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Fatigue Made Easy

Historical Introduction

Professor Darrell F. Socie

Mechanical Science and EngineeriU i it f Illi i



University of Illinois

Contact Information

Darrell Socie

Mechanical Science and Engineering1206 West Green

Urbana, Illinois 61801

Office: 3015 Mechanical Engineering La

[email protected]

mailto:[email protected]

mailto:[email protected]



Surveying Made Easy

1688 1st

1793 12th



… Made Easy



Shakespheare Made Easy

Original

Translation



Seminar Outline

1. Historical background

2. Physics of fatigue3. Characterization of materials

4. Similitude ( why fatigue modeling works )

5. Variability6. Mean stress

7. Stress concentrations

8. Surface effects9 Variable amplitude loading



19th Century

1829 Albert Repeated Load

1839 Poncelet “fatigue”

1843 Rankine Stress Concent

1860 Wohler Systematic Inve

1886 Baushinger Cyclic Deforma

1890 Goodman Mean Stresses

1903 Ewing & Humfrey Fatigue Mecha



The first major transportation

disaster-Versailles accident o

May 11, 1842

At the dawn of the industrial



Versailles



“I have this day to announce to you one of th

frightful events that has occurred in modern The train of the left bank was unusually long

1500 to 1800 passengers. On arriving betwe

Meudon and Bellevue the axle tree of the firs

broke. … The second engine … passed ove

the boiler burst … The carriages arrived of c

and passed over the wreck, when six of them

… instantly ignited. Three were totally consuwithout the possibility of escape to the unhap

‘The Times’, May 11, 1842



Early steam engine



Typical broken axle of the 1



Expert opinions of the time

“I never met one which did not present a

crystallization fracture…”

“the principal causes … are percussion, h

magnetism”

“the change … may take place instantane

“steam can speedily cause iron to becom

magnetic”



Rankine 1820 - 1872

Trained as a c



William Rankine’s second p

Stated that deterioration of axles is gradua

“the fractures appear to have commenced

smooth, regularly-formed, minute fissure,

all round the neck of the journal, and pene

an average to a depth of half an inch. … u

thickness of sound iron in the center becainsufficient to support the shocks to which

exposed.”



Rankine ...

“In all the specimens the iron remained fi

proving that no material change had take

the structure”

He noted that fractures occurred at sharp

He recommended that the journals be for

large curve in the shoulder (which is exac



Wöhler 1819 - 1914

Prussian Railway

Work done before the

of the metallurgica

Critical value of st

which failure wil



Wöhler Tests

Wöhler circa 1850



Wöhler Observations

Steel will rupture at stress less than the ela

the stress is repeated a sufficient number o

Stress range rather than maximum stress

determines the number of cycles

There appears to be a limiting stress range

may be applied indefinitely without failure

As the maximum stress increases, the limit

range decreases



Bauschinger 1834 - 1893

Cyclic Behavior o



Goodman

Mechanics Applied to Engineering

John Goodman, 1890

“.. whether the assumptions of the

theory are justifiable or not …. We

adopt it simply because it is theeasiest to use, and for all practical

purposes, represents Wöhlers data.



1903 - Ewing and Humfrey

Cyclic deforma

to the develop

bands and fati

N = 1,000 N = 2,000



Their Description of Fatigue

The course of the breakdown was as follows: Thexamination, made after a few reversals of the sshowed slip lines on some of the crystals … aftreversals of stress additional slip lines appeared

After many reversals they changed into compara

wide bands with rather hazily defined edges …parts of the crystals became almost covered witmarkings …. at this stage some of the crystals cracked.

