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Fatigue, How and Why
Physics of Fatigue
Professor Darrell F. Socie
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
2009 Darrell Socie, All Rights Reserved
Fatigue and Fracture
( Basic Course )
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Fatigue, How and Why
Physics of Fatigue
Material Properties
Similitude
Fatigue Calculator
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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 nucleation
Small crack growth in an elastic-plasticstress field
Macroscopic crack growth in a nominally
elastic stress field
Final fracture
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Mechanisms Crack Nucleation
Nucleation in Slip Bands inside Grain
Nucleation at Grain Boundaries
Nucleation at Inclusions
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1903 - Ewing and Humfrey
Cyclic deformation leadsto the development of slipbands and fatigue cracks
N = 1,000 N = 2,000
N = 10,000 N = 40,000 Nf= 170,000
Ewing, 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
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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 sinlecrystals 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
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Crack at Particle
Material: BS L65 Aluminum
Loading: 63 ksi, R=0 for500,000+ cycles, followed by 68ksi, 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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2219-T851 Cracked Particle
10m
J ames & Morris,ASTM STP 811 Fatigue Mechanisms: Advances in Quantitative Measurement of Physical
Damage, pp. 46-70, 1983.
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Crack at Bonded Particle
Material: BS L65 AluminumLoading: 63 ksi, R=0 for
500,000+ cycles, followed by 68ksi, 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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Crack Initiation at Inclusions
Langford and Kusenberger, Initiation of Fatigue Cracks in 4340 Steel, Metallurgical Transactions, Vol 4, 1977, 553-559
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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
FatigueStrength,M
Pa
0.6
0.5
0.35
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
FatigueStrength,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 deformation
Surface phenomena
Stochastic process
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100 m
bulksurface
10 m
surface
20-25 austenitic steel in symmetrical push-pull fatigue
(20C, p/2= 0.4%) : short cracks on the surface and in the bulk
Surface Damage
From Jacques Stolarz, EcoleNationaleSuperieuredes Mines
Presented at LCF 5 in Berlin, 2003
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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
S
Stage I crack is strongly affected by slipcharacteristics, microstructuredimensions, stress level, extent of neartip 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 718
= 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
CrackL
ength,mm
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 SmoothSpecimens 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
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Strain-Life Data
Reversals, 2Nf
StrainA
mplitude
2
10-5
10-4
0.01
0.1
1
100 101 102 103 104 105 106 107
10-3
10m100 m
1mmfracture Crack size
Most of the life is spent in microcrack growth in theplastic strain dominated region
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Stage II Crack Growth
Locally, the crack grows in shearMacroscopically it grows in tension
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Long Crack Growth
Plastic zone size is much larger than the materialmicrostructure so that the microstructure does notplay 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
Stresses Around a Crack
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Stresses Around a Crack (continued)
Minimum Load
cyclic plastic zone
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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
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5 mcrackgrowth
direction
Mode I Growth
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crack growth direction
10m
slip bandsshear stress
Mode II Growth
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1045 Steel - Tension
Nucleation
Shear
Tension
1.0
0.2
0
0.4
0.8
0.6
1 10 102
103
104
105
106
107
Fatigue Life, 2Nf
Damage
FractionN
/Nf
100 m crack
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Fatigue Life, 2Nf
Damage
FractionN
/Nf
f
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
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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 growingmicrocracks in the finite life region
Crack nucleation is dominate at long lives.
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Fatigue, How and Why
Physics of Fatigue
Material Properties Similitude
Fatigue Calculator
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Characterization
Stress Life Curve
Fatigue Limit Strain Life Curve
Cyclic Stress Strain Curve
Crack Growth CurveThreshold Stress Intensity
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Bending Fatigue
F
stress
time
stress amplitude
stress range
I
cM=
Bending stress:
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SN Curve
200
300
400
500
200
300
400
500
StressA
mplitude,M
Pa
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
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Fatigue Strength
105 106 107 108 109
2014-T4 290 235 186 152 138
2024-T4 297 214 166 145 138
6061-T6 186 152 117 104 90
7075-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
StressAm
plitude,
MP
a
103 104 105 106 107 108 109
fatigue limit
( )bf'f NS
2S =
The fatigue limit is usually only found in steel laboratory specimens
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Very High Cycle Fatigue of Steel
100
1000
104
Cycles
StressAm
plitude,
MP
a
1010103 104 105 106 107 108 109
conventionalfatigue limit
surface failureslarge inclusions
internalinclusions
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Fatigue Damage
100
1000
10000
StressAmplitu
de,
MPa
100
