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 dsocie@uiuc.edu 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 )