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New Life in FatigueShip structure ≡
a collection of a large number and variety of
fatigue prone locations, hot spots.
HOUSTON, WE HAVE A PROBLEM ...
21-11-2011
Challenge the future
DelftUniversity ofTechnology
hot spots.
KIVI NIRIA
Fatigue in High-Speed Aluminium Shipsa total stress concept and joint SN curve formulation
21-11-2011
Challenge the future
DelftUniversity ofTechnology
• For many years, aluminium alloys have become the standardfor high speed ships.
Introduction
Lpp = 12 …15 [m]
Fn ~ 1.0 [-]
3 | 48
• Primary joining method for ship structural components:
ARC-WELDING
fracture toughness: aluminium << steel
• Arc-welding:
� Reduces fatigue strength
� Fillet welds and butt welds introduce NOTCHES (stress concentrations):
+
Introduction
4 | 48
+
� Dynamic loading=
� WELD LINES fatigue governingparts of ship structure
X
Y
Z
• Some typical structural details: weld line + ends
Introduction
Mb
Fm
t bt c
M b
Fm
ct
t b
M b
Fm
M b
Fm
5 | 48
M b
Fmt b
ct
M b
Fm
Mb
Fm
t btc
• Maritime Innovation Project (MIP): VOMAS
• Consortium: Damen Shipyards, TUD, Marin, TNO, BV, LR, ABS, USCG
For high-speed aluminium vessels, a practical, efficient methodology to predict (impact induced) fatigue in an early design stage does not exist.
Introduction
6 | 48
Introduction
hydrodynamic loads
structural response
fatigue assessment
fatigue design method
7 | 48
loads
hydro-elasticity
response assessment
fatigue resistance
• Fatigue life prediction concepts
Motivation
(fictitious) notch stress
concept
structural (hot spot)
stressconcept
Battelle SS approach:• master SN curve • mesh insensitive• design environment
• 1 SN curve• fictitious notch radius
transforms nominal stress fatigue strength systems in a uniform local stress value
• fine solid mesh
8 | 48
nominalstress
concept• ∞ SN-curves / detail cat.• x SN-curves + SCF• design environment
HSS approach:• extrapolation
method sensitive• fine mesh• 1 or 2 SN-curves
Ship structure ≡a collection of a large
number and variety of fatigue prone locations,
hot spots.
HOUSTON, WE HAVE A PROBLEM ...
• Some modelling considerations:
� Ship structure = shell plated structure
� Governing parameter: tb << (a,b)
Motivation
single SN curve with stress based through-thickness criterion
9 | 48
� Shell FE environment: no weld modelling
� WELD LINES / basic joints / failure locations
� Include characteristic NOTCH crack propagation behaviour
� Relation to LEFM approach: welding process induced flaws exist
through-thickness criterion
• Combine and extend the advantages of the different fatigue life prediction concepts for applicability in a design environment.
Idea
(fictitious) notch stress
concept
∞
structural (hot spot)
stressconcept
∫√
10 | 48
nominalstress
concept
∞
A good scientist is a person with original ideas.
A good engineer is a person who makes a
design(method) that works with as few original ideas
as possible.
TOTAL STRESS CONCEPT
Total Stress Concept
Joint SN Curve Formulation
102
103
total stress concept, Tσ = 1 : 1.56
102
103
T
102
103
total stress concept, Tσ = 1 : 1.56
102
103
total stress concept, Tσ = 1 : 1.56
T
11 | 48
small scale specimen based large scale specimen fit
103
104
105
106
107
108
100
101
N
S R
10
310
410
510
610
710
810
0
101
N
S R
T-jointButt jointCruciform jointLongitudinal stiffener jointGusset plate / bracketPP Butt jointLC Cruciform joint
ST
103
104
105
106
107
108
100
101
NS R
10
310
410
510
610
710
810
0