Cycles
101 102 103 104 105 106 107
( )bf'f NS
2
S=
1
10
b
1
'f
fS2
SN
=
10SDamage
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Fatigue Limit Strength Correlation
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
FatigueS
trength,M
Pa
0.6
0.5
0.35
0 500 1000 1500 2000
250
500
750
1000
1250
Tensile Strength, MPa
FatigueS
trength,M
Pa
0.6
0.5
0.35
From Forrest, Fatigue of Metals, Pergamon Press, London, 1962
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Fatigue Limit Strength Correlation
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SN Materials Data
101 10 102 103 106 107105104
Fatigue Life, Reversals
100
1000
10000
StressAmplitude,
MPa
93 steels
17 aluminums
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Strain Controlled Testing
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Cyclic Hardening / Softening
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Stable Hysteresis Loop
ep
Hysteresis loop
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Strain-Life Data
0
100
200
300
400
500
600
0 0.004 0.008 0.012
Strain Amplitude
Stres
sAmplitude
2 2 2
1
= +
E K
n
'
/ '
During cyclic deformation, the material deforms on a path
described by the cyclic stress strain curve
2
2
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Cyclic Stress Strain Curve
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Strain-Life Data - 2Nf
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
StrainAmplitude
100 101 102 103 104 105 106 107
2 Reversals, 2Nf= 1 Cycle, Nf
2
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Elastic and Plastic Strain-Life Data
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
StrainAmplitude
100 101 102 103 104 105 106 107
2
Plastic
Elastic
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Strain-Life Curve
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
StrainAmplitude
100 101 102 103 104 105 106 107
cf
'f
bf
'f )N2()N2(
E2
+
=
c
b
'f
E
'f
2Nt
2
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Transition Fatigue Life
From Dowling, Mechanical Behavior of Materials, 1999
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N Materials Data
Fatigue Life, Reversals
93 steels
17 aluminums
1 10 102 103 106 10710510410-4
10-2
10-3
0.1
10
1
StrainAmplitude
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Crack Growth Testing
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Stress Concentration of a Crack
2 a
+=a21KT
a ~ 10-3for a crack
~ 10-9
KT ~ 2000
appliedlocal 2000=
Traditional material properties like tensile strengthare not very useful for cracked structures
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Stress Intensity Factor
2a
aK =
K characterizes the magnitude of thestresses, strains, and displacements in theneighborhood of a crack tip
Two cracks with the same K will havethe same behavior
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Crack Growth Measurements
2a
Cycles
Cra
cksize
dN
da
a1
a2
2 1
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Crack Growth Data
10-12
10-11
10-10
10-9
10-8
10-7
10-6
1 10 100
CrackGrowthRate,m/cycle
mMPa,K
mKC
dN
da=
KTH
Kc
m ~ 3
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Threshold Region
threshold stress intensity
>
w
afaKTH
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 >
Small cracks are frequently semielliptical surface cracks
2
THc
K63.0a
=
2
u
THc
K52.2a
=
Smooth specimen fatigue limit2
u
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Non-propagating Crack Sizes
Ultimate Strength, MPa
CrackSize,m
mmMPa5KTH =
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
CrackGrow
thRate,m/c
ycle
mMPa,K
mKC
dN
da=
KTH
Kc
Stable growth region
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Crack Growth Data
( )0.3
12
mMPaK109.6dN
da
=
( )25.2
10
mMPaK104.1dN
da
=
( )25.3
12
mMPaK106.5dN
da
=
Ferritic-Pearlitic Steel:
Martensitic Steel:
Austenitic Stainless Steel:
Barsom, Fatigue Crack Propagation in Steels of Various Yield StrengthsJ ournal of Engineering for Industry, Trans. ASME, Series B, Vol. 93, No. 4, 1971, 1190-1196
5 10 100
10-7
10-6
10-8
CrackGrowthRate,m/cycle
K, MPam
yield252273392
415
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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
CrackLength,mm
0 50 100 150 200 250 300 350
Cycles x103
Virkler, Hillberry and Goel, The Statistical Nature of Fatigue Crack Propagation, J ournal of Engineering Materials
and Technology, Vol. 101, 1979, 148-153
Things Worth Remembering
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Things Worth Remembering
MethodStress-LifeStrain-Life
Crack Growth
PhysicsCrack Nucleation
Microcrack GrowthMacrocrack Growth
Size0.01 mm
0.1 - 1 mm> 1mm
Fatigue, How and Why
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Fatigue, How and Why
Physics of Fatigue
Material Properties Similitude
Fatigue Calculator
Fatigue Analysis
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Fatigue Analysis
Material
Data
Component
Geometry
Service
Loading
Analysis
Fatigue
Life Estimate
?
The Similitude Concept
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The Similitude Concept
Why Fatigue Modeling Works !
What is the Similitude Concept
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p
The Similitude Concept allows engineers to
relate the behavior of small-scale cyclicmaterial test specimens, defined undercarefully controlled conditions, to the likely
performance of real structures subjected tovariable amplitude fatigue loads under eithersimulated or actual service conditions.
Fatigue Analysis Techniques
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g y q
Stress - Life
BS 7608, Eurocode 3Strain - Life
Crack Growth
Life Estimation
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MethodStress-LifeBS 7608
Strain-Life
Crack Growth
PhysicsCrack Nucleation
Crack GrowthMicrocrack Growth
Macrocrack Growth
Size0.01 mm1 - 10 mm0.1 - 1 mm
> 1mm
Stress-Life Fatigue Modeling
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g g
P
Fixed
End
The Similitude Concept states that if theinstantaneous loads applied to the test
structure (wing spar, say) and the testspecimen are the same, then the responsein each case will also be the same and canbe described by the materials S-N curve.
