WJ_1974_02_s59

8/20/2019 WJ_1974_02_s59

http://slidepdf.com/reader/full/wj197402s59 1/7

Strength of Transverse Fillet W elded Jo ints

Analysis yields a design formu la that is more rational

than the method of treating all fillets as though loaded

in the weakest direction

B Y B E N K A T O A N D KOJI M O R I T A

S U M M A R Y . T h e r e su l t a n t f o r ce o n a

f i l l e t w e l d m a y b e t r a n sve r se t o t h e

ax is o f the

w e l d ,

i n c l i ned to the ax is

o r pa ra l le l to the ax is . The s t ress d i s

t r i bu t ion in the we ld and i t s s ta t i c re

s i s t a n ce va r y m a t e r i a l l y w i t h t h e r e l a

t i ve o r ien ta t ion o f l oad and we ld ax is .

M o s t o f t h e b a s i c in ve s t i g a t i o n s o n

t h e s t a t i c s t r e n g t h a n d b e h a v i o r o f f i l

l e t w e l d s w e r e co n d u c t e d d u r i n g

1920's a n d 1930's (Ref. 1). I t h as

been sh ow n tha t b reak ing loads fo r

t r a n sve r se l y - l o a d e d f i ll e t s w e r e o f

the o rde r o f 40 % g rea te r th an th ose

fo r long i tud ina l l y - lo aded f i l l e ts o f the

sam e s ize and leng th . In th i s pape r

the te r m t ransv e rse f i l l e t w i l l be used

t o d e sc r i b e t h e f o r m e r , w h i l e l o n g i t u

d in a l f i l le t w i l l be used fo r th e la t te r .

A f e w d e s i g n sp e c i f i ca t i o n s (e .g . ,

Ref . 2 ) and des ign m e th ods take

t h e se d i f f e r e n ce s i n t o a cco u n t , b u t

mo st do no t , t rea t ing a l l f i l l e t we lds

a s t h o u g h o r i e n t e d i n t h e w e a ke s t

d i r e c t i o n .

T h e m a i n r e a so n s f o r

n e g l e c t i n g t h e g r e a t e r s t r e n g t h o f

t r a n sve r se f i l l e t w e l d s a r e p r o b a b l y

a n i n t e r e s t i n s i m p l i f y i n g d e s i g n a n d

BEN KATO is Professor and KOJI MORITA

is Assistant Professor in the Faculty of

Engineering, Department of Architecture,

University of Tokyo, Tokyo, Japan.

t h e f a c t t h a t t h e p e r f o r m a n ce o f a

t r a n s v e r s e f i l let w e l d i s co m p l e x .

Recen t l y , i n recogn i t i on o f the re

m a r ka b l e i m p r o v e m e n t i n q u a l i t y o f

s t e e l , e l e c t r o d e a n d w e l d i n g t e c h

n i q u e s , e x t e n s i ve i n ve s t i g a t i o n s o n

f i l l e t w e l d e d j o i n t s w e r e co n d u c t e d t o

o b t a i n m o r e r a t i o n a l d e s i g n f o r m u l a s

(Re fs .

3,4).

Rega rd less o f wh e t he r o r no t one

d i s t i n g u i sh e s b e t w e e n t h e d i f f e r e n t

types o f f i l l e t we ld loads in des ig n , i t

i s des i ra b le to make a s tudy o f the i r

p e r f o r m a n ce . It sh o u l d a i d i n a sse ss

i n g t h e t r u e e f f e c t i ve n e ss o f co n n e c

t i o n s p r o p o r t i o n e d b y co n ve n t i o n a l

m e t h o d s .

In th i s repo r t , the s ta t i c s t r eng th

a n d b e h a v i o r o f t r a n sve r se f i l l e t

w e l d s a r e s t u d i e d t h e o r e t i ca l l y . A n

a p p r o x i m a t e so l u t i o n b a se d o n t h e

theo ry o f e las t i c i t y i s rev iewed and

su p p l e m e n t e d by a n e l a s t i c - p l a s t i c -

s t r a i n h a r d e n i n g a n a l ys i s p e r f o r m e d

n u m e r i ca l l y u s i n g t h e f i n i t e e l e m e n t

t e ch n i q u e . T h e r e su l t s a r e co m p a r e d

w i th ava i lab le tes t resu l ts .

A n A p p r o x i m a t e A p p r o a c h f r o m

t h e T h e o r y o f E l a s t i c i t y

A n a p p r o x i m a t e t h e o r y o n t h e

s t r e n g t h o f t r a n sve r se f i l l e t w e l d s

w as p resen te d by a sen io r w r i te r (Re f .

5), b a se d o n t h e f o l l o w i n g a ssu m p

t ions: :

1 . T he d i rec t s t ress (q ) on the tens i le

face o f the we ld i s un i fo r m ly

d ist r ibu ted (F ig . 1 ) .

2 . The pa t te rn o f the e las t i c s t res s

d i s t r i b u t i o n r e m a i n s u n ch a n g e d

un t i l the b reak ing o f the

w e l d .

