fatigue made easy

1

Fatigue Made Easy

Historical Introduction

Professor Darrell F. SocieUniversity of Illinois at Urbana-Champaign

© 2002 Darrell Socie, All Rights Reserved

Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 35

Contact Information

Darrell SocieMechanical Engineering1206 West GreenUrbana, Illinois 61801

Office: 3015 Mechanical Engineering Laboratory

[email protected]: 217 333 7630Fax: 217 333 5634


Surveying Made Easy17711688 1st

1793 12th

<http://www.uzes.net/1600to1800books.htm>


… Made Easy


… Made Easy


Shakespheare Made EasyOriginal

Translation

Shakespheare Made Easy, Alan Durband, Hutchinson & Co Ltd, London, 1985

2


Seminar Outline

1. Historical background2. Physics of fatigue 3. Characterization of materials4. Similitude ( why fatigue modeling works )5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading 10. Welded structures


19th Century

Mean StressesGoodman1890

Fatigue MechanismsEwing & Humfrey1903

Cyclic DeformationBaushinger1886Systematic InvestigationsWohler1860Stress ConcentrationsRankine1843“fatigue”Poncelet1839Repeated LoadsAlbert1829


The first major transportation disaster-Versailles accident of

May 11, 1842

At the dawn of the industrial revolution


Versailles


“I have this day to announce to you one of the most frightful events that has occurred in modern times. … The train of the left bank was unusually long; … from 1500 to 1800 passengers. On arriving betweenMeudon and Bellevue the axle tree of the first engine broke. … The second engine … passed over it, and the boiler burst … The carriages arrived of course, and passed over the wreck, when six of them were … instantly ignited. Three were totally consumed, … without the possibility of escape to the unhappy inmates, who were locked up … The number of killed is variously estimated (between 40 and 80).”

‘The Times’, May 11, 1842


Early steam engine

3


Typical broken axle of the 1840s


Expert opinions of the time

“I never met one which did not present a crystallization fracture…”“the principal causes … are percussion, heat and magnetism”“the change … may take place instantaneously”“steam can speedily cause iron to become magnetic”


Rankine 1820 - 1872

Trained as a civil engineer


William Rankine’s second paper

Stated that deterioration of axles is gradual “the fractures appear to have commenced with a smooth, regularly-formed, minute fissure, extending all round the neck of the journal, and penetrating on an average to a depth of half an inch. … until the thickness of sound iron in the center became insufficient to support the shocks to which it was exposed.”


Rankine ...

“In all the specimens the iron remained fibrous; proving that no material change had taken place in the structure”He noted that fractures occurred at sharp cornersHe recommended that the journals be formed with a large curve in the shoulder (which is exactly right!)


Wöhler 1819 - 1914

Prussian Railway Service

Work done before the development of the metallurgical microscope

Critical value of stress below which failure will not occur

4


Wöhler Tests

Wöhler circa 1850

Fatigue Dynamics circa 2000


Wöhler Observations

Steel will rupture at stress less than the elastic limit if the stress is repeated a sufficient number of timesStress range rather than maximum stress determines the number of cyclesThere appears to be a limiting stress range which may be applied indefinitely without failureAs the maximum stress increases, the limiting stress range decreases


Bauschinger 1834 - 1893

Cyclic Behavior of MaterialsBauschinger EffectNatural Elastic Limit


Goodman

Mechanics Applied to EngineeringJohn 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 practical purposes, represents Wöhlers data.


1903 - Ewing and Humfrey

Cyclic deformation leads to the development of slip bands and fatigue cracks

N = 1,000 N = 2,000

N = 10,000 N = 40,000 Nf = 170,000Ewing and Humfrey (1903) The Fracture of Metals Under Repeated Alterations of Stress, Philosophical Transactions of the Royal Society, A, Vol 221, 241-253


Their Description of Fatigue

The course of the breakdown was as follows: The first examination, made after a few reversals of the stress, showed slip lines on some of the crystals … after more reversals of stress additional slip lines appeared …. After many reversals they changed into comparatively wide bands with rather hazily defined edges … some parts of the crystals became almost covered with dark markings …. at this stage some of the crystals had cracked.

Once an incipient crack forms across a set of crystals, the effect of further reversals is mainly confined to the neighborhood of the crack tip.

5


20th Century

Cycle CountingEndo1967Strain-Life MethodPeterson1963Crack GrowthParis1961Plastic StrainsCoffin & Manson1954Cumulative DamageMiner1945Fracture MechanicsGriffith1920


Circa 1910 Data Acquisition


Early Strip Chart


Griffith 1893-1963

Circa1920 studied scratches and the effect of surface finish on fatigue for the Royal Aircraft Establishment

E2a γ=πσ

Griffith (1920) The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society, A, 221, 163-198


Miner

Miner (1945) Cumulative Damage in Fatigue, Journal of Applied Mechanics, Vol. 12, 1945, A159-A164

The phenomenon of cumulative damage under repeated loads was assumed to be related to the net work absorbed by a specimen

“proved” linear damage rule


1954 - Coffin and Manson

Rec

ipro

cal o

f elo

ngat

ion

at fa

ilure

1/Σ

b

Cycles to failure

Manson (1953) Behavior of Materials Under Conditions of Thermal Stress, NACA Technical Note 2933

Cycles to failure

Ela

stic

+ in

elas

tic s

train

cha

nge

Coffin (1954) A Study of the Effects of Cyclic Thermal Stress on a Ductile Metal, Transactions ASME, Vol. 76, 931-950

6


1961 - Paris

Paris (1963) The Fracture Mechanics Approach to Fatigue, Proceedings of the Tenth Sagamore Army Materials Conference, 107-132


1963 Peterson

Peterson (1963) Fatigue of Metals: Part 3 Engineering and Design Aspects, Materials Research and Standards, 122-139


Endo 1925 - 1989

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


1980’s – Software DevelopmentDevelopment of the local strain approach.

