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8/18/2019 ZHANG-Æ£ÀÍÄÍ¾ÃÐÔ-3

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Recent Developments in Analysis and Testingof Spot and Seam Welds

Dr. Shicheng Zhang


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2

Brief review

•The recent developments are characterised y the progress in

local approach which was first proposed y !oo" in #$%&.

•The "ey to the local approach is the determination of local

stress parameter '(S!).

•Different concepts are *nder development to get (S!s at spot

welds+ especially for the a*tomotive str*ct*res.

•,ario*s specimens are proposed for spot weld testing.

So*rce- SA !apers 2//#0/#0/12 and 2//&0/#0/$/&+ Detroit+ 3SA4 565AT 3ser 6eeting+ 6ay $0##+ 2//%+ Steyr+ A*stria


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78A ao*t local stress parameters at spot welds

What are (S!s at spot welds9•They are str*ct*ral stress+ notch stress+ S.:.5.+ ;0integral+

ow to determine the (S!s9

•They can e n*merically calc*lated 'stress solver)+

analytically

appro?imated 'stress form*las) and e?perimentally meas*red

'strain ga*ge techni@*e).



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1

r

Str*ct*ral stresses aro*nd a spot weld Stress solver

Str*ct*ral stress is

•plate theory stress witho*t sing*larity

•linearly distri*ted over sheet thic"ness

•o*tp*t stress of shell elements '56)

Str*ct*ral stress is denoted as σ '*i ).



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&

Cotch stress aro*nd a spot weld Stress solver

Cotch stress is denoted as σ" .



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T

A stress solver for spot welds Stress solver

:np*t - σiEStress components aro*nd a spot weld

The Stress Solver A pac"age of analytic sol*tions to spot welds

=*tp*t - σr + σ" + F+ ;+ θ+ σ Str*ct*ral stress+ Cotch stress+ S.:.5.+ ;0integral+


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ρ

t

2 2

2 2

2 2

%

A pac"age of sol*tions to spot welds

σ r = ma?G σ ui + σ liH

Stress solver

σ k = σ n +#

1 πG σ ui − σ uo + σ li − σ lo ± I2' σ ui − σ li )2 + ' σ uo + σ lo )2

+ 2' σ ui + σ li − σ ui σ uo − σ ui σ lo − σ uo σ li − σ li σ lo )J#K 2 H

# K I = I ' σ ui − σ uo + σ li − σ lo ) + & 2 ' τ qu − τ ql )J t 2#

K II = I ' σ ui − σ li ) + 12

&' τ qu + τ ql )J t K eq = ± K I 2 + α K II + β K III

K III =2

2' τ ui − τ li ) t

J ='#− ν 2 )t

1L E I1' σ ui + σ li − σ ui σ li ) + ' σ uo + σ lo )2 − 2' σ ui σ uo + σ ui σ lo + σ uo σ li + σ li σ lo )J



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' σ ui − σ li )

T

σ lo = lo

L

A pac"age of sol*tions to spot welds

θ = − arctan σ ui − σ uo + σ li − σ lo

Stress solver

σ uo = σ uo + 2 σ ui − σ lo1

T T σ + σ + σ + σ

σ ui = σ li = uo ui li lo1T σ + 2 σ li − σ uo

1



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5inite element model Stress solver

Diameter of the spo"e pattern C*gget diameter Diameter of the central eam element C*gget diameter



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K2

0

0

#/

Application of the stress solver Stress solver

Tale #. Stress intensity factors F : and F :: at the leading verte? and F ::: at theside verte? of the weld spot+ all in CKmm + *nder tensile0shear force 5# "C

with n*gget diameter d& mm and sheet thic"ness t# mm

A*thors

!oo" I2J+ Analytic appro?imation

RadaE and SonsinoI2J+ 56

Smith and


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Application of the stress solver Stress solver



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πdt

+ 2

2

+ + )

ρ πdt

+ + + 24 4

#2

:nterface0force0ased estimations Stress solver

R*pp et al.-

6addo?-

σ r =

σ r =

F x M y

+#.L%2 K 2dt

2 F x M y

πdt t w

6O

5O 5y6y

5? 6?

