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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

Fatigue Seminar © 2003-2012 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 45

Outline

1. Comparison to Wrought Metals

2. Conceptual Models

3. Stress-Strain Behavior

4. Fatigue Behavior


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


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 fatigue

behavior

Accurate determination of Kf


Similitude

Plastic

Zone

Ds , De

Ds , De

DS Nominal stress


Fatigue Analysis: Strain-Life

Material

Data

Component

Geometry

Service

Loading

Analysis Fatigue

Life Estimate

eN curve

se curve

Kf

DS , Sm


Cyclic Hardening / Softening


Stable Hysteresis Loops

2,

sDs

2,

eDe

Ds

De


Stable Hysteresis Loops

2

sD

2

eD


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


Cyclic Stress Strain Curve


Stable Hysteresis Loop

Ds

De

Dee Dep

Hysteresis loop

Cyclic se

Masing behavior

Symmetrical


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


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


Neuber’s Rule

eDsDDD eSK f2KT S

KT e

s

e

se KKKT


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


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


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 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.


Inspiration

P d

1

2

Displacement, d

Load, P

Elastic

Elastic - Plastic

Fully Plastic

sys

e


Inspiration - Add Broken Bars


Strategy – Divide and Conquer


Problem - Elastic Modulus


Secant Modulus

sS linear 0(E ) E m

e e eS R

e s

s s

S S linear

0

/ (E )

/ (E m )


Remaining Plastic Strain

s e

1 n

RK

s s e

s

1 n

0E m KNew stress-strain equation


Monotonic Behavior – Gray Iron

s se

s

C1 n

0 C CE m K

s se

s

T1 n

0 T TE m K


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


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


Symmetric Area


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


Surface Behavior

Eu

Debonded graphite in tension

Unloading modulus provides evidence


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


Stress-Strain Model

s s s - seff B G eff ccA ( ) (1 A )


Crack Closure Stress

s e - e qcc maxQ( )

- e - e2 1 maxq (B / B )( )


Mean Stress

-s e 0.25max a f1.82(N )


Life Prediction Procedure


Stress-Strain Results


Model User’s

John Deere

Caterpillar

eFatigue.com

Safe Technology

nCode International


eFatigue

Cast Iron Fatigue

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