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Iowa State University Fracture Mechanics, Spring 2006 Ashraf Bastawros

Fatigue Crack GrowthFatigue Crack Growth

Ashraf Ashraf -- F. Bastawros F. BastawrosAerospace and Engineering Mechanics

Iowa State University [email protected] , X4-3039

Howe Hall Rm. 2347

Spring 2006


Importance of Fatigue

Bottom line: Fluctuating loads are more detriment than

monotonic loading

Example: Comet Airliner First jet propelled aircraft.

- Actual cabin differential pressure during flight 8.5psi (57kPa)

-The design pressure was 20psi (138kPa), [FOS >2].

- Pressurized once to double its working pressure of 114kPaThought would not fail under the action of fatigue {WRONGE }

Crack growth due to cyclic loading caused catastrophic

failure of the aircraft


Aloha Airlines, 4/28/1988. The aircraft lost 1/3 of its roof due to a stress fracture while cruising at 24,000 feet.

From: http://www.airdisaster.com/

Fatigue Failure


Types of Fatigue Loading

Mechanical Fatigue: pure fluctuation in applied load

Fretting Fatigue: cyclic stress with oscillatory relative motion

and frictional sliding. Contact Fatigue: rolling and sliding contact

Corrosion Fatigue: chemical aggressive or embitterment.

Creep Fatigue: cyclic loading at constant elevated temperature

Thermal Fatigue: cyclic temperature at constant or zero load

Thermo-mechanical Fatigue: combined cyclic variation of both

loading and temperature

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Cyclic Loading definitions

Typical stress history during cyclic loading


Parameters defining a cyclic loading history

- Stress Range:

- K-Range:

- Stress amplitude:

- Mean Stress:

- Loading ratio:

- N f : No. of cycle to failure

Cyclic Loading Definitions

( )( )

max min

max min

1max min2

1max min2

min min

max max

a

m

K K K

K R K

=

=

=

= +

= =


Frequency: f (Hz or cycle/s). Rotating machinery at 3000rpm,

f = 50Hz. The running frequency generally influences fatigue

crack growth if there are environmental effects present, such

as humidity or elevated temperature. The frequency of the

on/off cycle could be more detriment in limiting the life.

Waveform: is the profile of the stress history; sine wave,

square wave or any other regular or random profile. It would

influence the fatigue crack growth if there are environmental effects .

Cyclic Loading Definitions


Key difference between static and cyclic loading

Static: until applied K reaches

the crack will not grow

Cyclic: K applied can be few percent of

Over time, the crack grows .

The design could be safe under static loading, but any cyclic

loading must be considered.

Cyclic vs. Static Loading

( )30MPa m for examplec K

()

3MPa m

for example

c K

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Fatigue Crack Growth

Paris, Gomez and Anderson ( A rational analytical theory of fatigue, the Trend in

Engineering, Vol 13, 9-14, 1961 ) postulated that the rate of crack growthdepends on in the following way:

dadN

f = ( )loading

Cycle N

C r a c

k l e n g

t h ,

a da

dN

da

dN a a

F H G I

K J F

H G I

K J

1 2 1 1, ,

2 1>

B

a

K ( )ma da C K

N dN

=


( ) ;mda C K K Y adN Y

= =


is a geometric constant depends on the specimen type



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