101
NS R
bulb st - web fr conn with bracket: type a T st - web fr conn: type cweb fr - web fr conn with soft toe bracket: type aweb fr - web fr conn with nested bracket: type c st - web fr conn: type b
ST
• Fatigue governing parameters
Total Stress Concept
movingdislocations
cracknucleation
micro-crackpropagation
macro-crackpropagation
finalfracture
crack initiation crack propagation
SCF SIF
� Stress Concentration Factor � Stress Intensity Factor
12 | 48
• Welding process induced flaws already exist
fracture mechanics approach (LEFM, loading mode I)
• Include crack initiation period
modify SIF using SCF related notch stress distribution
Intensity Factor
• Weld ends (HS type a and b)
• Basic welded joint formulations (HS type c): toe root
� DS / SS butt joint: 4x / 2x 2x / 1x
� DS / SS cover plate: 4x / 2x NC / NC
Total Stress Concept
M b
Fm
M b
Fmt bt ct bt c
c
c
ab
t ct c
13 | 48
� DS / SS cover plate: 4x / 2x NC / NC
� DS / SS T-joint: 4x / 2x 2x / 1x
� DS / SS cruciform joint: 8x / 4x 4x / 2xM b
Fm
M b
Fmt b
ctct
t b
M b
Fm
M b
Fm
M b
Fm
M b
Fm
M b
Fm
M b
Fm
t bt b
t c
M b
Fm
M b
Fmt b
ct
t b
ct
M b
Fm
M b
Fm
• Notch stress formulation (force {F,M} induced, geometry and far fieldstress determined parameter):
equilibrium equivalent partfar field stress
self-equilibrating partweld geometry induced bending
+Williams’ asymptotic solution
+
Total Stress Concept
m brr rr
14 | 48
Fm
M b
t br
+
s
m b
=
+
rr
rr rr
• Notch stress formulation, force {F,M} induced:
� Notch angle α ≠ π (fillet weld config): weld toe
� Non-symmetry w.r.t. (tb / 2), e.g. DS T-joint
� Symmetry w.r.t. (t / 2), e.g. DS cruciform joint
Fm
M b
= +
s
t br
m b
=
+
rr
rr
Fm
M b
= +
s
t br
m b
=
+
Total Stress Concept
15 | 48
� Symmetry w.r.t. (tb / 2), e.g. DS cruciform joint
� Notch angle α = π (crack config): weld root / crack growth specimen
� Non-symmetry, e.g. DS LC cruciform joint
� Symmetry, e.g. DEN specimen
M b
t b
M b
Fm
t 'bbb
rr'
• QUESTION 1: effects of self-equilibrating stress part
Consider weld toe failure of a DS T-joint and DS cruciform joint. Will there be any difference in fatigue life and if so, which joint has a longer fatigue life?
� The far field stress is the same for both joints (membrane state).
� Please note that the nominal-, hot spot- and fict. notch stress is the same.
� Regarding the DS cruciform joint, consider fatigue failure from 1 side.
Total Stress Concept
16 | 48
� Regarding the DS cruciform joint, consider fatigue failure from 1 side.
A. Fatigue life is the same.B. DS T-joint has longer fatigue life.C. DS cruciform joint has longer fatigue life.D. There is not enough information to answer this question.
t br
++t b
r
• Residual stress formulation (welding induced):
� Non-symmetry w.r.t. (tb/2):
equilibrium equivalent+
self-equilibrating part
FE analysis,schematic
SS butt jointDS T-joint
Total Stress Concept
17 | 48
� Symmetry w.r.t. (tb/2):
DS butt joint:
measured [Pagel, 2011]
DS long. stiffener:
FE analysis,schematic
• Arc-welded joint: notch stress + residual stress formulation
� Equilibrium equivalent part: force induced + welding induced
� Force induced: {Fm,Mb}
Equilibrium equivalent part + self-equilibrating part
Total Stress Concept
18 | 48
� Welding induced: membrane + bending (angular distortion)
� Self-equilibrating part:
measured / design value / fatigue strength C
1
msS C N
−= ⋅measured / mean stress /
fatigue strength C
hypothesis: distribution is similar for notch stress and residual stress!
