5.3 finite s02

7/30/2019 5.3 Finite S02

http://slidepdf.com/reader/full/53-finite-s02 1/36

1

Materials Issues in

Fatigue and Fracture

n 5.1 Fundamental Concepts

n 5.2 Ensuring Infinite Life

n

5.3 Finite Lifen 5.4 Summary

7/30/2019 5.3 Finite S02


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

7/30/2019 5.3 Finite S02


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

7/30/2019 5.3 Finite S02


4

At sufficiently

high

alternatingstresses a

crack will

nucleate and

grow until the

component breaks.

Finite life - crack growth

Finite life

7/30/2019 5.3 Finite S02


5

Short and long life behavior

Crack nucleation dominates at long lives, crack growth

dominates at short lives.

7/30/2019 5.3 Finite S02


6

5.3 Finite Life

n Smooth specimens

n Short cracks

n Long cracks

7/30/2019 5.3 Finite S02


7

At sufficiently

high

alternatingstresses even

smooth

specimens

will nucleate a

crack andultimately fail

in fatigue.

Finite life - crack growth

Finite life

Smooth specimen

7/30/2019 5.3 Finite S02


8

Plastic strains cause fatigue

Plastic strains

cause the

nucleation of

fatigue cracks.The life to

fatigue failure

of smooth

specimens

correlates withthe plastic

strain.

1954 - Coffin and Manson

7/30/2019 5.3 Finite S02


9

106

105

104

103

.0001

.001

.01

.1

total strain ampltude

elastic strain ampltude

plastic strain ampltude

Reversals (2Nf)

σ'f b

c

ε' f

E

²e

∆ε t = ∆εe + ∆ε p =σ' f

E

2N f ( ) b + ε' f 2N f ( )c

Strain-life curve

Fatigue test data

from strain-

controlled tests on

smooth specimens.

Elastic component of

strain, ? εe

Plastic component of

strain, ? ε p

7/30/2019 5.3 Finite S02


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

S t r a i n A m

p l t u d e ,

² e t / 2

Strong materials give the best fatigue

resistance at long lives; whereas, ductile

materials give the best fatigue resistance

at short lives.

7/30/2019 5.3 Finite S02


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-H311Ti-6AL-4V

HY-80

Reversals, 2Nf

S t r a i n A m p i t u d e , ² e / 2

Strong materials give the best fatigue

resistance at long lives; whereas, ductile

materials give the best fatigue resistance

at short lives.

7/30/2019 5.3 Finite S02


12

Smooth specimen behavior

After Socie

7/30/2019 5.3 Finite S02


13

Transition Fatigue Life

10

6

10

5

10

4

10

3.0001

.001

.01

.1

total strain ampltude

elastic strain ampltude

plastic strain ampltude

Reversals (2Nf)

σ'f b

c

ε' f

E

²e

Transition fatigue life, Ntr

Elastic strains = plastic strains

2 N tr =ε f

' E

σ f '

1

b−c

7/30/2019 5.3 Finite S02


14

Aluminum - smooth specimens

Initiation and

small

crack growthdominate

so fatigue

strength

correlates with

UTS andsmall grain size.

7/30/2019 5.3 Finite S02


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.

7/30/2019 5.3 Finite S02


16

Titanium - smooth specimens

Lamellar α Equiaxed α Duplex

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

7/30/2019 5.3 Finite S02


17

5.3 Finite Life

n Smooth specimens

n Short cracks

n Long cracks

7/30/2019 5.3 Finite S02


18

Growth of Small Cracks

Here the ? K is the remote stress intensity

factor based on remote stresses….

7/30/2019 5.3 Finite S02


19

Short Cracks, Long Cracks

U =∆K eff

∆K =

Smax − Sopen

Smax − Smin

=1

1− R 1−

Sopen

Smax

? K eff = U ? K

7/30/2019 5.3 Finite S02


20

Crack Growth at a Notch

Cracks growing from notches

don’t know that that stress

field they are experiencing isconfined to the notch root.

7/30/2019 5.3 Finite S02


21

Crack closure

Plastic wake New plastic deformation

S = Smax

S = 0

S

S

R e m o t e S t r e s s , S

Time, t

Smax

Sopen, Sclose

R e m o t e S t r e s s , S

Time, t

Smax

Sopen, Sclose

Crack

open

Crack

closed

7/30/2019 5.3 Finite S02


22

Crack Closure Mechanisms

7/30/2019 5.3 Finite S02


23

Intrinsic, extrinsic crack closure

da

dn= C ∆K ( )m K max( ) p Extrinsic

Intrinsic

7/30/2019 5.3 Finite S02


24

Cyclic plastic zone size

r c = 1π ∆K I

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 and Stage II behavior.

7/30/2019 5.3 Finite S02


25

Effect of grain size

Greater Mode II displacement Lesser Mode II displacement

(slower) (faster)

7/30/2019 5.3 Finite S02


26

Effect mean stress

R ̃ 0 (slower) R ̃ 0.5 (faster)

7/30/2019 5.3 Finite S02


27

Effect stress range

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

7/30/2019 5.3 Finite S02


7/30/2019 5.3 Finite S02


29

Aluminum - crack growth

•Orientation of microstructural texture

•Grain size

•Strength

•Environment

7/30/2019 5.3 Finite S02


30

Steel - crack growth

Crack growth behavior of FP-steels does not vary much

upper bound scatter bands orientation

7/30/2019 5.3 Finite S02


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!

7/30/2019 5.3 Finite S02


32

5.3 Finite Life

n Smooth specimens

n Short cracks

n Long cracks

7/30/2019 5.3 Finite S02


33

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

C

1 10 100

m

Paris Power Lawda

dN= C (? K)

m

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

I II III

? K th

K C10-8

10-6

10-10

Behavior of long cracks

I Sensitive to

microstructure

and environment

II Paris power Law

III Approaching

fracture whenK max ˜ K IC.

Short cracks

Long cracks

L o g C r a c k G

r o w t h R a t e ,

d a / d N

( m / c y c l e )

7/30/2019 5.3 Finite S02


34

Stage II crack growth

Stage II

crack growth

(r c >> d)Plexiglas

7/30/2019 5.3 Finite S02


35

Ferritic-Pearlitic

steels all have

about the same

crack growth

rates

Behavior of structural metals

7/30/2019 5.3 Finite S02


36

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.

Crack Growth Rates of Metals

5.3 finite s02

Documents