Fatigue crack growth modeling established


1990’s Finite Element


2000’s Integrated Systems

Component Loads

Component Stress State

Loading Locations and Orientations

FE

Fatigue

MBD

7


Things Worth Remembering

The physics of fatigue has been well known for over 100 yearsApplication of this knowledge still poses challenges

Fatigue Made Easy

Physics of Fatigue Damage




Seminar Outline

1. Historical background2. Physics of fatigue3. Characterization of materials4. Similitude (why fatigue modeling works)5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading 10. Welded structures


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


The Fatigue Process

Crack nucleationSmall crack growth in an elastic-plastic stress fieldMacroscopic crack growth in a nominally elastic stress fieldFinal fracture


1903 - Ewing and Humfrey

Cyclic deformation leads to the development of slip bands and fatigue cracks

N = 1,000 N = 2,000

N = 10,000 N = 40,000 Nf = 170,000Ewing, 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

8


Crack Nucleation


Slip Band in Copper

Polak, J. Cyclic Plasticity and Low Cycle Fatigue Life of Metals, Elsevier, 1991


Slip Band Formation

Loading Unloading

Extrusion

Undeformedmaterial

Intrusion


Slip Bands

Ma, B-T and Laird C. “Overview of fatigue behavior in copper sinle crystals –II Population, size, distribution and growthKinetics of stage I cracks for tests at constant strain amplitude”, Acta Metallurgica, Vol 37, 1989, 337-348


Crack Initiation at Inclusions

Langford and Kusenberger, “Initiation of Fatigue Cracks in 4340 Steel”, Metallurgical Transactions, Vol 4, 1977, 553-559


Subsurface Crack Initiation

Y. Murakami, Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions, 2002

9


Fatigue Limit and Strength Correlation

0 500 1000 1500 2000

250

500

750

1000

1250

Tensile Strength, MPa

Fatig

ue S

treng

th, M

Pa

0.6

0.5

0.35

0 500 1000 1500 2000

250

500

750

1000

1250


Fatig

ue S

treng

th, M

Pa

0.6

0.5

0.35

From Forrest, Fatigue of Metals, Pergamon Press, London, 1962Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 49 of 35

Crack Nucleation Summary

Highly localized plastic deformationSurface phenomenaStochastic process


100 µm

bulksurface

10 µm

surface

20-25 austenitic steel in symmetrical push-pull fatigue (20°C, ∆εp/2= ±0.4%) : short cracks on the surface and in the bulk

Surface Damage

From Jacques Stolarz, Ecole Nationale Superieure des MinesPresented at LCF 5 in Berlin, 2003


Stage I Stage II

loading direction

freesurface

Stage I and Stage II


Stage I Crack Growth

Single primary slip system

individual grain

near - tip plastic zone

S

SStage I crack is strongly affected by slip characteristics, microstructure dimensions, stress level, extent of near tip plasticity


Small Cracks at Notches

D acrack tip plastic zone

notch plastic zone

notch stress field

Crack growth controlled by the notch plastic strains

10


Small Crack Growth

1.0 mm

N = 900

Inconel 718∆ε = 0.02Nf = 936


0

0.5

1

1.5

2

2.5

0 2000 4000 6000 8000 10000 12000 14000

J-603

F-495 H-491

I-471 C-399

G-304

Cycles

Cra

ck L

engt

h, m

m

Crack Length Observations


Crack - Microstructure Interactions

Akiniwa, Y., Tanaka, K., and Matsui, E.,”Statistical Characteristics of Propagation of Small Fatigue Cracks in Smooth Specimens of Aluminum Alloy 2024-T3, Materials Science and Engineering, Vol. A104, 1988, 105-115

10-6

10-7

0 0.005 0.01 0.015 0.02 0.0250.03 0.025 0.02 0.015 0.01 0.005

A B CD

F

E

Crack Length, mm

da/dN, mm/cycle


Strain-Life Data

Reversals, 2Nf

Stra

in A

mpl

itude

∆ε 2

10-5

10-4

0.01

0.1

1

100 101 102 103 104 105 106 107

10-3

10µm100 µm

1mmfracture Crack size

Most of the life is spent in microcrack growth in the plastic strain dominated region


Stage II Crack Growth

Locally, the crack grows in shear Macroscopically it grows in tension


Long Crack Growth

Plastic zone size is much larger than the material microstructure so that the microstructure does not play such an important role.

11


Material strength does not play a major role in fatigue crack growth

Crack Growth Rates of Metals


Maximum Load

monotonic plastic zone

σ

Stresses Around a Crack

σ

ε


Stresses Around a Crack (continued)

Minimum Load σ

ε

cyclic plastic zone

σ


Crack Closure

S = 250

b

S = 175

c

S = 0

a


Crack Opening LoadDamaging portion of loading history

Nondamaging portion of loading history

Opening load


Mode Iopening

Mode IIin-plane shear

Mode IIIout-of-plane shear

Mode I, Mode II, and Mode III

12


5 µmcrac

k gr

owth

dire

ctio

n

Mode I Growth


crack growth direction

10 µm

slip bandsshear stress

Mode II Growth


1045 Steel - Tension

NucleationShear

Tension

1.0

0.2

0

0.4

0.8

0.6

1 10 102 103 104 105 106 107

Fatigue Life, 2Nf

Dam

age

Frac

tion

N/N

f

100 µm crack


Fatigue Life, 2Nf

Dam

age

Frac

tion

N/N

ff

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



Fatigue is a localized process involving the nucleation and growth of cracks to failure.Fatigue is caused by localized plastic deformation.Most of the fatigue life is consumed growing microcracks in the finite life regionCrack nucleation is dominate at long lives.

Fatigue Made Easy

Characterization of Materials



13


Seminar Outline

1. Historical background2. Physics of fatigue3. Characterization of materials4. Similitude (why fatigue modeling works) 5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading 10. Welded structures


Characterization

Stress Life CurveFatigue Limit

Strain Life CurveCyclic Stress Strain Curve

Crack Growth CurveThreshold Stress Intensity


Bending Fatigue

F

stre

ss

time

stress amplitude

stress range

IcM

=σBending stress:

ω


SN Curve

200

300

400500

200

300

400

500

Stre

ss A

mpl

itude

, MPa

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


SN Curve

100

1000

10000

102

Cycles

Stre

ss A

mpl

itude

,MPa

103 104 105 106 107 108 109

fatigue limit

( )bf'f NS

2S

=∆

The fatigue limit is usually only found in steel laboratory specimens


Fatigue Damage

100

1000

10000

Stre

ss A

mpl

itude

, MPa

100

Cycles101 102 103 104 105 106 107

( )bf'f NS

2S

=∆

110

b1

'f

f S2SN

∆=

10SDamage ∆∝

14


Fatigue Limit Strength Correlation

0 500 1000 1500 2000

250

500

750

1000

1250


Fatig

ue S

treng

th, M

Pa

0.6

0.5

0.35

0 500 1000 1500 2000

250

500

750

1000

1250


Fatig

ue S

treng

th, M

Pa

0.6

0.5

0.35

From Forrest, Fatigue of Metals, Pergamon Press, London, 1962Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 79 of 35

