1

Materials Issues in Fatigue and Fracture

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

2

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

3

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

4

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

Finite life - crack growth

Finite life

5

Short and long life behavior

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

6

5.3 Finite Life

n Smooth specimensn Short cracksn Long cracks

7

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

8

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

9

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

10

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.

11

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.

12

Smooth specimen behavior

After Socie

13

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

14

Aluminum - smooth specimens

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

15

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.

16

Titanium - smooth specimens

Lamellar α Equiaxed α Duplex

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

17

5.3 Finite Life

n Smooth specimensn Short cracksn Long cracks

18

Growth of Small Cracks

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

19

Short Cracks, Long Cracks

U =∆K eff

∆K=

Smax − Sopen

Smax − Smin=

11 − R

1−Sopen

Smax

? Keff = U ? K

20

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.

21

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

22

Crack Closure Mechanisms

23

Intrinsic, extrinsic crack closure

dadn

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

24

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.

25

Effect of grain size

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

26

Effect mean stress

R ˜ 0 (slower) R ˜ 0.5 (faster)

27

Effect stress range

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

28

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

29

Aluminum - crack growth

•Orientation of microstructural texture•Grain size

•Strength•Environment

30

Steel - crack growth

Crack growth behavior of FP-steels does not vary much

upper bound scatter bands orientation

31

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!

32

5.3 Finite Life

n Smooth specimensn Short cracksn Long cracks

33

+

+

+

+

++

+

+

+

+

+

+

+

+

+

++

+

+

+

+

++

+

+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)

34

Stage II crack growth

Stage II crack growth (rc >> d)

Plexiglas

35

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

Behavior of structural metals

36

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