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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 Mechanical Components

Fatigue of Bolts Fretting Fatigue Welded Joints 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


Kf 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 Joint Loading

Force

Tensile Loading

P

P

P

Shear Loading

P

P


Tensile Loading

kb

kj


Bolt Preload Force

dFKT 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

Cum

ulat

ive

Prob

abilit

y


Bolted Joint Analysis

δb extension

bolt

F b

δj contraction

joint


Bolted Joint Analysis (continued)

F b

δb δj

Fi

preload force

kb kj


Bolted Joint Analysis (continued)

Fb

P

P

eP

P

e e

P

Pb

Pj

Pkk

kPjb

bb +

=


Fatigue Considerations

100

1000

10000

100

Cycles

Stre

ss A

mpl

itude

, MPa

101 102 103 104 105 106 107

b ~ -0.1

10f S1N

∆∝


Bolt Stiffness

Fb

e

Pb

Pj P

Pb

Pj P

Stiffer bolts carry more of the external force

e


Joint Seperation

Fb

e

Fb = P

kb kj


Bolt Stiffness

L1

L2

d

At EA

LEA

Lk1

k1

k1

k1

t

2

1

1

b

21b

+=

+=

springs in series


Joint Stiffness

3d

L

LEd8k

2

jπ

=


Joint Stiffness

Pkk

kFPjb

bib ++=

Define joint factor, C

jb

b

ib

kkkC

PCFP

+=

+=

kb should be small and and kj large

11.091

LEd8

LEd

LEd

C 22

2

==π

+π

π

=


Aluminum and Steel Joints Steel Bolt , Steel Flange Steel Bolt , Aluminum Flange

C = 0.11 C = 0.25

LEd8k steel

2

fπ

=LEd8k umminalu

2

fπ

=


Fatigue Design Traditional Method

Fi / At Mean stress

Alte

rnat

ing

stre

ss

S u 0

S e

Sa

tf

tiua A2

PCK21

A/FSS ∆=

+−

=


Shear Loading of Bolted Joints

Tensile Loading

P

P

P

Shear Loading

P

P

Fi Fi µFi µFi


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, JSME 21 (159) 1978


Loosening Fatigue limit


Retightening of a Bolt


Summary

Bolts have poor fatigue strength Bolt preload must be maintained


Fretting

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

shaft

Relative motion between bearing and 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 shear stresses at local contacts

Cold welding produces wear particles

Fretting fatigue crack 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

−

KS

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. JSME, 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 Joints, SAMPE Symposium, 1996, 65-79


Prevention

Reduce surface shear stress Reduce normal force Reduce coefficient of friction

Eliminate stress concentration Stepped shafts with large radii

Compressive residual stress Shot peening

Separation of surfaces Compliant coatings


Eliminate Contact

Kt = 3.5

Slotted hole From Schijve Fatigue of Structures and Materials, Kluer, 2001


Eliminate Stress Concentration


Attachments

Fretting at the bolt hole even when the bracket is unloaded


Summary

Fretting is caused by sliding surfaces Fretting is a long life fatigue problem


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 0

105 106 107 108

BS 7608 - Steel

Fatigue Life, Cycles


Crack Growth Data

( ) 0.312 mMPaK109.6dNda

∆×= −

( ) 25.210 mMPaK104.1dNda

∆×= −

( ) 25.312 mMPaK106.5dNda

∆×= −

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless Steel:

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

5 10 100

10-7

10-6

10-8

Cra

ck G

row

th R

ate,

m/c

ycle

∆K, MPa√m

σyield 252 273 392 415


0

25

50

75

100

125

105

B

C

D E

F

106 107 108

BS 7608 - Aluminum

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


Crack Growth Data

1 10 100

Cyclic Stress Intensity, MPa√m

Cra

ck G

row

th R

ate

m/c

ycle

A533B m/cycle

6061-T6 m/cycle

10-2

10-4

10-6

10-8

10-10

10-12

3X

Steel welds are 3 times stronger 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 toe is nearly the same for any cycle

∆ε

ε

σ

∆ε


Mean Stress Effects

As welded structures usually have the maximum 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

Stre

ss R

ange

, MPa

100

10

103 104 105 106 107


Failures Run outs

The good welds


Weld Terminations 1000

Stre

ss R

ange

, MPa

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 flaws 0.1 to 1 mm long. Reducing the size or eliminating these flaws will substantially improve fatigue lives.


Nominal Stress ?


