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1
Professor Darrell F. SocieMechanical Science and Engineering
University of Illinois
© 2004-2007 Darrell Socie, All Rights Reserved
Fatigue of Mechanical Components
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Fatigue of Mechanical Components
Fatigue of BoltsFretting FatigueMechanically Fastened JointsWidespread Fatigue DamageWelded Joints
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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
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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.
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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
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Bolted Joint Loading
Force
Tensile Loading
P
P
P
Shear Loading
P
P
3
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Tensile Loading
kb
kj
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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
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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
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Bolted Joint Analysis
δb extension
bolt
F bte
n sio
n
δj contraction
joint
F jco
mpr
essi
on
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Bolted Joint Analysis (continued)
F b -Fj
δb δj
Fi
preload force
kb kj
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Bolted Joint Analysis (continued)
Fb-Fj
P
P
eP
P
e e
P
Pb
Pj
Pkk
kPjb
bb +
=
5
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Fatigue Considerations
5f S1N
Δ∝
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Bolt Stiffness
Fb
e
Pb
Pj P
Pb
PjP
Stiffer bolts carry more of the external force
e
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Joint Seperation
Fb -Fj
e
Fb = P
kb kj
6
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Joint Stiffness
3d
L
LEd8k
2
jπ
=
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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
=
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Fatigue DesignTraditional Method
Fi / AtMean stress
Alte
rnat
ing
stre
ss
Su0
Se
Sa
tf
tiua A2
PCK21
A/FSS Δ=
+−
=
7
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Shear Loading of Bolted Joints
Tensile Loading
P
P
P
Shear Loading
P
P
Fi Fi μFiμFi
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Mechanics of Shear Loading
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Shear Failures of Bolts
8
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Shear Fatigue Testing
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Self Loosening of a Bolt
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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
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Loosening Fatigue limit
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Retightening of a Bolt
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Summary
Bolts have poor fatigue strengthBolt preload must be maintained
10
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Fatigue of Mechanical Components
Fatigue of BoltsFretting FatigueMechanically Fastened JointsWidespread Fatigue DamageWelded Joints
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Fretting
www.eren.doe.gov/wind/feature.html
shaft
Relative motion between bearing and shaft
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Interface Stresses
P
F
Clamping Force
F
σx
τ
Stresses in the bar
Stresses in the flange
11
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Localized Sliding
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Fretting Mechanism
www.nrim.go.jp:8080/public/english/act/1992/1718.html
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Fretting Mechanism
High shear stresses at local contacts
Cold welding produces wear particles
Fretting fatigue crack formed
12
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Fretting Cracks
100 μm
From Waterhouse, Fretting Corrosion, 1972 From ASM Fatigue and Fracture Handbook, 1996
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Fatigue Behavior
Hoeppner and Gates, “Fretting Fatigue Considerations in Engineering Design”, Wear, Vol. 70, 1981, 155-164
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Fretting Fatigue Limits
From Schijve Fatigue of Structures and Materials, Kluer, 2001
13
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Variables Affecting Fretting
Clamping pressureCyclic stress levelSliding displacementCoefficient of frictionMaterials strengthSurface roughnessEnvironment
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Fretting Testing
www.nrim.go.jp:8080/public/english/act/1992/1718.html
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Clamping Pressure
www.nrim.go.jp:8080/public/english/act/1992/1718.html
14
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Sliding Displacement
Funk, “Test Methods to Investigate the Influences of Fretting Corrosion on the Endurance” Materialprüfung, 1969, 221-227
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Modeling
Friction stress, μpo
Contact pressure, po
Cyclic stress, σa
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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
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Friction Coefficient
Wharton, “The Effect of Different Contact Materials on the Fretting Fatigue Strength of an Aluminum Alloy”, Wear, Vol. 26, 1973, 253-260
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Fasteners
σo
σh
p
q
θ
Farris et. Al. “Analysis of Widespread Fatigue Damage in Structural Joints, SAMPE Symposium, 1996, 65-79
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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
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Eliminate Contact
Kt = 3.5
Slotted holeFrom Schijve Fatigue of Structures and Materials, Kluer, 2001
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Eliminate Stress Concentration
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Attachments
Fretting at the bolt hole even when the bracket is unloaded
17
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Summary
Fretting is caused by sliding surfacesFretting is a long life fatigue problem
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Fatigue of Mechanical Components
Fatigue of BoltsFretting FatigueMechanically Fastened JointsWidespread Fatigue DamageWelded Joints
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Mechanically Fastened Joints
PinsBoltsRivetsAdhesive Bonding
18
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Pined Joints2024-T3 with steel pins
Sharp et.al. Fatigue Design of Aluminum Components and Structures , 1996
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Bolted Joints
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Test Data
Atzori et. al. “A Re-analysis on Fatigue Data of Aluminum Alloy Bolted Joints” International Journal of Fatigue, 1997, 579-588
19
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Design Curves
Atzori et. al. “A Re-analysis on Fatigue Data of Aluminum Alloy Bolted Joints” International Journal of Fatigue, 1997, 579-588
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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
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Eccentric Loading
1 2
3 4
L1
L3
Fe
20
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Bolted Joints (continued)
Fe
Fe
Q
Q
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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
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With PreloadF
e
Fi
Fi
Preload force reacted by pressure forces
Fe
Fi
Fi
21
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Shear Loading
1
2
3
4
F
Σ moment = 0
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Bolt Centroid