• Notch stress formulation:
� Analytical / characteristic (near) singularity / all geometry parameters
� Related to linear far field stress distribution (FEM)
� Example 1, (α ≠ π), non-symmetry: DS T-joint t
hw
l w
t c
26m b
sb b
f m
t tσ = − ⋅ 6
6b
sb b m
mR
m t f
⋅= −⋅ − ⋅
Total Stress Concept
19 | 48
� Example 1, (α ≠ π), non-symmetry: DS T-joint
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.2; lw/t b = 1.0; ρ/t b = 0.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.2; lw/t b = 1.0; ρ/t b = 0.0
weld notch stress σw /σs
far field stress σf /σs
FE result
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
weld notch stress σw /σs
far field stress σf /σs
FE result
Fm
M b
t b
• Notch stress formulation:
� Example 2, (α ≠ π), symmetry: DS cruciform joint
Fm
M b
t b
hw
l w
t c
Total Stress Concept
20 | 48
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
weld notch stress σw /σs
far field stress σf /σs
FE result
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 0.4; ρ/t b = 0.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σw /σ
s, σ
f /σ
s [ - ]
r/t b
[ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 0.4; ρ/t b = 0.0
weld notch stress σw /σs
far field stress σf /σs
FE result
• Notch stress formulation:
� Example 3, (α = π), non-symmetry: DS cruciform joint, SS butt joint
� Assumed crack path: weld leg section (cr. joint), weld throat (butt joint)
� Stress state mainly characterised by membrane and bending as well
Total Stress Concept
21 | 48
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σwr
/σsr, σ
lr /σ
sr [ - ]
r '/t
b' [ -
]
lw/t b = 10/8; hw/t b = 2/8; lw/hw = 10/2; ag/t b = 3/8; ρ/t b = 0/8
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σwr
/σsr, σ
lr /σ
sr [ - ]
r '/t
b' [ -
]
lw/t b = 10/8; hw/t b = 2/8; lw/hw = 10/2; ag/t b = 3/8; ρ/t b = 0/8
weld root notch stress σwr /σsr
weld root linear stress σlr /σsr
FEM
1r2r3
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σwr
/σsr, σ
lr /σ
sr [ - ]
r '/t
b' [ -
]
tc/t b = 10/10; lw/hw = 10/20; lw/t b = 10/10; ag/t b = 3/10; ρ/t b = 0/10
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
σwr
/σsr, σ
lr /σ
sr [ - ]
r '/t
b' [ -
]
tc/t b = 10/10; lw/hw = 10/20; lw/t b = 10/10; ag/t b = 3/10; ρ/t b = 0/10
weld root notch stress σwr /σsr
weld root linear stress σlr /σsr
FEM
r1
r2
r3
{σs,Rs} still defines far field stress
• Notch stress formulation: motivation
� Fatigue life effects: equilibrium equivalent stress part {σs,Rs}
0.00
0.25
0.50
0.75
1.00
s [ -
]
fatigue life: relative bending stress effects, far field stress only
0.00
0.25
0.50
0.75
1.00
s [ -
]
fatigue life: relative bending stress effects, far field stress only
edge crack formulationcentre crack formulation
Total Stress Concept
22 | 48
� Pure bending shows better performance compared to pure membrane:
� Non-monotonic behaviour means bad news
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-1.00
-0.75
-0.50
-0.25
N/NRs=0 [ - ]
Rs
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
-1.00
-0.75
-0.50
-0.25
N/NRs=0 [ - ]
Rs
fd
dr
σ
• Notch stress formulation: motivation
� Fatigue life effects: self-equilibrating part
Total Stress Concept
0.00
0.25
0.50
0.75
1.00
Rs [
- ]
fatigue life: relative bending stress effects
0.00
0.25
0.50
0.75
1.00
Rs [
- ]
fatigue life: relative bending stress effects
non-symmetric notch behaviour symmetric notch behaviour
0.00
0.25
0.50
0.75
1.00
Rs [
- ]
fatigue life: relative bending stress effects, far field stress only
0.00
0.25
0.50
0.75
1.00
Rs [
- ]
fatigue life: relative bending stress effects, far field stress only
edge crack formulationcentre crack formulation
edge crack formulation
23 | 48
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-1.00
-0.75
-0.50
-0.25
N/NRs(M)=0 [ - ]
R
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-1.00
-0.75
-0.50
