Transcript AME 324B Engineering Component Design

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
 Role of stress concentrations
Comet airplanes
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
Identifying Fatigue Fractures
beachmarks
Three Theories
Stress-Life
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 lowcycle fatigue
Low vs. High Cycle
>103 cycles, high cycle fatigue
car crank shaft – ~2.5 E8 Rev/105 miles
manufacturing equipment @ 100 rpm – 1.25 E8 Rev/year
<103 cycles, low cycle fatigue
ships, planes, vehicle chassis
Types of Fatigue Loading
Fully Reversed
Repeated
   max   min
stress range

a 
2
alternating
component
m 
 max   min
2
mean
component
Fluctuating
amplitude
ratio
stress ratio
a
A
m
 min
R
 max
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
Testing Fatigue Properties
 Rotating
Beam – most data is from this type
 Axial
lower or higher? Why?
 Cantilever
 Torsion
Fully Reversed Empirical Data
An S-N Curve (Stress-Life)
Wrought Steel
Fully Reversed Empirical Data
Aluminum
Endurance Limit
S e
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
Sf
for these, we use a FATIGUE STRENGTH defined for a certain
number of cycles (5E8 is typical)
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
Types of Fatigue Loading
Fully Reversed
Repeated
   max   min
stress range

a 
2
alternating
component
m 
 max   min
2
mean
component
Fluctuating
amplitude
ratio
stress ratio
a
A
m
 min
R
 max
Getting Fatigue Data
1)
2)
3)
4)
Test a prototype
Test the exact material used
Published fatigue data
Use static data to estimate
Estimating Se´ From Static Data
see page 345 in your book…
steels
Se  0.5Sut
Se  100 ksi
for Sut  200 ksi
for Sut  200 ksi
irons
Se  0.4 Sut
Se  24 ksi
for Sut  60 ksi
for Sut  60 ksi
S f @ 5 E 8  0.4 Sut
S f @ 5 E 8  19 ksi
for Sut  40 ksi
for Sut  40 ksi
aluminums
BUT, these are all for highly polished, circular rotating beams of a certain size
Correction Factors
Se  Cload Csize Csurf CtempCreliab Se
S f  Cload Csize Csurf CtempCreliab S f 
pages 348-353 in your book
Constructing Estimated S-N Curves
The material strength at 103 cycles, Sm:
Sm=0.9Sut
Sm=0.75Sut
for bending
for axial loading
The line from Sm to Se or Sf, Sn=aNb
or logSn=loga + blogN
Fatigue Stress Concentration
Kf = 1+q(Kt-1)
q = notch sensitivity
function of material, Sut,
Neuber constant, a
notch radius, r
q
1
a
1
r
Update
What is fatigue?
 Types of Fatigue Loading
 Empirical Data
 Estimating Endurance/Fatigue Strength
 Strategies for Analysis

 Uniaxial Fully Reversed
m  0 m  0
 Uniaxial Fluctuating
 Multiaxial
Uniaxial
 Crack Growth
Multiaxial
Types of Fatigue Loading
Fully Reversed
Repeated
   max   min
stress range

a 
2
alternating
component
m 
 max   min
2
mean
component
Fluctuating
amplitude
ratio
stress ratio
a
A
m
 min
R
 max
Uniaxial, Fully Reversed Strategy
Loading & Stress Half
N (umber of cycles)
Tentative Material
Fluctuating Load (Fa)
Tentative Design
a (nominal)
Kt
Kf
a
1, 2, 3 (principal)
´ (von Mises)
Uniaxial, Fully Reversed Strategy
Fatigue Half
Cload
Csurf
Csize
Ctemp
Creliab
Se´ or Sf´
Se or Sf
Estimated S-N Curve
Uniaxial Fully Reversed Strategy
N (umber of cycles)
Tentative Material
Fluctuating Load (Fa)
Tentative Design
a (nominal)
Kt
Kf
a
Cload
Csurf
Csize
Ctemp
Creliab
Se´ or Sf´
Se or Sf
1, 2, 3 (principal)
Estimated S-N Curve
´ (von Mises)
Sn
Nf 