Fatigue Limit Strength Correlation


SN Materials Data

101 10 102 103 106 107105104

Fatigue Life, Reversals

100

1000

10000

Stre

ss A

mpl

itude

, MPa

93 steels

17 aluminums


Strain Controlled Testing


Cyclic Hardening / Softening


Stable Hysteresis Loop

∆σ

∆ε

∆εe∆εp

Hysteresis loop

15


Strain-Life Data σ − ε

0

100

200

300

400

500

600

0 0.004 0.008 0.012

Strain Amplitude

Stre

ss A

mpl

itude

∆ε ∆σ ∆σ2 2 2

1

= +

E K

n

'

/ '

During cyclic deformation, the material deforms on a path described by the cyclic stress strain curve

∆ε2

∆σ 2


Cyclic Stress Strain Curve


Strain-Life Data ∆ε - 2Nf

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

Stra

in A

mpl

itude

100 101 102 103 104 105 106 107

2 Reversals, 2Nf = 1 Cycle, Nf

∆ε 2


Elastic and Plastic Strain-Life Data

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

Stra

in A

mpl

itude

100 101 102 103 104 105 106 107

∆ε 2 Plastic

Elastic


Strain-Life Curve

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

Stra

in A

mpl

itude

100 101 102 103 104 105 106 107

cf

'f

bf

'f )N2()N2(

E2ε+

σ=

ε∆

c

b

'fε

E

'fσ

2Nt

∆ε 2


Transition Fatigue Life

From Dowling, Mechanical Behavior of Materials, 1999

16


εN Materials Data


93 steels

17 aluminums

1 10 102 103 106 10710510410-4

10-2

10-3

0.1

10

1

Stra

in A

mpl

itude


Crack Growth Testing


Stress Concentration of a Crack

2 a

ρ

ρ+=

a21KT

a ~ 10-3

for a crack

ρ ~ 10-9

KT ~ 2000

appliedlocal 2000 σ=σ

Traditional material properties like tensile strength are not very useful for cracked structures


Stress Intensity Factor

σ

σ

2a

aK πσ=

K characterizes the magnitude of the stresses, strains, and displacements in the neighborhood of a crack tip

Two cracks with the same K will have the same behavior


Crack Growth Measurements

σ

σ

2a

Cycles

Cra

ck s

ize

dNda

a1

a2

σ2 σ1


Crack Growth Data

10-12

10-11

10-10

10-9

10-8

10-7

10-6

1 10 100

Cra

ck G

row

th R

ate,

m/c

ycle

mMPa,K∆

mKCdNda

∆=

∆KTH

Kc

m ~ 3

17


Threshold Region

threshold stress intensity

πσ∆>∆

wafaKTH

operating stresses

flaw size

flaw shape


Threshold Stress Intensity



Non-propagating Crack Sizes

a212.1KTH ππ

σ∆>∆

Small cracks are frequently semielliptical surface cracks

2TH

cK63.0a

σ∆∆

=

2

u

THc

K52.2a

σ

∆=

Smooth specimen fatigue limit 2

uσ≈


Non-propagating Crack Sizes

Ultimate Strength, MPa

Cra

ck S

ize,

mm mMPa5KTH =∆

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000


Stable Crack Growth

10-12

10-11

10-10

10-9

10-8

10-7

10-6

1 10 100

Cra

ck G

row

th R

ate,

m/c

ycle

mMPa,K∆

mKCdNda

∆=

∆KTH

Kc

Stable growth region


Crack Growth Data

( ) 0.312 mMPaK109.6dNda

∆×= −

( ) 25.210 mMPaK104.1dNda

∆×= −

( ) 25.312 mMPaK106.5dNda

∆×= −

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless Steel:

Barsom, “Fatigue Crack Propagation in Steels of Various Yield Strengths”Journal of Engineering for Industry, Trans. ASME, Series B, Vol. 93, No. 4, 1971, 1190-1196

5 10 100

10-7

10-6

10-8

Cra

ck G

row

th R

ate,

m/c

ycle

∆K, MPa√m

σyield252273392415

18



MethodStress-LifeStrain-Life

Crack Growth

PhysicsCrack Nucleation

Microcrack GrowthMacrocrack Growth

Size0.01 mm

0.1 - 1 mm> 1mm

Fatigue Made Easy

Similitude




Seminar Outline

1. Historical background2. Physics of fatigue3. Characterization of materials4. Similitude ( why fatigue modeling works )5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading 10. Welded structures


Fatigue Analysis

MaterialData

ComponentGeometry

ServiceLoading

Analysis FatigueLife Estimate

?


The Similitude Concept

Why Fatigue Modeling Works !


What is the Similitude Concept

The “Similitude Concept” allows engineers to relate the behavior of small-scale cyclic material test specimens, defined under carefully controlled conditions, to the likely performance of real structures subjected to variable amplitude fatigue loads under either simulated or actual service conditions.

19


Fatigue Analysis Techniques

Stress - LifeBS 7608, Eurocode 3 Strain - LifeCrack Growth


Life Estimation

MethodStress-LifeBS 7608

Strain-LifeCrack Growth


Crack GrowthMicrocrack GrowthMacrocrack Growth

Size0.01 mm

1 - 10 mm0.1 - 1 mm

> 1mm


Stress-Life Fatigue Modeling

P

FixedEnd

The Similitude Concept states that if the instantaneous loads applied to the ‘test’ structure (wing spar, say) and the test specimen are the same, then the response in each case will also be the same and can be described by the material’s S-N curve. Due account can also be made for stress concentrations, variable amplitude loading etc.

100

1000

10000

Stre

ss A

mpl

itude

, MPa

100

Cycles101 102 103 104 105 106 107


Fatigue Analysis: Stress-Life

MaterialData

ComponentGeometry

ServiceLoading


SN curveKa, Ks, …

Kf

∆S , Sm


Stress-Life

Major Assumptions:Most of the life is consumed nucleating cracksElastic deformationNominal stresses and material strength control fatigue lifeAccurate determination of Kf for each geometry and material


Stress-Life

Advantages:Changes in material and geometry can easily be evaluatedLarge empirical database for steel with standard notch shapes

20


Stress-Life

Limitations:Does not account for notch root plasticityMean stress effects are often in errorRequires empirical Kf for good results


BS 7608 Fatigue Modeling

The Similitude Concept states that if the instantaneous loads applied to the ‘test’ structure (welded beam on a bulldozer, say) and the test specimen (standard fillet weld) are the same, then the response in each case will also be the same and can be described by one of the standard BS 7608 Weld Classification S-N curves.