-0.25
N/NRs(M)=0 [ - ]
R
answer Question 1: C
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-1.00
-0.75
-0.50
-0.25
N/NRs=0 [ - ]
R
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
-1.00
-0.75
-0.50
-0.25
N/NRs=0 [ - ]
R
� Non-symmetry: weld geometry induced bending part amplifies effect
� Symmetry: 3 criteria, bending induced anti-symmetry require shift + scaling (no far field bending stress projection)
� Far field bending effect counter-acted by self-equilibrating stress (notch effect)
• Stress Intensity Factor formulation K: generalised formulation not available for basic welded joints
(α ≠ π), (α = π)
• Equilibrium equivalent stress part: consistent with far field stress / solutions for simple geometries
aYYK gmI ⋅π⋅σ⋅⋅= aYMK gkI ⋅⋅⋅⋅= πσ
Crack Propagation Model
24 | 48
Geometry factor: Yg
• Self-equilibrating unit stress part: notch effect / applied as crack face pressure
Magnification factor: Ym
• Geometry factor Yg: cracked geometry parameter
� Covers macro-crack effects: finite thickness (and free surface) � Superposition principle: membrane + bending
� Handbook solutions
( ) ( ) ( ){ }[ ]gbbgmmgmmg YMYFRYFY ⋅+⋅⋅+⋅= sgnsgnsgn
Crack Propagation Model
25 | 48
� Handbook solutions
• Weld root geometry correction Mk : cracked geometry, FEM
• Magnification factor Ym: uncracked geometry parameter
( )∫
−
σ⋅
π=
a
022
m drra
r2Y ( )
⋅⋅−
⋅=
bbw
s t
rR
t
rr 2
1 σσ
σ
• Stress Intensity Factor example
� Notch angle α ≠ π :
5.0
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
5.0
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
0.0
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.00
0.0
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.00
Yg dominates (a/tb) > 0.2Ym dominates (a/tb) ≤ 0.2
Williams’ asympt. sol. dominates (a/tb) ≤ 0.1
Cgb dominates 0.1 < (a/tb) ≤ 0.2
Crack Propagation Model
26 | 48
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
a/tb [ - ]
Yg,
Ym, Y
mY
g [ -
]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
a/tb [ - ]
Yg,
Ym, Y
mY
g [ -
]
Ym
Yg
YmYg
FEM
macro-crackmicro-
crack-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
σw /σs, σf /σs [ - ]
r/t b
[ -
]
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
σw /σs, σf /σs [ - ]
r/t b
[ -
]
weld notch stress σw /σs
far field stress σf /σs
FEM
• Stress Intensity Factor example
� Notch angle α = π : geometry with gap ag
� SIF is MkYg determined; square root notch behaviour included in K by definition
� MkYg < 1, bb < tb
Crack Propagation Model
27 | 48
� Ym (notch effect) affects crack propagation!
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
a/t b' [ - ]
MkY
g, Y
m ,
√ (
1/Y
m )
[ -
]
tc/t b = 10/10; lw/hw = 10/20; lw/t b = 10/10; ag/t b = 3/10; ρ/t b = 0/10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
a/t b' [ - ]
MkY
g, Y
m ,
√ (
1/Y
m )
[ -
]
tc/t b = 10/10; lw/hw = 10/20; lw/t b = 10/10; ag/t b = 3/10; ρ/t b = 0/10
MkYg
Ym
√ ( 1/Ym )
FEM
t b
hw
l w
c
M b
Fm
t
s , Rs
t 'bbb
agr
r' a,
srRsr
• QUESTION 2: fatigue life comparison for weld toe and weld root failure
Consider a DS cruciform joint. Will there be any difference in fatigue life for the weld toe and weld root failure case and if so, which one will be longer?
Total Stress Concept
tr r
t
3.0
3.5
4.0
4.5
5.0
( 1
/Ym )
[ -
]
tc/t b = 10/10; lw/hw = 10/10; lw/t b = 10/10; ag/t b = 5/10; ρ/t b = 0/10
3.0
3.5
4.0
4.5
5.0
( 1
/Ym )
[ -
]
tc/t b = 10/10; lw/hw = 10/10; lw/t b = 10/10; ag/t b = 5/10; ρ/t b = 0/10
Ym
MkYg
√ ( 1/Ym )
FEM
2.5
3.0
3.5
4.0
4.5
5.0
mY
g [ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
2.5
3.0
3.5
4.0
4.5
5.0
mY
g [ -
]
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
Ym
Yg
YmYg
FEM
28 | 48
A. Fatigue life is the same.B. Weld root has longer fatigue life.C. Weld toe has longer fatigue life.D. There is not enough information to answer this question.