Once an incipient crack forms across a set of cry



20th Century

1920 Griffith Fracture Mech

1945 Miner Cumulative Da

1954 Coffin & Manson Plastic Strains

1961 Paris Crack Growth1963 Peterson Strain-Life Met

1967 Endo Cycle Counting



Circa 1910 Data Acquisition



Early Strip Chart



Griffith 1893-1963

Circa1920 studied scr

the effect of surface fifatigue for the Royal A

Establishment

2a



Miner

The phenomenon

cumulative damag

repeated loads wato be related to th

absorbed by a sp

“proved” linear da



1954 - Coffin and Manson

R e c

i p r o c a l o f e l o n g a t i o n a t f a i l

u r e 1 / b

Cycles

E l a s t i c + i n e l a

s t i c s t r a i n c h a

n g e



1961 - Paris



1963 Peterson



Endo 1925 - 1989

What could be more



1980’s – Software Develop

Develop

the loca

approac

Fatigue

growth mestablis



1990’s Finite Element



2000’s

Integrated Systems

Gigacycle FatigueMicro/nano Fatigue



Integrated Systems

Component

Loads

LoadingLocations and

FE

MBD



Gigacycle Fatigue

surface

microcracksmicrocrack

arrest



Micro/ Nano Fatigue



Things Worth Rememberin

The physics of fatigue has been wel

for over 100 years Application of this knowledge still po

challenges



Fatigue Seminar



Fatigue Made Easy

Physics of Fatigue Damag


Mechanical Science and EngineeriUniversity of Illinois



Seminar Outline


2. Physics of fatigue

3. Characterization of materials

4. Similitude (why fatigue modeling works)

5. Variability

6. Mean stress


8. Surface effects

9 Variable amplitude loading



10-10 10-8 10-6 10-4 10-2 100

Specimens Atoms Dislocations Crystals

Size Scale for Studying Fa

Understand the physics on this scale



The Fatigue Process

Crack nucleation

Small crack growth in an elastic-plastress field

Macroscopic crack growth in a nom

elastic stress field

Final fracture



1903 - Ewing and Humfrey

Cyclic deform

to the develobands and fa

N = 1,000 N = 2,000



Crack Nucleation



Slip Band in Copper



Slip Band Formation

Extrusion

Undeformedmaterial

Intrusion



Slip Bands



Crack Initiation at Inclusion



Subsurface Crack Initiation



Fatigue Limit and Strength C

250

500

750

1000

1250

F

a t i g u e S t r e n g t h , M

P a

250

500

750

1000

1250

F


P a



Crack Nucleation Summary

Highly localized plastic deformation

Surface phenomena Stochastic process



bulksurface

10 µm

surface

Surface Damage



free

surface

Stage I and Stage II



Stage I Crack Growth

Single primary slip system

individual grain

S

S

Stage I crack is strongl



Small Cracks at Notches

D acrack tip plastic zone

notch plastic zone

notch stress fie



Small Crack Growth

Inconel 718

= 0.02



0.5

1

1.5

2

2.5

J-603

F-495 H-491

I-471 C-399

C r a c k L e n g t h , m m

Crack Length Observations



Crack - Microstructure Inte

10-6

Fda/dN, mm/cycle



Strain-Life Data

S t r a i n A

m p l i t u d e

2

10-5

10-4

0.01

0.1

1

100 101 102 103 104 105 1

10-3

10m100 m

1mmfracture Crack size



Stage II Crack Growth



Long Crack Growth

Plastic zone size is much larger than the m



Crack Growth Rates of Meta



Maximum Load

Stresses Around a Crack



Stresses Around a Crack (c

Minimum Load

cyclic plastic zone



Crack Closure

b ca



Crack Opening Load

Damaging portion of loading history

Opening load



Mode I

opening

Mode II

in-plane shear

Mode

out-of-plan

Mode I, Mode II, and Mode



5 m c r a c k g r o w t h d i r e c t i o n

Mode I Growth



crack gro

slip bandsshear stress

Mode II Growth



1045 Steel - Tension

Nucleation

Shear

Tension

1.0

0.2

0

0.4

0.8

0.6

D a m a g e

F r a c t i o n

N / N f

100 m crack



D a m a g e

F r a c t i o n

N / N f

f

Nucle

Shear

1.0

0.2

0

0.4

0.8

0.6

1045 Steel - Torsion




Fatigue is a localized process involv

nucleation and growth of cracks to fa Fatigue is caused by localized plasti

deformation.

Most of the fatigue life is consumed microcracks in the finite life region

Crack nucleation is dominate at long



Fatigue Seminar



Fatigue Made Easy

Characterization of Materia


Mechanical Science and EngineeriUniversity of Illinois



Seminar Outline





5. Variability

6. Mean stress


8. Surface effects




Characterization

Stress Life Curve

Fatigue Limit

Strain Life Curve

Cyclic Stress Strain Curve

Crack Growth Curve Threshold Stress Intensity



Bending Fatigue

F

s t r e s s

stress am

stress rang

cMBending stress:



SN Curve

200

300

400

500

200

300

400

500

S t r e s s A

m p l i t u d e , M

P a

1x108 2x108 3x108 4x108 5x1080Cycles to Failure

Monel Alloy



SN Curve

100

1000

10000

S t r e s s A m

p l i t u d e , M P

a

fatigue limit

bf 'f NS

2S



Fatigue Damage

100

1000

10000

S t r e s s A m p l i t u d e , M P a

100

Cycles

101 102 103 104 105 106 107

bf

'

f NS2

S

1

10

b

1

'

f

f

S2

SN



Fatigue Limit Strength Corr

250

500

750

1000

1250

F


P a

250

500

750

1000

1250

F


P a



Fatigue Limit Strength Corr



SN Materials Data

100

1000

10000

S t r e s s A m p

l i t u d e , M P a

93

17



Strain Controlled Testing



Cyclic Hardening / Softenin



Stable Hysteresis Loop

Hysteresis loop



Strain-Life Data

0

100

200

300

400

500

600

0 0 004 0 008 0 012

S t r e s s A m p l i t u d e

2 2 2

E K

2



Cyclic Stress Strain Curve



Strain-Life Data

- 2Nf

10-4

0.001

0.01

0.1

1

S t r a i n A m

p l i t u d e

2



Elastic and Plastic Strain-L

10-4

0.001

0.01

0.1

1

S t r a i n A m

p l i t u d e

2 Plastic

Elastic



Strain-Life Curve

10-4

0.001

0.01

0.1

1

S t r a i n A m

p l i t u d e

b

f

'

f )N2(

E2

c

b

'

f

E

'