3 . B r e a k i n g w i l l o ccu r w h e n t h e

shea r s t re ss a t a po in t o f the f i l l e t

reaches

Cmax.= <*>/£

where <7

T

= the tens i le s t re ng t h o f

th e w e l d m e t a l .

Fo r s im p l i c i t y , a f i l l e t we ld w i t h equa l

legs i s cons ide red .

T h e e l a s t i c s t r e ss co m p o n e n t s i n a

f i l l e t a re exp ressed in a po la r coo rd i

n a t e sys t e m w i t h t h e o r i g i n 0 a t t h e

toe o f the f i l l e t , as shown in F ig . 1 .

The com pa t i b i l i t y e qua t ion i s (Re f. 6 ) .

( f W a 7 * r ^ ) ( ^ T e T ^ l £ ) = 0

(D

T h e g e n e r a l so l u t i o n f o r t h i s e q u a t i o n

is

I =

a

0

log

r +

b

0

r

2

<-c

0

r

2

log

r •

d

0

r

2

e

* a^e

• ( a , r e s i n e ) / 2 ' ( b , r

3

* a ; r-Ub,'r logr)cos9

- (c , re cose ) /2+(d , r

3

tc, ' r- ' .d, ' r log r)sin 9

•

£,( a„r%

b

n

r

n

-

2

•

a '

r

•

b; r- -

2

)cos

ne

• S (c

n

r

n

*d

n

r

n

*

2

-.Cnr-

n

*dnr-

n, 2

)sin ne

n

»2

(2)

W E L D I N G R E S E A R C H S U P P L E M E N T I 5 9 - s

8/20/2019 WJ_1974_02_s59


Tak ing in to acco un t the boun da ry

co n d i t i o n s , s t r e ss co m p o n e n t s a r e o b

t a i n e d f r o m E q . (2) as

=

I S i , i aft

(3)

1

-»M

(y2sinecos(e-t/4)t(e-7r/A))

l i t

sr*

(4 ) q * —

9 — [J2 c o s e s in (e -» /4 ) - (8 - * /4 ) ] « —

j . 3 i .1 d x

r9

~ r

2

36 rarae

- q

(5)

1 -v/A

/2 sin9sin(e-n:/4))

T h e co o r d i n a t e 9 w h i c h y i e l d s m a x i

m u m s h e a r

T

0.

m

ax i s ob ta ined as

f o l

l o w s :

From Eq. (5 ) ,

f^=

:

T

L

£T(

sin6cos

(

6

-'

r

'

A

)

6 1 -* /A

4-cose

sin(e-»/4))=

o

F r o m w h i c h ,

0

= " 7 8 . I n t r o d u c i n g d

-

TT/Q in to Eq. (5).

•^rs max.=/2q(1-t/A) 'sin

2

f/8

The exp ress ion in te rm s o f the ex te r

nal l oadT , pe r one f i l l e t we ld i s

-<=re

max. =

<

1

* /4)- ' (

s in

2

* /8

)( T,/A

w

)

(6)

T h e m a x i m u m s t r e n g t h o f a t r a n s

ve rse f i l l e t we ld i s ob ta in ed by in t ro

duc ing

T

r

0.max.=

ff

T

/ / 3 i n E q . ( 6 ) :

h

m a

x . =

(1 - '

r

^ ) fe in -

2

* /8 )A

v v

f f

T

/ /3

(7)

The ob l ique p lane RP in F ig . 1 wh ich

is no rm a l to the coo rd ina te l i ne

$

=

n

/8 th ro ugh the roo t o f the we ld c an

b e co n s i d e r e d t h e f r a c t u r e p l a n e , t h a t

is , b reak ing w i l l occu r a long the p lane

RP mak ing the ang le 6

- f / 8

w i t h

the shea r face .

Fig. 1

—

Transverse fillet weld

For the case o f the long i tud in a l

f i l l e t we ld the c r i t i ca l sec t ion i s c lea r

ly the th roa t (RQ in F ig . 1 ) . Th en th e

m a x i m u m s t r e n g t h o f a l o n g i t u d i n a l

f i l l e t we ld o f the same s ize and leng th

is

T

l .max. A

w

0-

T

/73

From Eqs. (7 ) and (8),

T,max.

= ( 1 - * / 4 ) ( s i n -

2

* / 8 ) T , .

= 1.46 T,

m

„

(8)

(9)

T h u s , t h e p r e se n t m e t h o d p r e d i c t s

t h a t t r a n sve r se f i l l e t w e l d s a r e 4 6 %

s t r o n g e r t h a n l o n g i t u d i n a l f i l l e t w e l d s

o f the sam e s ize and le ng t h .

Tsrr

1

sxq

^£

^C

JSL

~

AQQ

flhfl

4 0 0

r_d

(a ) TEST SPECIMENS Cin mm.

Fig. 2— Test specimens (Test No. 1)

Compar ison wi th Test Resu l ts

T h e t h e o r e t i ca l p r e d i c t i o n o b t a i n e d

i n t h e p r e v i o u s se c t i o n i s n o w co m

pa red w i t h ava i lab le tes t resu l ts .

O n e t e s t w a s p e r f o r m e d u s i n g sp e c

imens o f the fo rm shown in F ig . 2 (a ) ,

w h e r e s l i ce - cu t sp e c i m e n s w i t h l a r g e

s ize f i l l e ts we re adop ted (Re f . 5 ) .

