experimental elastic stress analysis of partial penetration welded nozzle

8/16/2019 Experimental Elastic Stress Analysis of Partial Penetration Welded Nozzle

1/14

NUCLEAR ENGINEERING AND DESIGN 7 (1968) 73-86. NORTH-HOLLAND PUBLISHING COMPANY, AMSTERDAM

E X P E R I M E N T A L E L A ST IC S T RE S S A N A L Y S I S

O F P A R T IA L P E N E T R A T I O N W E L D E D N O Z Z LE S

I N A

SPHERICAL SHELL

E P R O C T E R a nd R F F L I N D E R S

Central Electricity Generating Board

Berkeley Nuclear Laboratories

Berkeley Glos. England

Received 12 May 1967

The initial stage of a test programme to investigate, in detail, the behaviour of radial and oblique

nozzle junctions in spheric al s hells , has been completed. Although this stage was designed to invest i-

gate elasti c and elas tic/ plas tic behaviour at ambient temperatu re, this repor t descri bes the elastic

analysis only.

Thre e basic desi gns of through nozzles wer e investiga ted, one of each design mounted radially and

the other at 45 ° obliquity. Four hundred E.R. stra in gauges were fixed on the inner and outer surf aces

of the shell plate and nozzles and optical equipment was set up to measu re t ilt of the nozzles . For t he

purpose of this elastic test the vessel was hydraulically pressurized to 240 psig.

Stres s distri butions in the form of stres s concentration factors (SCF = stres s magnitude divided by

the corres pondin g str es s in an unpiere ed sphere of the same rad ius and thickness) are shown for the

individual nozzle s. Maximum values of SCF and 'equivale nt' st res s are shown plotted against the rati o

of nozzle thickn ess to nozzle internal d iamet er, for both radial and oblique case s.

Compari sons are made with nozzl es designed accordi ng to BS.1500 and BS.3915, and the limit ation s

of elastic design methods allowing limited plasticity are demonstrated and discussed in the report.

1. INTRODUCTION

Opera t iona l in fo rma t ion of p re s su re c i rcu i t

components on nuclear and modern h igh eff ic iency

conventional p lant is s t i l l ex tr emel y l imited .

Ea r ly work a t Be rke ley Nuc lea r Labora to r ie s ,

on model vesse ls conta in ing s tandpipe nozzle

c lus ters and cyl indr lLcal support sk i r ts , provided

a basic unders tanding of geom etr ica l e ffec ts on

vesse l s sub jec ted to p re ssu re a lone and p ressu re

and tem pera tur e combined. However , in order to

modi fy ex i s t ing pa ra me te r s to achieve more

economi cal des igns ,.and to predic t more accura te ly

the working l i fe of exis t ing nuclear p lant , compo-

nents must be s tudied in greater de ta i l .

Throughout the Centra l Elec tr ic i ty Genera t ing

Board much effor t is be ing employed in theore t ica l

s tudies to improve the design of pre ssu re conta in-

ing stru ctu res . The.,~e studie s take into account

long te rm c reep behav iou r a t e leva ted tempe ra -

ture s as well as sho:ct te rm and cycl ic e las t i c /

p las t i c consider a t ions . Through these effor ts

so lu t ions fo r symmetr ica l a t t achmen ts a re be -

coming avai lable . I t wil l , however , be some t ime

befo re a sym metr ic p rob lems can be so lved .

De ta i led expe r imen ta l r e su l t s a re , the re fo re ,

requ i red fo r two ma in reasons :

1) Verif ica t ion of theore t ica l so lu t ions .

2) Predic t ion of the behaviour of typica l compo-

nents which cannot a t present be theore t ica l ly

analysed , ass is t ing both desig ners of fu ture

plant and oper a to rs of exis t ing p lant .

In order to obtain a maximum amount of infor-

mation with res pect to these req uir emen ts , a

ser ie s of tes ts has been in i t ia ted to invest iga te

both short and long te rm behavi our of typical

nozz le / she l l in te r sec t ions . Two des igns rep re -

sentat ive of exist ing plant, and a thir d design,

nominal ly pre ss ure s t rength , to provide a datum

and an indication of very high strain behaviour

are being tes ted . Fro m each design , one nozzle

is mounted r adia lly and a second at 45 ° obliquity.

Although the ves se l and nozzles re pres ent cur-

ren t r eac to r ves se l s ize s , the re su l t s a re , o f

course , appl icable to o ther types of vess e ls .

The f i rs t tes t of the ser ies was designed

p r i m a r i l y t o i n v es t i g at e s h o rt t e r m e l a s t i c / p l a s -

t ic behaviour , with par t icu l ar a t ten t ion being

paid to shakedown effects and the extension of

s t re s s d ie -away as p lac t ic i ty p roceeds . Also ,


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74 E. PROCTER and R. F. FLINDERS

since vir tual ly no exper imental data is avai lable

for s ingle through nozzles with par t ia l p enetra-

t ion welds , a full e las t ic s t re ss analysi s has

been ca rri ed out. Special attention was paid to

the distrib ution of st re ss in the shell plate adja-

cent to a radially mounted nozzle. This part of

the work is described in this report.

