Download pdf - Fatigue Analysis Techniques · Fatigue Analysis Techniques! Load-Life! Stress-Life! BS 5400 ( Eurocode 3 )! Strain-Life! Crack Growth

Fatigue AnalysisTechniques

Darrell SocieMechanical Engineering

University of Illinois

Fatigue AnalysisTechniques

! Load-Life! Stress-Life! BS 5400 ( Eurocode 3 )! Strain-Life! Crack Growth

Common Features

! Constant amplitude test data! Rainflow! Linear damage

Load-Life Data

10

100

1000

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

Cycles

Lat

eral

Fo

rce,

kN

Stress-Life Data

100

1000

10000

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

Cycles

Stre

ssA

mpl

itud

e,M

Pa

BS 5400 ( Eurocode 3 ) Data

100

200

300

400

B

C

D

E

F F2 G W0

105 106 107 108

Str

ess

Ran

g e,M

Pa Steel

BS 5400 ( Eurocode 3 ) Data

0

25

50

75

100

125

105

B

C

DE

F

Aluminum

106 107 108

Str

ess

Ran

g e,M

Pa

Cycles

BS 5400 ( Eurocode 3 )Weld Class F

Strain-Life Data∆ε - 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

Str

ain

Am

plit

ud

e

Strain-Life Data σ − ε

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Strain Amplitude

Str

ess

Am

plit

ud

e

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

Cra

ckG

row

thR

ate,

m/c

ycle

Rainflow Counting

AC

BD

E

F

G

H

I

Hysteresis Loops

AC

BD

E

F

G

H

I

A, I

B

C

D, F

E

G

H

Damage Accumulation

! Miner’s Linear Damage Rule

" Σ Ni / Nf = 1

Load-Life

! Major Assumption" Loads used to generate

baseline data are the same asservice loading

Load-Life

! Advantages" Actual test of structure" Manufacturing and local stress

concentration effectsautomatically included

" Stress analysis is not needed

Load-Life

! Limitations" Actual test of structure" New tests required for each

change in material, loading orgeometry

" Mean stress effects can not beincluded

Stress-Life

! Major Assumptions" Nominal stresses and material

strength control fatigue life" Accurate determination of Kf

for each geometry and material

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

Str

ess

Am

plit

ud

e

Kt or Kf

Stress-Life

! Advantages" Changes in material and

geometry can easily beevaluated

" Large emperical database forsteel with standard notchshapes

Stress-Life

! Limitations" Does not account for notch

root plasticity" Mean stress effects are often

in error" Requires emperical Kf for good

results

BS 5400 ( Eurocode 3 )

! Major Assumptions" Complex weld geometries can

be described by a standardclassification

" Crack growth dominatesfatigue life

" Results independant ofmaterial and mean stress forstructural steels


10

100

1000

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

Cycles

Str

ess

Ran

ge,

MP

a

Fatigue Limit

No Fatigue Limit


! Advantages" Manufacturing effects are

directly included" Large emperical database

exists


! Limitations" Difficult to determine weld

class for complex shapes" No benifit for improving

manufacturing process

Welded Structure

Strain-Life

! Major Assumptions" Local stresses and strains

control fatigue behavior" Accurate determination of Kf

Strain-Life

! Advantages" Plasticity effects" Mean stress effects

Mean Strain Example

Tensile Mean Stress

Compressive MeanStress

Neuber’s Rule

0

200

400

600

800

1000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Strain

Str

ess

K S ef2 ∆ ∆ ∆σ ∆ε=

Strain-Life

! Limitations" Requires emperical Kf

" Long life situations wheresurface finish and processingvariables are important

Crack Growth

! Major Assumptions" Nominal stress and crack size

control fatigue life" Accurate determination of

initial crack size

Crack Growth

! Advantage" Only method to directly deal

with cracks

Crack Growth

! Limitations

" Sequence effects∆Keff = f ( ∆K )

" ∆K = E ∆e Y( a ) √ a" Accurate determination of ai

Crack Closure

Crack Opened Crack Closed

Crack Opening Load

Damaging portion of loading history

Nondamaging portion of loading history

Opening load

Applications

! Material Selection /Improvement

! Fillet Weld! Scaling / Editing Load

Histories! Crack Size / Shape

Transmission History

-600

-400

-200

0

200

400

600

800

1000

No

min

alS

trai

n

Material Properties

BHN 187 277 336 410 545

σ f' ,MPa 1668 2978 3902 4593 5666

b -0.149 -0.158 -0.159 -0.167 -0.170

ε 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

Strength Variation

0

100

200

300

400

500

600

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

Blocks

Har

dn

ess,

BH

N

Kf Variation

1.5

2

2.5

3

3.5

4

4.5

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

Blocks

Fat

igu

eN

otc

hF

acto

r

Scale Factor Variation

0

0.5

1

1.5

2

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

Blocks

Sca

leF

acto

r

Cycle Histogram

0

1500

range (uE)

-1000

1000

mean (uE)

0

25

coun

ts

ε-N Damage

0

1500

range (uE)

-50

50

mean stress

0

10

%da

mag

e

Weld Geometry

Crack Depth

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 1.0a/W

Y(

a/W

)

Crack Length

0

0.001

0.002

0.003

0.004

0.005

0 200 400 600 800 1000

Blocks

Cra

ckL

eng

th,m