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Fatigue, How and Why Physics of Fatigue
Professor Darrell F. Socie Mechanical Science and Engineering
University of Illinois
© 2004-2013 Darrell Socie, All Rights Reserved
Fatigue and Fracture
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 1 of 141
Fatigue, How and Why
Physics of Fatigue Material Properties Similitude Fatigue Calculator
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 2 of 141
10-10 10-8 10-6 10-4 10-2 100 102
Specimens Structures Atoms 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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 3 of 141
The Fatigue Process
Crack nucleation Small crack growth in an elastic-plastic
stress field Macroscopic crack growth in a nominally
elastic stress field Final fracture
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 4 of 141
Mechanisms Crack Nucleation
Nucleation in Slip Bands inside Grain Nucleation at Grain Boundaries Nucleation at Inclusions
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 5 of 141
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 = 170,000 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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 6 of 141
Crack Nucleation
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 7 of 141
Slip Band in Copper
Polak, J. Cyclic Plasticity and Low Cycle Fatigue Life of Metals, Elsevier, 1991
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 8 of 141
Slip Band Formation
Loading Unloading
Extrusion
Undeformed material
Intrusion
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 9 of 141
Slip Bands
Ma, B-T and Laird C. “Overview of fatigue behavior in copper sinle crystals –II Population, size, distribution and growth Kinetics of stage I cracks for tests at constant strain amplitude”, Acta Metallurgica, Vol 37, 1989, 337-348
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 10 of 141
2124-T4 Cracking in Slip Bands
N = 60
N = 2000 N = 1200
N = 300 N = 240
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 11 of 141
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.
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 12 of 141
2219-T851 Cracked Particle
10µm James & Morris, ASTM STP 811 Fatigue Mechanisms: Advances in Quantitative Measurement of Physical
Damage, pp. 46-70, 1983.
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 13 of 141
Crack at Bonded 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.
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 14 of 141
7075-T6 Cracking at Inclusion
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 15 of 141
Crack Initiation at Inclusions
Langford and Kusenberger, “Initiation of Fatigue Cracks in 4340 Steel”, Metallurgical Transactions, Vol 4, 1977, 553-559
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 16 of 141
Subsurface Crack Initiation
Y. Murakami, Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions, 2002
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 17 of 141
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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 18 of 141
Crack Nucleation Summary
Highly localized plastic deformation Surface phenomena Stochastic process
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 19 of 141
100 µm
bulk surface
10 µm
surface
20-25 austenitic steel in symmetrical push-pull fatigue (20°C, ∆εp/2= ±0.4%) : short cracks on the surface and in the bulk
Surface Damage
From Jacques Stolarz, Ecole Nationale Superieure des Mines Presented at LCF 5 in Berlin, 2003
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 20 of 141
Stage I Stage II
loading direction
free surface
Stage I and Stage II
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 21 of 141
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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 22 of 141
Small Cracks at Notches
D a crack tip plastic zone
notch plastic zone
notch stress field
Crack growth controlled by the notch plastic strains
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 23 of 141
Small Crack Growth
1.0 mm
N = 900
Inconel 718 ∆ε = 0.02 Nf = 936
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 24 of 141
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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 25 of 141
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 0.025 0.03 0.025 0.02 0.015 0.01 0.005
A B C D
F
E
Crack Length, mm
da/dN, mm/cycle
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 26 of 141
Strain-Life Data
Reversals, 2Nf
Stra
in A
mpl
itude
∆ε
2
10-5
10-4
0.01
0.1
1
100 101 102 103 104 105 106 107
10-3
10µm 100 µm
1mm fracture Crack size
Most of the life is spent in microcrack growth in the plastic strain dominated region
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 27 of 141
Stage II Crack Growth
Locally, the crack grows in shear Macroscopically it grows in tension
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 28 of 141
Long Crack Growth
Plastic zone size is much larger than the material microstructure so that the microstructure does not play such an important role.