2. DESCRIPTI ON OF TES T VESSEL AND

NOZZLES

2.1. Materials

The behaviour of the vessel beyond yield is

influenced by the physical prope rti es of the ma-

ter ia ls as wel l as component geometry . I f com-

parisons are to be made with the full size proto-

type i t i s desi rable to obtain correct re la t ionship

between the var ious mater ia ls , i .e . , shel l p la te ,

nozzle forgings and deposited weld. In the case

of invest igatio ns into creep behaviour this re la-

tionship is also desir able , together with the

abi l i ty to accumulate creep s t ra in in reasona bly

short tes t durat ions .

The material chosen for the test plates was

boi le r plate to BS 1501(1958)-161-C and for the

nozz les , forged bar to BS 1503(1958)-161-B.

Standard tensi le s t rength requirements for both

these materials are 28 tsi rain., 32 tsi max.

Yield s t r e ss r equ i reme nts a re based on min imum

values only, 15 tsi for the plate material and

14 tsi for forged bar. To obtain simi lar it y of

physical proper t ies in the tes t vessel an upper

limit of 18 tsi was specified for both plate and

forged mater ia ls .

The man ufac ture rs ' analy sis for the two ma-

terials was as given in table 1.

Table 1

Plate Forged bar

to BS1501 (1958)- to BS1503 (1958)-

161-C 161-B

C

Si

S

Ph

Mn

Ni

Cr

Mo

Cu

YP

UTS

Elongation

Reduction

of area

0.22%

0.2%

0.02%

0.024%

0.78%

0.1%

0.08%

0.01%

0.12%

17.7 tsi

31.4 tsi

24% on 8 in.

gauge length

0.21%

0.233%

0.038%

0.028%

0.72%

17.15 tsi

31.9 tsi

35~0 on 4~A

61%

2.2. Nozzle weld proc edure s

To obtain reasonable repres enta t i on of the

nozzle welds on the model to those on full size

vessels , sui table weld procedures had to be

developed. Pre l im ina ry work was carr ied out a t

the C.E.G.B. 's N.W. Region R. & D. Department,

us ing f la t p la tes with edge preparat i ons rep re-

sentative of the various weld conditions. As a

resul t of th is work, tenta t ive weld procedu res

were suggested to the vessel manufacturer .

The manufacturers submit ted sect ions through

at least one each of the oblique nozzles, to show

that the specified requirements could be met.

Par t i cular a t tent ion was paid to the hardness and

width of heat affected zones , the hard ne ss of the

deposited weld mater i a l and the angular to ler-

ances .

2.3. Manufacture

The nozzles were posi t ioned in the vess el

such that e las t ic s t ress in terference between

nozzles was nil . Nozzle sections are shown in

figs. 1-3.

Fig. 1 shows the thickest pair of nozzles fit ted

in the vessel . These are nominal ly t rue to scale

of reacto r vesse l s tandpipe nozzles designed to

BS1500, in which design all rein for cem ent for

the opening in the shell plat e i s prov ided by the

nozzle. Fig. 2 shows nozzle s repres ent ati ve of

reactor vessel s tandpipe a t tachments , designed

to BS1500, but where the whole of the upper part

of the vessel is made in thicker plate than re-

qu i red by normal membrane s t re ss ca lcula t ions ,

i .e . , par t r e infor cemen t for the openings is pro-

vided by the nozzle and part by the use of thicker

shell plate. Fig. 3 shows the final pair of nozzles .

I t was desired to design these on a pure pre ssu re

strengt h basi s, i .e. , nozzle thic kness 0.035 in.

Owing to obvious welding pro ble ms the nozzl es

were made ~ in. thick. The radial nozzle is

slightly thicker than that required by BS3915

(t = 0.07 in.) and the oblique nozzle slightly thin-

ne r (BS3915, t = 0.21 in.).

Care was taken before and during manufacture

to ensure that to lerances would be representa t ive ,

a t th is scale , of reactor pract ice . The development

tests indicated that the angles of the oblique noz-

zles could be mai nta ine d within +2 ° . In the tes t

vesse l the max imum deviat ion f rom nominal was

1¼°. The test plate profile was checked by tem -

plates . The maxi mum deviation f rom true shape,

measured over a 4 ft chordal length was 0.050 in.,

and over a 1 ft chorda l length 0.025 in. Thes e

tolerances are wel l wi thin acceptable l imits ,

even when cons ideri ng the scale factor. The noz-

zles were machined to an accuracy of +0.005 in.


3/14

EXPERIMENTAL ELASTIC STRESS ANALYSIS 75

I

~ ]

" 6 8 7 "

W I

/ / ~ 2 .87

.

/ /

r i / / ' / / /

, ' / /

/ •

&

N O Z Z L E 4 ,

t / T = 0 . 6 0 3

~ D i = 0 " 0 1 4 8

~" /~ i = 0° 23 9

- 1 2 5 ~

N O Z Z L E . 2 , .

f

= o o , ,

.328~

/

, 3 2 1 1

N O Z Z L E 5 .

