Importance of Fatigue
• Bottom line: Fluctuating loads are more detriment than
monotonic loading
• Example: Comet Airliner– First jet propelled aircraft.
Fatigue Crack Growth
- Actual cabin differential pressure during flight 8.5psi (57kPa)
Ashraf -F. Bastawros
-The design pressure was 20psi (138kPa), [FOS >2].
Aerospace and Engineering Mechanics
Iowa State University
bastaw@iastate.edu, X4-3039
Howe Hall Rm. 2347
- Pressurized once to double its working pressure of 114kPa
Thought would not fail under the action of fatigue {WRONGE}
¾Crack growth due to cyclic loading caused catastrophic
failure of the aircraft
Spring 2006
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Types of Fatigue Loading
Fatigue Failure
• 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
Aloha Airlines, 4/28/1988. The aircraft lost 1/3 of its roof
due to a stress fracture while cruising at 24,000 feet.
• Thermal Fatigue: cyclic temperature at constant or zero load
• Thermo-mechanical Fatigue: combined cyclic variation of both
From: http://www.airdisaster.com/
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
loading and temperature
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
1
Cyclic Loading definitions
Cyclic Loading Definitions
Parameters defining a cyclic loading history
- Stress Range:
∆σ = σmax −σmin
- K-Range:
∆K = Kmax − Kmin
- Stress amplitude:
•Typical stress history during cyclic loading
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
σa = 12 (σmax −σmin )
- Mean Stress:
σm = 12 (σmax +σmin )
- Loading ratio:
R=
- Nf : No. of cycle to failure
Iowa State University
Cyclic Loading Definitions
σmin Kmin
=
σmax Kmax
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Cyclic vs. Static Loading
¾Frequency: 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.
Key difference between static and cyclic loading
¾ Static: until applied K reaches K c ( 30MPa m for example )
the crack will not grow
¾ Cyclic: K applied can be few percent of K c ( 3MPa m
Over time, the crack grows.
for example )
¾Waveform: 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.
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
The design could be safe under static loading, but any cyclic
loading must be considered.
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
2
Fatigue Crack Growth
Fatigue Crack Growth
σ
B
da
= f (loading)
dN
a
Crack length, a
σ 2 > σ1
FG da IJ
H dN K
a1 ,σ 2
FG da IJ
H dN K
a1 ,σ 1
Cycle N
σ
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 growth
depends on ∆ K in the following way:
Iowa State University
∆a
da
m
→
= C ( ∆K )
dN
∆N
Fracture Mechanics, Spring 2006
Ashraf Bastawros
da
m
= C ( ∆K )
; ∆K = Y ∆σ π a
dN
Y is a geometric constant depends on the specimen type
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
Fatigue Crack Growth
Iowa State University
Fracture Mechanics, Spring 2006
Ashraf Bastawros
3