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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

dsocie@illinois.edu

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

The phenomenon

cumulative damag

repeated loads wato be related to th

absorbed by a sp

“proved” linear da

1954 - Coffin and Manson

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

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

LoadingLocations and

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

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

Crack Nucleation Summary

Highly localized plastic deformation

Surface phenomena Stochastic process

bulksurface

10 µm

surface

Surface Damage

surface

Stage I and Stage II

Stage I Crack Growth

Single primary slip system

individual grain

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

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

Fda/dN, mm/cycle

Strain-Life Data

S t r a i n A

m p l i t u d e

100 101 102 103 104 105 1

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

Crack Opening Load

Damaging portion of loading history

Opening load

Mode I

opening

Mode II

in-plane shear

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

Tension

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

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

s t r e s s

stress am

stress rang

cMBending stress:

SN Curve

S t r e s s A

m p l i t u d e , M

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

Monel Alloy

SN Curve

S t r e s s A m

p l i t u d e , M P

fatigue limit

bf 'f NS

Fatigue Damage

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

Cycles

101 102 103 104 105 106 107

Fatigue Limit Strength Corr

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

Fatigue Limit Strength Corr

SN Materials Data

S t r e s s A m p

l i t u d e , M P a

Strain Controlled Testing

Cyclic Hardening / Softenin

Stable Hysteresis Loop

Hysteresis loop

Strain-Life Data

0 0 004 0 008 0 012

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

Cyclic Stress Strain Curve

Strain-Life Data

S t r a i n A m

p l i t u d e

Elastic and Plastic Strain-L

S t r a i n A m

p l i t u d e

2 Plastic

Elastic

Strain-Life Curve

S t r a i n A m

p l i t u d e

f )N2(

Transition Fatigue Life

N Materials Data

93 steels

17 alumin

S t r a i n

A m p l i t u d e

Crack Growth Testing

Stress Concentration of a C

a ~ 10-3

for a crack

~ 10-9

KT ~ 2000

aplocal 2000

Stress Intensity Factor

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

Crack Growth Data

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

y c l e

Threshold Region

threshold stress intensity

af aKTH

operating stresses

flaw size

flaw shape

Threshold Stress Intensity

Non-propagating Crack Siz

a212.1KTH

Small cracks are frequently semielliptical surfa

Smooth specimen fatigue limit2

Non-propagating Crack Siz

C r a c

k S i z e , m

mMP5KTH

Stable Crack Growth

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

y c l e

Stable growth region

Crack Growth Data

MK109.6dN

10 MK104.1

12 MK1065da

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless St

C r a c k G r o w t h

R a t e , m / c y c l

MethodStress-Life

Strain-Life

Crack Growth

PhysicsCrack Nucleation

Microcrack Growth

Macrocrack Growth

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

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

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

p l i t u d e , M P a

F i A l i S Li

Fatigue Analysis: Stress-Li

MaterialData

ComponentGeometry

Analysis

SN curveKa, Ks, …

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

e , M P a

W ld Cl ifi ti

Weld Classifications

F ti A l i BS 7608

Fatigue Analysis: BS 7608

MaterialData

ComponentGeometry

Analysis

Weld SN curve

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

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

p l i t u d e

F ti A l i St i Lif

Fatigue Analysis: Strain-Lif

MaterialData

ComponentGeometry

Analysis

N curve

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

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

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

Fatigue Analysis: Crack Gr

MaterialData

ComponentGeometry

Analysis

da/dN curve

Crack Growth

Major Assumptions:

Nominal stress and crack size control

Accurate determination of initial crack

Crack Growth

Advantage:

Only method to directly deal with c

Crack Growth

Limitations:

Complex sequence effects

Accurate determination of initial cra

Choose the Right Model

Similitude

Failure mechanism

Size scale

Design Philosophy

Safe Life

Damage Tolerant

Safe Life

104 105 106 107

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

Fatigue Life

99 90 1050

Percent Survival

104 105 106 107

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

Fatigue Life

99 90 105099 90 1050

Percent Survival

Damage Tolerant

r a c k s i z e

Safe Operating Life

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

3. Characterization of materials4. Similitude

5. Variability

6. Mean stress7. Stress concentrations

8. Surface effects

Sources of Variability

customers

m p l i t u d e

a i l u r e s

Stress

“Average” Load History

Average Load History

Gumble Probability Plot

99.9 %

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

F a t i g

u e L i v e s

Variability in Fatigue Lives

0.1 1 10 102 103

Normalized Life

Airplane (334)

Tractor ( ATV (19)