= 0 ' 2 8 7

~

: 0 - 0 1 4 8

~ t = 0 , I 1 4

Fig. 1. Section through nozzl es 1 and 4. Fig. 2. Section through nozz les 2 and 5.

on diam eter . Two holes, ~ in. diam ete r were

drilled through each nozzle wall and located be-

tween the inner and outer fi l led welds (see figs.

1-3). These were to facili t ate leak test s on the

root r uns . Any flaw:3 allowin g leakage rat es

gre ate r than 1 cusec', were rep air ed before fu r-

ther welding. After completion, the nozzle welds

were u ltr ason ical ly examined with the aid of

automatic scanning equipment suppl ied and

operate d by per son nel from C.E.G.B S.W. Region

R. & D. A thick ness surve y on the test plate at

3 in . p i tches , indicated th ickness var ia t i ons be-

tween 1.125 in. and :1.135 in.

3. INSTRUMENTATION

3.1. Slr ain gauges

The strain gauges used were Budd type HE 121,

having ~ in. gauge length and 120~ nominal re -

s is tance. Laboratory tes ts demons tra ted these

gauges to be sa t isfactory for measur ing s t ra ins

up to at least 7% when used with Budd type GA 5

adhesive [1].

The total number of gauges was restricted to

400, by the capacity of the rec ordi ng equipment.

The majority were fixed on nozzles and sur-

rounding plate, in positions chosen to provide


4/14

76

E. PROCTER and R. F. FLINDERS

t

125

N O Z Z L _ _ E _ 3

t / T - 0 " 1 1

¢L~/D. = 0"0148

~ / ~ ( - 0 " 0 4 3 4

"25~

,

Ux S

j / / , 4 s ' ~ N O Z Z L E 6

M ~ / / ~ / T " O ' "

~ - ~ , . . ~ I % ~ = 0 . 0 48

Fig. 3. Section through nozz les 3 and 6.

• INS IDE H OOP/CIRC .

X O U T S I D E H O O P / C I RC ,

i

-p 1 ~ - -

Q O~u'l"SIDE A X lAL/~4EI~I

% - /

2 " 0 1 "O O - I , O

S .C.F .

Fig. 5. St res s dist ribu tions for radial nozzle (No. 1).

L I G H T S O U R CE P R O J E C T I N G

C R O S 5 W I R E I M A G E ,

O P T I C A L L Y F L A T

M I R R O R . ~ . ~ " ~ /

RE CT A N G UL A R S CA L E .

Fig. 4. Diagrammatic arrangementof optical lever

system.

the most economical distribution with due con-

sideration of the information required. Gauges

were provided on both the inner and outer sur-

faces of the vessel and the nozzles. Since high

strain gradients were expected inside the noz-

zles particular care was taken to position

gauges at the expected maximum strain posi-

tions. Gauge positions are shown on the stress

plots in figs. 5-7 and 16-18. The gauges were

fixed inside the nozzles by an expanding mandrel

technique [2].

All strain gauges were connected to inter-

mediate junction boxes by light-gauge double

insulated twin core cable. Multi-core cables

were used for the lead outs from these junction

boxes to the permanent strain recording equip-

ment. The multi-core cables from inside the

vessel were brought through rubber packed seal-

ing glands [3] in the end flanges of the two I0 in.

b o re b ran ch e s . T h e v es s e l w a s t o b e p re s s u r i z ed


5/14

EXPERIMENTAL ELASTIC STRESS ANALYSIS 77

/

•

HOOP/CIRC.

• INSIDEHOOP/CIRC, GAUGE6

X OUTSIDEHOOP/CIRC. • OOP /CIRC.

e INSIDE AXIAL/tVlERID. 't" AXIA L/MER ID.

OUTSIDI.~AXIAL/MERD . ~ + ~

S.C.F'S.

• INSIDE HOOP/CIRC.

X OUTSIDEHOOP/CIRC.

• - IN$1 0E AXlAL/MERID.

,.I-

S.C.F_~_ 2 0 - t

S.C.F.

Fig. 6. Str ess distribut ions for radial nozzle (No. 2). Fig. 7. Str ess distributio ns for radial nozzle (No. 3).

with water , thus the inte rnal gaug es and junction

boxes were waterproofed with a b i tumast ic com-

pound [4].

Since the st rai n ga uges wer e all fixed to a

compara t ive ly sma l l a rea o f the t e s t vesse l ,

which i tse lf was f i l led with water , one compen-

sating gauge only was used. This was attached

to a p la te of the same mat er ia l as the vesse l ,

waterproofed and p laced in a drum of water

a longside the vesse l . To provide a check on zero

gauge drift one further gauge was attached to a

free p la te , waterpr oofed and posi t ioned ins ide

the vesse l and connected to the recording equip-

ment together with the ac t ive gauges . The re-

cording equipment employs a d ig i ta l vol tmeter

with v isual d isp lay and an associa ted pr in t-out

unit.

3.2. Nozzle deflections

Nozzle ro ta t ions or t i l t , re la t i ve to the tes t

p la te , were me asur ed by an opt ica l leve r sys tem.