Mechan ica l p rope r t ies o f s tee l p la tes

a n d w e l d m e t a l a r e sh o w n i n T a b l e 1;

t h o se o f w e l d m e t a l w e r e o b t a i n e d

f r o m sm a l l t e n s i l e t e s t p i e ce s m a

ch ined ou t o f the ac tua l f i l l e ts as

sh ow n in F ig . 2 (b ). The exp e r im en ta l

m a x i m u m s t r e n g t h o f j o i n t s i s co m

p a r e d w i t h t h e t h e o r e t i ca l p r e d i c t i o n

in Tab le 2 . F igu re 3 com pare s theo re t

i ca l and tes t resu l ts fo r the ang le the

b r e a k i n g p l a n e m a ke s w i t h t h e sh e a r

f ace .

A d d i t i o n a l t e s t s w e r e p e r f o r m e d

u s i n g sp e c i m e n s of t h e f o r m sh o w n

in F ig . 4 , cons is t ing o f seve ra l s i zes o f

f i l l e ts and a l im i ted f i l l e t l eng th (Re f .

7). M e ch a n i c a l p r o p e r t i e s of p l a t e s

a n d w e l d m e t a l s a r e sh o w n i n T a b l e

3 . Tes t resu l ts a re com pare d w i t h the

theo re t i c a l p red ic t ions in F ig . 5 and

Tab le 4 . F igu re 5 com par es the max

i m u m s t r e n g t h w h i l e t h e a n g l e o f

b reak ing p lane i s com pare d in Tab le

4 .

In bo th cases , the co r re la t ion be

tw ee n tes ts and theo ry i s qu i te good .

T h e a p p r o x i m a t e t h e o r y a l so se e m s

to be ab le to g ive a good exp lana t ion

fo r the resu l ts o f g roup tes ts c i ted

ear l ie r (Refs. 3 , 4 ) . The resu l ts o f tests

ca r r ied ou t by the task commi t tee o f

A W S S t ru c t u r a l W e l d i n g C o m m i t t e e

shows tha t fo r tes t spec imens o f A

4 4 1 s t e e l w e l d e d w i t h E 7 0 X X t yp e

( b ) T E S T P I E C E S M I L L E D O U T

OF THE WELD METAL (in mm. )

N o t a t i o n „ .

A

W

= I * a = t h r o a t a r e a

a = s / / 2 = t h r o a t

D

P

= e l a s t i c - p l a s t i c m a t e r i a l

s t i f f n e ss m a t r i x

E = Young 's modu lus

H ' = s t r a i n h a r d e n i n g m o d u l u s

I

= len gth o f a f i l l e t

q = u n i f o r m l y d i s t r i b u t e d s t r e ss o n

the ten s i le face o f a f i l l e t

s = size o f a f i l le t

T,

= ex te rna l l oad pe r one long i tu

d ina l f i l l e t we ld

T t = ex te rna l l oad pe r one t ra ns

ve rse f i l l e t w e ld

Af = i n c r e m e n t o f s t r a i n ve c t o r

A* = equ iv a len t p las t i c s t ra in i n

c r e m e n t

<• = Po iss on 's ra t io

rj,,o"

8

,o~

x

'Cfy

=

n o r m a l s t r ess co m p o

nen ts

o-

x

,<r

y

= dev ia to r i c s t ress

a = equ iv a len t s t ress

o-

T

= t e n s i l e s t r e n g t h o f t h e w e l d

me ta l

?

=

i n c rem en t o f s t ress vec to r

T ,r

r8

i

r

xv

= sh e a r s t re ss co m p o n e n t s

<E> = s t ress func t ion de f ined by Eq . (2 )

6 0 - s I F E B R U A R Y 1 9 7 4

8/20/2019 WJ_1974_02_s59


e l e c t r o d e s ,

t he

a v e r a g e r a t i o

of th e

s t r e n g t h o f t r a n s v e r s e f i l le t w e l d s t o

t h a t o f l o n g i t u d i n a l f i l le t w e l d s is 1.56

a n d f o r s p e c i m e n s o f A 5 1 4 s t e e l

w e l d e d w i t h E 1 1 0 X t y p e e l e c t r o d e ' s ,

t h e a v e r a g e r a t i o is 1.45 (F i e f . 3 ). It

h a s a l s o b e e n f o u n d t h a t t he r e s u l t s

o f t he i n t e r n a t i o n a l t e s t s c o n d u c t e d

u n d e r t he a e g i s of the I n t e r n a t i o n a l

I n s t i t u t e

o f

W e l d i n g , i n c o r p o r a t i n g

r e s u l t s f r o m m o r e t h a n t e n c o u n t r i e s ,

c o u l d

b e

w e l l i n t e r p r e t e d

o n the

b a s i s

o f t h i s t h e o r y ( R e f s . 4 , 8) .