Sheppard- σ ij = F ij

ωt #+

P

M ij

t i β+ F Ai

t i2'i+ j = #+2)

Zhang- σ r = 1 F M 1 F z πdt πdt 2 πd 2

' F = 2 2 F x2 + F y2 4 M = M x + M y

σ k =1 F

πdt '#+

+ #$ t M L π

) + 2 '#+2

π

t

ρ) + 1 F z

πd 2'#+

&d

t 2π

t

ρ)

K I = F 2 M & 2 F z

2πd t πdt t πd t K II =

2 F

πd t K III =

2 F 2 2 M z

πd t πd t



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2

#

Tensile0shear Stress form*las

σ r =#.2% F

dt ' σ r = 1 F

πdt )

σ k =#.2% F

dt

t '#+ /.1/ )

ρ

K eq =/.$1 F

d t K eq = ± K I 2 + K II



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>at0profile

σ r = /.%aM t dtA

Stress form*las

σ k = /.%aM t

dtA

t '#+ /.1% )

ρ

K eq =/.$2aM t

Ad t



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J

#&

Do*le0c*p Stress form*las

σ r =#.2% F

dt 'cos θ +

/./$L D

t sin θ )

σk

=

#.2% F

dt Icos

θ +

/./$L D

t sinθ

+ '/.1/cos θ +/./1&L D

t sin θ )

t

ρ

K eq =

/.#L F

d t

2 D2 2

'1.%&/cos θ + /.#/& 2 sin θ t D

+ /.2L# sin 2 θ )#K 2t



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cos φ sin2 θ J#K 2+

#

Do*le03 Stress form*las

σ r

=

#.2% F

dt Isin φ cos θ +η'b − d )

1t cos φ sin θ J

1t φ = arctan

η'b − d ) tanθ

σ k =#.2% F

dt

t I'#+ /.2L2 ) sin φ cosθ ρ

+ η'b − d )1t

'#+ /. t ρ

) cos φ sin θ J

1t '#+ /.2L2 t K ρ ) φ = arctanη'b − d )'#+ /. t K ρ ) tanθ

K eq =

/.% F

d t Isin2 φ cos2 θ + η 2 'b − d )2 2

#2t 2

φ / or πK2So*rce- SA !apers 2//#0/#0/12 and 2//&0/#0/$/&+ Detroit+ 3SA4 565AT 3ser 6eeting+ 6ay $0##+ 2//%+ Steyr+ A*stria


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2 2

#%

Do*le03 Stress form*las

σ r =#.2% F

dt

Isin φ cos θ +η'b − d )

1t

cos φ sin θ J '#)

σ k =#.2% F

dt

t I'# + /.2L2 ) sin φ cos θ + ρ

η'b − d )

1t

t '#+ /. ) cos φ sin θ J '2)

ρ

56-

K eq =/.% F

d t Isin φ cos θ +

@. '#)

η 2 'b − d )22

#2t cos2 φ sin2 θ J#K 2

@. '2) @. ')

')

Spo"e pattern N Stress solver



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#L

5atig*e test data condensation Stress form*lasacross different specimens



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#$

So*rces of scatter of fatig*e data Stress form*las

Local geometry:

- Sheet thickness t;

- Spot diameter d;

- Notch radius ρ.

Material:

- Composition;

- Micro-structure;

- Dislocation density.

Welding effects:

- esidual stress;

- Material inhomogeneity;

- Welding defects.

Load!"oundary condition:

- Stress ratio R;

- Definition of failure;

- #est conditions.

5

C



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2/

=ptimiOation of spot weld distri*tion Stress form*las

• Dura"ility reser$e for e$ery spot %eld:

R = −∆ F d t

N K mm K 2

• Critical spot %elds:

Spot %elds %ith R


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+

2#

Stress distri*tion aro*nd Strain ga*ge techni@*e

a spot or similar weld∞

σ ij 'r + θ ) = σ / + ∑I An 'r ) cos'n θ )n=#

+ n 'r ) sin'n θ )J

σ ij 'r + θ ) =

+

+

σ ij# 'r ) − σ ij 'r )2 σ ij# 'r ) + σ ij 'r )

2

σ ij2 'r ) − σ ij1 'r )2

σ ij2 'r ) + σ ij1 'r )2

cosθ

cos2 θ

sinθ

sin2 θ



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22

Con0destr*ctive testing

of spot weldsStrain ga*ge techni@*e

•:nside stress at n*gget edge is decisive.

