Materials Issues in Fatigue and Fracture -...

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Materials Issues in Fatigue and Fracture

n 5.1 Fundamental Conceptsn 5.2 Ensuring Infinite Lifen 5.3 Finite Lifen 5.4 Summary

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1. Will a crack nucleate? 2. Will it grow? 3. How fast will it grow?

A simple view of fatigue

Cyclic nucleation and arrested growth Crack growth

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Fatigue of a component

The fatigue life of an engineering component consists of two main life periods:

Initiation or nucleation of a fatigue crack (NI)

And

Its growth to failure (NP)

A smooth specimen

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At sufficiently high alternating stresses a crack will nucleate and grow until the component breaks.

Finite life - crack growth

Finite life

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Short and long life behavior

Crack nucleation dominates at long lives, crack growthdominates at short lives.

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5.3 Finite Life

n Smooth specimensn Short cracksn Long cracks

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At sufficiently high alternating stresses even smooth specimens will nucleate a crack and ultimately fail in fatigue.

Finite life - crack growth

Finite life

Smooth specimen

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Plastic strains cause fatigue

Plastic strains cause the nucleation of fatigue cracks. The life to fatigue failure of smooth specimens correlates with the plastic strain.

1954 - Coffin and Manson

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106

105

104

103

.0001

.001

.01

.1

total strain ampltudeelastic strain ampltudeplastic strain ampltude

Reversals (2Nf)

σ'f b

c

ε' f

E

²e

∆ε t = ∆ε e + ∆ε p =σ' fE

2Nf( )b + ε' f 2Nf( )c

Strain-life curve

Fatigue test data from strain-controlled tests on smooth specimens.

Elastic component of strain, ? εe

Plastic component of strain, ? εp

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Behavior of Aluminum Alloys

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07

1100

2014

2024

5456

7075

1015

4340

Reversals, 2Nf

Stra

in A

mpl

tude

, ²et

/2

Strong materials give the best fatigue resistance at long lives; whereas, ductilematerials give the best fatigue resistance at short lives.

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Comparison of various metals

0.001

0.01

0.1

1

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07

A36

5456-H311

Ti-6AL-4V

HY-80

Reversals, 2Nf

Stra

in A

mpi

tude

, ²e/

2

Strong materials give the best fatigue resistance at long lives; whereas, ductilematerials give the best fatigue resistance at short lives.

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Smooth specimen behavior

After Socie

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Transition Fatigue Life

106

105

104

103

.0001

.001

.01

.1

total strain ampltudeelastic strain ampltudeplastic strain ampltude

Reversals (2Nf)

σ'f b

c

ε' f

E

²e

Transition fatigue life, NtrElastic strains = plastic strains

2Ntr =ε f

' E

σ f'

1b−c

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Aluminum - smooth specimens

Initiation and small crack growth dominateso fatigue strength correlates with UTS andsmall grain size.

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Steel - smooth specimens

As with aluminum, both tensile strength (hardness) and grain size influence the long-life fatigue resistance. Ductility is more important at short lives. At lives of ˜ 5x103, all have the same fatigue resistance.

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Titanium - smooth specimens

Lamellar α Equiaxed α Duplex

SN curves for Ti (R = -1)..grain size effects

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5.3 Finite Life

n Smooth specimensn Short cracksn Long cracks

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Growth of Small Cracks

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

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Short Cracks, Long Cracks

U =∆K eff

∆K=

Smax − Sopen

Smax − Smin=

11 − R

1−Sopen

Smax

? Keff = U ? K

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Crack Growth at a Notch

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

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Crack closure

Plastic wake New plastic deformation

S = Smax

S = 0

S

S

Rem

ote

Stre

ss, S

Time, t

Smax

Sopen, Sclose

Rem

ote

Stre

ss, S

Time, t

Smax

Sopen, Sclose

Crack open

Crack closed

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Crack Closure Mechanisms

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Intrinsic, extrinsic crack closure

dadn

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

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Cyclic plastic zone size

rc =1π

∆KI

2σy'

2

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

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Effect of grain size

Greater Mode II displacement Lesser Mode II displacement(slower) (faster)

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Effect mean stress

R ˜ 0 (slower) R ˜ 0.5 (faster)

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Effect stress range

Near threshhold: closure important High stress range: closure less important

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The use of the effective stress intensity factor accounts for the effects of mean stress and short crack effects.

dadN

= C ∆K( )n

dadN

= C' ∆Keff( )n = C' U∆K( )n

?Keffective

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Aluminum - crack growth

•Orientation of microstructural texture•Grain size

•Strength•Environment

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Steel - crack growth

Crack growth behavior of FP-steels does not vary much

upper bound scatter bands orientation

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Titanium - crack growth

Orientation can make a large difference with Ti. As with steel and Al, grain size (also O2 content) make a large difference. Large GS = good!

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5.3 Finite Life

n Smooth specimensn Short cracksn Long cracks

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+

+

+

+

++

+

+

+

+

+

+

+

+

+

++

+

+

+

+

++

+

+C

1 10 100

m

Paris Power LawdadN

= C (? K)m

Log Range in Stress Intensity Factor, ? K (MPavm)

I II III

? Kth

KC

10-8

10-6

10-10

Behavior of long cracks

I Sensitive tomicrostructure and environment

II Paris power Law

III Approachingfracture whenKmax ˜ KIC.

Short cracks

Long cracks

Log

Cra

ck G

row

th R

ate,

da/d

N(m

/cyc

le)

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Stage II crack growth

Stage II crack growth (rc >> d)

Plexiglas

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Ferritic-Pearlitic steels all have about the same crack growth rates

Behavior of structural metals

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

Crack Growth Rates of Metals