A n a l y s i s by t h e F i n i t e

E l e m e n t M e t h o d

T h e a s s u m p t i o n s m a d e

in the d e r i

v a t i o n of the m e n t i o n e d s o l u t i o n a r e

n o t p r e c i s e . In c o n j u n c t i o n w i t h

( 1 ) ,

i t

i s k n o w n t h a t t he d i r e c t s t r e s s o n th e

t e n s i l e f a c e o f th e w e l d v a r i e s a p p r o x

i m a t e l y l i n e a r l y f r o m the to e to the

r o o t . A s f o r t h e a s s u m p t i o n (2) , the

p e a k s t r e s s p r e d i c t e d b y e l a s t i c

t h e o r y s h o u l d b e r e l i e v e d b y p l a s t i c

d e f o r m a t i o n

a s

s o o n

as i t

e x c e e d s

the

y i e l d s t r e s s a n d t h u s a r e d i s t r i b u t i o n

o f t he s t r e s s w i l l o c c u r . W i t h r e s p e c t

t o the t h i r d a s s u m p t i o n , t he b r e a k i n g

s t r e s s s h o u l d b e e v a l u a t e d a c c o r d i n g

t o a n a p p r o p r i a t e f a i l u r e t h e o r y .

I n a d d i t i o n , t he s h e a r s t r e s s a l o n g

t h e a s s u m e d b r e a k i n g p l a n e RP is e x

p r e s s e d a s

-c =, _2i=_£L

s i n 2

r j _ t;

r e C

os 2(3

|3=

5 * / 8

- 9

10)

F r o m Eqs. ( 3 ) , ( 4 ) , (5) a n d

( 1 0 ) ,

t he d i s

t r i b u t i o n o f s h e a r s t r e s s a l o n g the

p l a n e RP is g i v e n a s s h o w n i n Fig. 6 .

T h i s m e a n s t h a t rr fl. ma x. is no t the

m a x i m u m s h e a r s t r e s s a l o n g the

o b l i q u e p l a n e RP. O b v i o u s l y t h i s

r e s u l t c o m e s m a i n l y f r o m the a s s u m p

t i o n

(1 )

m e n t i o n e d a b o v e .

I n s p i t e o f t h o s e s h o r t c o m i n g s , the

p r e d i c t i o n f r o m t h i s a p p r o x i m a t e

t h e o r y ha d s h o w n s a t i s f a c t o r y a g r e e

m e n t w i t h v a r i o u s t e s t s r e s u l t s . M o r e

p r e c i s e s t u d y on the p e r f o r m a n c e o f

t h e t r a n s v e r s e f i l l e t w e l d in e l a s t i c -

p l a s t i c r a n g e is d e s i r a b l e i n o r d e r to

k n o w

h o w

t h i s a p p r o x i m a t e s o l u t i o n

c a n p r e d i c t

t he

a c t u a l b e h a v i o r

a n d

to

a s s e r t the g e n e r a l i t y o f t h i s s o l u t i o n .

F o r t h i s p u r p o s e , a n u m e r i c a l

a n a l

y s i s by the f i n i t e e l e m e n t m e t h o d ,

e x t e n d e d to the e l a s t i c - p l a s t i c - s t r a i n

h a r d e n i n g r a n g e b y P o p e a n d o t h e r s

( R e f s . 9, 10) , is a p p l i e d h e r e i n . A n a l

y s i s is p e r f o r m e d o n the b a s i s o f i n

c r e m e n t a l s t r a i n t h e o r y a n d a n i s o

t r o p i c a n d d u c t i l e m a t e r i a l a s s u m e d

t o o b e y

the vo n

M i s e s y i e l d c o n d i t i o n

w i t h

P r a n d t l - R e u s s

l o a d i n g f u n c t i o n .

T h e p r i n c i p a l f e a t u r e o f t h i s p r o b l e m

l i e s in the e v a l u a t i o n of the e l a s t i c -

p l a s t i c m a t e r i a l s t i f f n e s s m a t r i x

D

p

w h i c h r e l a t e s

t he

s t r a i n i n c r e m e n t

to

t h e s t r e s s i n c r e m e n t of the m a t e r i a l .

D° is g i v e n in R e f s . 9, 1 0 , a s f o l l o w s :

D = - P -

m u l t i p l i e d

b y

( 1 1 )

°x •

r

r

J

.2c, - t f j ^ v e ,

- S f i ^ h :

cr ;

2

* 2 c ,

xy

r S t i - i S L y r -

(SYM.)

A < T = D

P

A 6 , A O = { AO „,AO~y,,&Xxy}

A €

=

{ A €

X

, AGy ,Ar

X

y}

w h e r e ,

2H =2

T a b l e 1 — M e c h a n i c a l P r o p e r t i e s o f P l a t e a nd W e l d M e t a l ( T e s t No. 1)

W e l d m e t a l

P r o p e r t y

Y i e l d point

( UN / c m * )

1

T e n s i l e s t r e n g t h ,

( k N / c m

2

)

E l o n g a t i o n ,

%

Reduc t i on

o f

a rea (%)

S t e e l

p l a te

27.54

45.86

29.0

|_(b)

37.73

47.33

3 7 , 8

56 .1

D4316

T(b )

40.47

4 8 . 2 2

2 8 . 9

4 5 . 8

(a)

D5011

(a)

