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1
Professor Darrell F. SocieMechanical Science and Engineering
University of Illinois
© 2004-2007 Darrell Socie, All Rights Reserved
Fatigue, How and Why
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 1 of 108
Contact Information
Darrell SocieMechanical Engineering1206 West GreenUrbana, Illinois 61801
Office: 3015 Mechanical Engineering Laboratory
[email protected]: 217 333 7630Fax: 217 333 5634
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Fatigue, How and Why
Physics of FatigueMaterial PropertiesSimilitudeFatigue Calculator
2
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10-10 10-8 10-6 10-4 10-2 100 102
Specimens StructuresAtoms Dislocations Crystals
Size Scale for Studying Fatigue
Understand the physics on this scale
Model the physics on this scale
Use the models on this scale
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The Fatigue Process
Crack nucleationSmall crack growth in an elastic-plastic stress fieldMacroscopic crack growth in a nominally elastic stress fieldFinal fracture
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Mechanisms Crack Nucleation
Nucleation in Slip Bands inside GrainNucleation at Grain BoundariesNucleation at Inclusions
3
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1903 - Ewing and Humfrey
Cyclic deformation leads to the development of slip bands and fatigue cracks
N = 1,000 N = 2,000
N = 10,000 N = 40,000 Nf = 170,000Ewing, J.A. and Humfrey, J.C. “The fracture of metals under repeated alterations of stress”, Philosophical Transactions of the Royal Society, Vol. A200, 1903, 241-250
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Crack Nucleation
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Slip Band in Copper
Polak, J. Cyclic Plasticity and Low Cycle Fatigue Life of Metals, Elsevier, 1991
4
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Slip Band Formation
Loading Unloading
Extrusion
Undeformedmaterial
Intrusion
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Slip Bands
Ma, B-T and Laird C. “Overview of fatigue behavior in copper sinle crystals –II Population, size, distribution and growthKinetics of stage I cracks for tests at constant strain amplitude”, Acta Metallurgica, Vol 37, 1989, 337-348
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2124-T4 Cracking in Slip Bands
N = 60
N = 2000N = 1200
N = 300N = 240
5
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Crack at Particle
Material: BS L65 Aluminum
Loading: 63 ksi, R=0 for 500,000+ cycles, followed by 68 ksi, R=0 to failure. Cracks found
during 68 ksi loading.
S. Pearson, “Initiation of Fatigue Cracks in Commercial Aluminum Alloys and the Subsequent Propagation
of Very Short Cracks,” RAE TR 72236, Dec 1972.
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7075-T6 Cracking at Inclusion
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Subsurface Crack Initiation
Y. Murakami, Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions, 2002
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Fatigue Limit and Strength Correlation
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
Fatig
ue S
treng
th, M
Pa
0.6
0.5
0.35
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
Fatig
ue S
treng
th, M
Pa
0.6
0.5
0.35
From Forrest, Fatigue of Metals, Pergamon Press, London, 1962
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Crack Nucleation Summary
Highly localized plastic deformationSurface phenomenaStochastic process
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100 µm
bulksurface
10 µm
surface
20-25 austenitic steel in symmetrical push-pull fatigue (20°C, Δεp/2= ±0.4%) : short cracks on the surface and in the bulk
Surface Damage
From Jacques Stolarz, Ecole Nationale Superieure des MinesPresented at LCF 5 in Berlin, 2003
7
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Stage I Stage II
loading direction
freesurface
Stage I and Stage II
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Stage I Crack Growth
Single primary slip system
individual grain
near - tip plastic zone
S
SStage I crack is strongly affected by slip characteristics, microstructure dimensions, stress level, extent of near tip plasticity
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Small Cracks at Notches
D acrack tip plastic zone
notch plastic zone
notch stress field
Crack growth controlled by the notch plastic strains
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Small Crack Growth
1.0 mm
N = 900
Inconel 718Δε = 0.02Nf = 936
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0
0.5
1
1.5
2
2.5
0 2000 4000 6000 8000 10000 12000 14000
J-603
F-495 H-491
I-471 C-399
G-304
Cycles
Cra
ck L
engt
h, m
m
Crack Length Observations
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Crack - Microstructure Interactions
Akiniwa, Y., Tanaka, K., and Matsui, E.,”Statistical Characteristics of Propagation of Small Fatigue Cracks in Smooth Specimens of Aluminum Alloy 2024-T3, Materials Science and Engineering, Vol. A104, 1988, 105-115
10-6
10-7
0 0.005 0.01 0.015 0.02 0.0250.03 0.025 0.02 0.015 0.01 0.005
A B CD
F
E
Crack Length, mm
da/dN, mm/cycle
9
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Strain-Life Data
Reversals, 2Nf
Stra
in A
mpl
itude
Δε 2
10-5
10-4
0.01
0.1
1
100 101 102 103 104 105 106 107
10-3
10μm100 μm
1mmfracture Crack size
Most of the life is spent in microcrack growth in the plastic strain dominated region
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 25 of 108
Stage II Crack Growth
Locally, the crack grows in shear Macroscopically it grows in tension
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Long Crack Growth
Plastic zone size is much larger than the material microstructure so that the microstructure does not play such an important role.