•The stress is inaccessile to meas*re.

•Destr*ctive meas*res may e ta"en.

•Con0destr*ctive method is desired.

Strain ga*ge

C*gget :nside stress

Strain ga*ge

Destr*ctive-';apan)

Strain ga*ge

>ole'B6W+ Qermany)

Removed 'BA6+ Qermany)

Strain ga*ge

Con0destr*ctive-



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′ ′

#2'#− ν )d + ′

I' ′

ρt ′ ′ ′ ′

2 2 ′ ′

2

A strain ga*ge sol*tion

to spot0welded lap EointStrain ga*ge techni@*e

σr

=

αr Ed !

2'# − ν 2 )d I'2d !

− d )εuo

− 1εuo

J

εuo = 'εuo2 − εuo ) K ∆ x

α Ed t K I = I ! 2 GI

'd ! − 2d ) & 2t

2 Jεuo − εuoH

K II =2 α II Ed ! t 2d ! − d '#− ν 2 )d L

+t

$ &

ε)εuo − uo J

2

σ k = αk Ed !2'#− ν 2 )d

G'2d ! − d )εuo − 1εuo + #1 π

I'd ! − 2d )εuo − εuo + I'2d ! − d )εuo − 1εuo J2 + I'd ! − 2d )εuo − εuo J2 JH

J = α J Etd !2#$2'# − ν )d GI'2d ! − d )εuo − 1εuo J2 + I'd ! − 2d )εuo − εuo J2H



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2 K2

′

21

,irt*al testing Strain ga*ge techni@*e

εuo = 'εuo2 − εuo ) K ∆ x

Tale 1. (S!s determined y the strain ga*ge sol*tion in the virt*al

testing ',T) compared with their finite element '5) res*lts for a tensile0shear specimen with d& mm+ t# mm and ρ/.2 mm *nder tensile0

shear force of 5#/// C4 stresses are in CKmm + S:5s in CKmm and ;0

integral in CKmm

σr F : F :: σ" ;0:ntegral

Strain ga*ge sol*tion %1.& %%.$ #/./ 22.# /./L$

5inite element sim*lation %1.1 %%.$ #/./ 22.& /./L$



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2&

6onitoring (S!s

Strain ga*ge sol*tion

Strain ga*ge techni@*e

σr σ" F : F :: ;

t+*+5

Strain ga*ge apparat*s

5



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2


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2%

(imitations

•The res*lts presented are mainly valid for rittle fract*re+ high0cycle

fatig*e and high0speed crash of spot welds.

•5or *ltimate fail*re+ low0cycle fatig*e and low0speed crash+ the res*lts

are hardly applicale altho*gh they not necessarily always fail.

•The material heterogeneity+ resid*al stress and defects d*e to welding

are not considered.

•The res*lts are primarily linear sol*tions and large deformation+ finite

strain and large plasticity are not considered.



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2L

6otivation and =Eective

6otivation-

A*tomotive str*ct*res with a large n*mer of spot welds

need simplified finite element modeling of spot welds.

A *niform spot weld model is desired for oth C,> and fatig*e sim*lations.

=Eective-

Development of a simplified spot weld model capale of

delivering reliale nat*ral fre@*ency and modes



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2$

Test


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/


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#

Simplified Spot Weld 6odel

Beam element

O

y

?

Rigid ar element 'RB2)

:ndependent nodes

Dependent nodes



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0 0

0 01

&

%

0 0

2


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0 0

&


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#

1

O

Damping

in

6ode Type ?peri.


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dudt

&

6ass 0 Spring System for Analysis

,iration

d2

u M e 2 + Redt + K eu = F A cos ωt



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val*ation of Damping ,al*e

!rinciple of f*ll width at half ma?im*m

for eval*ating damping val*es M e

d 2 u2

dt + Re

du

dt + K e u = F A cos ω t

u A = F A

2 ω Re + 'ω M e − K eω

) 2

d =

" 2 − " #

" /

#

= z 2 − z # = = # Re

K e M eDamping val*e



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t

l

=

=

%


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•

•

•

•

L

sim*lations.

The model is validated y the co*pon and component tests.

The same model may also e *sed for fatig*e predictions with additional

data recovery.

A*tomatic generation of the model is s*pported at least y preprocessors li"e ACSA and 6D:CA.