M e a n

3 9 . 1 0

4 7 8 2

3 3 . 4

5 1 . 0

L

4 0 . 6 7

5 1 . 7 4

3 2 . 9

4 1 . 2

T M e a n

3 9 . 4 9 4 0 . 0 8

5 0 . 2 7 51 .06

33.4 33.2

39.4

40.3

(a) Type of electrode;

D4316 :

low hydrogen type; D 5 0 1 1 ; high cellulose

type,

lb) L - long i tud ina l . T = t ransverse; see

Fig 2(b)

(c) 1 k N / c m

J

= 1 45

ksi

c

2

=

o

x

'

2

• 2

u c - ' o -

y

'

~y

2 ( 1

- l-

2

) (

<s; = 2 c r

x

- o -

y

) / 3

cr

y

'

= ( 2 c r

y

- < T

x

) / 3

d e v i a t o r i c s t r e s s

E = Y o u n g ' s m o d u l u s

= P o i s s o n ' s r a t i o

cr

= Jcr

x

2

• (5-

y

2 _ o-

x

cr

y

3 t

x y

2

= e q u i v a l e n t s t r e s s

H ' = A C T /

A £

P

= s t r a i n h a r d e n i n g m o d u l u s

A

g P

=

l i t ( ( c r

x

' t * o - y ' ) A e

x

* ( o - ^ * < 5 -

x

Hey

3

c

2

• ( 1 - > ) t

x y

A l '

x y

)

= e q u i v a l e n t p l a s t i c s t r a i n i n c r e

m e n t .

T h e c o m p u t a t i o n a l p r o c e d u r e of th e

p r o b l e m is o u t l i n e d in the f l o w c h a r t

o f F ig . 7 . The d e t a i l e d d e s c r i p t i o n o f

t h e a n a l y t i c a l p r o c e s s fo r the s i m i l a r

p r o b l e m

is

g i v e n e l s e w h e r e ( R e f.

1 1 ) .

Fig. 3 — Breaking planes, theory and tests

T a b l e 2 — M a x i m u m L o ad s b y T e s t s a nd T h e o r y ( T e s t No . 1)

Tes ts

T h e o r y

M a x i m u m

load,

kN

L1 L2 L3 M e a n H I H2 H3 M e a n L H

3 0 1 . 8 4 2 8 6 1 6 3 1 9 .4 8 3 02 8 2 3 4 3 . 0 3 1 1 . 6 4 3 3 8 . 1 3 3 1 . 2 4 3 0 7 . 7 2 3 2 9 . 2 8

W E L D I N G R E S E A R C H S U P P L E M E N T 6 1 - s

8/20/2019 WJ_1974_02_s59


r b 1

f

-nSi*

T^

K»

2t

JL.

40

4.

s

b

t

S 5B

S 5 R

5

2 7

9

S 1 0 B

1 0

49.5

16 .5

5 1 5 B

S 1 5 R

1 5

7 2

2U

B:

Basic type elec trod e

,

R:

b=4.5(s*1) . t = 1.5(s*1), s,b

S 2 0 B

2 0

9 4 .5

31 .5

S30B

3 0

13 9.5

4 6.5

S 4 0 B

S 4 0 R

4 0

18 4.5

61.5

fut i le

type electrode

. t. in mm.

Fig. 4

—

Test specimens (Test No. 2)

2.0 +

r a l ' - C m a x .

1.5

. 1 . 0 -

m

— B -—re gres sion curve

o — R f r o m Eq.(4)

a —throat

I — l e n g t h o f w e l d

10 2 0 3 0

a

( m m )

Table 4 — Ang le of Breaking Plane w it h

Shear Face

Speci

men

S5 B

S5 R

S1 B

S15B

S15R

Angle,

deg

21.0

20.5

20.5

21.9

21 8

Speci

men

S2 B

S3 B

S4 B

S4 R

Theory

Angle,

deg

22.0

21.5

21.0

20.5

22.5

Fig. 5

—

Comp arison betwe en tests and theory (Test No. 2)

T h e sp e c i m e n i s m o d e l e d b y

t r i a n

gular e lemen ts as shown in F ig . 8 .

The imp o r ta n t resu l ts ob ta ined a re

co m p a r e d w i t h e xp e r i m e n t a l r e su l t s

a n d w i t h p r e v i o u s a p p r o x i m a t e

s o l u

t i o n i n t h e f o l l o w i n g .

Elastic Behavior

T h e d i s t r i b u t i o n o f p r i n c i p a l

s t resses in the f i l l e t and i t s v i c in i t y in

the e las t i c range i s shown in F ig . 9 .

M e a su r e d s t r e sse s a n d t h o se ca l cu

l a t ed b y t h e f i n i t e e l e m e n t m e t h o d

a r e co m p a r e d i n t h i s f i g u r e . M e a

su red s t resses a re ob ta ined f rom e lec

t r i c r e s i s t a n ce w i r e s t r a i n g a g e s i n

s t a l l e d o n t h e t e s t sp e c i m e n S 4 0 B

men t ioned ea r l i e r (Re f . 12 ) . In the

a c t u a l sp e c i m e n , so m e f r i c t i o n b e

tw ee n the inne r p la te and ou te r p la te

is inev i ta b le , w h i le in the ana ly t i ca l

m o d e l n o f r i c t i o n b e t w e e n t h e m i s

a s s u m e d .