100
1000
10000
StressAmplitude,
MPa
100
Cycles101 102 103 104 105 106 107
Fatigue Analysis: Stress-Life
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g y
MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
SN curveKa, Ks,
Kf
S , Sm
Stress-Life
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Major Assumptions:
Most of the life is consumed nucleating cracksElastic deformation
Nominal stresses and material strength controlfatigue life
Accurate determination of Kffor each geometryand material
Stress-Life
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Advantages:
Changes in material and geometry can easily beevaluated
Large empirical database for steel with standardnotch shapes
Stress-Life
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Limitations:
Does not account for notch root plasticity
Mean stress effects are often in error
Requires empirical Kffor good results
BS 7608 Fatigue Modeling
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The Similitude Concept states that if theinstantaneous loads applied to the teststructure (welded beam on a bulldozer, say)and the test specimen (standard fillet weld)
are the same, then the response in eachcase will also be the same and can bedescribed by one of the standard BS 7608Weld Classification S-N curves.
10
100
1000
105
Cycles
StressR
ange,
MPa
108107106
Weld Classifications
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D E
F2 G
Fatigue Analysis: BS 7608
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MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
Weld SN curve
Class
S
BS 7608
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Major Assumptions:
Crack growth dominates fatigue lifeComplex weld geometries can be described by a
standard classification
Results independent of material and mean stress
for structural steels
BS 7608
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Advantages:
Manufacturing effects are directly included
Large empirical database exists
BS 7608
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Limitations:
Difficult to determine weld class for complex
shapes
No benefit for improving manufacturing process
Strain-Life Fatigue Modeling
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The Similitude Concept states that if theinstantaneous strains applied to the teststructure (vehicle suspension, say) and thetest specimen are the same, then theresponse in each case will also be the same
and can be described by the materials e-Ncurve. Due account can also be made forstress concentrations, variable amplitudeloading etc.
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
StrainAmplitude
100 101 102 103 104 105 106 107
Fatigue Analysis: Strain-Life
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MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
N curve curve
Kf
S , Sm
Strain-Life
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Major Assumptions:
Local stresses and strains control fatigue
behavior
Plasticity around stress concentrations
Accurate determination of Kf
Strain-Life
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Advantages:
Plasticity effects
Mean stress effects
Strain-Life
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Limitations:
Requires empirical Kf Long life situations where surface finish and
processing variables are important
Crack Growth Fatigue Modeling
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The Similitude Conceptstates that if the stress
intensity (K) at the tip of acrack in the test structure(welded connection on an oilplatform leg, say) and thetest specimen are the same,
then the crack growthresponse in each case willalso be the same and can bedescribed by the Parisrelationship. Account can
also be made for localchemical environment, ifnecessary.
10-12
10-11
10-10
10-9
10-8
10-7
10-6
1 10 100
CrackG
rowthRate,m/cycle
mMPa,K
Fatigue Analysis: Crack Growth
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MaterialData
ComponentGeometry
ServiceLoading
Analysis FatigueLife Estimate
da/dN curve
K
S , Sm
Crack Growth
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Major Assumptions:
Nominal stress and crack size control fatigue life
Accurate determination of initial crack size
Crack Growth
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Advantage:
Only method to directly deal with cracks
Crack Growth
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Limitations:
Complex sequence effects
Accurate determination of initial crack size
Choose the Right Model
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Similitude
Failure mechanism
Size scale
Design Philosophy
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Safe Life
Damage Tolerant
Safe Life500500
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0
100
200
300
400
500
104 105 106 107 108 109
StressAmplitud
e,
MPa
Fatigue Life
99 90 11050
Percent Survival
0
100
200
300
400
500
104 105 106 107 108 109
StressAmplitud
e,
MPa
Fatigue Life
99 90 1105099 90 11050
Percent Survival
Choose an appropriate risk and replace critical partsafter some specified interval
Damage Tolerant
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Inspect for cracks larger than a1 and repairCycles
Cracksize
a1
a2
Safe Operating Life
Inspection
Inspection
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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
Things Worth Remembering
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Questions to ask
Will a crack nucleate ?
Will a crack grow ?
How fast will it grow ?
Similitude
Failure mechanism
Size Scale
Fatigue, How and Why
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Physics of Fatigue
Material Properties
Similitude
Fatigue Calculator
www.FatigueCalculator.com
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Constant Amplitude Calculators
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Finders
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Deterministic Analysis
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Deterministic Analysis (continued)
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Deterministic Analysis (continued)
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Deterministic Analysis Results
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Probabilistic Analysis
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Probabilistic Analysis (continued)
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Probabilistic Analysis (continued)
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Probabilistic Analysis Results
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Fatigue and Fracture( Basic Course )
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