Nf = fatigue safety factor; Sn = Fatigue strength at n cycles;
 ´= largest von Mises alternating stress
Uniaxial, Reversed Example
A
B
C
D
(mm)
3mm fillets
6.8 kN
250
10
75
125
100
10
30
30
32
38
MB
35
Mmax
Sut=690 MPa
Sy=580 Mpa
Mc
A
B
C
D
Update
What is fatigue?
 Types of Fatigue Loading
 Empirical Data
 Estimating Endurance/Fatigue Strength
 Strategies for Analysis

 Uniaxial Fully Reversed
m  0 m  0
 Uniaxial Fluctuating
 Multiaxial
Uniaxial
 Crack Growth
Multiaxial
Types of Fatigue Loading
Fully Reversed
Repeated
   max   min
stress range

a 
2
alternating
component
m 
 max   min
2
mean
component
Fluctuating
amplitude
ratio
stress ratio
a
A
m
 min
R
 max
Does Mean Stress Matter?
a
Fluctuating Stress Failure Plot
constructed for a given number of cycles N
Sy
Failure
Se or Sf
modified-Goodman
Safety
Sy
Sut
m
The Data
“Augmented” ModifiedGoodman Plot
a
Sy
 m
Sy

 m
S yc

 a
S yc
Syc
1
 a  S f
Se or Sf

 a
Sy
1
 m
Sut
Sy
von Mises calculated for a and for m separately

 a
Sf
1
Sut
m
Factors of Safety

Four cases
1)
2)
3)
4)


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)
Uniaxial Fluctuating Strategy
Stress & Loading
N (umber of cycles)
Tentative Material
Fluctuating Load (Fa)
Tentative Design
m (nom)
Kt
a (nom)
Kf
a
Kfm
m
1a, 2a, 3a; 1m, 2m, 3m (principal)
´a, ´m (von Mises)
Uniaxial Fluctuating Strategy
Fatigue Aspects
Cload
Csurf
Csize
Ctemp
Creliab
Se´ or Sf´
Se or Sf
Modified-Goodman Diagram
Uniaxial Fluctuating Strategy
N (umber of cycles)
Tentative Material
Fluctuating Load (Fa)
Tentative Design
m (nom)
Kt
a (nom)
Kf
a
Kfm
m
1a, 2a, 3a; 1m, 2m, 3m (principal)
´a, ´m (von Mises)
Cload
Csurf
Csize
Ctemp
Creliab
Se´ or Sf´
Se or Sf
Modified-Goodman Diagram
Nf
Uniaxial, Fluctuating Example
A
B Fm=1 kN C
Fa= 2 kN
250
10
75
D
125
100
(mm)
3mm fillets
10
30
30
32
38
MB
35
Mmax
Sut=690 MPa
Sy=580 Mpa
Mc
A
B
C
*NOT a rotating shaft*
D
Strategy
´a and ´m with appropriate stress
concentration factors
 Find Se
 Plot modified-Goodman diagram
 Find factor of safety
 Find
Update
What is fatigue?
 Types of Fatigue Loading
 Empirical Data
 Estimating Endurance/Fatigue Strength
 Strategies for Analysis

 Uniaxial Fully Reversed
m  0 m  0
 Uniaxial Fluctuating
 Multiaxial
Uniaxial
 Crack Growth
Multiaxial
Types of Fatigue Loading
Fully Reversed
Repeated
   max   min
stress range

a 
2
alternating
component
m 
 max   min
2
mean
component
Fluctuating
amplitude
ratio
stress ratio
a
A
m
 min
R
 max
Multiaxial Fatigue
 simple
multiaxial stress
periodic, synchronous, in-phase
 complex
multiaxial stress
everything else
 assuming
synchronicity and being inphase is usually conservative
Fully Reversed Multiaxial
 Find
von Mises equivalent stress for
alternating component
Cload implications
 a 
1
a
  2a
2   2
a
  3a
2
Sy
Nf 
 a
2   3a  1 2
a
Fluctuating Multiaxial
 Sines
Method
 Von Mises Method
 a 
1
a
  2a
2   2
a
  3a
2
 m 
1
m
2   3a  1 2
  2m
a
2   2
modified-Goodman diagram
m
  3m
2
2   3m  1 2
m
Fatigue Recap
What is fatigue?
 Types of Fatigue Loading
 Empirical Data
 Estimating Endurance/Fatigue Strength
 Strategies for Analysis

 Uniaxial Fully Reversed
m  0 m  0
 Uniaxial Fluctuating
 Multiaxial
Uniaxial
 Crack Growth
Multiaxial