10

100

1000

105

Cycles

Stre

ss R

ange

,MPa

108107106


Weld Classifications

D E

F2 G


Fatigue Analysis: BS 7608

MaterialData

ComponentGeometry

ServiceLoading


Weld SN curve

Class

∆S


BS 7608

Major Assumptions:Crack growth dominates fatigue lifeComplex weld geometries can be described by a standard classificationResults independent of material and mean stress for structural steels


BS 7608

Advantages:Manufacturing effects are directly includedLarge empirical database exists

21


BS 7608

Limitations:Difficult to determine weld class for complex shapesNo benefit for improving manufacturing process


Strain-Life Fatigue Modeling

The Similitude Concept states that if the instantaneous strains applied to the ‘test’ structure (vehicle suspension, say) and the test specimen are the same, then the response in each case will also be the same and can be described by the material’s e-N curve. Due account can also be made for stress concentrations, variable amplitude loading etc.

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

Stra

in A

mpl

itude

100 101 102 103 104 105 106 107


Fatigue Analysis: Strain-Life

MaterialData

ComponentGeometry

ServiceLoading


εN curveσε curve

Kf

∆S , Sm


Strain-Life

Major Assumptions:Local stresses and strains control fatigue behaviorPlasticity around stress concentrationsAccurate determination of Kf


Strain-Life

Advantages:Plasticity effectsMean stress effects


Strain-Life

Limitations:Requires empirical Kf

Long life situations where surface finish and processing variables are important

22


Crack Growth Fatigue Modeling

The Similitude Concept states that if the stress intensity (K) at the tip of a crack in the ‘test’ structure (welded connection on an oil platform leg, say) and the test specimen are the same, then the crack growth response in each case will also be the same and can be described by the Paris relationship. Account can also be made for local chemical environment, if necessary.

10-12

10-11

10-10

10-9

10-8

10-7

10-6

1 10 100

Cra

ck G

row

th R

ate,

m/c

ycle

mMPa,K∆


Fatigue Analysis: Crack Growth

MaterialData

ComponentGeometry

ServiceLoading


da/dN curve

K

∆S , Sm


Crack Growth

Major Assumptions:Nominal stress and crack size control fatigue lifeAccurate determination of initial crack size


Crack Growth

Advantage:Only method to directly deal with cracks


Crack Growth

Limitations:Complex sequence effectsAccurate determination of initial crack size


Choose the Right Model

SimilitudeFailure mechanismSize scale

23


Design Philosophy

Safe LifeDamage Tolerant


Safe Life

0

100

200

300

400

500

104 105 106 107 108 109

Stre

ss A

mpl

itude

, MPa

Fatigue Life

99 90 11050Percent Survival

0

100

200

300

400

500

104 105 106 107 108 109

Stre

ss A

mpl

itude

, MPa

Fatigue Life

99 90 1105099 90 11050Percent Survival

Choose an appropriate risk and replace critical partsafter some specified interval


Damage Tolerant

Inspect for cracks larger than a1 and repairCycles

Cra

ck s

ize

a1

a2

Safe Operating Life

Inspection


Inspection

A Boeing 777 costs $250,000,000

A new car costs $25,000

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



Questions to askWill a crack nucleate ?Will a crack grow ?How fast will it grow ?

SimilitudeFailure mechanismSize Scale

Fatigue Made Easy

Variability



24


Seminar Outline

1. Historical background2. Physics of fatigue3. Characterization of materials4. Similitude5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading 10. Welded structures


Sources of Variabilitycustomers

materials manufacturing

usage

107

Fatigue Life, 2Nf

1

10 102 103 104 105 106

0.1

10-2

1

10-3

10-4

Stra

in A

mpl

itude

time

50%

100 %

Failu

res

Strength

Stress


“Average” Load History

Take a loading history that produces “average” fatigue damage and multiply it by a scale factor to obtain the distribution of loads.


Gumble Probability Plot 99.9 %

99 %

80 %

50 %

10 %

1 %

200 400 600 800

Gumbel Distribution42 Data PointsLocation 362.94Scale 124.61

Maximum force from 42 drivers

Cum

ulat

ive

Pro

babi

lity


Maximum Load Correlation

0 200 400 600 800 1000

108

107

106

105

104

103

Maximum Load

Fatig

ue L

ives


Variability in Fatigue Lives

0.1 1 10 102 103 104

Normalized Life

Airplane (334)

Tractor (54)ATV (19)

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

Calculated fatigue lives for actual service usage data

Cum

ulat

ive

Pro

babi

lity

25


Variability in Loading

1 10

LogNormal Distribution54 Data PointsMean 1.01COV 0.47

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

n neq SS ∑∆=∆

n ~ 4 - 6

Equivalent LoadCum

ulat

ive

Pro

babi

lity

2


Statistical Variability of Fatigue Life

50

10

2

90

98

104 105 106 107 108

Cycles to Failure

Per

cent

Sur

viva

l

∆s=210∆s=245∆s=315∆s=280∆s=440

Sinclair and Dolan, “Effect of Stress Amplitude on the Variability in Fatigue Life of 7075T6 Aluminum Alloy”Transactions ASME, 1953


P-S-N Curve

0

100

200

300

400

500

104 105 106 107 108 109

Stre

ss A

mpl

itude

, MPa

Fatigue Life

99 90 11050Percent Survival


10/1b)N(S2S b

f'f ≈=

∆

Suppose has a COV = 0.1'fS

The variability in Nf will be:

( ) ( ) 3.11)1.0(11COV1COV22

'ff

102b2SN =−+=−+=

Variability in Strength and Life

A 10% variation in strength results in a factor of 20 in fatigue life


Strain Life Data for 980X Steel

102 103 104 105 106 107

Fatigue Life101

1

0.1

10-2

10-3

10-4

Stra

in A

mpl

itude

378 Data Points


Curve Fitting

102 103 104 105 106 107

Fatigue Life101

1

0.1

10-2

10-3

10-4

Stra

in A

mpl

itude

cf

'f

bf

'f )N2()N2(

E2ε+

σ=

ε∆

Assume a constant slope to get a distribution of properties

'fσ

26


Distribution

LogNormal Distribution378 Data PointsMean 802 MPaCOV 0.12

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

'fσ

'fσ

10 100 1000

Cum

ulat

ive

Pro

babi

lity


Material Property Simulation

102 103 104 105 106 107

Fatigue Life101

1

0.1

10-2

10-3

10-4

Stra

in A

mpl

itude


Typical Variability

Pit SizeBolt Preload ForceSurface Roughness


Pit Depth Variability

PitsLogNormal Distribution12 Data PointsMean 24.37

100

COV 0.33

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

10Pit Depth, µm

Dolly, Lee, Wei, “The Effect of Pitting Corrosion on Fatigue Life”Fatigue and Fracture of Engineering Materials and Structures, Vol. 23, 2000, 555-560

