5 Fatigue in Mechanical Components_F10

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Fatigue of Mechanical Components

Fatigue of Bolts

Professor Stephen D. Downing

Department of Mechanical Science and Engineering

© 2010 Darrell Socie, All Rights Reserved

Fatigue and Fracture

( Basic Course )



Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 1 of 113


Fatigue of Bolts

Fretting Fatigue

Welded J oints

Case Study




Fatigue Strength of Bolts

Su = 785 MPa

Fatigue Design Review Task 5 – Assembly of Available Fatigue Data Relevant to Pressure Equipment Design

TWI Report No: 123337/2/01, European Commission

3.6




K f for Bolts

SAE

Grade

Metric

Grade

Rolled

Threads

Cut

Threads

Head

Fillet

0 - 2 3.6 – 5. 8 2.2 2.8 2.1

4 - 8 6.6 – 10. 9 3.0 3.8 2.3

High strength bolts fail by crack growth.

Not much benefit, in fatigue, of very high strength bolts.




Cut and Rolled Threads

Fatigue Design Review Task 5 – Assembly of Available Fatigue Data Relevant to Pressure Equipment Design

TWI Report No: 123337/2/01, European Commission




Bolted J oint Loading

Force

Tensile Loading

P

P

P

Shear Loading

P

P


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Tensile Loading

kb

k j



Bolt Preload Force

dFK T i=

K Torque factor depending on bolt friction Typically in the range of 0.1 – 0.3

T Bolt torque

Fi Preload force

D Bolt diameter



Variability in Bolt Force

100 1000

Force

200 Data Points

Median 130

COV 0.14

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

Bolt Force, kN

Preload force in bolts tightened to 350 Nm

C u m u l a t i v e P r o b a b i l i t y



Bolted J oint Analysis

δb extension

bolt

F b

δ j contraction

joint



Bolted J oint Analysis (continued)

F b

δb δ j

Fi

preload force

kb k j



Bolted J oint Analysis (continued)

Fb

P

P

e

P

P

e e

P

Pb

P j

Pkk

kP

jb

bb +=



Fatigue Considerations

100

1000

10000

100

Cycles

S t r e s s A m

p l i t u d e ,

M P a

101 102 103 104 105 106 107

b ~ -0.1

10f S

1N

∆∝



Bolt Stiffness

Fb

e

Pb

P j P

Pb

P j

P

Stiffer bolts carry more of the external force

e



J oint Seperation

Fb

e

Fb = P

kbk j



Bolt Stiffness

L1

L2

d

AtEA

L

EA

L

k

1k

1

k

1

k

1

t

2

1

1

b

21b

+=

+=

springs in series



J oint Stiffness

3d

L

L

Ed8

k

2

j

π=



J oint Stiffness

Pkk

kFP jb

bib ++=

Define joint factor, C

jb

b

ib

kk

kC

PCFP

+=

+=

kb should be small and and k j large

11.09

1

L

Ed8

L

EdL

Ed

C22

2

==π

+π

π

=



Aluminum and Steel J oints

Steel Bolt , Steel Flange Steel Bolt , Aluminum Flange

C = 0.11 C = 0.25

L

Ed8k steel

2

f

π=

L

Ed8k umminalu

2

f

π=



Fatigue Design

Traditional Method

Fi / AtMean stress

A l t e r n a t i n g s t r e s s

Su0

Se

Sa

tf

tiua

A2

PC

K 21

A/FSS

∆=

+−

=



Shear Loading of Bolted J oints

Tensile Loading

P

P

P

Shear Loading

P

P

Fi FiµFiµFi



Mechanics of Shear Loading




Shear Failures of Bolts




Shear Fatigue Testing




Self Loosening of a Bolt




Self Loosening Mechanism (Sakai)

F

−∆N

Normal force increased

Normal force decreased

Net torque produced

+∆N

−∆µN

+∆µN

Sakai, Investigations of Bolt Loosening Mechanisms, J SME 21 (159) 1978




Loosening Fatigue limit




Retightening of a Bolt




Summary

Bolts have poor fatigue strength

Bolt preload must be maintained





Fatigue of Bolts

Fretting Fatigue

Welded J oints

Case Study




Fretting

www.eren.doe.gov/wind/feature.html

shaft

Relative motionbetween bearingand shaft




Interface Stresses

P

F

Clamping Force

F

σx

τ

Stresses in the bar

Stresses in the flange




Localized Sliding




Fretting Mechanism

www.nrim.go.jp:8080/public/english/act/1992/1718.html




Fretting Mechanism

High shearstresses at

local contacts

Cold weldingproduces

wear particles

Fretting fatiguecrack formed




Fretting Cracks

100 µm

From Waterhouse, Fretting Corrosion, 1972 From ASM Fatigue and Fracture Handbook, 1996




