2 Cast Iron Fatigue

7/30/2019 2 Cast Iron Fatigue

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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



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




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




Strain-Life – Wrought Metals

Major Assumptions:

Local stresses and strains control fatiguebehavior

Accurate determination of K f




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



Cyclic Hardening / Softening



Stable Hysteresis Loops

2,

σ∆σ

2,

ε∆ε

∆σ

∆ε



Stable Hysteresis Loops

2

σ ∆

2

ε ∆



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



Cyclic Stress Strain Curve



Stable Hysteresis Loop

∆σ

∆ε

∆εe∆εp

Hysteresis loop

Cyclic σε

Masing behavior

Symmetrical



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



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



Neuber’s Rule

ε∆σ∆=∆∆ eSK f 2K T S

K T e

σ

ε

σε= K K K T



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



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



Gray Iron Hysteresis Loop



Monotonic Behavior – Nodular Iron



Monotonic Behavior – Gray Iron

Much stiffer in compression

No linear region



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.




Inspiration

P δ

1

2

Displacement, δ

L o a

d ,

P

Elastic

Elastic - Plastic

Fully Plastic

σys

ε




Inspiration - Add Broken Bars




Strategy – Divide and Conquer




Problem - Elastic Modulus




Secant Modulus

= + σS linear 0(E ) E m

ε = ε + εS R

ε = σ

= σ + σ

S S linear

0

/ (E )

/ (E m )




Remaining Plastic Strain

σ ε =

1 n

RK

σ σ ε = + + σ

1 n

0E m KNew stress-strain equation




Monotonic Behavior – Gray Iron

σ σε = +

+ σ

C1 n

0 C CE m K

σ σε = +

+ σ

T1 n

0 T TE m K




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




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




Symmetric Area




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




Surface Behavior

Eu

Debonded graphite in tension

Unloading modulus provides evidence




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




Stress-Strain Model

σ = σ + σ + − σeff B G eff ccA ( ) (1 A )




Crack Closure Stress

σ = ε − ε qcc maxQ( )

′= − ε − ε2 1 maxq (B / B )( )




Mean Stress

−σ ε = 0.25max a f 1.82(N )




Life Prediction Procedure




Stress-Strain Results




Model User’s

J ohn Deere

Caterpillar

eFatigue.com

Safe Technology

nCode International




eFatigue



Cast Iron Fatigue

2 Cast Iron Fatigue

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