t br r
2ai t b
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
2.5
a/t b' [ - ]
MkY
g, Y
m ,
√ (
1/Y
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.5
1.0
1.5
2.0
2.5
a/t b' [ - ]
MkY
g, Y
m ,
√ (
1/Y
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
2.5
a/tb [ - ]
Ym, Y
g, Y
m
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.5
1.0
1.5
2.0
2.5
a/tb [ - ]
Ym, Y
g, Y
m
• Characteristic da/dn-∆K curve (long crack growth)
• Paris-based two-stage model: ignore region III
Crack Propagation Model
10-5
10-4
III
da/
dn
( )mth KK
KC
dn
da ∆⋅
∆∆−⋅=
γ
1
∆K = crack driving force
29 | 48
• Similitude hypothesis: da/dndepends only on (∆K, ∆Kth, Kmax, Kc)
100 101 102 1010-8
10-7
10-6
I
II
da/
dn
th K c
K
K
∆K = crack driving force
• Crack growth at NOTCHES: elasticity/plasticity
Crack Propagation Model
10-6
10-5
10-4
10-3
(da
/dn
) [ m
m/c
ycle
]
short (notch) crack growth
10-6
10-5
10-4
10-3
(da
/dn
) [ m
m/c
ycle
]
short (notch) crack growth
long crack growth10
-6
10-5
10-4
10-3
(da
/dn
) [ m
m/c
ycle
]
short (notch) crack growth
10-6
10-5
10-4
10-3
(da
/dn
) [ m
m/c
ycle
]
short (notch) crack growth
long crack growthplastic short (notch) crack growthelastic short (notch) crack growth
30 | 48
� Frost-Dugdale model: da/dn = C.a
� Generalised Frost-Dugdale model(Jones et. al, 2008)
( )mm
KaCdn
da ∆⋅⋅=
−2
1
- non-similitude behaviour- elastic crack growth at notch
101
102
103
104
10-7
∆K [ MPa √ mm ]
10
110
210
310
410
-7
∆K [ MPa √ mm ]
long crack growthplastic short (notch) crack growthelastic short (notch) crack growth
101
102
103
104
10-7
∆K [ MPa √ mm ]
10
110
210
310
410
-7
∆K [ MPa √ mm ]
• Crack growth at NOTCHES: elasticity/plasticity
� P. Dong: plasticity dominated micro-crack behaviour
� Elasticity/plasticity criterion:
Crack Propagation Model
( )mgk KM
dn
da ∆⋅= 2
31 | 48
� Model: work in progress because of slope dependency
elasticity
plasticity
r
r
crackp
notchp
:2
:2
,
,
<≥
( )mg
mn
m KYCdn
da ∆⋅⋅= −2 2,1=n
• Crack growth at NOTCHES: elasticity/plasticity
� Example: elastic behaviour
Crack Propagation Model
10-4
10-3
10-2
[ m
m/c
ycle
]
Al 5083, T-L config.
10-4
10-3
10-2
[ m
m/c
ycle
]
Al 5083, T-L config.
40 10 -5-
rolling direction
10-4
10-3
10-2
) [
mm
/cyc
le ]
Al 5083, T-L config.
10-4
10-3
10-2
) [
mm
/cyc
le ]
Al 5083, T-L config.
32 | 48
101
102
103
104
10-8
10-7
10-6
10-5
10
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
10
110
210
310
410
-8
10-7
10-6
10-5
10
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
base material; Rs = -1.0
base material; Rs = 0.0
101
102
103
104
10-8
10-7
10-6
10-5
10
∆K . √ ( Yl / Yn ) [ MPa √ mm ]
(da
/dn
) . ( Y
l / Y
n )
[ m
m/c
ycle
]
10
110
210
310
410
-8
10-7
10-6
10-5
10
∆K . √ ( Yl / Yn ) [ MPa √ mm ]
(da
/dn
) . ( Y
l / Y
n )
[ m
m/c
ycle
]
base material; Rs = -1.0
base material; Rs = 0.0
• Crack growth at NOTCHES: elasticity/plasticity
� Example: plastic behaviour incl. notch radius effects
Crack Propagation Model
10-2
[ m
m/c
ycle
]
R = 0.05 [-] 10
-2
[ m
m/c
ycle
]
R = 0.05 [-] 10
-2
[ m
m/c
ycle
]
R = 0.05 [-] 10
-2
[ m
m/c
ycle
]
R = 0.05 [-]
33 | 48
102
103
104
10-4
10-3
∆K [ MPa √ mm ]
(da
/dn
) [
mm
/cyc
le ]
10
210
310
4
10-4
10-3
∆K [ MPa √ mm ]
(da
/dn
) [
mm
/cyc
le ]
ρ = 0.0 [mm]
ρ = 0.4 [mm]
ρ = 0.7 [mm]
ρ = 1.4 [mm]
102
103
104
10-4
10-3
∆K . √ ( 1/Ym ) [ MPa √ mm ](d
a/d
n)
/ Y m
2 [ m
m/c
ycle
]
10
210
310
4
10-4
10-3
∆K . √ ( 1/Ym ) [ MPa √ mm ](d
a/d
n)
/ Y m
2 [ m
m/c
ycle
]
ρ = 0.0 [mm]
ρ = 0.4 [mm]
ρ = 0.7 [mm]
ρ = 1.4 [mm]
• Crack growth at NOTCHES:
� Notch / micro-crack fatigue life effects and notch radius influence
Crack Propagation Model
0.26
0.31micro-crack propagation fatigue life contribution
0.26
0.31micro-crack propagation fatigue life contribution
10-4
10-3 short (notch) crack growth
10-4
10-3 short (notch) crack growth
34 | 48
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.01
0.06
0.11
0.16
0.21
Ni /Ntot [ - ]
a i [ m
m ]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.01
0.06
0.11
0.16
0.21
Ni /Ntot [ - ]
a i [ m
m ]
101
102
103
104
10-7
10-6
10-5
10
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
10
110
210
310
410
-7
10-6
10-5
10
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
• QUESTION 3: effect of final crack length
Consider a DS T-joint with SIF behaviour as shown. At what (dimensionless) crack length do you expect that > 90 [%] of the fatigue life is consumed?