Cum

ulat

ive

Pro

babi

lity


Variability in Bolt Force

100 1000

ForceLogNormal Distribution200 Data PointsMean 130.45COV 0.14

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

Bolt Force, N

Preload force in bolts tightened to 350 Nm

Cum

ulat

ive

Pro

babi

lity


Surface Roughness Variability

100

LogNormal Distribution125 Data PointsMean 42.98COV 0.10

Machined aluminum casting

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

Force

10Surface Finish, µin

Cum

ulat

ive

Pro

babi

lity

27


Variability Summary

Source COVService Loading 0.47

Materials 0.12Manufacturing 0.14Surface Finish 0.10

Environment 0.33

Strength

Stress

( )∏=

−+=n

1i

a2X 1C1CCOV

2i

i

Largest variability dominates


Stress - Strength

initial cost

warranty costreputation cost

customer usage

strength

design and test loads



Fatigue data inherently contains a lot of variabilityThe variability is predictable and quantifiable

Fatigue Seminar

Fatigue Made Easy

Mean Stress




Seminar Outline


28


Mean Stresses

mean stress

stress range

stre

ss

2SSS minmax

mean+

=

Smax

Smin

max

min

SSR =


General Observations

Tensile mean stresses reduce the fatigue life or decrease the allowable stress rangeCompressive mean stresses increase the fatigue life or increase the allowable stress range


Mechanism

Fatigue damage is a shear process

∆S

Tensile mean stresses open microcracks and make sliding easier

2Smean


Goodman 1890

Mechanics Applied to EngineeringJohn 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 practical purposes, represents Wöhlers data.

Sultimate = Smin + 2 ∆S


Goodman Diagram

Mean stress

Alte

rnat

ing

stre

ss

Su0

Se

107 cycles

105 cycles

−

∆

=∆

−= ultimate

mean

1R SS1

2S

2S

R = -1 R = 1


Test Data ( 1941 )

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.2

0.4

0.6

0.8

1.0

1.2

0

Mean StressUltimate Strength

Alte

rnat

ing

Stre

ssFa

tigue

Lim

it

J.O. Smith, The Effect of Range of Stress on the Fatigue Strength of Metals,Engineering Experiment Station Bulletin 334, University of Illinois, 1941

29


Compression

Se

Su0R = -1 R = 1

-SuR = -∞

no influence

detrimental

beneficial


Modified Goodman ( no yielding )

Se

Su0R = -1 R = 1

-SuR = -∞

Sys

Sys

-Sys

ysmean SS2S

<+∆


Mean Stress Influence on Life

0.1

1

10

100

1000

-0.6 -0.4 -0.2 0 0.2 0.4 0.6Mean Stress

Ultimate Strength

Rel

ativ

e Fa

tigue

Life


Stress Concentrations

PlasticZone

∆ε

∆ε The elastic material surroundingthe plastic zone around a stressconcentration forces the material to deform in strain control


Mean Stresses at Notches

σ

ε

σ

ε

σ

ε

elastic plastic

NominalNotch

NotchNominal

Nominal mean stress is less than notch mean stress

Nominal mean stress is greater than notch mean stress

Nominal Notch


Morrow Mean Stress Correction

cf

'f

bf

mean'f )N2()N2(

E2ε+

σ−σ=

ε∆

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

Stra

in A

mpl

itude

100 101 102 103 104 105 106 107

Emeanσ

30


Smith Watson Topper

σ

ε

∆ε

σmaxcb

f'f

'f

b2f

2'f

max )N2()N2(E2

+εσ+σ

=ε∆

σ


Mean Stress Relaxation

Stadnick and Morrow, “Techniques for Smooth Specimen Simulation of Fatigue Behavior of Notched Members”ASTM STP 515, 1972, 229-252


Loading Histories


Test Results


Crack Growth Physics

σ

σMaximum load

Minimum load

σ

ε

Mean stresses in plastic zone are small


Mean Stress Effects

From: Dowling and Thangjitham, An Overview and Discussion of Basic Methodology for Fatigue,ASTM STP 1389,2000, 3-38

( )γ−∆

=R1KC

dNda m

0 < γ < 0.5

31


Compression

Crack open

Crack closed


Compressive Stresses

Compressive stresses are not very damaging in crack growth

Stre

ss

Crack opening level


Sources of Mean/Residual Stress

Loading HistoryFabricationShot PeeningHeat Treating


Loading History

Tension overloads produce favorable compressive residual stress

Compressive overloads produce unfavorable tensile residual stress

σ

ε

σ

ε


Fabrication


Cold Expansion

1965 Basic Cx process conceptualized (Boeing)The split sleeve is slipped onto the mandrel, 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.

When the puller is activated, the mandrel is drawn through the sleeve radially expanding the hole.

Courtesy of Fatigue Technology Inc.

32


Theory of Cold Expansion

Courtesy of Fatigue Technology Inc.Fatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 187 of 35

Fatigue Life Improvement

Courtesy of Fatigue Technology Inc.

100

200

300

0108107106105104103

Nom

inal

Stre

ss

Fatigue Life

Cold Expanded


Shot Peening

-600

-400

-200

0

200

0 0.2 0.4 0.6 0.8Depth (mm)

Res

idua

l Stre

ss (M

Pa)

Residual stress in a shot peened leaf springFatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 189 of 35

Shot Peening Results

www.metalimprovement.com

500

1000

1500

5000

0 1000 1500 2000 2500Fatig

ue s

treng

th a

t 2x1

06cy

cles

, MPa

Ultimate Tensile Strength, MPa

2SS u

FL =

Smooth

Notched

Shot PeenedSmooth & Notched


Heat Treating

200

600

400

00 5 10 15

Brin

ellH

ardn

ess

Depth, mm0 5 10 15

-1500

-1000

-500

0

500

1000

Depth, mm

Res

idua

l Stre

ss, M

Pa

Radial

Circumferential

Axial

50 mm diameter induction hardened 1045 steel shaft



Local mean stress rather than the nominal mean stress governs the fatigue lifeMean stress has the greatest effect on crack nucleation