99.9 %

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

Variability in Loading

LogNormal Distribution

54 Data Points

Mean 1.01COV 0.47

99.9 %

Equi C u m u l a t i v

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

Statistical Variability of Fati

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

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

99 90 11050

Percent Survival

Variability in Strength and L

10/1b)N(S2

Suppose has a COV = 0.1'

The variability in Nf will be:

)1.0(11COV1COV

Variability in Strength and L

Strain Life Data for 980X S

10-3 S t r a i n

A m p l i t u d e

378 Data Point

Curve Fitting

10-3 S t r a i n

A m p l i t u d e

f 2()N2(E2

Assume a constant

a distribution of prop

Distribution'

Distribution

378 Data PointsMean 802 MPa

COV 0.12

99.9 %

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

10-3 S t r a i n A m

p l i t u d e

Typical Variability

Pit Size

Bolt Preload Force

Surface Roughness

Pits That Initiated Cracks

Pre-corro

246 fai

Pit Size Distribution

100 200 400 500300

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

COV = 0.3

Variability in Bolt Force

200 Data Points

Mean 130.45COV 0.14

99.9 %

Bolt Force, N

Surface Roughness Variab

125 Data Points

Mean 42.98COV 0.10

99.9 %

10 Surface Finish, in

Variability Summary

Source COService Loading 0.4

Materials 0.1Manufacturing 0.1

Surface Finish 0.1

Environment 0.3

Strength

Stress

X 1C1CCOV

Stress - Strength

Stress Strength

initial cost

customer

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

SSS minmax

General Observations

Tensile mean stresses reduce the fa

or decrease the allowable stress ranCompressive mean stresses increas

fatigue life or increase the allowable

Mechanism

Fatigue damage is a shear process

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

Mean stress

A l t e r n a t i n

g s t r e s s

107 cycles

105 cycles

R = -1 R = 1

Test Data ( 1941 )

A l t e r

n a t i n g S t r e s

t i g u e L i m i t

Compression

no influence

detrimental

beneficial

Modified Goodman ( no yie

Mean Stress Influence on L

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

Stress Concentrations

Plastic

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

Reversals, 2Nf

t r a i n A m p l i t

100 101 102 103 104 105 10

Smith Watson Topper

max )N2(E2

Mean Stress Relaxation

Loading Histories

Test Results

Crack Growth Physics

Maximum load

Minimum load

Mean Stress Effects

Compression

Compressive Stresses

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

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

Cold Expanded

Shot Peening

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

Shot Peening Results

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

l e s ,

Shot PeenedSmooth & Notched

Heat Treating

00 5 10 15

i n e l l H a r d n e

Depth, mm

0 5-1500

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

Radial

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

Define K and K after Yield

Define: nominal stress, S

nominal strain, e

notch stress, notch strain,

Stress concentration K

Stress and Strain Concentr

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

Fi t i ldi

K and K

S t r e s s ( M P a )

Neuber’s Rule

e s s ( M P a )