C o n s i d e r i n g t h i s d i f f e r e n c e

o f co n d i t i o n , t h e co r r e l a t i o n b e t w e e n

tes t and theo ry seems to be good .

A n o t h e r co m p a r i so n o f e xp e r i

me n ta l and ca lcu la ted s t resse s i s

g iven in F ig . 1 0 . The c i ted tes t resu l ts

a re take n f rom Re fe rence B . Th is

tes t cons is ts o f tw o types o f spec

i m e n ; one has s l i t s a long the con tac t

faces o f j o ined p la tes as seen in F ig .

10(a) ,

the o the r has jo in ed p la tes

c lose ly in con tac t as seen in F ig .

10(b) .

S t res ses g iven in the f igu re a re

a lso those

at

the load leve l

T=441

kN .

S t r e ss m e a su r e m e n t s w e r e ca r

r ied ou t us ing an ex tenso me te r .

P r inc ipa l s t resses a re shown in the

r i g h t s id e of e a ch f i g u r e , w h e r e m a g -

Table 3

Steel )

platesf

used t

with '

Weld

metals

— Mechanical Properties

B-type

(a

>

electrode

R-type

(a)

electrode

S5 B

S10B

S15B

S20B

S30B

S40B

S5 R

S15R

S40R

of Plates a

Yield

point,

k N / c m

2

33.22

34.30

44.88

44.39

44.59

47.04

47.04

47.04

46.35

44.59

45.77

nd Weld Metals (Test No.

Tensile

st rength,

k N / c m

2

56.25

55.17

57.62

58.80

58.31

59.49

59.49

59.49

56.35

54.19

54.59

2 )

Elonga

t ion,

%

32.4

37.4

21.0

21.0

21.7

19.3

19.3

19.3

17.5

18.5

16.4

\ \

ty

\

\

v

x/8

s^v

§H

{a) B = basic; R = rutile

R

Fig.

6—Shear

stress distribution by Eq.(10)

6 2 - s F E B R U A R Y 1 9 7 4

8/20/2019 WJ_1974_02_s59


n i tudes a re g iven i r respe ct i ve o f the i r

o r i e n t a t i o n .a

x

,

<r

y

a n d T ^ in the

le f t s ide of each f igu re a re the no r ma l

s t r e ss co m p o n e n t p e r p e n d i cu l a r t o

the tens i le face , the no r ma l s t res s

co m p o n e n t p e r p e n d i cu l a r t o t h e

shea r face , and the shea r s t ress

a long tens i le face and shea r face ,

respect i ve ly .

In tes t spec ime n (b) , f r i c t io na l

f o r ce s w i l l b e i n d u ce d w h e n t h e sp e c

im en i s sub jec t to ten s io n ; no f r i c t i on

w i l l appea r in sp ec i me n (a) , bu t som e

a d d i t i o n a l b e n d i n g d u e t o e cce n t r i c i t y

w i l l appea r in th i s case . In the ana ly t

i ca l m o d e l f o r t h e f i n i t e e l e m e n t

ca l cu l a t i o n , h o w e ve r , t h e co n d i t i o n o f

n o g ap b ut n o f r i c t i o n b e t w e e n

con ta c t faces i s assum ed , as seen in

Fig. 8 . The resu l t f rom the f in i te

e lem en t me tho d , F ig . 10 (c ), sh ow s a n

i n t e r m e d i a t e f e a t u r e b e t w e e n t e s t

resu l ts o f (a ) an d (b) , and ta ki ng in to

a cco u n t a b o ve m e n t i o n e d s i t u a t i o n ,

the theo re t i c a l bas is o f the f in i te

e l e m e n t co m p u t a t i o n se e m s t o b e

r e a so n a b l e .

Plastic Behavior

F igu re

11

sh o w s t h e sp r e a d o f t h e

p las t i c zone fo r inc r eas ing load ing

s teps . W he n a ce r ta in load leve l

(T=849 kN) i s exceed ed th e sp rea d o f

t h e y i e l d - f l o w r e g i o n e xp a n d s n o f u r

the r , wh i le the rap id p rog ress o f p las

t i c d e f o r m a t i o n i n t o s t r a i n h a r d e n i n g

range i s obse rved a long a loca l i zed

a r e a ,

w h i ch a p p r o x i m a t e l y co i n c i d e s

w i t h t h e f o r m e r l y p r e d i c t e d b r e a k i n g

p lane .

D is t r ibu t ions o f shea r s t ress a long

the assumed b reak ing p lane RP a re

sh o w n i n F i g . 12 fo r va r iou s load ing

s teps . R

vsults frorr

t h e f i n i t e

:

^ment

method a re g iven in so l id

l i nes ,

fhese

a re d i f fe r en t f ro m the pa t te rn g ive n in

Fig. 6 th e resu l t f ro m the e las t i c

theo ry , and p resen t no s t ress peaks

a t the ends. Ra the r , the y sh ow good

a g r e e m e n t u p t o t h e u l t i m a t e s t a g e

w i th the p red ic t ion g iven by Eq .