33

Fatigue Made Easy

Stress Concentrations




Seminar Outline

1. Historical background2. Physics of fatigue3. Characterization of materials4. Similitude5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading 10. Welded structures


Stress Concentration Factor

Applied stressLocal stress

ρ+σ=σ

a21appliedlocal

Inglis Solution 1910

2aρ


Define Kσ and Kε after Yielding

S , e

σ , ε

Define: nominal stress, Snominal strain, e

notch stress, σnotch strain, ε

Stress concentration

Strain concentrationS

K σ=σ

eK ε

=ε


Stress and Strain Concentration

Kt

Nominal Stress

Stre

ss/S

train

Con

cent

ratio

n

1K →σ

2tKK →ε

First yieldingS

K σ=σ

eK ε

=ε


Kσ and Kε

Stre

ss (M

Pa)

Strain

KtS

Kte

σε

SK σ

=σ

eK ε

=ε

34


Neuber’s Rule

Stre

ss (M

Pa)

Strain

KtS

Kte

σ

ε εσ=eKSK tt

Stress calculated with elastic assumptions

Actual stress


Neuber’s Rule for Fatigue

2222eKSK tt ε∆σ∆

=∆∆

Stress and strain amplitudes

Elastic nominal stress

E2S

2e ∆

=∆

Substitute and rearrange

22E

2SKt

ε∆σ∆=

∆

The product of stress times strain controls fatigue life


SN Materials Data

101 10 102 103 106 107105104


100

1000

10000

Stre

ss A

mpl

itude

, MPa

93 steels

17 aluminums


εN Materials Data

93 steels

17 aluminums

10-4

10-2

10-3

0.1

10

1

Stra

in A

mpl

iture

1 10 102 103 106 107105104



1 106 10710510 102 103 104


1

10

102

105

104

103

22

EK

tε ∆

σ∆or

2S∆

22E

ε∆σ∆


A Dilemma

Stress analysis and stress concentration factors are independent of size and are related only to the ratio of the geometric dimensions to the loads

Fatigue is a size dependent phenomenon

How do you put the two together ?

35


Similitude


Fatigue of Notches


104 105 106 107 108

100

400

300

200

Fatigue Life

Nom

inal

Stre

ss, M

Pa

d d

Kt = 3.1

Kt = 3.1

Kf = 2.2

104 105 106 107 108

100

400

300

200

Fatigue Life

Nom

inal

Stre

ss, M

Pa

dd dd

Kt = 3.1

Kt = 3.1

Kf = 2.2


Notch Size

Kt KfKt

Kf

Large Notch Small Notch


Microstructure Size

Kt Kf

Kt Kf

Low Strength High Strength


Stress Gradient

Kt Kf

Kt

Kf

Low Kt High Kt


Kt vs Kf

0

2

4

6

8

10

0 2 4 6 8 10Kt

Kf

Kf = Kt

Experiments

Effe

ctiv

e st

ress

con

cent

ratio

n

Calculated stress concentration

36


Peterson’s Equation

ρα

+

−+=

1

1K1K tf

mmMPa2070025.08.1

u

σ

=α

0

1

2

3

4

10-4 10-3 10-2 0.1 1 10 102 103

Kf

ρα

No effect when ρ << αFull effect when ρ >> α


Peterson’s Constant

1000500 20001500

0.1

0.03

0.7

0.3


α, m

m


Static Strength

holeKt = 2.5

slotKt = 5

diamondKt = 20

edgeKt = 20


1018 Steel Test Data

0

20

40

60

80

100

0 2 4 6 8 10

load

, kN

displacement, mm

edgediamondslothole


Notched SN Curve

100

1000

10000

100

Cycles

Stre

ss A

mpl

itude

,MPa

101 102 103 104 105 106 107

Smooth specimen data

Notched specimenKf

Stress concentrations are not very important at short livesFatigue Seminar © 2002 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 215 of 35

Crack Growth Data

10-12

10-11

10-10

10-9

10-8

10-7

10-6

1 10 100

Cra

ck G

row

th R

ate,

m/c

ycle

mMPa,K∆

mKCdNda

∆=

∆KTH

Kc

a212.1KTH ππ

σ∆>∆

Nonpropagating cracks

37


Frost Datanucleation fracture

Rotating bendingNotched bar

Notched plate

1 3 5 7 9 11 13 15

1.0

0.8

0.6

0.4

0.2

0

Kt

Sno

min

al

Sfa

tigue

lim

it

tK1 nonpropagating cracks

Frost, “A Relation Between the Critical Alternating Propagation Stress and Crack Length for Mild Steel”Proceedings of the Institute for Mechanical Engineers, Vol. 173, No. 35, 1959, 811-836


Significance

DKS th

flπ

∆=

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

Kt does not play a role for sharp notches !

A stress concentration behaves like a crackonce a stress concentration becomes large (Kt > 4)


Cracks at Notches

D

a a D + a

KtS SS

a << D a >> D


Stress Intensity Factors

0 0.1 0.2 0.3 0.4 0.5 0.6

1.0

0

3.0

2.0

Da

DSK

aSKK t π=

( )aDSK +π=


Cracks at Holes

201 1 22

Once a crack reaches 10% of the hole radius, it behaves as if the hole was part of the crack


Specimens with Similar Geometry

Kt = 2.4Kt = 10.7

Ultimate Strength 780 MPaYield Strength 660 MPa

25 25

2.5 2.5

38


Test Results

1

100

1000

Nom

inal

Stre

ss A

mpl

itude

1 10 100 103 104 105 106 107

Total Fatigue Life, Cycles

Strength Limited

Crack Growth DominatedFatigue Strength Dominated

Threshold Stress Intensity Dominated

Kt = 2.4Kt = 10.7



Fatigue may be thought of as a failure of the average stress concept, consequently, fatigue usually begins at stress concentrators which are most frequently located on the surfaceThe severity of a stress concentrator in fatigue is size dependentSmall stress concentrators are more effective in high strength materials

Fatigue Made Easy

Surface Effects




Seminar Outline



Modern View of the Fatigue LimitThe fatigue limit is the stress where a crack may nucleate but will not grow through the first microstructural barrier such as the grain size, pearlite colony size, prior austenite grain size, eutectic cell size or precipitate spacing.

