia round specimen, highly polished
  • simply-supported rotating beam (R-1)
  • w 1725 rev/min (106 cycles in a day, 108
    cycles in 40 days)
  • Axial Test
  • more versatile (different R)
  • entire cross-section is uniformly stressed

13
Fatigue Strength/Endurance Limit
  • Materials with endurance limits include low
    strength carbon and alloy steels, some stainless
    steels, irons, titanium alloys, some polymers
  • Materials without endurance limits include
    aluminum, magnesium, copper, and nickel alloys,
    some stainless steels, high strength carbon and
    alloy steels

14
S-N Curve Estimation
  • Rotating bend or axial
  • AISI 4340 Steel, QT 1000F
  • Sut 170 kpsi
  • Use bilinear estimate in log S-log N space

103
106
15
S-N Curve Estimation Calculations
  • Rotating bend
  • Axial

16
Estimating a Fatigue Curve
17
Scatter in Fatigue Data
18
Parameters Affecting Fatigue Life
  • Mean Stress
  • Constant Amplitude vs. Variable Amplitude
  • Waveform
  • Frequency
  • Environment
  • Surface Finish

19
Estimating Fatigue Strength
20
Nonzero Mean Stress
  • Goodman
  • good fit to lowerbound data
  • Soderberg
  • sometimes too conservative
  • Gerber
  • good fit to mean data

21
Correction Factors
Correction factors to adapt rotating bend data to
other geometries and loadings (for steel)
Se Corrected (estimated) endurance limit Se?
Rotating bend endurance limit ka Surface finish
modification factor kb Size modification
factor kc Load modification factor kd
Temperature modification factor ke Reliability
factor kf Miscellaneous modification factor
22
Process Effects (Aluminum)
23
Surface Finish Effects
24
Dealing with Torsion
  • Reversed torsion of ductile materials
    Ses 0.58 Se? (this is von Mises criterion)
  • Use same factor for long-life fatigue
    Sfs 0.58 Sf?
  • Short-life S1000 0.9 Sus where Sus is ultimate
    strength in shear (0.8 Sut for steel, 0.7 Sut for
    other ductile metals)

25
Mean Stress Effects Torsion
  • Goodman equation for infinite life
  • Goodman equation for finite life

26
Combined Loading
  • Equivalent alternating stress
  • Equivalent mean stress

Treat these equivalent stresses as bending
stresses!
27
Dealing with Notches
  • Fatigue stress concentration factor Kf
  • Kf 1 (Kt - 1) q
  • Kt theoretical (geometric stress concentration
    factor)
  • q notch sensitivity factor (0 q 1)
  • q 0 implies Kf 1 (notch insensitive material
    such as cast iron)
  • q 1 implies Kf Kt (highly notch sensitive
    material)

28
(No Transcript)
29
Using q and Kf in Practice
  • q is a function of notch root radius
  • Use Kf in all calculations regardless of the
    number of cycles may be conservative for
    shorter lives
  • If calculated peak stress with Kf exceeds Sy,
    then a correction is needed for this fictitious
    elastic stress if yielding is contained

30
Residual Stress Method
  • Graphical method for Goodman equation
  • Correction does not change sea, but reduces the
    mean stress sem

Yield line
sa
Kf-Corrected sem, sea
Sy
Sn
Kf-Calculated sem, sea
Goodman line for 106 cycles
sm
Sut
Sy
31
Factor of Safety Determination
  • Same idea as in static calculations assume
    proportional loading
  • Static example max shear stress theory

s3
s2 0
Sy
failure pt
B
operating pt
A
Sy
O
s1
C
D
32
Factor of Safety Determination
  • Fatigue example Goodman equation for 106 cycles

sa
failure pt
operating pt
D
Sn
B
C
A
sm
O
Sut
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