Fatigue Behavior

Hoeppner and Gates, “Fretting Fatigue Considerations in Engineering Design”, Wear , Vol. 70, 1981, 155-164




Fretting Fatigue Limits

From Schijve Fatigue of Structures and Materials, Kluer, 2001




Variables Affecting Fretting

Clamping pressure

Cyclic stress level

Sliding displacement

Coefficient of friction

Materials strength

Surface roughness

Environment




Fretting Testing





Clamping Pressure





Sliding Displacement

Funk, “Test Methods to Investigate the Influences of Fretting Corrosion on the Endurance”Materialprüfung, 1969, 221-227




Modeling

Friction stress, µpo

Contact pressure, po

Cyclic stress, σa




Modeling (continued)

−µ−σ=σ

−K S

oflffl e1p

σffl fretting fatigue limit

σfl material fatigue limit

µ coefficient of friction

S sliding displacement, in mm

K material constant ~ 10-3 mm

Nishioka and Hirakawa, “Fundamental Investigations in Fretting Fatigue, Part 5 The Effect of Slip Amplitude”Bull. J SME, 1969, 692-697




Friction Coefficient

Wharton, “The Effect of Different Contact Materials on the Fretting Fatigue Strength of an Aluminum Alloy”,

Wear , Vol. 26, 1973, 253-260




Fasteners

σo

σh

p

q

θ

Farris et. Al. “Analysis of Widespread Fatigue Damage in Structural J oints, SAMPE Symposium, 1996, 65-79




Prevention

Reduce surface shear stressReduce normal force

Reduce coefficient of friction

Eliminate stress concentrationStepped shafts with large radii

Compressive residual stressShot peening

Separation of surfacesCompliant coatings




Eliminate Contact

K t = 3.5

Slotted hole

From Schijve Fatigue of Structures and Materials, Kluer, 2001




Eliminate Stress Concentration




Attachments

Fretting at the bolt hole evenwhen the bracket is unloaded




Summary

Fretting is caused by sliding surfaces

Fretting is a long life fatigue problem





Fatigue of Bolts

Fretting Fatigue

Welded Joints

Case Study




Types of Welds

Structural welds

Spot welds

Special Processes

Laser Electron Beam




Weld Classifications

D E

F2 G




100

200

300

400

B

C

D

E

F F2 G W

0105 106 107 108

BS 7608 - Steel

Fatigue Life, Cycles




Crack Growth Data

( ) 0.312 mMPaK 109.6

dN

da∆×= −

( ) 25.210 mMPaK 104.1

dN

da∆×= −

( ) 25.312 mMPaK 106.5

dNda ∆×= −

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless Steel:

Barsom, “Fatigue Crack Propagation in Steels of Various Yield Strengths” J ournal of Engineering for Industry, Trans. ASME, Series B, Vol. 93, No. 4, 1971, 1190-1196

5 10 100

10-7

10-6

10-8

C

r a c k G r o w t h R a t e

, m / c y c l e

∆K, MPa√m

σyield

252273392415




0

25

50

75

100

125

105

B

C

D

E F

106 107 108

BS 7608 - Aluminum


Sharp, “Behavior and Design of Aluminum Structures”,McGraw-Hill, 1992




Crack Growth Data

1 10 100

Cyclic Stress Intensity, MPa√m

C r a c k G r o w t h R a

t e m / c y c l e

A533B m/cycle

6061-T6 m/cycle

10-2

10-4

10-6

10-8

10-10

10-12

3X

Steel welds are 3 timesstronger than aluminum

1

3




Residual Stress from Welding

Y

X

X

X

X

Y

Y Y

tension

tension

compression

compression




Weld Distortion




Weld Toe Residual Stress

Yield

stress

Maximum stress at the weld toeis nearly the same for any cycle

∆ε

ε

σ∆ε




Mean Stress Effects

As welded structures usually have themaximum possible mean stress

Stress relief, peening, etc. will have a

substantial effect on the fatigue life




Butt and Fillet Weld Test Data

99% survival with 95% confidence

1000

S t r e s s R a n g e

, M P a

100

10

103 104 105 106 107


Failures Run outs

The good welds




Weld Terminations

1000

S t r e s s R a n g e ,

M P a

100

10

103 104 105 106 107


Failures Run outs

99% survival with 95% confidence

The bad welds




Sources of Inherent Scatter

Weld quality

Mean, fabrication and residual stresses

Stress concentrations (geometry)

Weldment size Material properties

Opportunities for Improvement !