An opt ica l ly f la t mir ror was a t tached to the end

of each nozzle and, to provi de a datum, to the

centre of the tes t p la te . Individual pro jec t i on

lamps were u sed to re f lec t a c ross -wi re image

on to sca les approximate ly 8 f t be low the mir-

ror s , as shown in f ig. 4. Closed c ircui t te l evi-

sion was used to provide a visual link between

the tes t ce l l and contro l area , thus enabl ing

nozzle ro ta t ions to be recorded remote f rom the

vesse l .

4 T E S T P R O C E D U R E

At zero pressure a l l gauges were indiv idual ly

balanced to indicate zero output from the wheat-

s tone br idge c irc ui t . To e l iminat e the poss ib i l i ty

o f gauge hys te re s i s the vesse l was p re ssu re

cycled severa l t imes between zero and 250 psig .

Gauge readings and nozzle cross-wire readings

were then recorded a t 40 ps i increments f rom

zero pressure to 240 psig and re turned to zero .

Vesse l press ure was indica ted by a s tandard

10 in. test gauge.


6/14


o

Fig. 8. Stress concentration factors inside radial noz-

zles.

• Maximum hoop SCF's

+ Axial SCF's at maximum hoop positions

Q Maximum axial SCF's

M E A N STRESS.

x\

x.

i

• 0 5 , I o

. . . e .. . - - f

l

• 2 0 . 2 Is

Fig. 9. Maximum stress concentration factors for shell

plate (radial nozzles).

Q Inside ci rcumfer ential

× Outside cir cumferent ial

• Inside and outside meri diona l

\

O . 0 5 . I O -1 5 " 2 0 - ;i S

Fig. 10. Equivalent str ess ratios. Radial nozzles.

® Equivalent stres s ratio at maximum axial positions

in nozzle.

• Equivalent stress ratio at maximum hoop positions,

maximum stress in nozzle.

× Equivalent stress ratio on outer surface of plate at

toe of weld

5.

R E S U L T S

5.1. Radia l no zzle s

Recorded s tra in readings for a l l gauges were

plo t ted against pressure up to 240 psig to ver ify

l inea r i ty . S t rain va lues at th i s p re s su re were

plo t ted against respect ive gauge posi t ions and,

f rom these graphs , s t r e s ses ca lcu lated and ex -

p res sed a s s t r e s s concent ra t ion fac to r s (SCF)

based on an expe r imen ta l she l l membrane s t re s s

of 11000 lb/ in, z. Due to the phys ical size of the

strain gauges it was not possible to position the

gauge grid centres closer than 0.15 in. to the

weld /sh el l p la te in ter sect io n , i .e . , the f i l le t weld

toe . Consequently the curves for s t ra in d is t r ibu-

tion along the plate were extended to the weld toe

posi t ion . The 'ex trapol a ted ' va lues were used to

calcula te s t resses a t these poin ts .

The ca lcula ted S CF's ar e shown plo t ted re l a-

tive to posit ions in figs. 5-7. Fig. 8 shows the

maximum hoop and corresponding axia l s t resses

and maximum axia l and corresponding hoop

s t re s ses in s ide the nozz le s , p lo t ted a s SCF's

against the ra t io of nozzle th ickness to in ternal

d iame te r , i . e . , t /d i . The curve showing hoop

str ess es has been extended on the assumption of


7/14

E X P E R I M E N T A L E L A S T I C S T R E S S A N A L Y S I S 7 9

K E Y : -

G & I J G E S .

• H O O P / C I R C .

÷ A X I A L / M E R I D .

[ ] 4 5 °

s , ( ; , ~ s .

• I N SI D E H O O P / C I R C

x O U T S I D E H O O P ] C I I

+ I N S I D E A X / A L ~ M E

O O U T S I D E A X I A L I M |

• I N S I D E M A X . P R IN q

• O U T S I D E M A X . P R I N

~ , I N S I D E M I N . P R I I~

[ ] O U T S I D E M I N . P R I N

f

/

f

\

2 I C

S C . F .

\

O - I

n °

/ J

i

\

I O °1

S . C . F .

S E C T I O N A - A

F i g . 1 1 . S t r e s s d i s t r i b u t i o n s f o r o b l i q u e n o z z l e n o . 4 .


8/14

80 E. PROC TER and R. F. FLINDER S

. K E Y : -

G A U G E S

• H O O P / C I R C .

+ A X I A L / M E R I D .

D 4 5 °

S , ~ . F ' S ,

• I N S ID E H O O P I C I R C .

x O U T S I D E H O O P ~ C l R C .

+ I N S I D E A X l A L I M E R I D .

O O U T S I D E A X I A L I M E R I D .

• I N S I D E M A X . P R I N C I P A L .

• O U T S I D E M A X . P R I N C I P A L .

~ . I N S I D E M I N . P R I N C I P A L ,

D O U T S I D E M I N . P R I N C I P A L .

i

2 I

2

0

I

J

2

d

o i

1 k

I

/ ~ l l , x

f

Q

i

I 0 - I

S E C T I O N A ' A S . C . F .

Fig . 12. S t r e s s d i s t r ibu t ions fo r ob l ique nozz le no. 5 .

