strength, fatigue and fracture - home | fracture control...
Post on 06-Feb-2018
234 Views
Preview:
TRANSCRIPT
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 of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 2 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 3 of 113
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.
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 4 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 5 of 113
Bolted Joint Loading
Force
Tensile Loading
P
P
P
Shear Loading
P
P
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 6 of 113
Tensile Loading
kb
kj
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 7 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 8 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 9 of 113
Bolted Joint Analysis
δb extension
bolt
F b
δj contraction
joint
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 10 of 113
Bolted Joint Analysis (continued)
F b
δb δj
Fi
preload force
kb kj
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 11 of 113
Bolted Joint Analysis (continued)
Fb
P
P
eP
P
e e
P
Pb
Pj
Pkk
kPjb
bb +
=
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 12 of 113
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
∆∝
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 13 of 113
Bolt Stiffness
Fb
e
Pb
Pj P
Pb
Pj P
Stiffer bolts carry more of the external force
e
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 14 of 113
Joint Seperation
Fb
e
Fb = P
kb kj
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 15 of 113
Bolt Stiffness
L1
L2
d
At EA
LEA
Lk1
k1
k1
k1
t
2
1
1
b
21b
+=
+=
springs in series
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 16 of 113
Joint Stiffness
3d
L
LEd8k
2
jπ
=
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 17 of 113
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 of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 18 of 113
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 of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 19 of 113
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 ∆=
+−
=
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 20 of 113
Shear Loading of Bolted Joints
Tensile Loading
P
P
P
Shear Loading
P
P
Fi Fi µFi µFi
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 21 of 113
Mechanics of Shear Loading
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 22 of 113
Shear Failures of Bolts
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 23 of 113
Shear Fatigue Testing
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 24 of 113
Self Loosening of a Bolt
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 25 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 26 of 113
Loosening Fatigue limit
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 27 of 113
Retightening of a Bolt
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 28 of 113
Summary
Bolts have poor fatigue strength Bolt preload must be maintained
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 29 of 113
Fatigue of Mechanical Components
Fatigue of Bolts Fretting Fatigue Welded Joints Case Study
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 30 of 113
Fretting
www.eren.doe.gov/wind/feature.html
shaft
Relative motion between bearing and shaft
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 31 of 113
Interface Stresses
P
F
Clamping Force
F
σx τ
Stresses in the bar
Stresses in the flange
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 32 of 113
Localized Sliding
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 33 of 113
Fretting Mechanism
www.nrim.go.jp:8080/public/english/act/1992/1718.html
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 34 of 113
Fretting Mechanism
High shear stresses at local contacts
Cold welding produces wear particles
Fretting fatigue crack formed
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 35 of 113
Fretting Cracks
100 µm
From Waterhouse, Fretting Corrosion, 1972 From ASM Fatigue and Fracture Handbook, 1996
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 36 of 113
Fatigue Behavior
Hoeppner and Gates, “Fretting Fatigue Considerations in Engineering Design”, Wear, Vol. 70, 1981, 155-164
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 37 of 113
Fretting Fatigue Limits
From Schijve Fatigue of Structures and Materials, Kluer, 2001
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 38 of 113
Variables Affecting Fretting
Clamping pressure Cyclic stress level Sliding displacement Coefficient of friction Materials strength Surface roughness Environment
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 39 of 113
Fretting Testing
www.nrim.go.jp:8080/public/english/act/1992/1718.html
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 40 of 113
Clamping Pressure
www.nrim.go.jp:8080/public/english/act/1992/1718.html
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 41 of 113
Sliding Displacement
Funk, “Test Methods to Investigate the Influences of Fretting Corrosion on the Endurance” Materialprüfung, 1969, 221-227
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 42 of 113
Modeling
Friction stress, µpo
Contact pressure, po
Cyclic stress, σa
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 43 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 44 of 113
Friction Coefficient
Wharton, “The Effect of Different Contact Materials on the Fretting Fatigue Strength of an Aluminum Alloy”, Wear, Vol. 26, 1973, 253-260
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 45 of 113
Fasteners
σo
σh
p
q
θ
Farris et. Al. “Analysis of Widespread Fatigue Damage in Structural Joints, SAMPE Symposium, 1996, 65-79
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 46 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 47 of 113
Eliminate Contact
Kt = 3.5
Slotted hole From Schijve Fatigue of Structures and Materials, Kluer, 2001
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 48 of 113
Eliminate Stress Concentration
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 49 of 113
Attachments
Fretting at the bolt hole even when the bracket is unloaded
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 50 of 113
Summary
Fretting is caused by sliding surfaces Fretting is a long life fatigue problem
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 51 of 113
Fatigue of Mechanical Components
Fatigue of Bolts Fretting Fatigue Welded Joints Case Study
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 52 of 113
Types of Welds
Structural welds Spot welds Special Processes Laser Electron Beam
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 53 of 113
Weld Classifications
D E
F2 G
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 54 of 113
100
200
300
400
B
C
D
E
F F2 G W 0
105 106 107 108
BS 7608 - Steel
Fatigue Life, Cycles
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 55 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 56 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 57 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 58 of 113
Residual Stress from Welding
Y
X
X
X
X
Y
Y Y
tension
tension
compression
compression
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 59 of 113
Weld Distortion
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 60 of 113
Weld Toe Residual Stress
Yield stress
Maximum stress at the weld toe is nearly the same for any cycle
∆ε
ε
σ
∆ε
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 61 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 62 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 63 of 113
Weld Terminations 1000
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 64 of 113
Sources of Inherent Scatter
Weld quality Mean, fabrication and residual stresses Stress concentrations (geometry) Weldment size Material properties
Opportunities for Improvement !