f

2Nt

2



Transition Fatigue Life



N Materials Data

93 steels

17 alumin

10-2

10-3

0.1

10

1

S t r a i n

A m p l i t u d e



Crack Growth Testing



Stress Concentration of a C

2 a

a21KT

a ~ 10-3

for a crack

~ 10-9

KT ~ 2000

aplocal 2000



Stress Intensity Factor

2a

aK

K characterizes the magnitude ostresses, strains, and displacem

neighborhood of a crack tip

Two cracks with the same K will

the same behavior



Crack Growth Measuremen

2a C r a c

k s i z e

a1

a2

2



Crack Growth Data

10-11

10-10

10-9

10-8

10-7

10-6

Cr

a c k G r o w t h R a t e , m / c

y c l e

mKCdN

da

Kc

m ~ 3



Threshold Region

threshold stress intensity

w

af aKTH

operating stresses

flaw size

flaw shape



Threshold Stress Intensity



Non-propagating Crack Siz

a212.1KTH

Small cracks are frequently semielliptical surfa

2

TH

c

K

63.0a

2

Smooth specimen fatigue limit2

u



Non-propagating Crack Siz

C r a c

k S i z e , m

mMP5KTH

0

0.2

0.4

0.6

0.8

1



Stable Crack Growth

10-11

10-10

10-9

10-8

10-7

10-6

C r a c k G r o w t h R a t e , m / c

y c l e

mKCdN

da

Kc

Stable growth region



Crack Growth Data

12

MK109.6dN

da

10 MK104.1

dNda

12 MK1065da

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless St

10-7

10-6

C r a c k G r o w t h

R a t e , m / c y c l

e

yield

252

273

392

415




MethodStress-Life

Strain-Life

Crack Growth

PhysicsCrack Nucleation

Microcrack Growth

Macrocrack Growth

0



Fatigue Seminar



Fatigue Made Easy

Similitude

Professor Darrell F. SocieMechanical Science and Engineeri




Seminar Outline




4. Similitude ( why fatigue modeling works )

5. Variability

6. Mean stress


8. Surface effects




Fatigue Analysis

Material

Data

ComponentGeometry

Service

AnalysisFa

Life E

?



The Similitude Concept

Why Fatigue Modeling Wo



What is the Similitude Conc

The “Similitude Concept” allows engi

relate the behavior of small-scalmaterial test specimens, definedcarefully controlled conditions, to thperformance of real structures subjvariable amplitude fatigue loads und

simulated or actual service conditions



Fatigue Analysis Technique

Stress - Life

BS 7608, Eurocode 3

Strain - Life

Crack Growth



S Lif F i M d li



Stress-Life Fatigue Modelin

P

Fixed

End

The Similitude Conceptinstantaneous loads apstructure (wing spar, sspecimen are the same,in each case will also be

1000

10000

A m

p l i t u d e , M P a

F i A l i S Li



Fatigue Analysis: Stress-Li

MaterialData

ComponentGeometry

S

Analysis

SN curveKa, Ks, …

Kf

St Lif



Stress-Life

Major Assumptions:

Most of the life is consumed nucleating

Elastic deformation

Nominal stresses and material strength

fatigue life Accurate determination of Kf for each g

and material

St Lif



Stress-Life

Advantages:

Changes in material and geometry canevaluated

Large empirical database for steel withnotch shapes

St Lif



Stress-Life

Limitations:

Does not account for notch root pla

Mean stress effects are often in er

Requires empirical Kf for good resu

BS 7608 F ti M d li



BS 7608 Fatigue Modeling

The Similitude Concept instantaneous loads appstructure (welded beam o

and the test specimen (sare the same then the100

1000

a n g

e , M P a

W ld Cl ifi ti



Weld Classifications

D E

F2 G

F ti A l i BS 7608



Fatigue Analysis: BS 7608

MaterialData

ComponentGeometry

S

Analysis

Weld SN curve

Class

BS 7608



BS 7608

Major Assumptions:

Crack growth dominates fatigue life

Complex weld geometries can be descstandard classification

Results independent of material and mfor structural steels

BS 7608



BS 7608

Advantages:

Manufacturing effects are directly i

Large empirical database exists



St i Lif F ti M d li



Strain-Life Fatigue Modelin

The Similitude Conceptinstantaneous strains astructure (vehicle suspentest specimen are the

response in each case w0.001

0.01

0.1

1

n A m

p l i t u d e

F ti A l i St i Lif



Fatigue Analysis: Strain-Lif

MaterialData

ComponentGeometry

S

Analysis

N curve

curve

Kf

St i Lif



Strain-Life

Major Assumptions:

Local stresses and strains control f

behavior

Plasticity around stress concentrat

Accurate determination of Kf

Strain Life



Strain-Life

Advantages:

Plasticity effects

Mean stress effects

Strain Life



Strain-Life

Limitations:

Requires empirical Kf

Long life situations where surface fprocessing variables are important

Crack Growth Fatigue Mod



Crack Growth Fatigue Mod

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 Paris

relationship Account canl b d f l l

10-9

10-8

10-7

10-6

o w t h R a t e , m / c y c l e

Fatigue Analysis: Crack Gr



Fatigue Analysis: Crack Gr

MaterialData

ComponentGeometry

S

Analysis

da/dN curve

K

Crack Growth



Crack Growth

Major Assumptions:

Nominal stress and crack size control

Accurate determination of initial crack

Crack Growth



Crack Growth

Advantage:

Only method to directly deal with c

Crack Growth



Crack Growth

Limitations:

Complex sequence effects

Accurate determination of initial cra

Choose the Right Model



Choose the Right Model

Similitude

Failure mechanism

Size scale

Design Philosophy



Design Philosophy

Safe Life

Damage Tolerant

Safe Life



Safe Life

0

100

200

300

400

500

104 105 106 107

S t r e s s A m p l i t u d e ,

M P a

Fatigue Life

99 90 1050

Percent Survival

0

100

200

300

400

500

104 105 106 107

S t r e s s A m p l i t u d e ,

M P a

Fatigue Life

99 90 105099 90 1050

Percent Survival

Damage Tolerant



Damage Tolerant

C

r a c k s i z e

a1

a2

Safe Operating Life

Inspection

Inspection



Inspection

A Boeing 777 costs $250,000,000

A new car costs $25,000

For every $1 spent inspecting and maintaiB 777 you can spend only 0.01¢ on a car





Questions to ask

Will a crack nucleate ?

