fatique analysis

8/9/2019 Fatique Analysis

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Fatigue Analysis

Techniques

Darrell Socie

Mechanical Engineering

University of Illinois


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Fatigue Analysis

Techniques

! Load-Life

! Stress-Life

! BS 5400 ( Eurocode 3 )

! Strain-Life

! Crack Growth


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Common Features

! Constant amplitude test data

! Rainflow

! Linear damage


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Load-Life Data

10

100

1000

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

Cycles

L

ateralForce,

kN


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Stress-Life Data

100

1000

10000

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

Cycles

Stre

ssAmplitude,MPa


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BS 5400 ( Eurocode 3 ) Data

100

200

300

400

B

C

D

E

FF2 G W

0105 106 107 108

Str

es

sR

ang

e,

MP

a Steel


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BS 5400 ( Eurocode 3 ) Data

0

25

50

75

100

125

105

B

C

DE

F

Aluminum

106 107 108

Str

es

sR

ang

e,

MP

a

Cycles


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BS 5400 ( Eurocode 3 )

Weld Class F


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Strain-Life Data

- 2Nf

0.00001

0.0001

0.001

0.01

0.1

1

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

Reversals

StrainAmplitude


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Strain-Life Data

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Strain Amplitude

StressAmplitude


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Crack Growth Data

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

1.00E+00 1.00E+01 1.00E+02

Cyclic Stress Intensity, MPa m

CrackGrowthRate,m/cycle


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Rainflow Counting

AC

BD

E

F

G

H

I


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Hysteresis Loops

AC

BD

E

F

G

H

I

A, I

B

C

D, F

E

G

H


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Damage Accumulation

! Miners Linear Damage Rule

" Ni / Nf = 1


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Load-Life

! Major Assumption

" Loads used to generatebaseline data are the same asservice loading


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Load-Life

! Advantages

" Actual test of structure

" Manufacturing and local stressconcentration effectsautomatically included

" Stress analysis is not needed


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Load-Life

! Limitations

" Actual test of structure

" New tests required for eachchange in material, loading orgeometry

" Mean stress effects can not beincluded


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Stress-Life

! Major Assumptions

" Nominal stresses and materialstrength control fatigue life

" Accurate determination of Kffor each geometry and material


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Notched S-N Curve

10

100

1000

10000

1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07

Cycles

StressAmplitud

e

Kt or Kf


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Stress-Life

! Advantages

" Changes in material andgeometry can easily beevaluated

" Large emperical database for

steel with standard notchshapes


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Stress-Life

! Limitations

" Does not account for notchroot plasticity

" Mean stress effects are oftenin error

" Requires emperical Kf for goodresults


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! Major Assumptions

" Complex weld geometries canbe described by a standardclassification

" Crack growth dominates

fatigue life" Results independant of

material and mean stress forstructural steels


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10

100

1000

1E+05 1E+06 1E+07 1E+08

Cycles

StressRange,

MPa

Fatigue Limit

No Fatigue Limit


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! Advantages

" Manufacturing effects aredirectly included

" Large emperical databaseexists


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! Limitations

" Difficult to determine weldclass for complex shapes

" No benifit for improvingmanufacturing process


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Welded Structure


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Strain-Life

! Major Assumptions

" Local stresses and strainscontrol fatigue behavior

" Accurate determination of Kf


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Strain-Life

! Advantages

" Plasticity effects

" Mean stress effects


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Mean Strain Example


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Compressive Mean

Stress


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Neubers Rule

0

200

400

600

800

1000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Strain

Stress

K S ef2 =


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Strain-Life

! Limitations

" Requires emperical Kf" Long life situations where

surface finish and processingvariables are important


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Crack Growth

! Major Assumptions

" Nominal stress and crack sizecontrol fatigue life

" Accurate determination ofinitial crack size


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Crack Growth

! Advantage

" Only method to directly dealwith cracks


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Crack Growth

! Limitations

" Sequence effectsKeff = f ( K )

" K = E e Y( a ) a

" Accurate determination of ai


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Crack Closure

Crack Opened Crack Closed


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Crack Opening Load

Damaging portion of loading history

Nondamaging portion of loading history

Opening load


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Applications

! Material Selection /

Improvement! Fillet Weld

! Scaling / Editing LoadHistories

! Crack Size / Shape


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Transmission History

-600

-400

-200

0

200

400

600

800

1000

NominalStrain


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Material Properties

BHN 187 277 336 410 545

f' ,MPa 1668 2978 3902 4593 5666

b -0.149 -0.158 -0.159 -0.167 -0.170

f' 0.556 0.700 0.563 0.381 0.068

c -0.522 -0.578 -0.595 -0.589 -0.603

K, MPa 1460 1743 2051 2381 4438

n 0.234 0.189 0.163 0.172 0.169

E, GPa 206 206 208 206 205


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Strength Variation

0

100

200

300

400

500

600

1E+03 1E+04 1E+05 1E+06 1E+07

Blocks

Hardness,

BHN


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Kf Variation

1.5

2

2.5

3

3.5

4

4.5

1E+03 1E+04 1E+05 1E+06 1E+07

Blocks

FatigueNotchFactor


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Scale Factor Variation

0

0.5

1

1.5

2

1E+03 1E+04 1E+05 1E+06 1E+07

Blocks

ScaleFactor


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Cycle Histogram

0

1500

range(uE)

-1000

1000

mean (u

E)

0

25

counts


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-N Damage

0

1500

range(uE)

-50

50

mean

stress

0

10

%

damage


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Weld Geometry

Crack Depth


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Geometry Factor

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.2 0.4 0.6 0.8 1.0

a/W

Y(a/W

)


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Crack Length

0

0.001

0.002

0.003

0.004

0.005

0 200 400 600 800 1000

Blocks

CrackLength,m

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