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$


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1/

;oint Type in


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1#

!rinciple of SSZK6SZ 6ethod

σst2

Q!0force

σs#

t#

t2#

σs22

σs2#

t#

!roced*re-#) :dentification of weld line2) Definition of critical locations) Determination of line forces1)


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12

Determination of (ine 5orces Based on Qrid0!oint5orces 'Codal 5orces)

Averaged over lements

Codes

Averagedon Codes

(ine forces and moments

6ethod of Dong+Battelle



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1

(ine 5orces Averaged over lements

(inearly distri*ted line force f to e determined y grid0

point forces 5 C-

,N',N/

/

f

,N00

Qrid !oint

'

Weld line



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# 2

# 2

11

Total Q!05orces Weighted y lement (ength

l5 = 5 ⋅ # C+# C+total l + l

l/

N

,Ntotal1,N/2,N02,N'

l5 = 5 ⋅ 2 C+2 C+total l + l

l0

/'

0



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'&

1

,alidation of (ine 5orce


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1%

,alidation of (ine 5orce


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d t2

2

1L

Derivation of Str*ct*ral Stresses according to Zhang'SSZ)

f m @

σ !

Qeometry-

Sheet thic"ness-

Throat thic"ness-

;oint angle-

Weld angle-

Weld penetration rate-

6odel siOe-

t#+ t2aα

β η η = sin α

h#+ h2+ ht 2

m2

f 2

@2

t#

h

σ ! 2#

σ ! 22α

d

aβ #

σ !#

f #

@#m#

h2 h#



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t

1$

Derivation of SSZ '?ample- σS2#)

Simple eam theory-

" m σ ! = σ m + σ b = + 2

t

ffective height-

t = t 2# = a + ηt 2 sin β

sin α

(ine force and moment-

" = " cos' α − β ) − q sin' α − β )m = m + %# [ " sin' α − β ) + q cos' α − β )] − %2 [ " cos' α − β ) − q sin' α − β )]



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t

=

+

&/

Derivation of SSZ '?ample- σS2#)

σ ! 2# = " m

+ 2t " cos' α − β ) − q sin' α − β )

ηt sin β a + 2

sin α

{m + %# [ " sin' α − β ) + q cos' α − β )] − %2 [ " cos' α − β ) − q sin' α − β )]} 2 ηt 2 sin β a + sin α



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− −

=

2 sin α " 2 −2

"

t 2 t # − − σ !

Derivation of SSZ 'S#+ σS22 and σS)

Similarly-

σ !# " #

t #

m# + q# ++

t # t 2 a 2 tan α 2 sin α sin β t #2

σ ! 22

t '# − 2 η )m2 + q2 &2 + 2= −

t # t #

t # 2 tan α

m + q & += −

t 2

a

2 tan α 2 sin α sin' α − β ) 2

t 2



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&2

6SZ Cotch Stresses

Analytic Appro?imation of Cotch ffects in Seam Welds yσsE- SSZ stresses

σ k j = σ ! j ⋅ # + ! ⋅

t j

ρ j

σ"E- 6SZ notch stresses 'appro?imate)

ρ j - Cotch radi*sti - ffective thic"ness

s - 5actor

Basis- .+ !aris+ !. and :rwin+ Q. #$L&. The stress analysis of crac"s >andoo"+

!aris !rod*ctions :ncorporated and Del Research


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&1

Determination of s05actor

σ k j = σ ! j ⋅ # + ! ⋅

t j

ρ j

M0Eointsingle fillet

=verlap Eoint B*tt Eoint M0Eointdo*le fillets

! #./ /.&L /.L& #./



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&&


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Applied5orceAmplit*de5 aICJ

(

&

?ample of 5atig*e Test

/&3

T0;oint 'Al*) 5ail*re criterion-(oad case-(oad angle- / 45/&'

2 loss of stiffness 'piston stro"eU)

that corresponds appro?imately

to crac" initiation

t

/&'

45/&0

?periment

/&0

/&3 /&4 /&( /&6


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AppliedloadinN C7raftamplitudein

MS8-7er"spannungsamplitudeinM9a6SZStressin6!a

M$/5/DQ1/

#N/&

#N/1

M1&5$/DQ$/#N/

M$/5/DQ%/

M$/5$/DQ1/

:AVDQ#//

Sch%ingspiel*ahl N 5

#N/1

M$/5$/DQ1/

:B:DQ%/

:B:,S/%

:B:,S#&

M$/5$/DQ%/

&%


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MS8-7er"spannungsamplitudeinM9a