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 65 of 113
The Good and Bad
Good weld design
Bad weld design
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 66 of 113
Typical Butt Weld
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 67 of 113
Weld Toe
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 68 of 113
Macroscopic LOF
3 mm
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 69 of 113
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.
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 70 of 113
Nominal Stress ?
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 71 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 72 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 73 of 113
σpeak
σn σhs
Peak and Hot Spot Stress
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 74 of 113
σpeak
t
σn V
P
σn
V
t
σn σn
P
Physical Meaning of Hot Spot Stress
IMc
AP
n +=σ
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 75 of 113
Hot Spot SN Curves
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 76 of 113
Weld Improvement
Reduce weld toe stresses Stress relieve Improve local geometry
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 77 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 78 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 79 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 80 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 81 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 82 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 83 of 113
Structural Stress Correlation
101
102
103
104
102 103 104 105 106 107
Fatigue Life
Stru
ctur
al S
tress
, MPa
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 84 of 113
Things Worth Remembering
Local weld toe stresses, geometry and flaws control the life of weldments
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 85 of 113
Fatigue of Mechanical Components
Fatigue of Bolts Fretting Fatigue Welded Joints Case Study (Merrimac Ferry)
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 86 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 87 of 113
Merrimac Wisconsin
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 88 of 113
Merrimac Ferries
http://www.shopstop.net/ferry/default.htm
1847 1963
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 89 of 113
Merrimac Free Ferry
Merrimac Ferry
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 90 of 113
Merrimac Free Ferry
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 91 of 113
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)
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 92 of 113
Basic Design
Supported by two 10’ by 80’ barges
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 93 of 113
Welded Box Beam
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 94 of 113
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?
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 95 of 113
Heavy Loads?
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 96 of 113
Remote Monitoring System
Merrimac WI Evanston IL
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 97 of 113
Installing Strain Gages
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 98 of 113
Typical Gage Installation
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 99 of 113
Strain Gage Locations
3
1 2
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 100 of 113
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.
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 101 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 102 of 113
Barge End
541.028 1100.712Time (Secs)-875
875
Strain Gage (ustrain)
Note: strain offset indicating plastic deformation
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 103 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 104 of 113
BS 7608 - Steel
500
1000
F F2
G W
0 105 106 107 108
Fatigue Life, Cycles
F2
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 105 of 113
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.
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 106 of 113
Crack Growth Calculations mKC
dNda
∆=
m
WafaC
dNda
πσ∆=
∫∫
πσ∆
=f
i
a
am
N
0
WafaC
dadN
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 107 of 113
Major Variables
Initial and final crack size Material properties Stress intensity factor Loading history
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 108 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 109 of 113
Edge Cracked Plate in Tension
π
π−++ππ
=
b2acos
)b2asin1(37.0
ba02.2752.0
b2atan
ab2
baF
3
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 110 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 111 of 113
Results for Center Cracks
0
2
4
6
8
10
12
0 500 1000 1500 2000
Years of Service
Cra
ck L
engt
h
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 112 of 113
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?
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 113 of 113
Frozen Tundra of the Wisconsin River
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 114 of 113
Thermal Loading
Constant Temperature Water
Variable Temperature Air
Thermal Expansion/Contraction on Deck
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 115 of 113
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
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 116 of 113
Colsac III
http://fun.co.columbia.wi.us/fun/colsac/construction.asp
May 16, 2003 Construction
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 117 of 113
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.
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 118 of 113
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.
Fatigue of Mechanical Components © 2011 Darrell Socie, All Rights Reserved 119 of 113
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”
Strength, Fatigue and Fracture
top related