The Good and Bad

Good weld design

Bad weld design




Typical Butt Weld




Weld Toe




Macroscopic LOF

3 mm




Weld Flaws

Even good welds contain initial crack like flaws0.1 to 1 mm long. Reducing the size or eliminatingthese flaws will substantially improve fatigue lives.




Nominal Stress ?




Various stress distributions in a T-butt weldment with transverse fillet welds;

r

t

t1

ED

BC

A

σ peak

σ

n

σhs

FP

M

C

Θ

• Normal stress distribution in the weld throat plane (A),•Through the thickness normal stress distribution in the weld toe plane (B),

•Through the thickness normal stress distribution away from the weld (C),

•Normal stress distribution along the surface of the plate (D),

•Normal stress distribution along the surface of the weld (E),

•Linearized normal stress distribution in the weld toe plane (F).

Stress Distributions in Weldments




Experimental Shellelements

Fine 3-D FEmesh

Coarse 3-D FEmesh

Stress magnitudes and distributions obtained from various FEmodels

Finite Element Models




σ peak

σn σhs

Peak and Hot Spot Stress




σ peak

t

σn

V

P

σn

V

t

σn σn

P

Physical Meaning of Hot Spot Stress

I

Mc

A

Pn +=σ




Hot Spot SN Curves




Weld Improvement

Reduce weld toe stresses

Stress relieve

Improve local geometry




Macroscopic Shape

t

r

θ

0.05 0.20.150.1

2

3

4

1

r / t

tK

θ = 15º

θ = 30º

θ = 45º

θ = 60º




K fmax

mMPatS15.01K umaxf β+=

r

t1K

t β+=

ρα+

−+=

1

1K 1K t

f

2

3

4

5

ρ =α Weld toe radius

f t K orK β ~ 0.3 axial

β ~ 0.2 bending

t

r

θ




Spot Weld Fatigue Data

10

102

103

104

105

102 103 104 105 106 107 108


M a x i m u m

L o a d ,

N Tensile Shear

Coach-peel

1

4

Fatigue Data Bank for Spot Welds, University of Illinois




Spot Weld Modeling

Beams are used as " force transducers " to obtain forces and momentstransmitted through the spot welds

Forces and moments are used to calculate " structural stresses "

Spotweld “Nugget” Beam Element




Structural Stress Calculations

Structural stresses are calculated from theforces and moments on each beam element :

Sheet 2

Nugget

Sheet 1

My

Fy

Fx

Mx

Fz

My

Fy

Fx

Mx

Fz

My

Fy

Fx

Mx

Fz




Structural Stresses

Stresses in sheet :

θσ+θσ+σ+θσ−θσ−=θ∆ cos)M(sin)M()F(sin)F(cos)F()(S yxxyx

dt

F)F( x

x

π

=σ

dt

F)F(

y

y π=σ

2

zz

t

F744.1t6.0)F( =σ

2

xx

td

M872.1t6.0)M( =σ

2

Y Y

td

M872.1t6.0)M( =σ

Fz

Mx

t

d

Fx

Fy

My




Structural Stress Correlation

101

102

103

104

102 103 104 105 106 107

Fatigue Life

S t r u c t u r a l S t r e s s ,

M P a




Things Worth Remembering

Local weld toe stresses, geometry and flawscontrol the life of weldments





Fatigue of Bolts

Fretting Fatigue

Welded J oints

Case Study (Merrimac Ferry)

ll b




Collaborators

David W. Prine

Infrastructure Technology Institute

Northwestern University

Darrell Socie

Department of Mechanical EngineeringUniversity of Illinois at Urbana Champaign

Continuous Remote Monitoringof The Merrimac Free Ferry

M i Wi i




Merrimac Wisconsin

M i F i




Merrimac Ferries

http://www.shopstop.net/ferry/default.htm

1847 1963

M i F F




Merrimac Free Ferry

Merrimac Ferry

M i F F




Merrimac Free Ferry

M i F C l II




Merrimac Ferry Colsac II

State Highway 113 over the Wisconsin River atMerrimac

Began operation in 1963

33’ wide by 80’ longCable driven (two cables)

B i D i




Basic Design

Supported by two 10’ by 80’ barges

W ld d B B




Welded Box Beam

C k F d i H ll




Cracks Found in Hull

Many cracks found in the ends where theramps are attached

Cracks also found in the center of the hull that couldlead to catastrophic failure, is the ferry safe?

H L d ?




Heavy Loads?