S . C . F .

- I


9/14

EXPE RIME NTAL ELASTIC STRESS ANALYSIS 81

K E Y : -

~AUGt~ S

• H O O P / C I R C .

+ A X I A L / M E R I D I O N A L .

a 4 5 °

. s . c . F s .

• I N S ID E H O O P / C I R C .

x O U T S ID E H O O P / C I R C .

+ I N S ID E A X I A L / M E R I D I O N A L .

O O U T S I[ )E A X I A L / M E R I O I O N A L .

• I N S ID E M A X . P R I N C I P A L ,

• O U T S I D E M A X , P R I N C I P A L ,

h I N S I D E M t N . P R I N C I P A L .

E 1 0 U T S I r p E M I N , P R I N C I P A L .

2 I O

$ . C . I ~

2 I

S . C . E

- I

U

I 0 - I

S . C . F .

S E C T I O N ' A A

Fig. 13. Str ess dis tri but ion s for obl ique nozzle no. 6 .


10/14

8 2 E . P R O C T E R a n d R . F . F L I N D E R S

3 ~ :

2.~

\

- - J ' C

~

A X l S ' E '

X - - A X I S ~ A M A X . H O O P S .C , F. IS .

F ' I - - A X I S ' B ' M A X . H O O P S .C . F? S .

• - - A X I S .~ s A X I A L 5 .C , F? S . A T M A X . H O O P S T R E S S P O S I T I O N S .

( ~ - - A X I S ~B * A X I A L S . C , F . ~ .A T M A X H O O P S T R E S S P O S I T I O N S .

I . S A - - A X I S *C * P R I N C I P A L S ~ 'F , ~S . H A V I N G M A X , E O U I V A L E N T S T R E S S

V A L U E .

I .O " 2 L I

•O S • • - ~ " - -

F i g . 1 4 . S t r e s s c o n c e n t r a t i o n f a c t o r s i n s i d e o b l i q u e

n o z z l e s .

x A x i s A m a x i m u m h o o p S C F ' s

[ ] A x i s B m a x i m u m h o o p S C F ' s

• A x i s A a x i a l S C F Ts a t m a x i m u m h o o p s t r e s s p o s i -

t i o n s

@ A x i s B. A x i a l 8 C F ' s a t m a x i m u m h o o p s t r e s s p o s i -

t i o n s

~ A x i s C . P r i n c i p a l S C FT s h a v i n g m a x i m u m e q u i v a l e n t

s t r e s s v a l u e

O ' ~ ' t : . . . . .

" O I " 1 " 2 5

F i g . 1 5 a . M a x i m u m c i r c u m f e r e n t i a l a n d m e r i d i o n a l

S C F ' s a t t o e o f w e l d s ( o b l iq u e n o z z l e s ) .

× ( a C A ) c i r c u m f e r e n t i a l S C F a t A o u t s i d e v e s s e l

• ( a C B ) c i r c u m f e r e n t i a l S C F at B o u t s i d e v e s s e l

® (C rM A ) m e r i d i o n a l S C F a t A o u t s i d e v e s s e l

+ ( O MB ) m e r i d i o n a l S C F a t B i n s i d e v e s s e l

' O S " I O " I S " ~ O . 2 5

F i g . 1 5 b . M a x i m u m c i r c u m f e r e n t i a l a n d m e r i d i o n a l

S C F ' s a t t o e o f w e l d s ( o b li q u e n o z z l e s ) .

y ( ( rC c ) c i r c u m f e r e n t i a l S C F a t C o u t s i d e v e s s e l

[ ] ((~ C D) c i r c u m f e r e n t i a l S C F a t D i n s id e v e s s e l

) . ( (r M c ) m e r i d i o n a l S C F a t C o u t s i d e v e s s e l

• ((Y M D ) m e r i d i o n a l S C F a t D i n s i d e v e s s e l

s t r e s s r a t i o s o f 2 . 0 f o r a p l a i n c y l i n d r i c a l o p e n -

i n g w i t h o u t r e i n f o r c e m e n t , i . e . , t / d i = 0 , a n d 1 . 0

f o r f u l l c o m p e n s a t i o n . S i m i l a r c u r v e s a r e s h o w n

i n f i g . 9 f o r m a x i m u m c i r c u m f e r e n t i a l a n d m e r -

i d i o n a l S C F ' s i n s i d e a n d o u t s i d e t h e s h e l l p l a t e .

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

t h e m e a n c i r c u m f e r e n t i a l a n d m e r i d i o n a l S C F ' s

t o b e 2 . 0 a n d 0 r e s p e c t i v e l y , f o r a p l a i n c y l i n d -

r i c a l o p e n i n g w i t h o u t r e i n f o r c e m e n t , i . e . , t / d i =0 .

N o z z l e t h i c k n e s s e s h a v e b e e n c a l c u l a t e d f o r t h e

t e s t c a s e a c c o r d i n g t o B S 1 5 0 0 a n d B S 3 9 1 5 r e -

s p e c t i v e l y . T h e t h i c k n e s s / d i a m e t e r r a t i o f o r

e a c h c a s e i s s h o w n o n t h e p l o t s i n f i g s . 8 a n d 9

t o i n d i c a t e c o m p a r a t i v e s t r e s s r a t i o s .