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Material strength does not play a major role in fatigue crack growth
Crack Growth Rates of Metals
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Maximum Load
monotonic plastic zone
σ
Stresses Around a Crack
σ
ε
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Stresses Around a Crack (continued)
Minimum Load σ
ε
cyclic plastic zone
σ
11
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Crack Closure
S = 250
b
S = 175
c
S = 0
a
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Crack Opening LoadDamaging portion of loading history
Nondamaging portion of loading history
Opening load
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Mode Iopening
Mode IIin-plane shear
Mode IIIout-of-plane shear
Mode I, Mode II, and Mode III
12
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5 μmcrac
k gr
owth
dire
ctio
n
Mode I Growth
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crack growth direction
10 μm
slip bandsshear stress
Mode II Growth
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1045 Steel - Tension
NucleationShear
Tension
1.0
0.2
0
0.4
0.8
0.6
1 10 102 103 104 105 106 107
Fatigue Life, 2Nf
Dam
age
Frac
tion
N/N
f
100 μm crack
13
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Fatigue Life, 2Nf
Dam
age
Frac
tion
N/N
ff
Nucleation
Shear
Tension
1 10 102 103 104 105 106 107
1.0
0.2
0
0.4
0.8
0.6
1045 Steel - Torsion
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 37 of 108
Things Worth Remembering
Fatigue is a localized process involving the nucleation and growth of cracks to failure.Fatigue is caused by localized plastic deformation.Most of the fatigue life is consumed growing microcracks in the finite life regionCrack nucleation is dominate at long lives.
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Fatigue, How and Why
Physics of FatigueMaterial PropertiesSimilitudeFatigue Calculator
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Characterization
Stress Life CurveFatigue Limit
Strain Life CurveCyclic Stress Strain Curve
Crack Growth CurveThreshold Stress Intensity
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Bending Fatigue
F
stre
ss
time
stress amplitude
stress range
IcM
=σBending stress:
ω
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SN Curve
200
300
400500
200
300
400
500
Stre
ss A
mpl
itude
, MPa
105 106 107 108 109
1x108 2x108 3x108 4x108 5x1080
Cycles to Failure
Cycles to Failure
Monel Alloy
1 hour 1 day 1 month 1 yearTesting time @ 30 Hz
15
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Fatigue Strength
105 106 107 108 109
2014-T4 290 235 186 152 1382024-T4 297 214 166 145 1386061-T6 186 152 117 104 907075-T6 276 200 166 152 145
Fatigue LifeAlloy
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6061-T6 Aluminum Test Data
Sharpe et. al. Fatigue Design of Aluminum Components and Structures , 1996
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SN Curve for Steel
100
1000
104
102
Cycles
Stre
ss A
mpl
itude
, MPa
103 104 105 106 107 108 109
fatigue limit
( )bf'f NS
2S
=Δ
The fatigue limit is usually only found in steel laboratory specimens
16
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Very High Cycle Fatigue of Steel
100
1000
104
Cycles
Stre
ss A
mpl
itude
, MPa
1010103 104 105 106 107 108 109
conventionalfatigue limit
surface failureslarge inclusions
internalinclusions
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Fatigue Damage
100
1000
10000
Stre
ss A
mpl
itude
, MPa
100
Cycles101 102 103 104 105 106 107
( )bf'f NS
2S
=Δ
110
b1
'f
f S2SN ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Δ=
10SDamage Δ∝
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 47 of 108
Fatigue Limit Strength Correlation
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
Fatig
ue S
treng
th, M
Pa
0.6
0.5
0.35
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
Fatig
ue S
treng
th, M
Pa
0.6
0.5
0.35
From Forrest, Fatigue of Metals, Pergamon Press, London, 1962
17
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Fatigue Limit Strength Correlation
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Strain Controlled Testing
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Cyclic Hardening / Softening
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Stable Hysteresis Loop
Δσ
Δε
ΔεeΔεp
Hysteresis loop
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Strain-Life Data σ − ε
0
100
200
300
400
500
600
0 0.004 0.008 0.012
Strain Amplitude
Stre
ss A
mpl
itude
Δε Δσ Δσ2 2 2
1
= + ⎛⎝⎜
⎞⎠⎟E K
n
'
/ '
During cyclic deformation, the material deforms on a path described by the cyclic stress strain curve
Δε2
Δσ 2
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Cyclic Stress Strain Curve
19
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Strain-Life Data Δε - 2Nf
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
Stra
in A
mpl
itude
100 101 102 103 104 105 106 107
2 Reversals, 2Nf = 1 Cycle, Nf
Δε 2
