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

Fatigue Analysis Techniques

Darrell Socie Mechanical Engineering

University of Illinois

Fatigue Analysis Techniques

! 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

L at

er al

F o

rc e,

kN

Stress-Life Data

100

1000

10000

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

Cycles

St re

ss A

m pl

it ud

e, M

P a

BS 5400 ( Eurocode 3 ) Data

100

200

300

400

B

C

D

E

F F2 G W 0

105 106 107 108

S tr

es s

R an

g e ,M

P a Steel

BS 5400 ( Eurocode 3 ) Data

0

25

50

75

100

125

105

B

C

D E

F

Aluminum

106 107 108

S tr

es s

R an

g e ,M

P a

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

S tr

ai n

A m

p lit

u d

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

S tr

es s

A m

p lit

u d

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

C ra

ck G

ro w

th R

at e,

m /c

yc le

Rainflow Counting

A C

B D

E

F

G

H

I

Hysteresis Loops

A C

B D

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 as service loading

Load-Life

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

concentration effects automatically included

" Stress analysis is not needed

Load-Life

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

change in material, loading or geometry

" Mean stress effects can not be included

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

S tr

es s

A m

p lit

u d

e

Kt or Kf

Stress-Life

! Advantages " Changes in material and

geometry can easily be evaluated

" Large emperical database for steel with standard notch shapes

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 standard classification

" Crack growth dominates fatigue life

" Results independant of material and mean stress for structural steels

BS 5400 ( Eurocode 3 )

10

100

1000

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

Cycles

S tr

es s

R an

g e,

M P

a

Fatigue Limit

No Fatigue Limit

BS 5400 ( Eurocode 3 )

! Advantages " Manufacturing effects are

directly included " Large emperical database

exists

BS 5400 ( Eurocode 3 )

! 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 Mean Stress

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

S tr

es s

K S ef 2 ∆ ∆ ∆σ ∆ε=

Strain-Life

! Limitations " Requires emperical Kf " Long life situations where

surface finish and processing variables 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

N o

m in

al S

tr ai

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

H ar

d n

es s,

B H

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

F at

ig u

e N

o tc

h F

ac to

r

Scale Factor Variation

0

0.5

1

1.5

2

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

Blocks

S ca

le F

ac to

r

Cycle Histogram

0

1500

range (uE)

-1000

1000

mea n (u

E)

0

25

co un

ts

ε-N Damage

0

1500

range (uE)

-50

50

mea n st

ress

0

10

% da

m ag

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 1.0 a/W

Y (

a/ W

)

Crack Length

0

0.001

0.002

0.003

0.004

0.005

0 200 400 600 800 1000

Blocks

C ra

ck L

en g

th ,m