Fatigue of Mechanical Components - utmis.org.loopiadns.comutmis.org.loopiadns.com/media/2016/08/3.-Fatigue-of-Mechanical-Components.pdfProfessor Darrell F. Socie Mechanical Science

1

Professor Darrell F. SocieMechanical Science and Engineering

University of Illinois

© 2004-2007 Darrell Socie, All Rights Reserved

Fatigue of Mechanical Components

Fatigue of Mechanical Components © 2004-2007 Darrell Socie, All Rights Reserved 1 of 123


Fatigue of BoltsFretting FatigueMechanically Fastened JointsWidespread Fatigue DamageWelded Joints


Fatigue Strength of Bolts

Su = 785 MPa

Fatigue Design Review Task 5 – Assembly of Available Fatigue Data Relevant to Pressure Equipment DesignTWI Report No: 123337/2/01, European Commission

3.6

2


Kf for Bolts

SAEGrade

MetricGrade

Rolled Threads

Cut Threads

HeadFillet

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


Bolted Joint Loading

Force

Tensile Loading

P

P

P

Shear Loading

P

P

3


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

Force200 Data PointsMedian 130COV 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

abili

ty

4


Bolted Joint Analysis

δb extension

bolt

F bte

n sio

n

δj contraction

joint

F jco

mpr

essi

on


Bolted Joint Analysis (continued)

F b -Fj

δb δj

Fi

preload force

kb kj


Bolted Joint Analysis (continued)

Fb-Fj

P

P

eP

P

e e

P

Pb

Pj

Pkk

kPjb

bb +

=

5


Fatigue Considerations

5f S1N

Δ∝


Bolt Stiffness

Fb

e

Pb

Pj P

Pb

PjP

Stiffer bolts carry more of the external force

e


Joint Seperation

Fb -Fj

e

Fb = P

kb kj

6


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

=


Fatigue DesignTraditional Method

Fi / AtMean stress

Alte

rnat

ing

stre

ss

Su0

Se

Sa

tf

tiua A2

PCK21

A/FSS Δ=

+−

=

7


Shear Loading of Bolted Joints

Tensile Loading

P

P

P

Shear Loading

P

P

Fi Fi μFiμFi


Mechanics of Shear Loading


Shear Failures of Bolts

8


Shear Fatigue Testing


Self Loosening of a Bolt


Self Loosening Mechanism (Sakai)

F

−ΔN

Normal force increased

Normal force decreased

Net torque produced

+ΔN

−ΔμN

+ΔμN

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

9


Loosening Fatigue limit


Retightening of a Bolt


Summary

Bolts have poor fatigue strengthBolt preload must be maintained

10





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

11


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

12


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

13


Variables Affecting Fretting

Clamping pressureCyclic stress levelSliding displacementCoefficient of frictionMaterials strengthSurface roughnessEnvironment


Fretting Testing



Clamping Pressure


14


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

15


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 stressReduce normal forceReduce coefficient of friction

Eliminate stress concentrationStepped shafts with large radii

Compressive residual stressShot peening

Separation of surfacesCompliant coatings

16


Eliminate Contact

Kt = 3.5

Slotted holeFrom Schijve Fatigue of Structures and Materials, Kluer, 2001


Eliminate Stress Concentration


Attachments

Fretting at the bolt hole even when the bracket is unloaded

17


Summary

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





Mechanically Fastened Joints

PinsBoltsRivetsAdhesive Bonding

18


Pined Joints2024-T3 with steel pins

Sharp et.al. Fatigue Design of Aluminum Components and Structures , 1996


Bolted Joints


Test Data

Atzori et. al. “A Re-analysis on Fatigue Data of Aluminum Alloy Bolted Joints” International Journal of Fatigue, 1997, 579-588

19


Design Curves

Atzori et. al. “A Re-analysis on Fatigue Data of Aluminum Alloy Bolted Joints” International Journal of Fatigue, 1997, 579-588


Joint Types

FrictionLoads transferred by contact friction forcesGross section nominal stressFailures at edge of cover plate in gross section

BearingLoads transferred by shear of boltsNet section nominal stressFretting fatigue failures at bolt holes


Eccentric Loading

1 2

3 4

L1

L3

Fe

20


Bolted Joints (continued)

Fe

Fe

Q

Q


Bolted Joints (continued)

Let the bolt forces be: Q1, Q2 , Q3 , Q4

The geometry requires:4

4

3

3

2

2

1

1

LQ

LQ

LQ

LQ

===

Moment balance:

[ ]24

23

22

21

1

1

1

231

1

231

1

221

11

LLLLLQFe

LLQ

LLQ

LLQLQFe

+++=

+++=

Load is concentrated on only a few bolts ( largest L )