Will a crack grow ?

How fast will it grow ?

Similitude Failure mechanism

Size Scale



Fatigue Seminar



Fatigue Made Easy

Variability


Mechanical Science and Engineeri


Seminar Outline



Seminar Outline



3. Characterization of materials4. Similitude

5. Variability

6. Mean stress7. Stress concentrations

8. Surface effects


Sources of Variability



Sources of Variability

customers

1

0.1

10-2

m p l i t u d e

time

50%

100 %

F

a i l u r e s

Stress

“Average” Load History



Average Load History

Gumble Probability Plot



Gumble Probability Plot

99.9 %

99 %

80 %

50 % 200 400 600 80

Gumbel Distribution

42 Data Points

Location 362.94

Scale 124.61

Maximum force from 42 drivers

C u m u l a t i v e

P r o b a b i l i t y

Maximum Load Correlation



Maximum Load Correlation

108

107

106

105

104

103

F a t i g

u e L i v e s

Variability in Fatigue Lives



Variability in Fatigue Lives

0.1 1 10 102 103

Normalized Life

Airplane (334)

Tractor ( ATV (19)

99.9 %

99 %

90 %

50 %

10 %

C

u m u l a t i v e P r o b a b i l i t y

Variability in Loading



Variability in Loading

1

LogNormal Distribution

54 Data Points

Mean 1.01COV 0.47

99.9 %

99 %

90 %

50 %

10 %

1 % S

Equi C u m u l a t i v

e P r o b a b i l i t y

2

Statistical Variability of Fati



Statistical Variability of Fati

50

10

2

90

98

P e r c e n

t S u r v i v a l

s=210s=245s=315

s=280s=440

P-S-N Curve



P S N Curve

100

200

300

400

500

S t r e s s A m p l i t u d e , M

P a

99 90 11050

Percent Survival

Variability in Strength and L



10/1b)N(S2

S b

f

'

f

Suppose has a COV = 0.1'

f S

The variability in Nf will be:

)1.0(11COV1COV

22

'

f f

102b2

SN

Variability in Strength and L

Strain Life Data for 980X S



Strain Life Data for 980X S

1

0.1

10-2

10-3 S t r a i n

A m p l i t u d e

378 Data Point

Curve Fitting



Curve Fitting

1

0.1

10-2

10-3 S t r a i n

A m p l i t u d e

'

f

b

f

'

f 2()N2(E2

Assume a constant

a distribution of prop

'

f

Distribution'

f



Distribution


378 Data PointsMean 802 MPa

COV 0.12

99.9 %

99 %

90 %

50 %

10 %

f

'

f

10 100

C u m u l a t i v e P r o b a b i l i t y

Material Property Simulatio



Material Property Simulatio

1

0.1

10-2

10-3 S t r a i n A m

p l i t u d e

Typical Variability



Typical Variability

Pit Size

Bolt Preload Force

Surface Roughness

Pits That Initiated Cracks



Pits That Initiated Cracks

701

Pre-corro

300 s

246 fai

Pit Size Distribution



Pit Size Distribution

40

30

20

10

100 200 400 500300

F r e q u e n c y Mean = 23

COV = 0.3

Variability in Bolt Force



Variability in Bolt Force

100

Force


200 Data Points

Mean 130.45COV 0.14

99.9 %

99 %

90 %

50 %

10 %

1 %

Bolt Force, N


Surface Roughness Variab



Surface Roughness Variab


125 Data Points

Mean 42.98COV 0.10

99.9 %

99 %

90 %

50 %

10 %

1 %

Force

10 Surface Finish, in


Variability Summary



Variability Summary

Source COService Loading 0.4

Materials 0.1Manufacturing 0.1

Surface Finish 0.1

Environment 0.3

Strength

Stress

na2

X 1C1CCOV

2i

Stress - Strength



Stress Strength

initial cost

customer

usage

strength

design andtest loads





Fatigue data inherently contains a lo

variability

The variability is predictable and qua



Fatigue Seminar



Fatigue Made Easy

Mean Stress




Seminar Outline





3. Characterization of materials4. Similitude (why fatigue modeling works)

5. Variability


8. Surface effects


Mean Stresses



mean stress

stress range

s t r e s s

2

SSS minmax

mean

Smax

Smin

General Observations



Tensile mean stresses reduce the fa

or decrease the allowable stress ranCompressive mean stresses increas

fatigue life or increase the allowable

range

Mechanism



Fatigue damage is a shear process

S

2

Smean

Goodman 1890



Mechanics Applied to Engineering

John Goodman, 1890

“.. whether the assumptions of the

theory are justifiable or not …. We

adopt it simply because it is the

easiest to use, and for all practicalpurposes, represents Wöhlers data.

