fatigue analysis techniques
TRANSCRIPT
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
BS 5400 ( Eurocode 3 )
10
100
1000
1E+05 1E+06 1E+07 1E+08
Cycles
Str
ess
Ran
ge,
MP
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 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