Slip Bands Crack


Intrinsic Flaws

Little effect of surface pit because it is smaller than the grain size

Large effect of defect because it is larger than the grain size

39


Surface Finish Influence

MethodStress-LifeStrain-Life

Crack Growth


Microcrack GrowthMacrocrack Growth

Size0.01 mm

0.1 - 1 mm> 1mm

Influence ofSurface Finish

StrongModerate

None


Sources of Surface EffectsMachining

CuttingGrinding

CorrosionGeneralPitting

ProcessingCutting/ShearingCastingForgingPlating

Foreign Object DamageNicksScratches


Machining

σ1

Cracks start in machining marks not in the direction of the maximum principal stress

100 µm


Casting

100 µm

Surface flaw in gray cast iron


Nodular Iron Surface

Flake graphite formed on the surface of a nodular iron casting

Starkey and Irving, “A Comparison of the Fatigue Strength of Machined and As-cast Surfaces of SG Iron”International Journal of Fatigue, July, 1982, 129-136


Test Data10-1

10-2

10-3

10-4

102 103 104 105 106 107 108101

Stra

in A

mpl

itude


Cast Surface

Machined Surface

40


Surface Reduction Factors

400 600 800 1000 1200 1400 1600


0.2

0.4

0.6

0.8

1.0

0

Sur

face

Fac

tor

Polished

Ground

Forged

Hot Rolled

Machined

5.0

2.5

1.7

1.2

1.0

Fatig

ue N

otch

Fac

tor


Noll and Lipson 1945

0

200

400

600

800

1000

400 600 800 1000 1200 1400 1600 18002000 2000


Fatig

ue L

imit,

MP

a

Ground

Machined

Hot RolledForged


Hiam and Pietrowski 1978

Driven for 1 or 2 years in Southern Ontariobefore making specimensto evaluate corrosion effects

Hiam and Pietrowski, “The Influence of Forming and Corrosion on the Fatigue Behavior of Automotive Steels”, SAE Paper 780040, 1978

Strain controlled fatigue testing


Kf for pitting

Hot RolledSurface

CorrodedSurface

950X 1.12 1.49

0.06% C HSLA 1.18 1.65

0.18% C HSLA 1.90

Surface finish factor predicts Kf = 1.6 for a Hot Rolled Surface

from Hiam and Pietrowski


Pit Depth Effects on Life106

105

104

0.1 0.30.20Pit Depth, mm

Fatig

ue L

ife, C

ycle

s

from Hiam and Pietrowski

950X Steel


Fatigue Notch Factor for Pits

1.00.1 0.30.20

Pit Depth, mm

1.1

1.2

1.3

1.4

1.5

Kf

41


Suspension


Spring Failures


Microscopic Examination

Corrosion Pits

Corrosion Pits


Chrome Plating

105 107106 108104

Stre

ss A

mpl

itiud

e, M

Pa500

200

400

300

Life, Cycles

Almen, “Fatigue Loss and Gain by Electroplating” , Product Engineering, Vol. 22, No. 5, 1951, 109-116

Chrome plated

Shot peened andchrome plated

Base steel


Hard Chrome Plating

coating

Metals Handbook, Volume 9, Fractography and Atlas of Fractographs

In addition to cracks, coatings frequently have high tensile residual stresses


Galvanized Steel

3

0.50

1

2

1

225 MPa

305 MPa

240 MPa

Life Fraction

Cra

ck D

ensi

ty m

m-1

Vogt, Boussac, Foct, “Prediction of Fatigue Resistance of a Hot-dip Galvanized Steel”Fatigue and Fracture of Engineering Materials and Structures, Vol. 23, No. 1, 2001,33-40

42


Fatigue Limit for Galvanized Steel

10010 100 1000

200

300

400

Fatig

ue L

imit

Coating Thickness, t µm

Uncoated Fatigue Limit

tKS TH

FL π∆

=

Coatings can be modeled with a crack equal to the coating thickness


Foreign Object Damage

http://www.eng.ox.ac.uk/~ftgwww/frontpage/fod2.html


Foreign Object Damage

http://www.eng.ox.ac.uk/~ftgwww/frontpage/fod2.html


Upper Control Arm


Serial Number



Fatigue crack nucleation is a surface phenomena and everything about the surface affects the fatigue lifeMost of the design rules are conservative having been developed for materials of the 1950’s

43

Fatigue Made Easy

Variable Amplitude Loading




Seminar Outline

1. Historical background2. Physics of fatigue3. Characterization of materials4. Similitude (why fatigue modeling works)5. Variability6. Mean stress 7. Stress concentrations8. Surface effects9. Variable amplitude loading10. 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

A

F

D

B

E

I, AH G

C

AD

BC

CB

DA

Counts 1/2 cycles


Rainflow and HysteresisA

CB

D EF G

H I

ε

σ

44


Cumulative Damage

….….

…. ….

High - Low

Low - HighnH nL

nL nH

∆SL

∆SH


Linear Damage

∆SH

∆SL

Nf H Nf L

Lf

L

Hf

H

F Nn

Nn

NnDamage +==∑

Miner’s Rule:


Nonlinear Damage

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

00

Cycle ratio,

Dam

age

fract

ion

nNf

0040.=ε∆

0200.=ε∆

ΣD = 0.7

ΣD = 1.3

ΣD ~ 1


Periodic Overload Results

10 100 103 104 105 106 107 108 109

10-3

10-4

0.01

0.1S

train

Am

plitu

de

Fatigue Life

….

….

The fatigue limit is reduced by a factor of 3 when a few large cycles are applied

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

100

1000

10000

Stre

ss A

mpl

itude

, MPa

100

Cycles101 102 103 104 105 106 107

( )bf'f NS

2S

=∆

110

b1

'f

f S2SN

∆=

10SDamage ∆∝


Crack Growth Data

10-12

10-11

10-10

10-9

10-8

10-7

10-6

1 10 100

Cra

ck G

row

th R

ate,

m/c

ycle

mMPa,K∆

mKCdNda

∆=

∆KTH

Kc

1

3

45


Crack Growth Data

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

Crack Growth Rate, m/cycle

1

10

100

mM

Pa

,K∆3SDamage ∆∝

( )2/m1SC

aaN2m

m

2/m1i

2/m1f

f

−π∆

−=

−−


Multiple Choice

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

1

10

100

Ampl

itude

100

Cycles101 102 103 104 105 106 107

1000

n = 10

n = 5

n = 3nSDamage ∆∝


Loading History

Time (Secs)

50 100 150 200 250 300

750

500

250

0

-250

-500

-750

Stra

in G

age

(ust

rain

)

Bracket.sif-Strain_b43

0

1500

Range (ustrain)

-750

750Mean (ustrain)