S = S + 2 S

Goodman Diagram



g

Mean stress

A l t e r n a t i n

g s t r e s s

Su0

Se

107 cycles

105 cycles

R = -1 R = 1

Test Data ( 1941 )



( )

0.2

0.4

0.6

0.8

1.0

1.2

0

A l t e r

n a t i n g S t r e s

s

F a

t i g u e L i m i t

Compression



p

Se

0

R = 1

-Su

R =

no influence

detrimental

beneficial

Modified Goodman ( no yie



( y

Se

Sys

mS2

S

Mean Stress Influence on L



0.1

1

10

100

1000

R e l a t i v e F a t i g u e L i f e

Stress Concentrations



Plastic

Zone

The elastic materia

the plastic zone aro

concentration force

to deform in strain

Mean Stresses at Notches



elastic p

NominalNotch

NotchNominal

Nominal

Morrow Mean Stress Corre



10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

S

t r a i n A m p l i t

u d e

100 101 102 103 104 105 10

E

mean

Smith Watson Topper



max

b2

f

2'

f

max )N2(E2

Mean Stress Relaxation



Loading Histories



Test Results



Crack Growth Physics



Maximum load

Minimum load

Mean Stress Effects



d

d

Compression



Crack

C k

Compressive Stresses



S t

r e s s

Crack ope

Sources of Mean/Residual



Loading History

Fabrication

Shot Peening

Heat Treating

Loading History



Tension overloads produce favorable

compressive residual stress

Compressive overloads produce

unfavorable tensile residual stress

Fabrication



Cold Expansion



1965 Basic Cx process conceptualized

The split sleeve is

slipped onto themandrel, which is

attached to the

hydraulic puller unit.

The mandrel and sleeve are

inserted into the hole with the

nosecap held firmly against the

workpiece.

Wh th ll i ti t d

Theory of Cold Expansion



Fatigue Life Improvement



100

200

300

N o m i n a l S t r e s s

Cold Expanded

Shot Peening



600

-400

-200

0

200

R e s i d u a l S t r e s s ( M P a

)

Shot Peening Results



500

1000

1500

0 u e s t r e n g t h a t 2 x 1 0 6

c y c

l e s ,

M P a

Smoo

Notc

Shot PeenedSmooth & Notched

Heat Treating



200

600

400

00 5 10 15

B r

i n e l l H a r d n e

s s

Depth, mm

0 5-1500

-1000

-500

0

500

1000

De

R e s i d u a l S t r e s s ,

M P a

Radial

Axial




Local mean stress rather than the n

mean stress governs the fatigue life

Mean stress has the greatest effectnucleation



Fatigue Seminar



Fatigue Made Easy

Stress Concentrations



U i it f Illi i

Seminar Outline





3. Characterization of materials4. Similitude

5. Variability


8. Surface effects

9 V i bl lit d l di

Stress Concentration Facto



appliedlocal

Inglis Solu

2

Define K and K after Yield



S , e

,

Define: nominal stress, S

nominal strain, e

notch stress, notch strain,

Stress concentration K

Stress and Strain Concentr



Kt

S t r e s s / S t r

a i n C o n c e n t r a t i o n

K

KK

Fi t i ldi

K and K



S t r e s s ( M P a )

KtS

Neuber’s Rule



S t r

e s s ( M P a )

KtS

eKSK tt

Stress calc

elastic ass

A

Neuber’s Rule for Fatigue



2222

eKSK tt

Stress and strain amplitudes

Elastic nominal stress

E2

S

2

e

Substitute and rearrange

22E

2

SK t

SN Materials Data



100

1000

10000

S t r e s s A m

p l i t u d e ,

M P

a

93 stee

17 alum

N Materials Data



93 steels

17 aluminu

10-2

10-3

0.1

10

1

S t r a

i n A m p l i t u r e

22E



10

102

105

104

103

2

2

E

K t

o r

2 S

A Dilemma



Stress analysis and stress concentration fac

independent of size and are related only to tof the geometric dimensions to the loads

Fatigue is a size dependent phenomenon

H d t th t t th ?