Bolt force:∑

= 2i

nn L

LeFQ


With PreloadF

e

Fi

Fi

Preload force reacted by pressure forces

Fe

Fi

Fi

21


Shear Loading

1

2

3

4

F

Σ moment = 0


Bolt Centroid

1

2

3

4

Find bolt centroid∑∑=

i

ii

AxA

x∑∑=

i

ii

AyA

y


Moment Balance

1

2

3

4

4F

4F

4F

4F

r4Externalmoment

ResultantMost of the force is taken by a few bolts

22


Rivets



Deformed Shape

Tensile and Bending Stress


Joint Design

Gro

ss S

ecti

on S

tres

s, k

si


23


Stress Concentration Factors

Peterson’s Stress Concentration Factors, 1997


Fabrication Induced Stresses

Gro

ss S

ecti

on S

tres

s, k

si

Cycles



Lap and Flange Joints


24


Flange Joint

P

P


Adhesive Bonding


Load Transfer

Krieger, “Stress Analysis Concepts for Adhesive Bonding of Aircraft Primary Structure” ASTM STP 981, 1988, 264-275

25


Shear Strength of AdhesivesRoom Temperature Dry

Elevated Temperature Dry (180 F)

Elevated Temperature Wet (180 F)

Shear Stress Strain Data for Structural Adhesives, DOT/FAA/AR-02/97


Adhesive Stresses

Shear Stress

Peel Stress


Debonding

Zhang and Shang, “Subcritical Crack Growth at Bimetal Interfaces: Part 1. Flexural Peel TechniqueMetallurgical Transactions A, 1996, 205-211

26


Fatigue Strength

Adhesive Bonded RivetedBolick et. al. “Comparative Study of Riveted and Adhesively Bonded Joints Subjected to Fatigue Loading”Fatigue 2002, Stockholm, 2002


Static and Fatigue Results


Summary

Local stress concentrators determine the strength of a joint

27





Aloha Flight 243


Aloha Flight 243

28


Widespread Fatigue Damage WFD

Multiple site damage MSD

Multiple element damage MED


WFD - MSD


Drilled HolesFighter Spectrum154 Data PointsMedian 126,750COV 0.22 in life

99.9 %

99 %

90 %

50 %

10 %

1 %

0.1 %

Cum

ulat

ive

Prob

abili

ty

105 Cycles

From: J.P. Butler and D.A. Rees, "Development of Statistical Fatigue Failure Characteristics of 0.125-inch 2024-T3 Aluminum Under Simulated Flight-by-Flight Loading," ADA-002310 (NTIS no.), July 1974.

180 drilled holes in a single plate

COV 0.07 in strength

29


Crack Interactions


Experiments


Crack Nucleation

Silva et. Al. “Multiple-site Damage in Riveted Lap-Joints: Experimental Simulation and Finite Element Prediction”International Journal of Fatigue, 2000, 319-338

30


Crack Nucleation



Crack Growth



Summary

WSD is an important failure mode in aircraft structures

31





Types of Welds

Structural weldsSpot weldsSpecial Processes

LaserElectron Beam


Weld Classifications

D E

F2 G

32


100

200

300

400

B

C

D

E

F F2 G W0

105 106 107 108

Stre

ss R

a nge

, MP a

BS 7608 - Steel

Fatigue Life, Cycles


Crack Growth Data

( ) 0.312 mMPaK109.6dNda

Δ×= −

( ) 25.210 mMPaK104.1dNda

Δ×= −

( ) 25.312 mMPaK106.5dNda

Δ×= −

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

ΔK, MPa√m

σyield252273392415


0

25

50

75

100

125

105

B

C

DE

F

106 107 108

Stre

ss R

a nge

, MP a

BS 7608 - Aluminum

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

33


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

YY

tension

tension

compression

compression


Weld Distortion

34


Weld Toe Residual Stress

Yieldstress

Maximum stress at the weld toe is nearly the same for any cycle

Δε

ε

σ

Δε


Mean Stress Effects

As welded structures usually have the maximum possible mean stressStress 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

35


Weld Terminations1000

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 qualityMean, fabrication and residual stressesStress concentrations (geometry)Weldment sizeMaterial properties

Opportunities for Improvement !


The Good and Bad

Good weld design

Bad weld design

36


Typical Butt Weld


Weld Toe


Macroscopic LOF

3 mm

37


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

ED

BC

A

σpeak

σn

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

38


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

σnσhs

Peak and Hot Spot Stress


σpeak

t

σn

V

P

σn

V

t

σnσn

P

Physical Meaning of Hot Spot Stress

IMc

AP

n +=σ

39


Hot Spot SN Curves


Weld Improvement

Reduce weld toe stressesStress relieveImprove 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

40


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 axialβ ~ 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

41


Structural Stress Calculations

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

Sheet 2

NuggetSheet 1

My

Fy

Fx

Mx

Fz

My

Fy

Fx

Mx

Fz

My

Fy

Fx

Mx

Fz


Structural StressesStresses in sheet :

θσ+θσ+σ+θσ−θσ−=θΔ 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

Mxt

d

Fx

FyMy


Structural Stress Correlation

101

102

103

104

102 103 104 105 106 107

Fatigue Life

Stru

ctur

al S

tress

, MPa

42


Things Worth Remembering

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

Documents

Fatigue of Mechanical Components - utmis.org.loopiadns.comutmis.org.loopiadns.com/media/2016/08/3.-Fatigue-of-Mechanical-Components.pdfProfessor Darrell F. Socie Mechanical Science