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 29 of 141
Material strength does not play a major role in fatigue crack growth
Crack Growth Rates of Metals
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 30 of 141
Maximum Load
monotonic plastic zone
σ
Stresses Around a Crack
σ
ε
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 31 of 141
Stresses Around a Crack (continued)
Minimum Load σ
ε
cyclic plastic zone
σ
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 32 of 141
Crack Closure
S = 250
b
S = 175
c
S = 0
a
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 33 of 141
Crack Opening Load Damaging portion of loading history
Nondamaging portion of loading history
Opening load
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 34 of 141
Mode Iopening
Mode IIin-plane shear
Mode IIIout-of-plane shear
Mode I, Mode II, and Mode III
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 35 of 141
5 µmcrac
k gr
owth
dire
ctio
n
Mode I Growth
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 36 of 141
crack growth direction
10 µm
slip bands shear stress
Mode II Growth
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 37 of 141
1045 Steel - Tension
Nucleation Shear
Tension
1.0
0.2
0
0.4
0.8
0.6
1 10 10 2 10 3 10 4 10 5 10 6 10 7
Fatigue Life, 2N f
Dam
age
Frac
tion
N/N
f
100 µm crack
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 38 of 141
Fatigue Life, 2N f
Dam
age
Frac
tion
N/N
f f
Nucleation
Shear
Tension
1 10 10 2 10 3 10 4 10 5 10 6 10 7
1.0
0.2
0
0.4
0.8
0.6
1045 Steel - Torsion
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 39 of 141
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 region
Crack nucleation is dominate at long lives.
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 40 of 141
Fatigue, How and Why
Physics of Fatigue Material Properties Similitude Fatigue Calculator
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 41 of 141
Characterization
Stress Life Curve Fatigue Limit
Strain Life Curve Cyclic Stress Strain Curve
Crack Growth Curve Threshold Stress Intensity
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 42 of 141
Bending Fatigue
F
stre
ss
time
stress amplitude
stress range
IcM
=σBending stress:
ω
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 43 of 141
SN Curve
200
300
400 500
200
300
400
500 St
ress
Am
plitu
de, M
Pa
105 106 107 108 109
1x108 2x108 3x108 4x108 5x108 0
Cycles to Failure
Cycles to Failure
Monel Alloy
1 hour 1 day 1 month 1 year Testing time @ 30 Hz
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 44 of 141
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 Life Alloy
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 45 of 141
6061-T6 Aluminum Test Data
Sharpe et. al. Fatigue Design of Aluminum Components and Structures , 1996
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 46 of 141
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
=∆
The fatigue limit is usually only found in steel laboratory specimens
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 47 of 141
Very High Cycle Fatigue of Steel
100
1000
104
Cycles
Stre
ss A
mpl
itude
, MPa
1010 103 104 105 106 107 108 109
conventional fatigue limit
surface failures large inclusions
internal inclusions
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 48 of 141
Fatigue Damage
100
1000
10000
Stre
ss A
mpl
itude
, MP
a
100
Cycles 101 102 103 104 105 106 107
( )bf'f NS
2S
=∆
1
10
b1
'f
f S2SN
∆=
10SDamage ∆∝
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 49 of 141
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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 50 of 141
Fatigue Limit Strength Correlation
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 51 of 141
SN Materials Data
10 1 10 102 103 106 107 105 104
Fatigue Life, Reversals
100
1000
10000
Stre
ss A
mpl
itude
, MP
a
93 steels
17 aluminums
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 52 of 141
Strain Controlled Testing
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Cyclic Hardening / Softening
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Stable Hysteresis Loop
∆σ
∆ε
∆εe ∆εp
Hysteresis loop
