department of mechanical science and engineering...

Professor Stephen D. DowningDepartment 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 Illinois at Urbana-Champaign, All Rights Reserved 1 of 45

1. Comparison to Wrought Metals2. Conceptual Models3. Stress-Strain Behavior4. Fatigue Behavior


Cast iron is a composite materialSteel matrixGraphite particles of different shapes

Graphite makes cast ironMore prone to surface crackingStiffer in compression than tension

New methods need to account for differences


Nodular IronSpheroidal graphiteFairly consistent sizeBehavior similar to steel

Gray IronGraphite flakesBehavior very different from steel

Compacted Flake IronIntermediate behavior


Major Assumptions:Local stresses and strains control fatigue behaviorAccurate determination of Kf


PlasticZone

,

,

S Nominal stress


MaterialData

ComponentGeometry

ServiceLoading

Analysis FatigueLife Estimate

N curvecurve

Kf

S , Sm


0

100

200

300

400

500

600

0 0.004 0.008 0.012Strain Amplitude

During cyclic deformation, the material deforms on a path described by the cyclic stress strain curve


ep

Hysteresis loop

Cyclic

Masing behaviorSymmetrical


f

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

100 101 102 103 104 105 106 107

cf

'f

bf

'f )N2()N2(

E2c

b

'f

E

'f

2Nt

2 Reversals, 2Nf = 1 Cycle, Nf


AC

BD

E

F

G

H

I

B

D

A, I

C

E

G

H

F

Loading history Stress-strain response


eSKf2KT S

KT e

KKKT


max

Smith Watson Topper

cbfff

bf

f NNE

)2()2(2

''22'

max

2max

bff N2

2'

max

For R = -1 loading only,

leads to a formulation in terms of the standard strain-life curve


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 strainsA new model for stress-strain response is needed


Much stiffer in compression

No linear region


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.


P

1

2

Displacement,

ElasticElastic - Plastic

Fully Plastic

ys


S linear 0(E ) E m

S R

S S linear

0

/ (E )

/ (E m )


1 n

R K

1 n

0E m K New stress-strain equation


C1 n

0 C CE m K

T1 n

0 T TE m K


m m g g

m g g g

F A A1 A A

m g g gF E 1 A E AElastic


Dominated by steel matrixSymmetric?Masing Behavior?Material Memory?

m g gE E , A 0.25

1 nB B

0 B B BE m K

B B Bi i 1

1 nB B

0 B B B2

E m 2 2K


Greater stiffness in compressionGraphite approaches incompressibilityCompressive stress is transferred to to the inherently stiffer matrix

G M BC C if 0

0 if 0


Eu

Debonded graphite in tensionUnloading modulus provides evidence


u 0 uE E m

u u maxeff

0 0

E mA 1E E

M T eff B T( ) A ( )

0 M TB T

0 u M T

E ( )( )E m ( )

Easier way to get bulk stress


eff B G eff ccA ( ) (1 A )


qcc maxQ( )

2 1 maxq (B / B )( )


0.25max a f1.82(N )


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Cast Iron Fatigue

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