Fatigue How and Why

7/29/2019 Fatigue How and Why

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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 2009 Darrell Socie, All Rights Reserved 1 of 120


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


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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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


FatigueS

trength,M

Pa

0.6

0.5

0.35

0 500 1000 1500 2000

250

500

750

1000

1250


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



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MethodStress-LifeStrain-Life

Crack Growth

PhysicsCrack Nucleation

Microcrack GrowthMacrocrack Growth

Size0.01 mm

0.1 - 1 mm> 1mm



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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


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


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


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



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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



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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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Fatigue How and Why

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