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Notches in Fatigue
Professor Stephen Downing
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
© 2002-2012 Darrell Socie, All Rights Reserved
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 50
Outline
1. Notch Rules
2. Fatigue Notch Factor
3. Stress Intensity Factors for Notches
4. Frost Data and Kf
5. Small Crack Growth
6. Small Notches
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Stress Concentration Factor
Applied stress
Local stress
a21appliedlocal
Inglis Solution 1910
2a
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 50
Notch Rules
Neuber
Glinka
Seeger
n
1
2
tKE
eSK
n
1
2
tKn1
1
EdeSK
SK
K*S
KSK
KEeSK
p
t
y
tLimitp
n
1
**2
p
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Define K and K after Yielding
S , e
,
Define: nominal stress, S
nominal strain, e
notch stress,
notch strain,
Stress concentration
Strain concentration
SK
eK
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 5 of 50
K and K
Str
ess (
MP
a)
Strain
KtS
Kte
SK
eK
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Stress and Strain Concentration
Kt
Nominal Stress
Str
ess/S
train
Concentr
ation
1K
2
tKK
First yielding
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Neuber’s Rule S
tress (
MP
a)
Strain
KtS
Kte
eKSK tt
Stress calculated with
elastic assumptions
Actual stress
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 8 of 50
Neuber’s Rule for Fatigue
2222
eKSK tt
Stress and strain amplitudes
Elastic nominal stress
E2
S
2
e
Substitute and rearrange
22E
2
SK t
The product of stress times strain controls fatigue life
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SN Materials Data
10 1 10 102 103 106 107 105 104
Fatigue Life, Reversals
100
1000
10000
Str
ess A
mplit
ude, M
Pa
93 steels
17 aluminums
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N Materials Data
93 steels
17 aluminums
10-4
10-2
10-3
0.1
10
1
Str
ain
Am
plit
ure
1 10 102 103 106 107 105 104
Fatigue Life, Reversals
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1 106 107 105 10 102 103 104
Fatigue Life, Reversals
1
10
102
105
104
103
2
2
E
K t
or
2 S
2 2 E
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Outline
1. Notch Rules
2. Fatigue Notch Factor
3. Stress Intensity Factors for Notches
4. Frost Data and Kf
5. Small Crack Growth
6. Small Notches
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 13 of 50
A Dilemma
Stress analysis and stress concentration factors are
independent of size and are related only to the ratio
of the geometric dimensions to the loads
Fatigue is a size dependant phenomena
How do you put the two together ?
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 14 of 50
Similitude
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 15 of 50
Fatigue of Notches
From Dowling, Mechanical Behavior of Materials, 1999
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Notch Size
Kt Kf
Kt
Kf
Large Notch Small Notch
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Microstructure Size
Kt Kf
Kt Kf
Low Strength High Strength
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Stress Gradient
Kt Kf
Kt
Kf
Low Kt High Kt
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Kt vs Kf
0
2
4
6
8
10
0 2 4 6 8 10
Kt
Kf
Kf = Kt
Experiments
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 20 of 50
Peterson’s Equation
1
1K1K t
f
mmMPa2070
025.0
8.1
u
0
1
2
3
4
10-4 10-3 10-2 0.1 1 10 102 103
Kf
No effect when <<
Full effect when >>
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Pererson’s Constant
1000 500 2000 1500
0.1
0.03
0.7
0.3
Ultimate Strength, MPa
, m
m
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Static Strength
hole
Kt = 2.5
slot
Kt = 5
diamond
Kt = 20
edge
Kt = 20
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 23 of 50
1018 Steel Test Data
0
20
40
60
80
100
0 2 4 6 8 10
load, kN
displacement, mm
edge
diamond
slot
hole
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Notched SN Curve
100
1000
10000
100
Cycles
Str
ess A
mplit
ude,
MP
a
101 102 103 104 105 106 107
Smooth specimen data
Notched specimen Kf
Stress concentrations are not very important at short lives
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Outline
1. Notch Rules
2. Fatigue Notch Factor
3. Stress Intensity Factors for Notches
4. Frost Data and Kf
5. Small Crack Growth
6. Small Notches
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Cracks at Notches
D
a a D + a
KtS S S
a << D a >> D
aSKK t aDSK
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Stress Intensity Factors
0 0.1 0.2 0.3 0.4 0.5 0.6
1.0
0
3.0
2.0
D
a
DS
K
aSKK t
aDSK
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Cracks at Holes
10 1 1 12
Once a crack reaches 10% of the hole radius,
it behaves as if the hole was part of the crack
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Outline
1. Notch Rules
2. Fatigue Notch Factor
3. Stress Intensity Factors for Notches
4. Frost Data and Kf
5. Small Crack Growth
6. Small Notches
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Crack Growth Data
10-12
10-11
10-10
10-9
10-8
10-7
10-6
1 10 100
Cra
ck G
row
th R
ate
, m
/cycle
mMPa,K
mKCdN
da
KTH
Kc
a2
12.1KTH
Nonpropagating cracks
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Frost Data
nucleation fracture
Rotating bending
Notched bar
Notched plate
1 3 5 7 9 11 13 15
1.0
0.8
0.6
0.4
0.2
0
Kt
Snom
inal
Sfa
tigue lim
it
tK
1 nonpropagating cracks
Frost, “A Relation Between the Critical Alternating Propagation Stress and Crack Length for Mild Steel”
Proceedings of the Institute for Mechanical Engineers, Vol. 173, No. 35, 1959, 811-836
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Significance
D
KS th
fl
For Kt > 4, the notch acts like a crack with a depth D
Kt does not play a role for sharp notches !
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Specimens with Similar Geometry
Kt = 2.4 Kt = 10.7
Ultimate Strength 780 MPa
Yield Strength 660 MPa
25 25
2.5 2.5
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Test Results
1
100
1000
Nom
inal S
tress A
mplit
ude
1 10 100 103 104 105 106 107
Total Fatigue Life, Cycles
Strength Limited
Crack Growth Dominated
Fatigue Strength Dominated
Threshold Stress Intensity Dominated
Kt = 2.4
Kt = 10.7
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Outline
1. Notch Rules
2. Fatigue Notch Factor
3. Stress Intensity Factors for Notches
4. Frost Data and Kf
5. Small Crack Growth
6. Small Notches
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Small Crack Growth
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Threshold
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Normalized Thresholds
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Growth from Notches
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Cracks at Notches
D a crack tip plastic zone
notch plastic zone
notch stress field
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Crack Growth
K or a
Cra
ck g
row
th r
ate
Long cracks
Crack tip plasticity controls
Short cracks
Notch plasticity
controls
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Closure Observations
a b
d c c 1st subcycle
d 500th subcycle
a
b
1026 steel
1/2 = 0.005
2/2 = 0.001
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Closure Correlation
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 44 of 50
Outline
1. Notch Rules
2. Fatigue Notch Factor
3. Stress Intensity Factors for Notches
4. Frost Data and Kf
5. Small Crack Growth
6. Small Notches
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area
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Small Notches
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Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 47 of 50
Threshold Stress Intensity
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Hardness Corelation
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Flaw Sensitivity
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Fatigue Limit
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Notches in Fatigue