eKSK tt

Stress calc

elastic ass

Neuber’s Rule for Fatigue

eKSK tt

Stress and strain amplitudes

Elastic nominal stress

Substitute and rearrange

SN Materials Data

S t r e s s A m

p l i t u d e ,

93 stee

17 alum

N Materials Data

93 steels

17 aluminu

S t r a

i n A m p l i t u r e

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

N o m i n a

l S t r e s s ,

Kt = 3.1

Kf = 2.2100

N o m i n a

l S t r e s s ,

Kt = 3.1

Kf = 2.2

Notch Size

Microstructure Size

Stress Gradient

Kt vs 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

M2070025.0

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

Peterson’s Constant

Static Strength

1018 Steel Test Data

diamond

Notched SN Curve

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

Smooth specimen dat

Notched specimen

Crack Growth Data

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

y c l e

12.1KTH

Nonpropagatin

Frost Data

Rotating bending

Notched bar

Notched plate

n o m i n a l

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

1 nonpropagating

Significance

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

a a D + a

Stress Intensity Factors

aSKK t

Cracks at Holes

201 1 22

Once a crack reaches 10% of the hole

Specimens with Similar Ge

Kt = 2.4Kt = 10.7

2.5 2.5

Test Results

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

Sources of Surface Effects

Machining

Cutting

Grinding

Corrosion

General

Pitting

Processing

Cutting/Shearing

Casting

Forging

Machining

Casting

Nodular Iron Surface

Test Data

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

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

Polished

Ground

Forged

Hot Rolled

Machined

Noll and Lipson 1945

F a t i g

u e L i m i t , M

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

950X 1.12 1

0.06% C HSLA 1.18 1

0.18% C HSLA 1

Pit Depth Effects on Life

F a t i g u

e L i f e ,

950X Steel

Fatigue Notch Factor for Pi

Suspension

Spring Failures

Microscopic Examination

Corrosion Pits

Chrome Plating

S t r e s s

A m p l i t i u d e

, M P a

Chrome plated

Shot peened a

chrome plate

Base steel

Hard Chrome Plating

coating

Galvanized Steel

C r a c k D e n s

i t y m m - 1

Fatigue Limit for Galvanize

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

Foreign Object Damage

Upper Control Arm

Serial Number

Fatigue crack nucleation is a surface phen

and everything about the surface affects th

Most of the design rules are conservative

been developed for materials of the 1950’s

Fatigue Seminar

Fatigue Made Easy

Variable Amplitude Loading

Mechanical Science and Engineering

Seminar Outline

2 Physics of fatigue

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

I, AH G

Counts 1/2 cycles

Rainflow and Hysteresis

Cumulative Damage

High - Low

….….

…. ….

Low - HighnH nL

Linear Damage

Nf H Nf L

nDamage +==∑

Miner’s Rule:

Nonlinear Damage

0.2 0.4 0.6 0.8 1.0

Cycle ratio,

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

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

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

d e , M P a

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

Cycles

101 102 103 104 105 106 107

10SDamage ∆∝

Crack Growth Data

1 10 100

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

mMPa,K∆

da∆=

∆KTH

Crack Growth Data

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

Crack Growth Rate, m/cycle

, K ∆

3SDamage ∆∝

( )2/m1SC

−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

n = 10

p l i t u d e

Cycles

101 102 103 104 105 106 107

n = 3nSDamage ∆∝

Loading History

500i n

Bracket.sif-Strain_b43

Time (Secs)

50 100 150 200 250 300

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

C o u n t s

rf_000.sif-Strain_b43

Slope = 3

Damage

m a g e

Slope = 5

Damage

m a g e

Slope = 10

Damage

% d a m

Mechanisms and Slopes

u d e , M P a

Crack Nucleation

Structures

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

Cycles101 102 103 104 105 106 107

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

Crack Growth Rate, m/cycle

, K ∆

Crack Growth

103 104 105 106 107 108

Total Fatigue Life, Cycles

E q u i v a l e

n t L o a d ,

Structures

A combination of nucleation and growth

Equivalent Load

Equivalent constant amplitude loading

Typically n ranges from 4 to 6 for structures

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

SAE Keyhole Specimen

Bracket

Suspension

Transmission

SAE Keyhole Test DataManTen RQC 100

Suspension

Transmission

Bracket

103 104 105 106 107 108

Total Fatigue Life, Cycles

Constant Amplitude

E q u i v a l e n

t L o a d ,

How Many Cycles ?

Engine:

2 starts/day for 10 years = 7000 cycles

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

How Many Cycles ? (continued)

250r a i n )

Bracket.sif-Strain_b43

Time (Secs)

50 100 150 200 250 300

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

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 Made Easy

Welded Structures

Mechanical Science and Engineering

Seminar Outline

5. Variability

6. Mean stress

8. Surface effects

9. Variable amplitude loading

10. Welded structures

Analyzing Welds

Nominal Stress

Structural or Hot Spot Stress

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

BS 7608 - Steel

0105 106 107 108

Fatigue Life, Cycles

Crack Growth Data

( ) 0.312

mMPaK109.6da

∆×= −

Ferritic-Pearlitic Steel:10-6

σyield

273392

( )mMPaK109.6dN

( ) 25.2

mMPaK104.1dN

∆×= −

( ) 25.312

mMPaK106.5

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

C r a c k G r o w t h

R a t e , m / c y c

∆K, MPa√m

Nominal Stress - Aluminum

106 107 108

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

Crack Growth Data

c y c l e 10

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

stronger than aluminum

Residual Stress from Welding

Ytension

YYtension

compression

Weld Distortion

Weld Toe Residual Stress

stress

Maximum stress at the weld toe

is nearly the same for any cycle

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

The good welds

99% survival with 95% confidence

S t r e s s R

a n g e ,

103 104 105 106 107

Failures Run outs

Weld Terminations

The bad welds

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

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 ?

σ peak

Stress Distributions in Weldments

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

• 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

Finite Element Models

Experimental Shell

elements

Coarse 3-D FE

Stress magnitudes and distributions obtained from various FE

models

Peak and Hot Spot Stress

σ peak

σn σhs

σn σn

Physical Meaning of Hot Spot Stress

σ peak

n +=σ

Hot Spot SN Curves

Typical Butt Weld

Weld Toe

Macroscopic LOF

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

0.05 0.20.150.1

θ = 15º

θ = 30º

θ = 45º

θ = 60º

mMPatS15.01Kumaxf

t β+=

1K1K t

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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