Similitude



Fatigue of Notches



100

400

300

200

N o m i n a

l S t r e s s ,

M P a

d d

Kt =

Kt = 3.1

Kf = 2.2100

400

300

200

N o m i n a

l S t r e s s ,

M P a

dd dd

Kt =

Kt = 3.1

Kf = 2.2

Notch Size



Kt

Kf

Kt

K

Microstructure Size



Kt

Kf

Kt

Stress Gradient



Kt

Kf

Kt

Kt vs Kf



2

4

6

8

10

Kf

Kf = K

Experiments

f f e c t i v e s t r e

s s c o n c e n

t r a t i o n

Peterson’s Equation



1K f

M2070025.0

u

0

1

2

3

4

10-4 10-3 10-2 0.1 1 10 102 10

Kf

Peterson’s Constant



0.1

0.03

0.7

0.3

, m m

Static Strength



1018 Steel Test Data



20

40

60

80

100

l o

a d ,

k N

edge

diamond

slot

hole

Notched SN Curve



1000

10000

S t r e s s A m p l i t u d e , M

P a

Smooth specimen dat

Notched specimen

Crack Growth Data



10-11

10-10

10-9

10-8

10-7

10-6

C r a c k G r o w t h R a t e , m / c

y c l e

mKCdN

da

Kc

12.1KTH

Nonpropagatin

Frost Data



nu

Rotating bending

Notched bar

Notched plate

1.0

0.8

0.6

0.4

0.2

S

n o m i n a l

S f a t i g u e l i m i t

1 nonpropagating

Significance



D

K

Sth

fl

For Kt > 4, the notch acts like a crack with

Kt does not play a role for sharp notch

A stress concentration behaves like a crac

Cracks at Notches



D

a a D + a

KtSS

Stress Intensity Factors



1.0

3.0

2.0

DS

K

aSKK t

aDSK

Cracks at Holes



201 1 22

Once a crack reaches 10% of the hole

Specimens with Similar Ge



Kt = 2.4Kt = 10.7

25 25

2.5 2.5

Test Results



100

1000

N o m i n a l S t r e s s A m p l i t u d e

Strength Limited

Crack Growth Dominated

Fatigue S

Threshold Stress Inte

Kt = 2

Kt = 1




Fatigue may be thought of as a failu

average stress concept, consequent

fatigue usually begins at stress concwhich are most frequently located on

surface

The severity of a stress concentratofatigue is size dependent

Small stress concentrators are more



Fatigue Seminar



Seminar Outline





3. Characterization of materials4. Similitude (why fatigue modeling works)

5. Variability


8. Surface effects

Modern View of the Fatigue



The fatigue limit is the stress where a crac

nucleate but will not grow through the first

microstructural barrier such as the grain s

pearlite colony size, prior austenite grain seutectic cell size or precipitate spacing.

Intrinsic Flaws



Little effect of surface pit because Large effect of def

Surface Finish Influence



MethodStress-Life

Strain-Life

Crack Growth

PhysicsCrack Nucleation

Microcrack Growth

Macrocrack Growth

Size0.01 mm

0.1 - 1 mm

> 1mm

Sources of Surface Effects



Machining

Cutting

Grinding

Corrosion

General

Pitting

Processing

Cutting/Shearing

Casting

Forging

Machining



100 m

Casting



Nodular Iron Surface



Test Data



10-1

10-2

10-3

10-4

2 3 4 5 6 7

S t r a i n A m p l i t u d e

Cast Surface

Machined Surface

Surface Reduction Factors

P li h d



0.2

0.4

0.6

0.8

1.0

S u r f a c e F a c t o r

Polished

Ground

Forged

Hot Rolled

Machined

5

2

1

1

1

Noll and Lipson 1945



200

400

600

800

1000

F a t i g

u e L i m i t , M

P a

Hiam and Pietrowski 1978



Driven for 1 or 2 y

in Southern Ontar

before making spto evaluate corros

Strain controlled f

Kf for pitting



Hot RolledSurface

CorSu

950X 1.12 1

0.06% C HSLA 1.18 1

0.18% C HSLA 1

Pit Depth Effects on Life

106



106

105

F a t i g u

e L i f e ,

C y c

l e s

950X Steel

Fatigue Notch Factor for Pi

1 5



1.1

1.2

1.3

1.4

1.5

Kf

Suspension



Spring Failures



Microscopic Examination



Corrosion Pits

Corrosion Pits

Chrome Plating

500



S t r e s s

A m p l i t i u d e

, M P a

500

200

400

300

Chrome plated

Shot peened a

chrome plate

Base steel

Hard Chrome Plating



coating

Galvanized Steel



3

0

1

2

Life

C r a c k D e n s

i t y m m - 1

Fatigue Limit for Galvanize

400



10010

200

300

400

F a t i g u e L i m i t Uncoated Fatigue Limit

t

KS TH

FL



Foreign Object Damage



Upper Control Arm



Serial Number



Fatigue crack nucleation is a surface phen

and everything about the surface affects th

life

Most of the design rules are conservative

been developed for materials of the 1950’s



Fatigue Seminar

Fatigue Made Easy



Fatigue Seminar © 2002-2011 Darrell Socie, All Rights Reserved 1 of 25




5. Variability

6. Mean stress


8. Surface effects

9. Variable amplitude loading

10. Welded structures

Variable Amplitude Loading




How to you identify cycles ?

How do you assess fatigue damage for a cycle ?

Rainflow Cycle Counting




What could be more basic than

learning to count correctly?

Matsuishi and Endo (1968) Fatigue of Metals Subjected to Varying Stress – Fatigue Lives Under

Random Loading, Proceedings of the Kyushu District Meeting, JSME, 37-40

Rainflow

strain

AC t 1/2 l




A

F

D

B

E

I, AH G

C

AD

BC

CB

DA

Counts 1/2 cycles

Rainflow and Hysteresis

A

C

B




C D E

F G

H I

ε

σ

Cumulative Damage

High - Low




….….

…. ….