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

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

r a t i o s h a v e b e e n c a l c u l a t e d , b a s e d o n V o n M i s e s

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

t o b e z e r o . T h e s e v a l u e s a r e s h o w n i n f i g . 1 0 .

5 . 2 .

O b l iq u e n o z z l e s

S t r a i n v a l u e s w e r e p l o t t e d a n d S C F ' s c a l c u l a t -

e d o n t h e s a m e b a s i s a s t h e r a d i a l n o z z l e s . H o w -

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

n o t b e f i x e d a t t h e s a m e p o s i t i o n . T h e r e f o r e , i n

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

w e r e i n t e r p o l a t e d i n o r d e r t o o b t a i n t h e s t r a i n

c o m p o n e n t s a t t h e s a m e l o c a t i o n .

T h e c a l c u l a t e d S C F ' s a r e s h o w n p l o t t e d r e l a -

t i v e t o p o s i t i o n i n f i g s . 1 1 - 1 3 . F i g . 1 4 s h o w s t h e


11/14

E X P E R I M E N T A L E L A S T I C S T R E S S A N A L Y S I S 8 3

• O - 2 0

, 3 0 I N S I D E ~ ' V I ~ C I' O R ~ A L E

S ~ : £ ' 1 . O

F i g . 1 6 . M a x i m u m a n d m i n i m u m S C F ' s a n d d i r e c t i o n s a t t o e o f w e l d s . O b l i q u e n o z z l e s .

O ~ P E m a x i m u m p r i n c i p a l S C F ' s a t : I i n s i d e v e s s e l

[ ] ~ P E m i n i m u m p r i n c i p a l S C F ' s a t

[ ] ( ~ PF m a x i m u m p r i n c i p a l S C F ' s a t F t o u t s i d e v e s s e l

/h ~ P F m i n i m u m p r i n c i p a l S C F ' s a t F

× f f CA

• f f C B

G f f M A

+ f f M B

8

•0 5 - l O . I 5 . 2 0 . 2 S

~ ;

F i g . 1 7 . M a x i r a u m S C F ' s i n s h e l l p l a t e .

O b L i q u e n o z z l e s .

y f f C C ® O ' PE m a x .

~ E C rC D s e e f i g . 1 5 [ ] ( r p E m i n .

~ k a M C [ ] ( r p F m a x .

O O - M D A O ' p F r a i n .

s e e f i g . 1 6

L ~ q)

~ B

2

O . O 5 - IO - IS . 2 0 , 2 S

F i g . 1 8 . E q u i v a l en t s t r e s s r a t i o s f o r o b l i q u e n o z z l e s .

X a x i s A s e e + p o s i t i o n A [ ] p o s i t i o n E s e e

s e e [ ] p o s i t i o n F f i g .

a x i s B f i g . [ ] p o s i t i o n B f i g .

• a x i s C 1 4 ® p o s i t i o n C 1 5 1 6

p o s i t i o n D


12/14


maximum hoop and corresponding axia l SCF's

inside the nozzles on axial planes through the

majo r axis of the in ter sect ion e l l ipse , p lo t ted

against

t / d i .

In addition SCF's of maximum and

min imum p r inc ipa l s t r e s ses on the ax i s no rma l

to the above are shown, these l att er valu es being

located a t the posi t ion of maximum equivalent

st re ss . In this case the value for the thinnest

nozzle tested is not shown due to the failure of a

gauge. Figs. 15 and 16 show si mil ar curv es for

the SCF's at the weld toes on the inner and outer

sur fac es of the shell plate. In fig. 16 the dire c-

t ions of the pr incipal s t res ses are a lso shown.

To i l lus tra te more c lear ly the posi t ion of the

absolu te maximu m the curves are shown plo t ted

together in fig. 17.

The equivalent s t ress ra t ios ca lcula ted f rom

the above values for both nozzles and shell plate

are shown in fig. 18.

Nozzle th icknesses have again been ca lcula ted

according to BS1500 and BS3915 and thickness

diameter ra t ios shown a t the appropria te values

on the above curves , indica t ing comparat ive

s tr ess ra t ios . In order to inc lude the value for

BS1500 i t was necessary to extrapola te the curves .

6. DISCUSSION OF RES ULT S

6 .1 . R a d i a l n o z z l e s

The max imum s t re s ses occu r r ing a t the rad ia l

nozz les are on the outer su rface of the shell

p la te , a t the weld toe , in the c ir cumfe rent ia l

d irec t ion . For the nozzle tes ted , the SCF' s range

from 1.7 to 1.16 with increasing nozzle thickness.

The re is so me bending of the shell plate, how-

ever , which increases with the reduct ion in noz-

zle thickne ss (fig. 9). Maximu m hoop st re ss ra -

tios inside the nozzles range from 1.61 to 1.03,

i.e. , slightly lower than those in the shell plate

(fig. 8). The mean st re ss in the plate app roxi mat es

to hoop s tress in the nozzle a t the smaller th ick-

nesses .