Remote Monitoring S stem




Remote Monitoring System

Merrimac WIEvanston IL

Installing Strain Gages




Installing Strain Gages

Typical Gage Installation




Typical Gage Installation

Strain Gage Locations




Strain Gage Locations

3

12

Data Gathering




Data Gathering

Ferry load tested with 34,000 # county truck

Time history data for both load test and live traffic

for 16 hours to check out system

Rainflow counting and burst history recorded for ~4months until winter closing in December 1998.

Strain for Single Load Test




Strain for Single Load Test

Gage Maximum Minimum Range

1_1 131 26 105

1_2 70 1 69

2_1 123 -158 281

2_2 44 -79 1232_3 184 -922 1106

3_1 140 -562 702

3_2 123 -61 184

Barge End




Barge End

541.028 1100.712 Time (Secs)-875

875

Strain Gage (ustrain)

Note: strain offset indicating plastic deformation

Strain Readings




Strain Readings

Gage Static 10-8-98 11-6-98

1_1 105 466 427

1_2 69 350

2_1 281 311 291

2_2 123 252

2_3 1106 1089

3_1 702 602 544

3_2 184 213

Live Traffic Tests:30,772 cars35 busses291 trucks

BS 7608 Steel




BS 7608 - Steel

500

1000

FF2

GW

0105 106 107 108


F2

Fatigue Analysis for Ends




Fatigue Analysis for Ends

No fatigue analysis needed if there is plasticdeformation in this welded structure.

WIDoT has lowered posted limit to excludeall but passenger cars and pickup trucks.

Crack Growth Calculations




Crack Growth Calculations

mK CdN

da∆=

m

W

af aC

dN

da

πσ∆=

∫∫

πσ∆

=f

i

a

a

m

N

0

W

af aC

dadN

Major Variables




Major Variables

Initial and final crack sizeMaterial properties

Stress intensity factor

Loading history

Crack Growth Data




Crack Growth Data

( ) 0.312 mMPaK 109.6

dN

da∆×= −

( ) 25.210 mMPaK 104.1

dN

da∆×= −

( ) 25.312 mMPaK 106.5

dN

da∆×= −

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless Steel:

From Dowling, Mechanical Behavior of Materials, 1999

Edge Cracked Plate in Tension




Edge Cracked Plate in Tension

π

π−++

ππ=

b2

acos

)

b2

asin1(37.0

b

a02.2752.0

b2atan

ab2

baF

3

Loading History for 1 Month




Loading History for 1 Month

0

20

40

60

80

100

120

0 300100 200 400 500

Strain Range, µε

N u m b e r o f C y c l e s

Results for Center Cracks




Results for Center Cracks

0

2

4

6

8

10

12

0 500 1000 1500 2000

Years of Service

C r a c k L e n g t h

Results




Results

Data shows overloads are driving end cracks.

Data shows center cracks are not being drivenby traffic loading.

Where do the strains come from to drive thecenter cracks?

Frozen Tundra of the Wisconsin River




Frozen Tundra of the Wisconsin River

Thermal Loading




Thermal Loading

Constant Temperature Water

Variable Temperature Air

Thermal Expansion/Contraction on Deck

Winter Tests in Ice




Winter Tests in Ice

-15

-10

-5

0

5

10

15

A i r T e m p e r a t u r e º C

22 days

-600

-400

-200

0

200

400

S t r a i n , µ ε

Colsac III




Colsac III

http://fun.co.columbia.wi.us/fun/colsac/construction.asp

May 16, 2003Construction

2 weeks later




2 weeks later

The Associated Press - J une 7, 2003

MADISON — The new Merrimac Ferry, which hasbeen closed for repairs, will not operate for the

foreseeable future due to a breakdown in repairnegotiations with the contractor.

The new $2.2 million ferry, known as the ColSac III,broke down May 23 about a week after openingto the public.

New and Improved




New and Improved

Portage Daily Register February 1,2004

The new Merrimac Ferry has spent more time beingdown for repairs than the 40 year old vessel it replaced

did in its last three years.

Since its launch on May 16, The Colsac III has brokendown 69 times and spent 48 days out of service.

The old ferry was down 48 times since 2000 but neverout of service for a full day.

More …




More …

The last breakdown came December 2, when valvesthat control the braking system locked, stranding theboat and vehicles in the middle of the river.

J ohn Vesperman chief operations engineer, “We had topull it ashore with a huge tow truck after we were ableto free the stuck valves”

Strength Fatigue and Fracture



Strength, Fatigue and Fracture

5 Fatigue in Mechanical Components_F10

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