Low - HighnH nL

nL nH

∆SL

∆SH

Linear Damage




∆SH

∆SL

Nf H Nf L

Lf

L

Hf

H

F N

n

N

n

N

nDamage +==∑

Miner’s Rule:

Nonlinear Damage

1.0

ΣD 0




0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

00

Cycle ratio,

D a m a g e f r a c t i o n

n

Nf

0040.=ε∆

0200.=ε∆

ΣD = 0.7

ΣD = 1.3

ΣD ~ 1

Periodic Overload Results0.1

The fatigue limit is reduced by a factor of 3

when a few large cycles are applied




10 100 103

104

105

106

107

108

109

10-3

10-4

0.01

S t r a i n

A m p l i t u d e

Fatigue Life

….

….

Bonnen and Topper, “The Effects of Periodic Overloads on Biaxial Fatigue of Normalized SAE 1045 Steel”

ASTM STP 1387, 2000, 213-231

Fatigue Damage Calculations

10000

d e , M P a

( )b

f

'

f NS2

S

=

∆




100

1000

S t r e s s A m p l i t u d

100

Cycles

101 102 103 104 105 106 107

( )1

10

b

1

'

f

f S2

SN

∆=

10SDamage ∆∝

Crack Growth Data

10-7

10-6

ycl e

K




10-12

10-11

10-10

10-9

10-8

1 10 100

C r a c k G r o w t h R a t e , m / c y

mMPa,K∆

mKCdN

da∆=

∆KTH

Kc

1

3

Crack Growth Data

100




10-1210-1110-1010-910-810-710-6

Crack Growth Rate, m/cycle

1

10

m

M P a

, K ∆

3SDamage ∆∝

( )2/m1SC

aaN2

m

m

2/m1

i

2/m1

f f

−π∆

−=

−−

Multiple Choice

Whi h l d th t f ti d ?




Which cycles do the most fatigue damage ?

(a) a few large cycles

(b) a moderate number of intermediate cycles

(c) a large number of small cycles

Fatigue Data

1000

n = 10




1

10

100

A m

p l i t u d e

100

Cycles

101 102 103 104 105 106 107

0

n = 5

n = 3nSDamage ∆∝

Loading History

750

500i n

)

Bracket.sif-Strain_b43




Time (Secs)

50 100 150 200 250 300

250

0

-250

-500

-750

S t r a i n G a g e ( u s t r a

0

1500

-750

750

0

750

C o u n t s

rf_000.sif-Strain_b43

Slope = 3

Damage




0

1500

-750

750

3.15

% d a

m a g e

Slope = 5

Damage




0

1500

-750

750

5.14

% d a

m a g e

Slope = 10

Damage




0

1500

-750

750

20.78

% d a m

a g e

Mechanisms and Slopes

104

u d e , M P a

Crack Nucleation

Structures




100

103

S t r e s s A m p l i t u

100

Cycles101 102 103 104 105 106 107

1

10

10-1210-1110-1010-910-810-710-6

Crack Growth Rate, m/cycle

1

10

100

m

M P a

, K ∆

1

3

Crack Growth

10

100

103 104 105 106 107 108

Total Fatigue Life, Cycles

1

51

E q u i v a l e

n t L o a d ,

k N

Structures

A combination of nucleation and growth

Equivalent Load

Equivalent constant amplitude loading




n

N

1i

n

i

N

S

S

∑=

∆

=∆

q p g

Typically n ranges from 4 to 6 for structures

N cycles at an amplitude of does as muchdamage as the entire loading history

S∆

SAE Keyhole Specimen

Bracket




Suspension

Transmission

SAE Keyhole Test DataManTen RQC 100

100

Suspension

Transmission

Bracket




10

103 104 105 106 107 108

Total Fatigue Life, Cycles

1

Constant Amplitude

5

1

E q u i v a l e n

t L o a d ,

k N

How Many Cycles ?

Engine:

2 starts/day for 10 years = 7000 cycles




y y y

3000 rpm for 100,000 miles (2000 hrs) = 3.6 x 108 cycles

How Many Cycles ? (continued)

750

500

250r a i n )

Bracket.sif-Strain_b43




Time (Secs)

50 100 150 200 250 300

250

0

-250

-500

-750

S t r a i n G a g e ( u s t r

0

2 minutes

Bracket Vibration:

0.5 per minute for 100,000 miles (2000 hrs) = 60,000 cycles

12 hz continuous vibration for 2000 hrs = 8.6 x 107 cycles

Things Worth Remembering

Rainflow counting is employed to identifycycles




g p y ycycles

The slope of the fatigue curve ( damage

mechanism) has a large influence on how

much damage is caused by smaller cycles

Fatigue Seminar



Fatigue Seminar

Fatigue Made Easy

Welded Structures



Fatigue Seminar © 2002-2010 Darrell Socie, Universit y of Illinoi s at Urbana-Champaign, All Rights Reserved 1 of 34



5. Variability

6. Mean stress


8. Surface effects

9. Variable amplitude loading

10. Welded structures

Analyzing Welds

Nominal Stress

Structural or Hot Spot Stress




p

Local Stress Strain

Crack Growth

Nominal Stress

Nominal stress approaches are based onextensive tests of welded joints and




extensive tests of welded joints andconnections. Weld joints are classified bytype , loading and shape. For example, atransversely loaded butt weld. It is

assumed and confirmed by experiments that welds of asimilar shape have the same general fatigue behavior sothat a single design SN curve can be employed for anyweld class. The designer need only determine the nominalstress and select a weld class. There is no need to directlyconsider the stress concentration effects of the weld.