Fig . 5 , i l lus tra t ing in some deta i l the d is t r i -

bution of st re ss in the shell plate, shows that

the c i rcumfe ren t ia l s t r e s s inc reases smoo th ly a s

the weld toe is approached, while the merid ion al

s tr ess de cre ase s unt i l , a t a d is tance approxim-

ating to nozzle thickness from the weld toe, a

sharp incre ase occurs . Bending s tr ess in the

merid ional d irec t ion is e l iminated a t the weld toe .

The SCF' s shown in f igs . 5-7 i l lus tra te tha t

the maximum stress ins ide each nozzle occurs in

the hoop direction and coincides with the shell

th ickness centre l ine . The s t res ses d ie away

rapidly , dependent upon nozzle thic kness , each

side of the peak. The axia l SCF's produce curve s

peaking at a number of points with a max imu m

value which is compress ive and coincident with

the nozzl e/w eld inte rfac e on the outside of the

shell. Whilst the magnitude of maximum axial

st re ss is dependent on both nozzle thick ness and

weld penetr ation , its position is dependent on

penet ratio n only; as the weld appr oache s full

penetra t ion the maximum axia l s t ress wil l ap-

proach a position coincident with the centre line

of the plate and maximum hoop str es s.

The design of nozzl es a ccor ding to the two

pressure vesse l codes were based on ac tual tes t

p la te th ickness and ambient temperature condi-

tions. The curv es in fig. 9 indicate that the max-

imum SCF's in the shell would be 1.1 for a noz-

zle designed to BS1500 and 1.86 if designed to

BS3915. Fig. 8 indic ates that corres pondi ng

maximum SCF's in the nozzles would be 1.0 and

1.75.

The maximum SCF values for the BS3915 de-

sign are well within the acceptable limit of 2.25

stated in Appendix A of the code. However , fir st

y ie ld does not occur a t the maximum stress po-

sition. Fig. 10 cle arl y indic ates that, ba sed on

Von Mises cr i t er ion , f i rs t y ie ld occur s ins ide

the nozzle a t the maximum axia l s t ress posi t ion ,

i.e., coincident with the centre line of the weld

f i l le t .

For the BS3915 design the maximum equiva-

lent st re ss ratio is shown, on extra polati on, to

be 2.35. Since, in this code, design memb ran e

stress is based on 2 uniaxia l y ie ld s t ress for the

ma te r ia l the p re s su re to f i r s t y ie ld wi ll be ex -

ceeded 1.57 times at design pressure and 1.96

t imes a t proo f t e s t p re ss u re , a s suming thi s to

be 1 .25 t ime s the design value . At tes t pr ess ure

the volume of nozzle mater ia l subjec ted to p las t ic

conditions will be litt le m ore than that contained

with in the shel l p la te th ickness . Plas t ic s t res ses

in the shell plate w ill be contained within a cir cle ,

inscr ibed fro m the nozzle centre of radius ap-

proxim ating to nozzle bore . The l imit ing fac tor

on th ickness of radia l nozzles des igned to th is

code may well be gover ned by welding techniques .

For ins tance , a t four t imes the s ize of the tes t

vesse l , which corres ponds with exis t ing rea cto r

ves se l s , a radia l nozzle would be of the order of

0.28 in. thick w elde d into ~t 4 in. thic k shel l plate.

In the case of BS1500 based on a design stress

of UTS/4 , des ign pre ss ure is of the order of 0 .68

t imes p r e ssu re to f i r s t y ie ld wh i ls t t e s t p re s -

sure , wMch is 1 .5 t im es design value , approx-

ima tes to f i r s t y ie ld.


13/14

EXPERIMENTAL ELASTIC STRESS ANALSYSIS 85

6.2. Oblique nozzles~

In the case of the n ozz les mounted at 45 °

obl iqui ty the maxim um st res ses occur ins ide the

nozz les and not on the shell plate, as in the case

o f rad ia l nozz le s . These max imum s t re s s es a re

in the hoop direction at positions coincident with

the c ent re of the we].d in the outer ob tuse angle.

The SCF's range from 2.91 to 2.1 with increasing

nozzle thi ckness (fi~:. 14). Axial str es se s in the

nozzles on this and the other axes peak at a num-

ber of posi t ions in s imil ar manner to the radia l

cases . The magnitude and posi t ion of these s t re ss

peaks are obviously dependent on nozzle thickness

and depth of weld penetration.

Maximum str ess es in the shel l p la te occur , as

expected, at the weld toes. Fig. 17 ill ust rat es

that, for values of l//di 0 .17 , max imum SCF's occu r

in the merid ional d irec t ion a t the major axis po-

sit ions (fig. 17). Fig. 15 shows that the max imu m

stress d irec t ions a t these posi t ions change from

merid i onal to c ir cumfe rent ia l for va lues of t /d <

0.17. Fig. 14 indica tes that the absolute ma xim um

SCF's would be 2.0 for a nozzle designed to

BS1500 and 2.7 if desi gned to BS3915, which is

in excess of tha t conside red as the l im it ing value

in Appendix A of the code, i.e ., 2.25. Max imu m

shell plate st re ss es would be 1.4 and 1.89, re -

spec tive ly, as shown in fig. 17.

