HOUSTON, WE HAVE A PROBLEM New Life in Fatigue life in fatigue... · New Life in Fatigue Ship...

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


102

103


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


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


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

+


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

=

+


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.


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


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


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

⋅= −⋅ − ⋅


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

[ -

]


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

[ -

]


-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

[ -

]




FE result

Fm

M b

t b


� Example 2, (α ≠ π), symmetry: DS cruciform joint

Fm

M b

t b

hw

l w

t c


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

[ -

]


-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

[ -

]




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

[ -

]


-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

[ -

]




FE result


� 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


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' [ -

]


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 [ -

]


edge crack formulationcentre crack formulation


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


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 [

- ]


0.00

0.25

0.50

0.75

1.00

Rs [

- ]


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


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


5.0


0.0


0.0


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


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

[ -

]



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


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 )

[ -

]


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 )

[ -

]


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?


tr r

t

3.0

3.5

4.0

4.5

5.0

( 1

/Ym )

[ -

]


3.0

3.5

4.0

4.5

5.0

( 1

/Ym )

[ -

]


Ym

MkYg

√ ( 1/Ym )

FEM

2.5

3.0

3.5

4.0

4.5

5.0

mY

g [ -

]


2.5

3.0

3.5

4.0

4.5

5.0

mY

g [ -

]


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


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


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

]


long crack growth10

-6

10-5

10-4

10-3

(da

/dn

) [ m

m/c

ycle

]


10-6

10-5

10-4

10-3

(da

/dn

) [ m

m/c

ycle

]


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 ]


101

102

103

104

10-7

∆K [ MPa √ mm ]

10

110

210

310

410

-7

∆K [ MPa √ mm ]


� P. Dong: plasticity dominated micro-crack behaviour

� Elasticity/plasticity criterion:


( )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


� Example: elastic behaviour


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

]


40 10 -5-

rolling direction

10-4

10-3

10-2

) [

mm

/cyc

le ]


10-4

10-3

10-2

) [

mm

/cyc

le ]


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


� Example: plastic behaviour incl. notch radius effects


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


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?


3.5

4.0

4.5

5.0


3.5

4.0

4.5

5.0


Ym

Yg

YmYg

FEM10

-4

10-3

[ m

m/c

ycle

]


10-4

10-3

[ m

m/c

ycle

]


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 ]


• 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?


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:


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):


( ) 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.


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

]


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

]


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

]


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 ]


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 ]


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 ]


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 ]


R = -1.00R = 0.10R = 0.50R = 0.75

• Basquin type of equation:

with and

• Initial crack size effect:


( ) ∫

⋅⋅

=

−

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




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


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:


102

103

S s

master curve formulation; Tσ = 1 : 3.50

102

103

S s


102

103

S R


102

103

S R


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.?


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?


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:


( ) 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



102

103


102

103

T

102

103


102

103


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.


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?

HOUSTON, WE HAVE A PROBLEM New Life in Fatigue life in fatigue... · New Life in Fatigue Ship...

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