materials issues in fatigue and fracture -...
TRANSCRIPT
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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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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