2 cast iron fatigue
TRANSCRIPT
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Cast Iron Fatigue
Professor Stephen D. Downing
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
© 2011-2013 Stephen Downing, All Rights Reserved
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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 2 of 45
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 fordifferences
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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 3 of 45
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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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 4 of 45
Strain-Life – Wrought Metals
Major Assumptions:
Local stresses and strains control fatiguebehavior
Accurate determination of K f
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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 5 of 45
Similitude
Plastic Zone
∆σ , ∆ε
∆σ , ∆ε
∆S Nominal stress
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Fatigue Analysis: Strain-Life
MaterialData
ComponentGeometry
ServiceLoading
AnalysisFatigue
Life Estimate
εN curveσε curve
K f
∆S , Sm
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Cyclic Hardening / Softening
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Stable Hysteresis Loops
2,
σ∆σ
2,
ε∆ε
∆σ
∆ε
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Stable Hysteresis Loops
2
σ ∆
2
ε ∆
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Strain-Life Data σ − ε
0
100
200
300
400
500
600
0 0.004 0.008 0.012
Strain Amplitude
S t r e s s A m
p l i t u d e
∆ε ∆σ ∆σ2 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
∆σ
∆ε
∆εe∆εp
Hysteresis loop
Cyclic σε
Masing behavior
Symmetrical
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Strain-Life Data ∆ε - 2Nf
10-5
10-4
0.001
0.01
0.1
1
Reversals, 2Nf
S
t r a i n A m p l i t u d e
100 101 102 103 104 105 106 107
c
f
'
f
b
f
'
f )N2()N2(E2
ε+σ
=ε∆
c
b
'f ε
E
'
f σ
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
s t r a i n
Loading history Stress-strain response
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Neuber’s Rule
ε∆σ∆=∆∆ eSK f 2K T S
K T e
σ
ε
σε= K K K T
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Mean Stresses
σ
ε
σmax
∆ε
Smith Watson Topper
cbf f f
bf
f NNE
+εσ+σ
=ε∆
σ )2()2(2
''2
2'
max
2max
ε∆σ
( )bf f N22
'max σ=
σ∆=σ
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 fatiguelife
Rainflow counting is used to determine damaging eventscorresponding to closed elastic-plastic hysteresis loops.
Mean stresses are tracked according to input loadingsequences
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 notonly associated with elastic and plastic deformationof the matrix, but is also due to volume increase inthe spaces occupied by the graphite.
2. This volume increase is most pronounced on thespecimen surface where graphite flakes, orientedperpendicularly to the load can actually crack ordebond from the matrix.
3. Gray iron is stiffer in compression than tensionbecause the spaces occupied by the graphite donot see corresponding decreases in volume.
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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 22 of 45
Inspiration
P δ
1
2
Displacement, δ
L o a
d ,
P
Elastic
Elastic - Plastic
Fully Plastic
σys
ε
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Inspiration - Add Broken Bars
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Inspiration - Add Broken Bars
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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 25 of 45
Strategy – Divide and Conquer
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Problem - Elastic Modulus
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Secant Modulus
= + σS linear 0(E ) E m
ε = ε + εS R
ε = σ
= σ + σ
S S linear
0
/ (E )
/ (E m )
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Remaining Plastic Strain
σ ε =
1 n
RK
σ σ ε = + + σ
1 n
0E m KNew stress-strain equation
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Fatigue Seminar © 2003-2013 Stephen Downing, University of Illinoi s at Urbana-Champaign, All Rights Reserved 29 of 45
Monotonic Behavior – Gray Iron
σ σε = +
+ σ
C1 n
0 C CE m K
σ σε = +
+ σ
T1 n
0 T TE m K
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Composite Rule of Mixtures
( )= σ + σ= σ − + σ
m m g g
m g g g
F A A1 A A
( ) = ε − + 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
σ σε = +
+ σ
1 n
B B
0 B B BE m K
( ) ( )−
σ = σ ± ∆σB B Bi i 1
( ) ∆σ ∆σ∆ε = +
+ ∆σ
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
( ) ( )σ = σ − σ ε ≤
= ε >
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
= + σu 0 uE E m
σ= = +u u max
eff 0 0
E mA 1
E E
σ = σM T eff B T( ) A ( )
σσ =
+ σ0 M T
B T0 u M T
E ( )( )
E m ( )
Easier way to get bulk stress
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Stress-Strain Model
σ = σ + σ + − σeff B G eff ccA ( ) (1 A )
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Crack Closure Stress
σ = ε − ε qcc maxQ( )
′= − ε − ε2 1 maxq (B / B )( )
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Mean Stress
−σ ε = 0.25max a f 1.82(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
J ohn Deere
Caterpillar
eFatigue.com
Safe Technology
nCode International
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eFatigue
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Cast Iron Fatigue