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 55 of 141
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
∆ε ∆σ ∆σ2 2 2
1
= +
E K
n
'
/ '
During cyclic deformation, the material deforms on a path described by the cyclic stress strain curve
∆ε 2
∆σ
2
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 56 of 141
Cyclic Stress Strain Curve
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Strain-Life Data ∆ε - 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
∆ε
2
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 58 of 141
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
∆ε
2 Plastic
Elastic
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 59 of 141
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=
ε∆
c
b
'fε
E
'fσ
2Nt
∆ε
2
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 60 of 141
Transition Fatigue Life
From Dowling, Mechanical Behavior of Materials, 1999
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 61 of 141
εN Materials Data
Fatigue Life, Reversals
93 steels
17 aluminums
1 10 102 103 106 107 105 104 10-4
10-2
10-3
0.1
10
1
Stra
in A
mpl
itude
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 62 of 141
Crack Growth Testing
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 63 of 141
Stress Concentration of a Crack
2 a
ρ
ρ+=
a21KT
a ~ 10-3
for a crack
ρ ~ 10-9
KT ~ 2000
appliedlocal 2000σ=σ
Traditional material properties like tensile strength are not very useful for cracked structures
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 64 of 141
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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 65 of 141
Crack Growth Measurements
σ
σ
2a
Cycles
Cra
ck s
ize
dNda
a1
a2
σ2 σ1
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 66 of 141
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,K∆
mKCdNda
∆=
∆KTH
Kc
m ~ 3
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 67 of 141
Threshold Region
threshold stress intensity
πσ∆>∆
wafaKTH
operating stresses
flaw size
flaw shape
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Threshold Stress Intensity
From Dowling, Mechanical Behavior of Materials, 1999
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 69 of 141
Non-propagating Crack Sizes
a212.1KTH ππ
σ∆>∆
Small cracks are frequently semielliptical surface cracks
2TH
cK63.0a
σ∆∆
=
2
u
THc
K52.2a
σ
∆=
Smooth specimen fatigue limit 2
uσ≈
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 70 of 141
Non-propagating Crack Sizes
Ultimate Strength, MPa
Cra
ck S
ize,
mm mMPa5KTH =∆
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 71 of 141
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,K∆
mKCdNda
∆=
∆KTH
Kc
Stable growth region
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 72 of 141
Crack Growth Data
( ) 0.312 mMPaK109.6dNda
∆×= −
( ) 25.210 mMPaK104.1dNda
∆×= −
( ) 25.312 mMPaK106.5dNda
∆×= −
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
∆K, MPa√m
σyield 252 273 392 415
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 73 of 141
Aluminum Crack Growth Rate Data
Sharp, Nordmark and Menzemer, Fatigue Design of Aluminum Components and Structures, 1996
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 74 of 141
Crack Growth Data
0
10
20
30
40
50
Cra
ck L
engt
h, m
m
0 50 100 150 200 250 300 350 Cycles 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 © 2004-2013 Darrell Socie, All Rights Reserved 75 of 141
Things Worth Remembering
Method Stress-Life Strain-Life
Crack Growth
Physics Crack Nucleation
Microcrack Growth Macrocrack Growth
Size 0.01 mm
0.1 - 1 mm > 1mm
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 76 of 141
Fatigue, How and Why
Physics of Fatigue Material Properties Similitude Fatigue Calculator
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 77 of 141
Fatigue Analysis
Material Data
Component Geometry
Service Loading
Analysis Fatigue Life Estimate
?
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 78 of 141
The Similitude Concept
Why Fatigue Modeling Works !
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 79 of 141
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.
