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Single primary slip system

S

S

II Fatigue Mechanisms

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Current Theory of Fatigue

3. Intrusions,extrusions

2. Persistent slip bands

4. Stage I (shear) fatigue crack

5. Stage II fatigue crack

1. Cyclic slip

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Outline

n 1. Cyclic slipn 2. Persistent slip bands (PSB)n 3. Intrusions and extrusionsn 4. Stage I crack growthn 5. Stage II crack growth

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Process of fatigue

3. Intrusions,extrusions

2. Persistent slip bands

4. Stage I (shear) fatigue crack

5. Stage II fatigue crack

1. Cyclic slip

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1. Cyclic slip

First cycle

Many cycles later - cyclic hardening

Cyclic slip occurs within a grain and therefore operates on an atomic scale and are thus is controlled by features seen at that scale.

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1. Cyclic slip

d =G b2 b3( )

2π γ

Material γ Stacking Fault Energy ergs cm-2

Aluminum 250

Iron 200

Nickel 200

Copper 90

Gold 75

Silv er 25

Stainl ess Steel <10

α Brass <10

n Planar or wavy slip?

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1. Cyclic slip

Planarslip inCu-Al

Wavy slip in steel

Cu-Al alloys, Cu-Zn, Aust. SS

Ni, Cu, Al Fe

n Stacking-fault energy effects

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1. Cyclic slipWavy slip materials Planar slip materials

n Planar and wavy slip materials

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1. Cyclic slip

γ = 10-3

γ =10-5

Dislocation cell structuresin copper

n Development of cell structures

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Example

5µm

60 cycles

1,000 cycles

5,000 cycles

20,000 cycles

80,000 cycles (failure)

OM surface OM etch pit

TEM

Stress range = ±25 ksi.

n Fatigue of an Fe single crystal

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Outline

n 1. Cyclic slip

n 2. Persistent slip bands (PSB)

n 3. Intrusions and extrusionsn 4. Stage I crack growthn 5. Stage II crack growth

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2. Persistent slip bands (PSB)

•Development of cell structures (hardening)•Increase in stress amplitude (under strain control)•Break down of cell structure to form PSBs•Localization of slip in PSBs

PSB

Cyclic hardening Cyclic softening

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Outline

n 1. Cyclic slipn 2. Persistent slip bands (PSB)

n 3. Intrusions and extrusionsn 4. Stage I crack growthn 5. Stage II crack growth

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3. Intrusions and extrusions

Intrusions and extrusions on thesurface of a Nispecimen

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3. Intrusions and extrusions

Cyclically hardened material

Extrusion

Cyclically hardened material

Intrusion

Cyclically hardened material

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3. Intrusions and extrusions

Fatigue crack initiation at an inclusionCyclic slip steps (PSB)Fatigue crack initiation at a PSB

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Outline

n 1. Cyclic slipn 2. Persistent slip bands (PSB)n 3. Intrusions and extrusions

n 4. Stage I crack growthn 5. Stage II crack growth

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4. Stage I crack growth

Single primary slip system

individual grain

near - tip plastic zone

S

S

Stage I fatigue cracks are the size of the grains and are thus controlled by features seen at that scale: grain boundaries, mean stresses, environment.

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4. Stage I crack growth

rc =1π

∆KI

2σy'

2

Cyclic plastic zone is the region ahead of a growing fatigue crack in which slip takes place. Its size relative to the microstructure determines the behavior of the fatigue crack, i.e.. Stage I andStage II behavior.

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4. Stage I crack growth

n Short Cracks, Long Cracks

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Cracks growing from notches don’t know that that stress field they are experiencing is confined to the notch root.

4. Stage I crack growth

n Crack Growth at a Notch

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4. Stage I crack growth

Here the ?K is the remote stress intensity factor based on remote stresses….

n Growth of Small Cracks

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Outline

n 1. Cyclic slipn 2. Persistent slip bands (PSB)n 3. Intrusions and extrusionsn 4. Stage I crack growth

n 5. Stage II crack growth

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5. Stage II crack growth

Plexiglas

Stage II fatigue cracks much larger than the grain size and are thus sensitive only to large scale microstructural features - texture, global residual stresses, etc.

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Example

n Stage II fatigue crack in a weldment

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5. Stage II crack growth

Scanning electronmicroscope image -striations clearly visible

Schematic drawing ofa fatigue fracturesurface

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5. Stage II crack growth

Plastic wake New plastic deformation

S

S

Rem

ote

Stre

ss, S

Time, t

Smax

S , Sop cl

S

S

Rem

ote

Stre

ss, S

Time, t

Smax

S , Sop cl

a.

b.

S = 0

S = Sop

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5. Stage II crack growth

Plastic wake New plastic deformation

S

S

Rem

ote

Stre

ss, S

Time, t

Smax

S , Sop cl

S

S

Rem

ote

Stre

ss, S

Time, t

Smax

S , Sop cl

c.

d.

S = Smax

S = 0

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Elastic stresses near a crack tipS

c

σx

σy

σxy

x

y

R

θ

σx =S πc

2πRcos

θ2

1− sinθ2

sin3θ2

=

KI2πR

f1 θ( )

σy =S πc

2πRcos

θ2

1+ sinθ2

sin3θ2

=

KI2πR

f2 θ( )

τxy =S πc

2πRcos

θ2

sinθ2

cosθ2

sin3θ2

=

KI2πR

f3 θ( )

The magnitude stress field near a crack tip depends upon the stress intensity factor (KI). Wouldn’t it be nice if this quantity correlates with the speed with which fatigue cracks grow? Let’s see if it works! Rather, let’s see if we can MAKE it work!

∆K ≡ Y∆S πaRange of stress intensity factor

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Geometry correction factor (Y)

2c

2c 2c

c

SS

S S

S

SS

S

Y=1

Y=1.12

Y=2/p

W

Y = secπcW

Infinite width center cracked panel

Finite width center cracked panel

Edge cracked panel

Disc shaped crack in an infinite body

B

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Crack growth rate (da/dN) is related to the crack tip stress field and is thus strongly correlated with the range of stress intensity factor: (? K=Y? Svpa).

dadN

= C ∆K( )n

Paris power law

5. Stage II crack growth

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5. Stage II crack growth

n Crack Closure Mechanisms

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5. Stage II crack growth

dadn

= C ∆K( )m K max( )p ExtrinsicIntrinsic

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Example

•Orientation of microstructural texture•Grain size •Strength•Environment

n Aluminum - crack growth

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5. Stage II crack growth

A. Dissolution of crack tip.

B. Dissolution plus H+ acceleration.

C. H+ acceleration

D. Corrosion products may retard crack growth at low ?K.

A B

C Dn Effects of

Environment

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The fatigue crack growth rates for Al and Ti are much more rapid than steel for a given ?K. However, when normalized by Young’s Modulus all metals exhibit about the same behavior.

Example

n Crack Growth Rates of Metals

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Summary

n Fatigue is a complex process involving many steps but it may be broken down into the initiation and growth of fatigue cracks.

n The growth of fatigue cracks is often considered to be the most important feature of fatigue from an engineering perspective.