(6),

sh ow n by dash ed l i nes in the f igu re .

T h e a b o ve o b se r va t i o n s se e m t o e x

p l a i n t h e r e a so n w h y t h e a p p r o x i m a t e

so lu t io n g iven by Eq . (7 ) can p r ov ide a

sa t i s f a c t o r y e s t i m a t i o n o f t h e a c t u a l

s t r e n g t h o f t h e t r a n sve r se f i l l e t

w e l d e d j o i n t s .

Conclusion

I t h a s b e e n sh o w n t h a t t h e s t r e n g t h

o f t r a n sve r s e f i l l e t w e l d e d j o i n t s

cou ld be es t ima ted by Eq . (7 ) sa t i s fac

to r i l y i n sp i te o f theo re t i c a l sho r t

com ings inv o lved in the bas is o f i t s a r

g u m e n t . A n e l a s t i c - p l a s t i c a n a l ys i s b y

t h e f i n i t e e l e m e n t t e ch n i q u e m a d e

he re in seems to exp la in the reason

w hy the p re d ic t i on by Eq . (7 ) ag rees

w i th tes ts resu l ts and thus to suppo r t

the va l id i t y o f Eq . (7 ) f ro m th e the o re t

ica l s ide .

y>

Start)

fpata

I n p u t

I

—

] P r in t InputJ jataJ

S e t u p Overall S t i f f n e ss

Ma t r i x K

T

4_

Setu p Load Vector F.

Modify

K

T

by Su ppo r t

I C o n d i t i o n

T

S o lve S t i f f n e ss E q u a t i o n

K T - * *

= F

Calcu la te £ . a<T

Determ ine Load Incr em ent — •

Factor,

U

Subrou t ine Inpu t

Subrout ine

D£M(Calculate

D* )

Subrout ine DPM (Ca lcu la te D* )

•Sub rou t ine

QSRM

(Ca lcu la te e lem en t

s t i f f n e ss m a t r i x

K e (

e m

s u p e r p o s e

K

e l e m .

o n K

i )

Subrout ine SOLVE

S u b r o u t i n e LDINCR

Determine Stress, Str a in ,

D isp lac eme nt, e tc . a t th is S tep

<r=<r» ( j * f f ' .

t = E» |j «e

• s

=

s \ i S.

etc. ,

1

Output ResuJisJ Subrout ine PRINT

£ " <r

« » ^ - ~ ~

t

y

e s

1

jt_——

. yes

Stop

Step2>>

' yes

no

..

\

n o ,

— ^ N

<

Output Data Cards

fo r the Next Run

y e s

H 1

N o t a t i o n s .

€

p

= equivalen1 p las t i c s t ra in

e^s p las t i c s t ra in a t the

b e g i n n i n g o f n e c k i n g

f = e q u i va l e n t s t r e s s

0~,

= t ru e s t re ss a t the be g in n in g

o f n e ck i n g

S = d i sp l a c e m e n t ve c t o r

Fig. 7 — Flow chart for computational procedure

T/8

Fig. 8 — Subdivision of the

spec/men

into triangular elements

W E L D I N G R E S E A R C H S U P P L E M E N T l 6 3 - s

8/20/2019 WJ_1974_02_s59


0 t(

20

^ T

Elast ic Range

( T=44t kN )

«-

-->

tens ion

>- -^compression

observed

by Fini te Element M ethod

Fig. 9

—

Distribution of principal stress

L .

J

I ;

(a) Slits Along Contact Faces (b) Plates Closely Contacted (c) Calc ulate d by Finite Elem ent Method

Fig.

10 —

Comparison of stress distributions

985kN

T = 7 7 8 k N

T=840 k N

Ta 849 kN

3 Y i e l d - f l o w R e g i o n

Fig. 11 — Spread of plastic region in a fillet

64-s I F E B R U A R Y 1 9 7 4

Sirain-hardening

Region

6A8kN

5 3 0 k N

319 kN

from Finite Element Method

from Eq.(6)

i

Fig.

12 —

Shear stress distribution ob

tained

by

finite element method

References

1. S p r a r a g e n , W. and Claussen , G. E . ,

S ta t i c Tes ts o f F i l l e t and P lug W e ld s , a

Re v i e w o f L i t e r a t u r e f r o m 1932 t o J a n u a r y

1, 1 9 4 0 , Welding Journal, A p r i l , 1 9 4 2 .

2 . A m e r i c a n W a t e r w o r k s A s s o c i a t i o n

S t a n d a r d f o r S t e e l T a n k s , S t a n d a r d P i p e s ,

Re s e r v o i r s a n d E l e v a t e d T a n k s f o r W a t e r

S t o r a g e , 1 9 5 9

ed . ,

(fo r exam p le ) .

3 . H ig g ins , T . R. an d Preece , F . R., " P r o

p o s e d W o r k i n g S t r e s s f o r F i l le t W e l d s i n

B u i l d i n g C o n s t r u c t i o n , " Engineering Jour

nal,

A I S C , V o l . 6 , No .

1, 1 9 6 9 .

4 .

L i g t e n b e r g , F. K ., I n t e r n a t i o n a l T e s t

S e r i e s , F i n a l Re p o r t , Do c . X V - 2 4 2 - 6 8 ,

I.I.W.,

1 9 6 8 .