1
2
3
4
Find bolt centroid∑∑=
i
ii
AxA
x∑∑=
i
ii
AyA
y
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Moment Balance
1
2
3
4
4F
4F
4F
4F
r4Externalmoment
ResultantMost of the force is taken by a few bolts
22
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Rivets
Sharp et.al. Fatigue Design of Aluminum Components and Structures , 1996
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Deformed Shape
Tensile and Bending Stress
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Joint Design
Gro
ss S
ecti
on S
tres
s, k
si
Sharp et.al. Fatigue Design of Aluminum Components and Structures , 1996
23
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Stress Concentration Factors
Peterson’s Stress Concentration Factors, 1997
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Fabrication Induced Stresses
Gro
ss S
ecti
on S
tres
s, k
si
Cycles
Sharp et.al. Fatigue Design of Aluminum Components and Structures , 1996
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Lap and Flange Joints
Sharp et.al. Fatigue Design of Aluminum Components and Structures , 1996
24
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Flange Joint
P
P
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Adhesive Bonding
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Load Transfer
Krieger, “Stress Analysis Concepts for Adhesive Bonding of Aircraft Primary Structure” ASTM STP 981, 1988, 264-275
25
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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
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Adhesive Stresses
Shear Stress
Peel Stress
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Debonding
Zhang and Shang, “Subcritical Crack Growth at Bimetal Interfaces: Part 1. Flexural Peel TechniqueMetallurgical Transactions A, 1996, 205-211
26
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Fatigue Strength
Adhesive Bonded RivetedBolick et. al. “Comparative Study of Riveted and Adhesively Bonded Joints Subjected to Fatigue Loading”Fatigue 2002, Stockholm, 2002
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Static and Fatigue Results
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Summary
Local stress concentrators determine the strength of a joint
27
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Fatigue of Mechanical Components
Fatigue of BoltsFretting FatigueMechanically Fastened JointsWidespread Fatigue DamageWelded Joints
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Aloha Flight 243
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Aloha Flight 243
28
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Widespread Fatigue Damage WFD
Multiple site damage MSD
Multiple element damage MED
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WFD - MSD
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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
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Crack Interactions
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Experiments
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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
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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
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Crack Growth
Silva et. Al. “Multiple-site Damage in Riveted Lap-Joints: Experimental Simulation and Finite Element Prediction”International Journal of Fatigue, 2000, 319-338
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Summary
WSD is an important failure mode in aircraft structures
31
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Fatigue of Mechanical Components
Fatigue of BoltsFretting FatigueMechanically Fastened JointsWidespread Fatigue DamageWelded Joints
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Types of Welds
Structural weldsSpot weldsSpecial Processes
LaserElectron Beam
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Weld Classifications
D E
F2 G
32
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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
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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
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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
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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
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Residual Stress from Welding
Y
X
X
X
X
Y
YY
tension
tension
compression
compression
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Weld Distortion
34
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Weld Toe Residual Stress
Yieldstress
Maximum stress at the weld toe is nearly the same for any cycle
Δε
ε
σ
Δε
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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
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Butt and Fillet Weld Test Data
99% survival with 95% confidence
1000
Stre
ss R
ange
, MPa
100
10
103 104 105 106 107
Fatigue Life, Cycles
Failures Run outs
The good welds
35
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Weld Terminations1000
Stre
ss R
ange
, MPa
100
10
103 104 105 106 107
Fatigue Life, Cycles
Failures Run outs
99% survival with 95% confidence
The bad welds
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Sources of Inherent Scatter
Weld qualityMean, fabrication and residual stressesStress concentrations (geometry)Weldment sizeMaterial properties
Opportunities for Improvement !
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The Good and Bad
Good weld design
Bad weld design
36
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Typical Butt Weld
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Weld Toe
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Macroscopic LOF
3 mm
37
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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.
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Nominal Stress ?
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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
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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
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σpeak
σnσhs
Peak and Hot Spot Stress
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σpeak
t
σn
V
P
σn
V
t
σnσn
P
Physical Meaning of Hot Spot Stress
IMc
AP
n +=σ
39
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Hot Spot SN Curves
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Weld Improvement
Reduce weld toe stressesStress relieveImprove local geometry
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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
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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
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Spot Weld Fatigue Data
10
102
103
104
105
102 103 104 105 106 107 108
Fatigue Life, Cycles
Max
imum
Loa
d, N
Tensile Shear
Coach-peel
1
4
Fatigue Data Bank for Spot Welds, University of Illinois
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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
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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
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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
Fatigue of Mechanical Components © 2004-2007 Darrell Socie, All Rights Reserved 122 of 123
Structural Stress Correlation
101
102
103
104
102 103 104 105 106 107
Fatigue Life
Stru
ctur
al S
tress
, MPa
42
Fatigue of Mechanical Components © 2004-2007 Darrell Socie, All Rights Reserved 123 of 123
Things Worth Remembering
Local weld toe stresses, geometry and flaws control the life of weldments