σ6SZin6!a

σ6SZin6!aMS8-7er"spannungsamplitudeinM9a

#N/

&L

6aster S0C


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N

N

&$

Two Cew 6od*les in !rinciple

SSZ06ethod-

SSZ Stresses

6SZ06ethod-

SSZ Stresses

Cotch 5actors

from 565AT Standard

Cotch 5actors

from 6SZ0Appro?imation

S0C


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/


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#


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Damage-

B*tt;oint(ap;oint B*tt;oint(ap;oint B*tt;ointdo*leM0;oint

do*leM0;oint

do*leM0;oint

(ap;ointTMK;oint TMK;oint TMK;oint

2

Application ?ample on


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Scenario Analysis 'M0;oint+ Single 5illet)

Qood+ Cormal+ Bad Weld 7*ality

!arameter-a0,al*e- a = λ 't # + t 2 ) K 2Weld angle- β = καWeld penetration- η

Defa*lt ,al*e- λ = /+ κ = /+& η = /+

?treme ,al*es-/+& ≤ λ ≤ /+%/%/+1 ≤ κ ≤ /+/+# ≤ η ≤ /+&

d η = sin α t 2 Cormal Weld 7*ality Bad Weld 7*ality Qood Weld 7*ality



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1

Scenario Analysis 'M0;oint+ Do*le 5illets)


!arameter-

a0,al*e #- a# = λ# 't # + t 2 ) K 2a0,al*e 2- a2 = λ2 't # + t 2 ) K 2

Defa*lt ,al*e-λ# = /+λ2 = /+

?treme ,al*es-/+& ≤ λ# ≤ /+%/%

/+& ≤ λ2 ≤ /+%/%Weld angle #-

Weld angle 2-β# = κ#α β 2 = κ 2α

κ# = /+& κ 2 = /+&

/+1 ≤ κ# ≤ /+

/+1 ≤ κ 2 ≤ /+

Cormal Weld 7*ality Bad Weld 7*ality Qood Weld 7*ality



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βη

t 2

&

Scenario Analysis '=verlap ;oint)


!arameter- Defa*lt ,al*e- ?treme ,al*es-

a0,al*e-

Weld angle-

Weld penetration-

a = λt 2 λ = /+ β = 1&°

η = /

/+& ≤ λ ≤ /+%/%/° ≤ β ≤ 1&° − /+2& ≤ η ≤ /+2&

(a ≤ t 2 cos β ) d η =




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Scenario Analysis 'B*tt ;oint)


!arameter- Defa*lt ,al*e- ?treme ,al*es-

Weld width- b = κt # κ = #+/ /+L ≤ κ ≤ 2+/Weld reinforcement- e = λ#t # λ# = / − /+2 ≤ λ# ≤ /+2Sheet offset- ' = λ2 't 2 − t # ) K 2 λ2 = #+/ '−#+/ ≤ λ2 ≤ #+/) PToe c*t depth-

Root c*t depth-

Toe c*r depth-

Root c*t depth-

%# = k #t #%2 = k 2t #% = k t 2%1 = k 1t 2

k # = /+#k 2 = /+#k = /+#k 1 = /+#

/+2 ≥ k # ≥ /

/+2 ≥ k 2 ≥ −/+#

/+2 ≥ k ≥ /

/+2 ≥ k 1 ≥ −/+#

P not a weld @*ality parameter




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!otentials and (imitations of the 6ethod

!otentials-

• The SSZK6SZ method allows weld geometry to e considerede?plicitly in fatig*e assessment.

• 5ail*re locations+ notaly+ at weld root and toe+ are clearly

indicated y the SSZK6SZ stresses.

• Weld @*ality can e eval*ated y scenario analysis in three

classes of good+ normal and ad weld @*ality.

(imitations-

• 6SZ notch stresses are only appro?imations.

• SSZK6SZ method is still not s*fficiently validated in 565AT.

• The relation etween weld @*ality and weld geometry sho*ld e

f*rther verified y e?periment or e?perience.

ZHANG-Æ£ÀÍÄÍ¾ÃÐÔ-3

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