Total Stress Concept
3.5
4.0
4.5
5.0
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
3.5
4.0
4.5
5.0
tc/t b = 1.0; hw/lw = 1.0; lw/t b = 1.0; ρ/t b = 0.0
Ym
Yg
YmYg
FEM10
-4
10-3
[ m
m/c
ycle
]
short (notch) crack growth
10-4
10-3
[ m
m/c
ycle
]
short (notch) crack growth
35 | 48
A. 0.1 (af/tb)B. 0.3 (af/tb)C. 0.5 (af/tb)D. 0.7 (af/tb)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
a/tb [ - ]
Yg,
Ym, Y
mY
g [ -
]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
a/tb [ - ]
Yg,
Ym, Y
mY
g [ -
]
FEM
101
102
103
104
10-7
10-6
10-5
∆K [ MPa √ mm ]
(da
/dn
) [
mm
/cyc
le ]
10
110
210
310
410
-7
10-6
10-5
∆K [ MPa √ mm ]
(da
/dn
) [
mm
/cyc
le ]
long crack growthplastic short (notch) crack growthelastic short (notch) crack growth
• QUESTION 3: effect of final crack length
Consider a DS T-joint with SIF behaviour as shown. At what (dimensionless) crack length do you expect that > 90 [%] of the fatigue life is consumed?
Total Stress Concept
0.7
0.8
0.9
1.0fatigue life: effect of final crack length
0.7
0.8
0.9
1.0fatigue life: effect of final crack length
36 | 48
A. 0.1 (af/tb)B. 0.3 (af/tb)C. 0.5 (af/tb)D. 0.7 (af/tb)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
af / tb [ - ]
N/N
af=
tb [
- ]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
af / tb [ - ]
N/N
af=
tb [
- ]
• Fatigue test results suggest a non-linear mean stress dependency.
• Exponential relation (Kwofie, 2001):
• First order approximation:
Crack Propagation Model
1
R
us
R
eσασσ
σ
− ⋅
−
=
generalization of several empirical models
1
1 R
R us
σσ ασ σ−
= − ⋅
37 | 48
� Goodman, α = 1 high-cycle fatigue: low σ / small σR
• High-cycle fatigue: low σ / large σR
� Walker, α = {σus /(γ.σR)} .ln{(1-R)/2}
1
1
2R
Rγσ
σ −
− =
• Walker’s mean stress model using :
superior curve fitting results: γ ≈ 0.5 for R ≥ 0γ = 0.0 for R < 0
• Another definition of ∆σeff (Kim, Dong, 2006):
Crack Propagation Model
( ) γσσ −−
∆=∆ 11 s
effR
R
us
eff eσασσ σ
⋅ = ⋅
+∆⋅=∆ σσσ maxeff= +
38 | 48
� R ≥ 0: γ = 0.5
� R < 0: γ = 0.0
Walker’s model: loading dependent mean stress
( )121
eff
R
σσ ∆∆ =−
( )1eff R
σσ ∆∆ =−
min
max
mean
t
min
maxmean
+
t
• Welded joints: alternating material zones
� Weld (filler) material� Heat Affected Zone (HAZ)� Base (parent) material
• Base material, loading induced mean stress:micro- and macro crack prop.
Crack Propagation Model
weldHAZ
base material
1 m−
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
Al 7075-T651; T-L config.
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
Al 7075-T651; T-L config.
R = -1.00R = 0.10R = 0.50R = 0.75
50.8
P
P61.0
~ 6
39 | 48
micro- and macro crack prop.
region affected according to Ym:
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
Al 5083, T-L config.
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K [ MPa √ mm ]
(da
/dn
) [ m
m/c
ycle
]
Al 5083, T-L config.
R = -1.0R = 0.0
40 10 -5-
rolling direction
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K . √ ( Yl / Yn ) / √ (1-R) 1- γ [ MPa √ mm ]
(da
/dn
) . ( Y
l / Y
n )
. (1-R
) 1- γ [
mm
/cyc
le ]
Al 5083, T-L config.
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K . √ ( Yl / Yn ) / √ (1-R) 1- γ [ MPa √ mm ]
(da
/dn
) . ( Y
l / Y
n )
. (1-R
) 1- γ [
mm
/cyc
le ]
Al 5083, T-L config.