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Elastic and Plastic Strain-Life Data
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
Stra
in A
mpl
itude
100 101 102 103 104 105 106 107
Δε 2 Plastic
Elastic
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Strain-Life Curve
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
Stra
in A
mpl
itude
100 101 102 103 104 105 106 107
cf
'f
bf
'f )N2()N2(
E2ε+
σ=
εΔ
c
b
'fε
E
'fσ
2Nt
Δε 2
20
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Transition Fatigue Life
From Dowling, Mechanical Behavior of Materials, 1999
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Crack Growth Testing
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Stress Concentration of a Crack
2 a
ρ
ρ+=
a21KT
a ~ 10-3
for a crack
ρ ~ 10-9
KT ~ 2000
appliedlocal 2000 σ=σ
Traditional material properties like tensile strength are not very useful for cracked structures
21
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Stress Intensity Factor
σ
σ
2a
aK πσ=
K characterizes the magnitude of the stresses, strains, and displacements in the neighborhood of a crack tip
Two cracks with the same K will have the same behavior
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Crack Growth Measurements
σ
σ
2a
Cycles
Cra
ck s
ize
dNda
a1
a2
σ2 σ1
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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/c
ycle
mMPa,KΔ
mKCdNda
Δ=
ΔKTH
Kc
m ~ 3
22
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Threshold Region
threshold stress intensity
⎟⎠⎞
⎜⎝⎛πσΔ>Δ
wafaKTH
operating stresses
flaw size
flaw shape
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Threshold Stress Intensity
From Dowling, Mechanical Behavior of Materials, 1999
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Non-propagating Crack Sizes
a212.1KTH ππ
σΔ>Δ
Small cracks are frequently semielliptical surface cracks
2TH
cK63.0a ⎟
⎠⎞
⎜⎝⎛
σΔΔ
=
2
u
THc
K52.2a ⎟⎟⎠
⎞⎜⎜⎝
⎛σ
Δ=
Smooth specimen fatigue limit 2
uσ≈
23
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Non-propagating Crack Sizes
Ultimate Strength, MPa
Cra
ck S
ize,
mm mMPa5KTH =Δ
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000
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Stable Crack Growth
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/c
ycle
mMPa,KΔ
mKCdNda
Δ=
ΔKTH
Kc
Stable growth region
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Crack Growth Data
( ) 0.312 mMPaK109.6dNda
Δ×= −
( ) 25.210 mMPaK104.1dNda
Δ×= −
( ) 25.312 mMPaK106.5dNda
Δ×= −
Ferritic-Pearlitic Steel:
Martensitic Steel:
Austenitic Stainless Steel:
Barsom, “Fatigue Crack Propagation in Steels of Various Yield Strengths”Journal of Engineering for Industry, Trans. ASME, Series B, Vol. 93, No. 4, 1971, 1190-1196
5 10 100
10-7
10-6
10-8
Cra
ck G
row
th R
ate,
m/c
ycle
ΔK, MPa√m
σyield252273392415
24
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Aluminum Crack Growth Rate Data
Sharp, Nordmark and Menzemer, Fatigue Design of Aluminum Components and Structures, 1996
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Crack Growth Data
0
10
20
30
40
50
Cra
ck L
engt
h, m
m
0 50 100 150 200 250 300 350Cycles x103
Virkler, Hillberry and Goel, “The Statistical Nature of Fatigue Crack Propagation”, Journal of Engineering Materials and Technology, Vol. 101, 1979, 148-153
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 71 of 108
Things Worth Remembering
MethodStress-LifeStrain-Life
Crack Growth
PhysicsCrack Nucleation
Microcrack GrowthMacrocrack Growth
Size0.01 mm
0.1 - 1 mm> 1mm
25
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Fatigue, How and Why
Physics of FatigueMaterial PropertiesSimilitudeFatigue Calculator
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Fatigue Analysis
MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
?
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The Similitude Concept
Why Fatigue Modeling Works !
26
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What is the Similitude Concept
The “Similitude Concept” allows engineers to relate the behavior of small-scale cyclic material test specimens, defined under carefully controlled conditions, to the likely performance of real structures subjected to variable amplitude fatigue loads under either simulated or actual service conditions.
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Fatigue Analysis Techniques
Stress - LifeBS 7608, Eurocode 3 Strain - LifeCrack Growth
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Life Estimation
MethodStress-LifeBS 7608
Strain-LifeCrack Growth
PhysicsCrack Nucleation
Crack GrowthMicrocrack GrowthMacrocrack Growth
Size0.01 mm
1 - 10 mm0.1 - 1 mm
> 1mm
27
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Stress-Life Fatigue Modeling
P
FixedEnd
The Similitude Concept states that if the instantaneous loads applied to the ‘test’structure (wing spar, say) and the test specimen are the same, then the response in each case will also be the same and can be described by the material’s S-N curve.