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

r

t

t1

E D

B C

A

σpeak

σn

σhs

F P

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 Shell elements

Fine 3-D FE mesh

Coarse 3-D FE mesh

Stress magnitudes and distributions obtained from various FE models

Finite Element Models


σpeak

σn σhs

Peak and Hot Spot Stress


σpeak

t

σn V

P

σn

V

t

σn σn

P

Physical Meaning of Hot Spot Stress

IMc

AP

n +=σ


Hot Spot SN Curves


Weld Improvement

Reduce weld toe stresses Stress relieve Improve local geometry


Macroscopic Shape

t

r

θ

0.05 0.2 0.15 0.1

2

3

4

1

r / t

tK

θ = 15º

θ = 30º

θ = 45º

θ = 60º


Kfmax

mMPatS15.01K umaxf β+=

rt1Kt β+=

ρα

+

−+=

1

1K1K tf

2

3

4

5

ρ = α Weld toe radius

ft KorK 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


Max

imum

Loa

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 moments transmitted 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 the forces 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

dtF)F( x

x π=σ

dtF

)F( yy π

=σ

2z

z tF744.1t6.0)F( =σ

2x

x tdM872.1t6.0)M( =σ

2Y

Y tdM872.1t6.0)M( =σ

Fz

Mx

t

d

Fx

Fy

My


Structural Stress Correlation

101

102

103

104

102 103 104 105 106 107

Fatigue Life

Stru

ctur

al S

tress

, MPa


Things Worth Remembering

Local weld toe stresses, geometry and flaws control the life of weldments



Fatigue of Bolts Fretting Fatigue Welded Joints Case Study (Merrimac Ferry)


Collaborators

David W. Prine Infrastructure Technology Institute

Northwestern University Darrell Socie

Department of Mechanical Engineering University of Illinois at Urbana Champaign

Continuous Remote Monitoring of The Merrimac Free Ferry


Merrimac Wisconsin


Merrimac Ferries

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

1847 1963


Merrimac Free Ferry

Merrimac Ferry


Merrimac Free Ferry


Merrimac Ferry Colsac II

State Highway 113 over the Wisconsin River at Merrimac

Began operation in 1963 33’ wide by 80’ long Cable driven (two cables)


Basic Design

Supported by two 10’ by 80’ barges


Welded Box Beam


Cracks Found in Hull

Many cracks found in the ends where the ramps are attached

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


Heavy Loads?


Remote Monitoring System

Merrimac WI Evanston IL


Installing Strain Gages


Typical Gage Installation


Strain Gage Locations

3

1 2


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 ~4

months until winter closing in December 1998.


Strain for Single Load Test

Gage Maximum Minimum Range1_1 131 26 1051_2 70 1 692_1 123 -158 2812_2 44 -79 1232_3 184 -922 11063_1 140 -562 7023_2 123 -61 184


Barge End

541.028 1100.712Time (Secs)-875

875

Strain Gage (ustrain)

Note: strain offset indicating plastic deformation


Strain Readings

Gage Static 10-8-98 11-6-981_1 105 466 4271_2 69 3502_1 281 311 2912_2 123 2522_3 1106 10893_1 702 602 5443_2 184 213

Live Traffic Tests: 30,772 cars 35 busses 291 trucks


BS 7608 - Steel

500

1000

F F2

G W

0 105 106 107 108


F2


Fatigue Analysis for Ends

No fatigue analysis needed if there is plastic deformation in this welded structure. WIDoT has lowered posted limit to exclude all but passenger cars and pickup trucks.


Crack Growth Calculations mKC

dNda

∆=

m

WafaC

dNda

πσ∆=

∫∫

πσ∆

=f

i

a

am

N

0

WafaC

dadN


Major Variables

Initial and final crack size Material properties Stress intensity factor Loading history


Crack Growth Data

( ) 0.312 mMPaK109.6dNda

∆×= −

( ) 25.210 mMPaK104.1dNda

∆×= −

( ) 25.312 mMPaK106.5dNda

∆×= −

Ferritic-Pearlitic Steel:

Martensitic Steel:

Austenitic Stainless Steel:

From Dowling, Mechanical Behavior of Materials, 1999


Edge Cracked Plate in Tension

π

π−++ππ

=

b2acos

)b2asin1(37.0

ba02.2752.0

b2atan

ab2

baF

3


Loading History for 1 Month

0

20

40

60

80

100

120

0 300 100 200 400 500

Strain Range, µε

Num

ber o

f Cyc

les


Results for Center Cracks

0

2

4

6

8

10

12

0 500 1000 1500 2000

Years of Service

Cra

ck L

engt

h


Results

Data shows overloads are driving end cracks. Data shows center cracks are not being driven

by traffic loading. Where do the strains come from to drive the

center cracks?


Frozen Tundra of the Wisconsin River


Thermal Loading

Constant Temperature Water

Variable Temperature Air

Thermal Expansion/Contraction on Deck


Winter Tests in Ice

-15 -10 -5 0 5

10 15

Air

Tem

pera

ture

ºC

22 days

-600

-400

-200

0

200

400 S

train

, µε


Colsac III

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

May 16, 2003 Construction


2 weeks later

The Associated Press - June 7, 2003 MADISON — The new Merrimac Ferry, which has been closed for repairs, will not operate for the foreseeable future due to a breakdown in repair negotiations with the contractor. The new $2.2 million ferry, known as the ColSac III, broke down May 23 about a week after opening to the public.


New and Improved

Portage Daily Register February 1,2004

The new Merrimac Ferry has spent more time being down 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 broken down 69 times and spent 48 days out of service.

The old ferry was down 48 times since 2000 but never out of service for a full day.


More …

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

John Vesperman chief operations engineer, “We had to pull it ashore with a huge tow truck after we were able to free the stuck valves”

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