R = -1.0R = 0.0
( ) ( )
12
1 1
21 1
m
m mg
Y YdaC K
dn R Rγ γ
−
− −
= ⋅ ⋅ ⋅ ∆
− −
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K . √ ( Yl / Yn ) / √ (1-R) 1- γ [ MPa √ mm ]
(da
/dn
) . ( Y
l / Y
n )
. (1-R
) 1- γ [
mm
/cyc
le ]
Al 7075-T651; T-L config.
101
102
103
104
10-8
10-7
10-6
10-5
10-4
10-3
10-2
∆K . √ ( Yl / Yn ) / √ (1-R) 1- γ [ MPa √ mm ]
(da
/dn
) . ( Y
l / Y
n )
. (1-R
) 1- γ [
mm
/cyc
le ]
Al 7075-T651; T-L config.
R = -1.00R = 0.10R = 0.50R = 0.75
• Basquin type of equation:
with and
• Initial crack size effect:
Joint SN Curve Formulation
( ) ∫
⋅⋅
=
−
b
f
b
i
t
a
t
a bm
b
mg
mn
m
s t
ad
t
aYY
RI
2
2
1
3total stress concept, Tσ = 1 : 1.53
3total stress concept, Tσ = 1 : 1.53
3total stress concept, Tσ = 1 : 1.18
3total stress concept, Tσ = 1 : 1.18
mT NCS
1 −
⋅=( )m
sm
m
b
sT
RItS 1
2
2
⋅
∆=⋅−
σ
40 | 48
103
104
105
106
107
108
100
101
102
103
N
S R
σ
103
104
105
106
107
108
100
101
102
103
N
S R
σ
T-joint
Butt joint
Cruciform joint
Longitudinal stiffener joint
103
104
105
106
107
108
100
101
102
103
N
S R
σ
103
104
105
106
107
108
100
101
102
103
N
S R
σ
T-joint
Butt joint
Cruciform joint
Longitudinal stiffener joint
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0
10
20
30
40
50
60
a i /t b [ - ]
p [
- ]
initial crack size (Weibull) distribution, m = 3, µ = 0.02
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0
10
20
30
40
50
60
a i /t b [ - ]
p [
- ]
initial crack size (Weibull) distribution, m = 3, µ = 0.02
• Mean stress effects:
� Micro-crack region: HAZ
Joint SN Curve Formulation
The fatigue strength of welded joints is mean stress independent.�
Welding induced residual stress acts as high-tensile mean stress.
welding induced high-tensile residual stress dominates loading induced part
41 | 48
� Macro-crack region: base material (weld toe) / weld material (weld root)
� Weld performance improvement (technique dependent) factor Ri
( ) ( )( )( )
2 1
11 1 1i
meq iR R R
γγ
⋅ −⋅ −= − − ⋅ −
stress dominates loading induced part
loading induced part only in macro-crack region
micro-crack region correction and loadinginduced part in macro-crack region
( ) ( )ms
m
m
b
sT
RItRS 1
2
2
2
1
1 ⋅−
∆=⋅−⋅−γ
σ
• Mean stress effects:
Joint SN Curve Formulation
102
103
S s
master curve formulation; Tσ = 1 : 3.50
102
103
S s
master curve formulation; Tσ = 1 : 3.50
102
103
S R
master curve formulation; Tσ = 1 : 1.60
102
103
S R
master curve formulation; Tσ = 1 : 1.60
42 | 48
103
104
105
106
107
108
100
101
N
10
310
410
510
610
710
810
0
101
N
T-joint; R = 0.0T-joint; R = -1.0Butt joint; R = 0.0Butt joint; R = -1.0Long. stiff. joint; R = 0.1Long. stiff. joint; R = 0.5Long. stiff. joint; UIT
103
104
105
106
107
108
100
101
N
10
310
410
510
610
710
810
0
101
N
T-joint; R = 0.0T-joint; R = -1.0Butt joint; R = 0.0Butt joint; R = -1.0Long. stiff. joint; R = 0.1Long. stiff. joint; R = 0.5Long. stiff. joint; UIT
• QUESTION 4: stress component for fatigue life calculation
Consider the structural response of the stiffened panel, loaded with space averaged pressure (sea side). The welding induced residual stress is assumed to be tensile. What stress value needs to be used at Pos. 2 for fatigue life calc.?