Structural Stress

Structural stress approaches are often

referred to as "hot-spot methods". Thestructural stress includes the




structural stress includes themacroscopic stress concentratingeffects of the weld detail but not thelocal peak stress caused by the notch

at the weld toe. There are various methods used todetermine the structural stress. They involveextrapolating the computed or measured stresses fromtwo points near the weld to a structural stress at the weldtoe. This method works in situations where there is noclear definition of the nominal stress.

Local Stress Strain

Local stress or strain approachesinclude both the macroscopic




include both the macroscopicstress concentration due to theweld shape and the local stressconcentration at the weld toe. To

apply traditional methods of fatigue analysis towelds, an appropriate value of the stressconcentration factor and residual stress must beselected. Although the smallest radius produces thelargest stress concentration factor, its effect infatigue is smaller because of the gradient effect. Asa result there is a critical radius for fatigue that canbe used to compute the fatigue notch factor.

Crack Growth

Many weld details have planarl k f f i d f t Thi i




lack of fusion defects. This is

particularly true of fillet welds. In

this case fracture mechanics

models for crack growth are the most appropriatefatigue technology.

Nominal Stress Weld Classifications

DE




F2 G

400

B

BS 7608 - Steel




100

200

300C

D

E

FF2

G W

0105 106 107 108

Fatigue Life, Cycles

Crack Growth Data

( ) 0.312

mMPaK109.6da

∆×= −

Ferritic-Pearlitic Steel:10-6

c l e

σyield

252

273392

415




( )mMPaK109.6dN

∆

( ) 25.2

10

mMPaK104.1dN

da

∆×= −

( ) 25.312

mMPaK106.5

dN

da∆×= −

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

10-8

C r a c k G r o w t h

R a t e , m / c y c

∆K, MPa√m

100

125

Nominal Stress - Aluminum




0

25

50

75

100

105

B

C

DE

F

106 107 108


Sharp, “Behavior and Design of Aluminum Structures”,McGraw-Hill, 1992

Crack Growth Data

c y c l e 10

-2

Steel welds are 3 times




1 10 100

Cyclic Stress Intensity, MPa√m

C r a c k G r o w t h R a t e m / c

A533B m/cycle

2024-T3 m/cycle10-4

10-6

10-8

10-10

10-12

3X

stronger than aluminum

1

3

Residual Stress from Welding

Y

XX

Ytension




Y

XX

Y

YYtension

compression

compression

Weld Distortion




Weld Toe Residual Stress

∆ε

σ

∆ε




Yield

stress

Maximum stress at the weld toe

is nearly the same for any cycle

ε

Mean Stress Effects

As welded structures usually have the

maximum possible mean stress




Stress relief, peening, etc. will have a

substantial effect on the fatigue life

Butt and Fillet Weld Test Data

1000

a

The good welds




99% survival with 95% confidence

S t r e s s R

a n g e ,

M P a

100

10

103 104 105 106 107


Failures Run outs

Weld Terminations

1000

P a

The bad welds




S t r e s s R a n g e ,

M P

100

10

103 104 105 106 107


Failures Run outs

99% survival with 95% confidence

Sources of Inherent Scatter

Weld quality

Mean, fabrication and residual stresses




Stress concentrations (geometry)

Weldment size

Material properties

Opportunities for Improvement !

The Good and Bad

Good weld design




Bad weld design

Nominal Stress ?




r

t1

ED

σ peak

Stress Distributions in Weldments




Various stress distributions in a T-butt weldment with transverse fillet welds;

r

t

D

BC

A

σ

n

σhs

FP

M

C

Θ

• Normal stress distribution in the weld throat plane (A),

• Through the thickness normal stress distribution in the weld toe plane (B),

• Through the thickness normal stress distribution away from the weld (C),

• Normal stress distribution along the surface of the plate (D),

• Normal stress distribution along the surface of the weld (E),

• Linearized normal stress distribution in the weld toe plane (F).

Fine 3-D FE

mesh

Finite Element Models




Experimental Shell

elements

Coarse 3-D FE

mesh

Stress magnitudes and distributions obtained from various FE

models

Peak and Hot Spot Stress




σ peak

σn σhs

V

t

σn σn

P

Physical Meaning of Hot Spot Stress




σ peak

t

σn V

P

σn

I

Mc

A

P

n +=σ

Hot Spot SN Curves




Typical Butt Weld




Weld Toe




Macroscopic LOF




3 mm

Weld Flaws

Even good welds contain initial crack like flaws

0.1 to 1 mm long. Reducing the size or eliminating

these flaws will substantially improve fatigue lives




these flaws will substantially improve fatigue lives.

Weld Improvement

Reduce weld toe stresses

Stress relieve

I l l t




Improve local geometry

Macroscopic Shape

t

θ4




r

0.05 0.20.150.1

2

3

1

r / t

tK

θ = 15º

θ = 30º

θ = 45º

θ = 60º

Kfmax

4

5

t

r

θ




mMPatS15.01Kumaxf

β+=

r

t1K

t β+=

ρ

α+

−+=

1

1K1K t

f

2

3

ρ = α Weld toe radius

f t Kor K β ~ 0.3 axial

β ~ 0.2 bending

Things Worth Remembering

Local weld toe stresses, geometry and flaws

control the life of weldments




Fatigue Seminar

fatigue made easy 1

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