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 80 of 141
Fatigue Analysis Techniques
Stress - Life BS 7608, Eurocode 3 Strain - Life Crack Growth
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 81 of 141
Life Estimation
Method Stress-Life BS 7608
Strain-Life Crack Growth
Physics Crack Nucleation
Crack Growth Microcrack Growth Macrocrack Growth
Size 0.01 mm
1 - 10 mm 0.1 - 1 mm
> 1mm
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 82 of 141
Stress-Life Fatigue Modeling
P
Fixed End
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
, MP
a
100
Cycles 101 102 103 104 105 106 107
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 83 of 141
Fatigue Analysis: Stress-Life
Material Data
Component Geometry
Service Loading
Analysis Fatigue Life Estimate
SN curve Ka, Ks, …
Kf
∆S , Sm
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 84 of 141
Stress-Life
Major Assumptions: Most of the life is consumed nucleating cracks Elastic deformation Nominal stresses and material strength control
fatigue life Accurate determination of Kf for each geometry
and material
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 85 of 141
Stress-Life
Advantages: Changes in material and geometry can easily be
evaluated Large empirical database for steel with standard
notch shapes
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 86 of 141
Stress-Life
Limitations: Does not account for notch root plasticity Mean stress effects are often in error Requires empirical Kf for good results
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 87 of 141
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
, MP
a
108 107 106
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 88 of 141
Weld Classifications
D E
F2 G
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 89 of 141
Fatigue Analysis: BS 7608
Material Data
Component Geometry
Service Loading
Analysis Fatigue Life Estimate
Weld SN curve
Class
∆S
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 90 of 141
BS 7608
Major Assumptions: Crack growth dominates fatigue life Complex weld geometries can be described by a
standard classification Results independent of material and mean stress
for structural steels
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 91 of 141
BS 7608
Advantages: Manufacturing effects are directly included Large empirical database exists
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 92 of 141
BS 7608
Limitations: Difficult to determine weld class for complex
shapes No benefit for improving manufacturing process
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 93 of 141
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
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 94 of 141
Fatigue Analysis: Strain-Life
Material Data
Component Geometry
Service Loading
Analysis Fatigue Life Estimate
εN curve σε curve
Kf
∆S , Sm
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 95 of 141
Strain-Life
Major Assumptions: Local stresses and strains control fatigue
behavior Plasticity around stress concentrations Accurate determination of Kf
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 96 of 141
Strain-Life
Advantages: Plasticity effects Mean stress effects
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 97 of 141
Strain-Life
Limitations: Requires empirical Kf
Long life situations where surface finish and processing variables are important
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 98 of 141
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,K∆
Fatigue, How and Why © 2004-2013 Darrell Socie, All Rights Reserved 99 of 141
Fatigue Analysis: Crack Growth
Material Data
Component Geometry
Service Loading
Analysis Fatigue Life Estimate
da/dN curve
K
∆S , Sm
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Crack Growth
Major Assumptions: Nominal stress and crack size control fatigue life Accurate determination of initial crack size
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Crack Growth
Advantage: Only method to directly deal with cracks
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Crack Growth
Limitations: Complex sequence effects Accurate determination of initial crack size
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Choose the Right Model
Similitude Failure mechanism Size scale
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Design Philosophy
Safe Life Damage Tolerant
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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 parts after some specified interval
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Damage Tolerant
Inspect for cracks larger than a1 and repair Cycles
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 ask Will a crack nucleate ? Will a crack grow ? How fast will it grow ?
Similitude Failure mechanism Size Scale
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Fatigue, How and Why
Physics of Fatigue Material Properties Similitude eFatigue
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Some Observations
Most fatigue failures are not the result of an expert using the wrong analysis etc.
Most fatigue failures are a result of a non-expert not considering fatigue because it is too complicated, not enough data etc.
Fatigue will no longer be taught in the major research universities as they focus on new science.
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Prof Yukitaka Murakami
Science in the Sunlight Science in the Shade
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Science in the Sunlight
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Science in the Shade
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A Common Viewpoint (controversial)
Fatigue is reasonably well understood, major problems are solved and current research is applications driven towards investigating special cases and improving the accuracy of our evaluations.
Fatigue is assessment is just like finite element
analysis, buy some software and make a color plot.
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Fatigue Calculators
There is a need for some fatigue analysis tools that take only a few minutes to learn so non-experts can reliably conduct a fatigue assessment.
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www.eFatigue.com
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Summary
eFatigue – Bring fatigue assessment out of the shade into the sunlight where many people can have access fatigue technology on demand.
Fatigue and Fracture