100
1000
10000
Stre
ss A
mpl
itude
, MPa
100
Cycles101 102 103 104 105 106 107
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Fatigue Analysis: Stress-Life
MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
SN curveKa, Ks, …
Kf
ΔS , Sm
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Stress-Life
Major Assumptions:Most of the life is consumed nucleating cracksElastic deformationNominal stresses and material strength control fatigue lifeAccurate determination of Kf for each geometry and material
28
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Stress-Life
Advantages:Changes in material and geometry can easily be evaluatedLarge empirical database for steel with standard notch shapes
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Stress-Life
Limitations:Does not account for notch root plasticityMean stress effects are often in errorRequires empirical Kf for good results
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BS 7608 Fatigue Modeling
The Similitude Concept states that if the instantaneous loads applied to the ‘test’structure (welded beam on a bulldozer, say) and the test specimen (standard fillet weld) are the same, then the response in each case will also be the same and can be described by one of the standard BS 7608 Weld Classification S-N curves.
10
100
1000
105
Cycles
Stre
ss R
ange
, MPa
108107106
29
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Weld Classifications
D E
F2 G
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 85 of 108
Fatigue Analysis: BS 7608
MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
Weld SN curve
Class
ΔS
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BS 7608
Major Assumptions:Crack growth dominates fatigue lifeComplex weld geometries can be described by a standard classificationResults independent of material and mean stress for structural steels
30
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BS 7608
Advantages:Manufacturing effects are directly includedLarge empirical database exists
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BS 7608
Limitations:Difficult to determine weld class for complex shapesNo benefit for improving manufacturing process
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Strain-Life Fatigue Modeling
The Similitude Concept states that if the instantaneous strains applied to the ‘test’structure (vehicle suspension, say) and the test specimen are the same, then the response in each case will also be the same and can be described by the material’s e-N curve. Due account can also be made for stress concentrations, variable amplitude loading etc.
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
Stra
in A
mpl
itude
100 101 102 103 104 105 106 107
31
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Fatigue Analysis: Strain-Life
MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
εN curveσε curve
Kf
ΔS , Sm
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 91 of 108
Strain-Life
Major Assumptions:Local stresses and strains control fatigue behaviorPlasticity around stress concentrationsAccurate determination of Kf
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Strain-Life
Advantages:Plasticity effectsMean stress effects
32
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Strain-Life
Limitations:Requires empirical Kf
Long life situations where surface finish and processing variables are important
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 94 of 108
Crack Growth Fatigue Modeling
The Similitude Concept states that if the stress intensity (K) at the tip of a crack in the ‘test’ structure (welded connection on an oil platform leg, say) and the test specimen are the same, then the crack growth response in each case will also be the same and can be described by the Paris relationship. Account can also be made for local chemical environment, if necessary.
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/c
ycle
mMPa,KΔ
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 95 of 108
Fatigue Analysis: Crack Growth
MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
da/dN curve
K
ΔS , Sm
33
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Crack Growth
Major Assumptions:Nominal stress and crack size control fatigue lifeAccurate determination of initial crack size
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 97 of 108
Crack Growth
Advantage:Only method to directly deal with cracks
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 98 of 108
Crack Growth
Limitations:Complex sequence effectsAccurate determination of initial crack size
34
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Choose the Right Model
SimilitudeFailure mechanismSize scale
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Design Philosophy
Safe LifeDamage Tolerant
Fatigue, How and Why © 2004-2007 Darrell Socie, All Rights Reserved 101 of 108
Safe Life
0
100
200
300
400
500
104 105 106 107 108 109
Stre
ss A
mpl
itude
, MPa
Fatigue Life
99 90 11050Percent Survival
0
100
200
300
400
500
104 105 106 107 108 109
Stre
ss A
mpl
itude
, MPa
Fatigue Life
99 90 1105099 90 11050Percent Survival
Choose an appropriate risk and replace critical partsafter some specified interval
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Damage Tolerant
Inspect for cracks larger than a1 and repairCycles
Cra
ck s
ize
a1
a2
Safe Operating Life
Inspection
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Inspection
A Boeing 777 costs $250,000,000
A new car costs $25,000
For every $1 spent inspecting and maintaining a B 777 you can spend only 0.01¢ on a car
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Things Worth Remembering
Questions to askWill a crack nucleate ?Will a crack grow ?How fast will it grow ?
SimilitudeFailure mechanismSize Scale
36
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Fatigue, How and Why
Physics of FatigueMaterial PropertiesSimilitudeFatigue Calculator
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www.FatigueCalculator.com
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Constant Amplitude Calculators
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Finders