5 . K a t o , B . a n d Na k a , T . , " De f o r m a t i o n

a n d S t r e n g t h o f E n d F i l l e t W e l d s , " Jour,

of

the Faculty of Engineering, Un i v e r s i t y o f

T o k y o , V o l . X X V I I I , No . 3 , 1 9 6 6 .

6 . T i m o s h e n k o , S . ,

Theory of Elasticity,

M c G r a w - H i l l Book Co .

7 . Ka to , B . , e t a l . , " U l t i m a t e S t r e n g t h o f

F i l le t W e l d e d J o i n t s , " T r a n s , o f A r c h i t e c

t u r a l I n s t i t u t e o f J a p a n , O c t . 1 9 6 8 , ( i n J a p

anese) .

8 . K a t o , B . a n d M o r i t a , K „ T h e S t r e n g t h

o f F i l l e t W e l d e d J o i n t s , Do c . X V - 2 6 7 - 6 9 ,

I.I.W., 1 9 6 9 .

9 . Pope , G. G. , "T he App l i ca t i o n o f the

M a t r i x D i s p l a c e m e n t M e t h o d i n P l a n e

E las to -P las t i c P rob lems , " P roc . o f the C o n

f e r e n c e h e l d a t W r i g h t - P a t t e r s o n A i r

Fo rce Base , Oh io , Oc t . 19 65 .

1 0 . Y a m a d a , Y „ e t a l , "P l a s t i c S t r e s s -

S t r a i n M a t r i x a n d i t s A p p l i c a t i o n f o r t h e

So lu t i on o f E las t i c -P las t i c P rob lems by the

F i n i te E l e m e n t M e t h o d , International Jour

nal of Mechanical Sciences, Vo l . 10 , No .

5 , M a y , 1 9 6 8 .

1 1 . K a t o , B . a n d A o k i , H . , "D e f o r m a t i o n

Ca p a c i t y o f S t e e l P l a t e E l e m e n t s , " P u b l i c a

t i o n s o f I A B S E , V o l . 3 0 - I , Z u r i c h ,

1 9 7 0 .

1 2 . K a t o , B . , e t a l , "U l t i m a t e S t r e n g t h o f

T r a n s v e r s e F i l l e t W e l d e d J o i n t s , " Trans,

of Architectural Institute of Japan, A u g u s t ,

1 9 6 9 ,

( i n Japanese ) .

1 3 .

B i e r e t t , G . a n d G r i i n i n g , G . , " S p a n -

n u n g s z u s t a n d u n d F e s t i g k e i t v o n S t i r n -

k e h l n a h t v e r b i n d u n g e n ,

Stahlbau,

1 0 ,

1 9 3 3 .

8/20/2019 WJ_1974_02_s59


WRC Bul le t in

No. 184

Ju n e

1973

" S u b m e r g e d - A r c - W e l d H a r dn e s s a n d

Crack ing in W et Sul f ide Se rv ice "

by D. J. Kotecki and D. G. How den

This s tudy was under taken to dete rmine:

(1) The causes of higher-than-normal hardness in submerged-arc welds in p la in-

carbon steels

(2) The levels of st rength or hardness which will not be susceptible to sulf ide-

cor rosion c racking

(3) Welding proc edur es whic h will ass ur e tha t nonsusc eptible welds will be

produced.

Concent ra t ion i s p r imar i ly on weld metal , though some considera t ion to the

weld heat-affected zone is given. The study covered a two-year period. The f i rst

year was concerned wi th a macroscopic v iew of the weldments . In that f i r s t -year

s tudy, some inhomogenei t ies were observed in weldments which a re not obvious

in a macroscopic view of the weldment. It appeared l ikely that these

inhomogeneit ies could affect the behavior of the weldment in aqueous hydrogen-

sulf ide serv i ce . Ac cor dingly , thei r p r esenc e and effec ts w ere invest igated dur in g

the second year .

The price of WRC Bullet in 184 is $3.50 per copy. Orders should be sent to the

Welding Researc h Counc il , 345 Ea st 47th Stree t , New York, N.Y. 10017.

WRC Bul le t in

No.

185

July

1973

" I m p r o v e d D i s c o n t in u i t y D e t e c t i o n U s in g

Computer-

Aided U l t rasonic Pulse -Echo Techniques"

by

J.

R. Frederick an d J. A. Seydel

The purpose of th is p ro jec t , sponsored by the Pressure Vessel Research Com

mit tee of the Welding Research Counci l , was to invest igate means fo r obta in ing

improved charac te r izat ion of the s ize , shape and locat ion of subsurface d is

cont inui t ies in metals . This objec t ive was met by applying computer ized data-

processing techniques to the s ignal obta ined in convent ional u l t rasonic pulse-

echo sy stems. The pr inc ipal benef i t s w ere improved s ignal- to-noise ra t io and

resolution.

The price of WRC Bullet in 185 is $3.50 per copy. Orders should be sent to the

Welding Resear ch Counc il , 345 E as t 47th Str eet , New York, N.Y. 10017.

Documents

WJ_1974_02_s59