Strength, Fatigue and Fracture - fcp.mechse.illinois.edu
Transcript of Strength, Fatigue and Fracture - fcp.mechse.illinois.edu
Introduction
Professor Darrell F. Socie Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
© 2011 Darrell Socie, All Rights Reserved
Fatigue and Fracture ( Basic Course )
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Contact Information
Darrell Socie Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign 1206 West Green Urbana, Illinois 61801 Office: 3015 Mechanical Engineering Laboratory [email protected] Tel: 217 333 7630 Fax: 217 333 5634
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
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Stress-Strain Response
Stre
ss (M
Pa)
Strain (%) 0.1 10 100
ceramics
metals
polymers
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Strain Energy
Stre
ss, σ
(MP
a)
Strain,ε (%)
E2U
2σ=
Strain energy per unit volume
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Ashby
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Strength vs Modulus
From M F Ashby, Materials Selection in Mechanical Design, 1999, pg 424
E
2fσ
High energy
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Component Stiffness
EALFy =
L4Ed
LEA
yFk
2
axialπ
===
IE3FLy
3
=
3
4
3bending L64Ed3
LIE3
yFk π
===
L F
L
F
d
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Relative Stiffness
L F
2
2
3
4
2
bending
axial
d3L16
L64Ed3
L4Ed
kk
=π
π
=
500kk10
dL
bending
axial ≈≈
L
F
d
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Relative Stresses
L F
L
F
d
2axial dF4
π=σ
3bending dLF32
π=σ
L16d
dLF32
dF4
3
2
bending
axial =
π
π=σσ
006.01.0Ld
bending
axial =σσ
≈
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Critical Speed ( whirling )
L
y
F = myω2
Instability occurs when the deflection due centrifugal force exceeds the deflection due to bending stiffness
3LyIE192F=
3LyIE48F=
Fixed ends
Free ends
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Spinning Tubular Shaft
ρ=
ρ=
ρππ
=
ρρπ=π=
EL2
r3.94n
L2r
Ltr2tr
mI
densityLtr2mtrI
4
2
cr
23
3
Consider a tube of length L, radius r, and thickness t
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Materials Selection
From M F Ashby, Materials Selection in Mechanical Design, 1999, pg 419
CFRP
Al Ti Fe
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
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Kansas City Hyatt Regency
www.sgh.com/expertise/investigations/ kchyatt/kchyatt.htm
http://ethics.tamu.edu/ethics/hyatt/hyatt2.htm
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Kansas City Hyatt Regency
http://www.rose-hulman.edu/Class/ce/HTML/publications/momentold/winter96-97/hyatt.html
Proposed design Actual design
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
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Buckling
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Buckling
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Buckling Theory
L
P
P
y
L
P
P
y
M
Equilibrium
M = Py
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Euler Buckling
2
22
cr LIEnP π
=
2
2
cr LIECP π
=
CFixed-Free 0.25Round_Round 1Fixed_Round 2Fixed-Fixed 4
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Delamination Buckling
σ
σc
σ
σc
h
L
( )2
2
2
c Lh
13E
ν−π
=σ
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Plastic Buckling
2
2
cr LIECP π
= 2t
2
cr LIECP π
=
E
Et
strain
Elastic Elastic - Plastic
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Fire Design of Steel Members
www.civil.canterbury.ac.nz/fire1/pdfreports/KLewis.pdf
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“Standard Fire” ISO 834
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80 90
Tem
pera
ture
, °C
Time, minutes
)1t8(log345T 10 +=
Steel melts at 1493 °C
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Elastic Modulus of Steel
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000
Temperature, °C
)25(E)T(E
600T
1100Tln2000
T1)25(E)T(E
<
+=
600T5.53T
1100T1690
)25(E)T(E
>−
−
=
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Yield Strength of Steel
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000Temperature, °C
)25()T(
ys
ys
σ
σ
600T
1750Tln767
T1)25(E)T(E
<
+=
600T440T1000
T1108
)25()T(
ys
ys >−
−
=σ
σ
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Design Loads
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000
Temperature, °C
)25(E)T(E
Safety factor of 5 is typically used for column buckling
~ 850 °C
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Design Loads
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000
Temperature, °C
)25(E)T(E
Safety factor of 5 is typically used for column buckling
~ 850 °C
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Time to Failure
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80 90
Tem
pera
ture
, °C
Time, minutes
~ 30 minutes before steel columns will buckle in a building fire
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
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Fractures
1943 1972
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Griffith 1893-1963
Circa1920 studied scratches and the effect of surface finish on fatigue for the Royal Aircraft Establishment
E2a γ=πσ
Griffith (1920) The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society, A, 221, 163-198
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
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Early steam engine
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Typical broken axle of the 1840s
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Expert opinions of the time
“I never met one which did not present a crystallization fracture…”
“the principal causes … are percussion, heat and magnetism”
“the change … may take place instantaneously” “steam can speedily cause iron to become
magnetic”
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Rankine 1820 - 1872
Trained as a civil engineer
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William Rankine’s second paper
Stated that deterioration of axles is gradual “the fractures appear to have commenced with a
smooth, regularly-formed, minute fissure, extending all round the neck of the journal, and penetrating on an average to a depth of half an inch. … until the thickness of sound iron in the center became insufficient to support the shocks to which it was exposed.”
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Rankine ...
“In all the specimens the iron remained fibrous; proving that no material change had taken place in the structure”
He noted that fractures occurred at sharp corners He recommended that the journals be formed with a
large curve in the shoulder (which is exactly right!)
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Aloha Flight 243
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
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Alaska Airlines Flight 261
January 31, 2000
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Jackscrew
http://www.ntsb.gov/events/2000/aka261
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Gimbal Nut
http://www.ntsb.gov/events/2000/aka261
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Report
The threads of the gimbal nut from the accident aircraft are stripped, and metal shreds made of the same material as that nut were found on the jackscrew. There are also impact marks on the outside of the gimbal nut and the lower stop nut; the Board will try to determine if those impact marks - as well as the stripping of both nuts’ threads - were made before the aircraft contacted the water or after.
http://www.ntsb.gov/events/2000/aka261
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Adhesive Wear
Attractive force between atoms tend to pull material from the asperity contacts
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Abrasive Wear
Hard particle microcuts a softer workpiece
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Surface Fracture
subsurface inclusion
Subsurface crack nucleation leads to spalling failures
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Fretting
Sliding with small displacements nucleates fatigue cracks
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Wear Process
A typical junction will deform with a load ∆L until the load and contact area reach the material strength.
∆L
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Mechanisms
∆L
Clean metal surfaces form a solid junction which shears off to form a wear particle.
The formation of a particle is a rare event, estimates are 1 in 10,000 contacts
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Adhesive Wear Law
P3xLkV =
V - volume of material removed x - sliding distance P - hardness L - load k - wear coefficient 3 - hemispherical particle assumption 1 - cubic shaped particles
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Typical Values of k
kMild steel on mild steel 10-2
Brass on hard steel 10-3
Lead on steel 2x10-5
PTFE on steel 2x10-5
Stainless steel on hard steel 2x10-5
Tungsten Carbide on Tungsten Carbide 10-6
Polyethylene on steel 10-7
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Lubrication
10-6
10-5
10-4
10-3
10-2
Wea
r coe
ffici
ent
clean poor lubrication
average lubrication
excellent lubrication
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Failure Modes
Elastic Deformation Plastic Deformation Buckling Fracture Fatigue Surface Damage
Fatigue and Fracture ( Basic Course )