0

750

Cou

nts

rf_000.sif-Strain_b43


Slope = 3

0

1500

range (ustrain)

-750

750mean (ustrain)

3.15

% d

amag

e

Damage


Slope = 5

0

1500

range (ustrain)

-750

750mean (ustrain)

5.14

% d

amag

e

Damage

46


Slope = 10

0

1500

range (ustrain)

-750

750mean (ustrain)

20.78

% d

amag

e

Damage


Mechanisms and Slopes

100

103

104

Stre

ss A

mpl

itude

, MP

a

100

Cycles101 102 103 104 105 106 107

110

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

Crack Growth Rate, m/cycle

1

10

100

mM

Pa

,K

∆

1

3

Crack Nucleation

Crack Growth10

100

103 104 105 106 107 108


1

51

Equ

ival

ent L

oad,

kN

Structures

A combination of nucleation and growth


Equivalent Load

n

N

1i

ni

N

SS

∑=

∆=∆

Equivalent constant amplitude loading

Typically n ranges from 4 to 6 for structures

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

S∆


SAE Keyhole Specimen

Suspension

Transmission

Bracket


SAE Keyhole Test DataManTen RQC 100

10

100

103 104 105 106 107 108


1

SuspensionTransmission

Bracket

Constant Amplitude

51

Equ

ival

ent L

oad,

kN


How Many Cycles ?

Engine:2 starts/day for 10 years = 7000 cycles3000 rpm for 100,000 miles (2000 hrs) = 3.6 x 108 cycles

47


How Many Cycles ? (continued)

Time (Secs)

50 100 150 200 250 300

750

500

250

0

-250

-500

-750

Stra

in G

age

(ust

rain

)

Bracket.sif-Strain_b43

0

2 minutes

Bracket Vibration:

0.5 per minute for 100,000 miles (2000 hrs) = 60,000 cycles12 hz continuous vibration for 2000 hrs = 8.6 x 107 cycles



Rainflow counting is employed to identify cyclesThe slope of the fatigue curve ( damage mechanism) has a large influence on how much damage is caused by smaller cycles

Fatigue Made Easy

Welded Structures




Seminar Outline



Types of Welds

Structural weldsSpot weldsSpecial Processes

LaserElectron Beam


Weld Classifications

D E

F2 G

48


100

200

300

400

B

C

D

E

F F2 G W0

105 106 107 108

Stre

ss R

a nge

, MP

a

BS 7608 - Steel

Fatigue Life, Cycles


Crack Growth Data

( ) 0.312 mMPaK109.6dNda

∆×= −

( ) 25.210 mMPaK104.1dNda

∆×= −

( ) 25.312 mMPaK106.5dNda

∆×= −

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless Steel:

Barsom, “Fatigue Crack Propagation in Steels of Various Yield Strengths”Journal of Engineering for Industry, Trans. ASME, Series B, Vol. 93, No. 4, 1971, 1190-1196

5 10 100

10-7

10-6

10-8

Cra

ck G

row

th R

ate,

m/c

ycle

∆K, MPa√m

σyield252273392415


0

25

50

75

100

125

105

B

C

DE

F

106 107 108

Stre

ss R

a nge

, MP

a

BS 7608 - Aluminum

Fatigue Life, CyclesSharp, “Behavior and Design of Aluminum Structures”,McGraw-Hill, 1992


Crack Growth Data

1 10 100

Cyclic Stress Intensity, MPa√m

Cra

ck G

row

th R

ate

m/c

ycle

A533B m/cycle

2024-T3 m/cycle

10-2

10-4

10-6

10-8

10-10

10-12

3X

Steel welds are 3 times stronger than aluminum

1

3


Residual Stress from Welding

Y

X

X

X

X

Y

YY

tension

tension

compression

compression


Weld Distortion

49


Weld Toe Residual Stress

Yieldstress

Maximum stress at the weld toe is nearly the same for any cycle

∆ε

ε

σ

∆ε


Mean Stress Effects

As welded structures usually have the maximum possible mean stressStress relief, peening, etc. will have a substantial effect on the fatigue life


Butt and Fillet Weld Test Data

99% survival with 95% confidence

1000

Stre

ss R

ange

, MP

a

100

10

103 104 105 106 107


Failures Run outs

The good welds


Weld Terminations1000

Stre

ss R

ange

, MP

a

100

10

103 104 105 106 107


Failures Run outs

99% survival with 95% confidence

The bad welds


Sources of Inherent Scatter

Weld qualityMean, fabrication and residual stressesStress concentrations (geometry)Weldment sizeMaterial properties

Opportunities for Improvement !


The Good and Bad

Good weld design

Bad weld design

50


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.


Macroscopic Shape

t

r

θ

0.05 0.20.150.1

2

3

4

1

r / t

tK

θ = 15º

θ = 30º

θ = 45º

θ = 60º


Kfmax

mMPatS15.01K umaxf β+=

rt1Kt β+=

ρα

+

−+=

1

1K1K tf

2

3

4

5

ρ = α Weld toe radius

ft KorK β ~ 0.3 axialβ ~ 0.2 bending

t

r

θ

51


Weld Improvement

Reduce weld toe stressesStress relieveImprove local geometry


Spot Weld Fatigue Data

10

102

103

104

105

102 103 104 105 106 107 108


Max

imum

Loa

d, N

Tensile Shear

Coach-peel

1

4

Fatigue Data Bank for Spot Welds, University of Illinois


Spot Weld Modeling

Beams are used as " force transducers " to obtain forces and moments transmitted through the spot welds

Forces and moments are used to calculate " structural stresses "

Spotweld “Nugget” Beam Element


Structural Stress Calculations

Structural stresses are calculated from the forces and moments on each beam element :

Sheet 2

NuggetSheet 1

My

Fy

Fx

Mx

Fz

My

Fy

Fx

Mx

Fz

My

Fy

Fx

Mx

Fz


Structural Stresses

Stresses in sheet :

θσ+θσ+σ+θσ−θσ−=θ∆ cos)M(sin)M()F(sin)F(cos)F()(S yxxyx

dtF)F( x

x π=σ

dtF

)F( yy π

=σ

2z

z tF744.1t6.0)F( =σ

2x

x tdM872.1t6.0)M( =σ

2Y

Y tdM872.1t6.0)M( =σ

Fz

Mxt

d

Fx

FyMy


Structural Stress Correlation

101

102

103

104

102 103 104 105 106 107

Fatigue Life

Stru

ctur

al S

tress

, MPa

52



Local weld toe stresses, geometry and flaws control the life of weldments

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