Joint SN Curve Formulation
1NODAL SOLUTION
STEP=1SUB =1TIME=1SEQV (AVG)DMX =.695882SMN =.159884SMX =68.802
1NODAL SOLUTION
STEP=1SUB =1TIME=1SX (AVG)RSYS=0DMX =.695882SMN =-70.953SMX =37.5
1 MNNODAL SOLUTION
STEP=1SUB =1TIME=1SZ (AVG)RSYS=0DMX =.695882SMN =-62.401SMX =54.793
1ELEMENTS
REAL NUM
2
43 | 48
A. σx (mode I stress component)B. σVM (Von Mises stress component)C. |σx | (absolute value of mode I stress component)D. |σx / 2| (absolute value of half mode I stress component)
X
Y
Z
LS specimen
.1598847.787
15.41423.04
30.66738.294
45.92153.548
61.17568.802
X
Y
Z
LS specimen
-70.953-58.903
-46.852-34.802
-22.752-10.701
1.34913.4
25.4537.5
MX
X
Y
Z
LS specimen
-62.401-49.38
-36.358-23.337
-10.3152.706
15.72828.75
41.77154.793
X
Y
Z
LS specimen
3
2
1
• QUESTION 5: effect of tensile/compressive loading
Assuming that the welding induced residual stress is tensile, what will be the relative mean stress ratio Rw for compressive loading relative to tensile loading?
Joint SN Curve Formulation
s
s sas
tension
minσ=R
44 | 48
A. Rw = -1B. Rw = -2C. Rw = -3D. Rw = -4
t
s r smax
smincompression
max
min
σσ=R
• Compressive cyclic loading:
� SN curves data: tensile residual stress + TENSILE cyclic loading
� Walker model, welding induced tensile residual stress:
Joint SN Curve Formulation
( ) γσσ −−
∆=∆ 11 w
effR γ = 0.5
45 | 48
� Predominantly, the micro-crack propagation region is affected!
� Total stress parameter: region I correction
( ) ( )ms
m
m
b
sT
RItRS 1
2
2
2
1
1 ⋅−
∆=⋅−⋅−γ
σ
( )−1 wR
( ) ( )ms
m
m
b
s
T
RItRS 1
2
2
2
1
1
2
⋅−
∆
=⋅−⋅−γ
σ
0 for ≥σ 0 for <σ
answer Question 4: D
Total Stress Concept
Joint SN Curve Formulation
102
103
total stress concept, Tσ = 1 : 1.56
102
103
T
102
103
total stress concept, Tσ = 1 : 1.56
102
103
total stress concept, Tσ = 1 : 1.56
T
46 | 48
small scale specimen based large scale specimen fit
103
104
105
106
107
108
100
101
N
S R
10
310
410
510
610
710
810
0
101
N
S R
T-jointButt jointCruciform jointLongitudinal stiffener jointGusset plate / bracketPP Butt jointLC Cruciform joint
ST
103
104
105
106
107
108
100
101
NS R
10
310
410
510
610
710
810
0
101
NS R
bulb st - web fr conn with bracket: type a T st - web fr conn: type cweb fr - web fr conn with soft toe bracket: type aweb fr - web fr conn with nested bracket: type c st - web fr conn: type b
ST
• QUESTION 6: effect of compressive stresses on fatigue life
Consider the structural response of the stiffened panel, loaded with space averaged pressure (sea side). At what weld location is the first crack expected?
� The welding induced residual stress is assumed to be tensile.
Total Stress Concept
1NODAL SOLUTION
STEP=1SUB =1TIME=1SEQV (AVG)DMX =.695882
1NODAL SOLUTION
STEP=1SUB =1TIME=1SX (AVG)RSYS=0
1 MNNODAL SOLUTION
STEP=1SUB =1TIME=1SZ (AVG)RSYS=0
1ELEMENTS
REAL NUM
2
47 | 48
A. Position 1.B. Position 2.C. Position 3.D. Position 1 and 3
X
Y
Z
LS specimen
.1598847.787
15.41423.04
30.66738.294
45.92153.548
61.17568.802
DMX =.695882SMN =.159884SMX =68.802
X
Y
Z
LS specimen
-70.953-58.903
-46.852-34.802
-22.752-10.701
1.34913.4
25.4537.5
RSYS=0DMX =.695882SMN =-70.953SMX =37.5
MX
X
Y
Z
LS specimen
-62.401-49.38
-36.358-23.337
-10.3152.706
15.72828.75
41.77154.793
RSYS=0DMX =.695882SMN =-62.401SMX =54.793
X
Y
Z
LS specimen
3
2
1
Pos 1. σz = -42.0 [MPa] Pos 2. σx = -63.5 [MPa] Pos 3. σx = 15.5 [MPa]
QUESTIONS?
Thank you for your attention!
Henk, thank you foryour presentation, but...
N=C·S-m
48 | 48
QUESTIONS?
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