Post on 30-Apr-2018
Cast Iron Fatigue
Professor Stephen D. Downing
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
© 2011-2012 Stephen Downing, All Rights Reserved
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Outline
1. Comparison to Wrought Metals
2. Conceptual Models
3. Stress-Strain Behavior
4. Fatigue Behavior
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Cast Iron vs. Wrought Steel
Cast iron is a composite material
Steel matrix
Graphite particles of different shapes
Graphite makes cast iron
More prone to surface cracking
Stiffer in compression than tension
New methods need to account for
differences
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Nodular Iron
Spheroidal graphite
Fairly consistent size
Behavior similar to steel
Gray Iron
Graphite flakes
Behavior very different
from steel
Compacted Flake Iron
Intermediate behavior
Microstructure
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Strain-Life – Wrought Metals
Major Assumptions:
Local stresses and strains control fatigue
behavior
Accurate determination of Kf
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Similitude
Plastic
Zone
Ds , De
Ds , De
DS Nominal stress
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Fatigue Analysis: Strain-Life
Material
Data
Component
Geometry
Service
Loading
Analysis Fatigue
Life Estimate
eN curve
se curve
Kf
DS , Sm
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Cyclic Hardening / Softening
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Stable Hysteresis Loops
2,
sDs
2,
eDe
Ds
De
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Stable Hysteresis Loops
2
sD
2
eD
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Strain-Life Data s - e
0
100
200
300
400
500
600
0 0.004 0.008 0.012
Strain Amplitude
Str
ess A
mplit
ude
De Ds Ds
2 2 2
1
E K
n
'
/ '
During cyclic deformation, the material deforms on a path
described by the cyclic stress strain curve
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Cyclic Stress Strain Curve
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Stable Hysteresis Loop
Ds
De
Dee Dep
Hysteresis loop
Cyclic se
Masing behavior
Symmetrical
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Strain-Life Data De - 2Nf
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
Str
ain
Am
plit
ude
100 101 102 103 104 105 106 107
c
f
'
f
b
f
'
f )N2()N2(E2
es
eD
c
b
'
fe
E
'
fs
2Nt
2 Reversals, 2Nf = 1 Cycle, Nf
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Cyclic Deformation
A
C
B
D
E
F
G
H
I
B
D
A, I
C
E
G
H
F
str
ain
Loading history Stress-strain response
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Neuber’s Rule
eDsDDD eSK f2KT S
KT e
s
e
se KKKT
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Mean Stresses
s
e
smax
De
Smith Watson Topper
cbfff
bf
f NNE
ess
eD
s )2()2(2
''2
2'
max
2max
eDs
bff N22
'max s
sDs
For R = -1 loading only,
leads to a formulation in terms of
the standard strain-life curve
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Cast Iron Analysis – Strain Life
Elastic-plastic behavior in stress concentrations control fatigue
life
Rainflow counting is used to determine damaging events
corresponding to closed elastic-plastic hysteresis loops.
Mean stresses are tracked according to input loading
sequences
Smith-Watson-Topper parameter accounts for mean stress
Neuber' Rule is used to determine notch root stress and
strains
A new model for stress-strain response is needed
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Gray Iron Hysteresis Loop
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Monotonic Behavior – Nodular Iron
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Monotonic Behavior – Gray Iron
Much stiffer in compression
No linear region
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Important Observations (Gilbert)
1. Curvature in the tensile stress/strain curve is not
only associated with elastic and plastic deformation
of the matrix, but is also due to volume increase in
the spaces occupied by the graphite.
2. This volume increase is most pronounced on the
specimen surface where graphite flakes, oriented
perpendicularly to the load can actually crack or
debond from the matrix.
3. Gray iron is stiffer in compression than tension
because the spaces occupied by the graphite do
not see corresponding decreases in volume.
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Inspiration
P d
1
2
Displacement, d
Load, P
Elastic
Elastic - Plastic
Fully Plastic
sys
e
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Inspiration - Add Broken Bars
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Inspiration - Add Broken Bars
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Strategy – Divide and Conquer
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Problem - Elastic Modulus
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Secant Modulus
sS linear 0(E ) E m
e e eS R
e s
s s
S S linear
0
/ (E )
/ (E m )
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Remaining Plastic Strain
s e
1 n
RK
s s e
s
1 n
0E m KNew stress-strain equation
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Monotonic Behavior – Gray Iron
s se
s
C1 n
0 C CE m K
s se
s
T1 n
0 T TE m K
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Composite Rule of Mixtures
s s
s - s
m m g g
m g g g
F A A
1 A A
e - m g g gF E 1 A E AElastic
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Bulk Response Like Steel?
Dominated by steel matrix
Symmetric?
Masing Behavior?
Material Memory?
m g gE E , A 0.25
s se
s
1 n
B B
0 B B BE m K
-
s s DsB B Bi i 1
Ds Ds
De Ds
1 n
B B
0 B B B
2E m 2 2K
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Symmetric Area
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Internal Graphite Behavior
Greater stiffness in compression
Graphite approaches incompressibility
Compressive stress is transferred to to the
inherently stiffer matrix
s s - s e
e
G M BC Cif 0
0 if 0
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Surface Behavior
Eu
Debonded graphite in tension
Unloading modulus provides evidence
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Surface Behavior Equations
su 0 uE E m
s u u max
eff0 0
E mA 1
E E
s sM T eff B T( ) A ( )
ss
s
0 M TB T
0 u M T
E ( )( )
E m ( )
Easier way to get bulk stress
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Stress-Strain Model
s s s - seff B G eff ccA ( ) (1 A )
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Crack Closure Stress
s e - e qcc maxQ( )
- e - e2 1 maxq (B / B )( )
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Mean Stress
-s e 0.25max a f1.82(N )
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Life Prediction Procedure
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Stress-Strain Results
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Stress-Strain Results
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Stress-Strain Results
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Stress-Strain Results
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Model User’s
John Deere
Caterpillar
eFatigue.com
Safe Technology
nCode International
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eFatigue
Cast Iron Fatigue