Equivalent s t res s ra t ios ins ide the nozzles and

on each s ide of the sh ell plate , shown in fig. 18

indica tes where f i rs t y ie ld wil l occur in the var-

ious nozzles . The fac t tha t f i rs t y ie ld does not

necessa r i ly occu r a t max imum s t re s s pos i t ions

was endorsed in the la ter p las t ic tes ts . For a

nozzle designed to BS3915 the maximum equiva-

lent s t r ess ra t io is shown to be approximate ly

2 .4, thus design and proof tes t pr ess ure s wil l be

approximate ly 1 .6 and 2 .0 t imes the pressure to

f i r s t y ield , r e spec t ive ly . These max imum equ i -

va len t s t r e s ses a re s imi la r to those fo r the ra -

dial nozzle, although in this case the maximum

SCF is appreciably large r . At tes t pre ssu re the

volume of mater ia l in the nozzle in excess of

yield point will be th:~t contained within lines

drawn, at a distance roughly equal to half the

shel l pla te th ickness , f rom each s ide of the shel l

plate. Pla stic ity in the shell plate will 'be con-

tained within a distance approximating to nozzle

radius from the toe of the weld.

In the cas e of the BS 1500 design the ma xi mu m

equivalent s t res s ra t io wil l be of the order of

2 .15 , thus design press ure wil l be marginal ly in

exce ss of f i rs t y ie ld , while proof tes t pre ssu re

will be 1.61 time s that to cause f irs t yield.

The design of obliquely mounted nozzles is

usual ly based on the ' equivalent ' rad ia l nozzle ,

i .e . , obl ique nozzle th ickness is that ca lcula t ed

for a radial nozzle having a diameter equal to

that of the maj or axis of the ellipse fo rme d at

the intersection of the nozzle and shell plate.

Stre sses have been ca lculated , by the O'Connel l

and Chubb [5] method, for the radial nozzle

equivalent of the BS3915 oblique design for the

te s t vesse l . The max imum equ ivalen t s t r e s s

ratio was shown to be almost identical to the

experimenta l ly obta ined value for the obl ique

case . This therefor e supports the method of

design , by consider ing the 'equivalent ' rad ia l

case .

7. CONCLUSIONS

1. Although maximu m st res ses a t radia l noz-

z le to shel l in tersec t ions occur in the surrounding

shel l p la te , the maximum equivalent s t r ess es ,

based on Von Mises cr i ter ion for y ie ld , occur in

the nozzles at positions coincident with the centres

of the weld fillets. In the oblique nozzle to shell

in ters ect ions the posi t ion of max. s t res s and max.

equivalent s t r ess coincide a t t / d i> 0.] . This is

on the inner surf ace of the nozzle opposite the

outer obtuse weld f i l le t . For th inner nozzles ,

maximum equivalent s t ress occurs on the inner

surface of the nozzle coincident with the inner

obtuse weld fillet , although the peak st re ss posi -

t ion rema ins the same. I t has a lso been demon-

stra ted tha t d if ferent nozzles having s ignif icant ly

different SCF's can have s imilar maximum equi-

valent s t r ess ra t ios . For ins tance in the BS3915

designs the maximum equivalent s t res s ra t ios

are appro ximat ely 2.4 for both radi al and 45 °

nozzles while the SCF's a t the corresponding

positions are 1.75 and 2.7 respectively.

These fac to r s p rov ide p rac t ica l demons t ra t ion

of the l imita t i ons of des ign methods accept i ng

plas t ic i ty but des igned on e las t ic analysis by

al lowing specif ied values for maximum SCF.

2. For both radi al and oblique nozz les de-

signed to BS3915 it has been shown that proof


14/14


test pressure is of the order of twice f i rs t y ie ld

pres sure , a l though the maximu m SCF's are ap-

preci ably differe nt and in the oblique case, the

limi ting design considera tion is exceeded. Since

the volume of material subject to plasticity is

comparatively small, this is quite acceptable by

modern design s tandards for ve ssels subjected to

norm al power plant requi reme nts . However ,

more conservat ive design may wel l be considered

neces sary for components required to have long

fat igue l i fe . Fur ther , to overcome dis tor t ional

problems of welding such nozzles into thick shell

pla te i t may be necessary to increase nozzle

thickne ss beyond the req uir eme nts of BS3915.

3. In view of 1 and 2 above, it is suggested

that the design limit for nozzles should be based

on a max imu m allowable equivalent st re ss, which

occur s inside the nozzle. The acceptable value

may be decided on cons idera tion of the fatigue

life req uir em ent s of the vesse l. For the avoid-

ance of low cycle fatigue the maxi mum allowable

equivalent s t r ess could be determ ined on the

basi s of fir st yield pres su re not exceeding 0.5 x

proof tes t pressure .

Oblique nozzle design, based on the 'e quival ent '

radia l case , appears sa t isfactory provided i t i s

based on maximum equivalent s t ress .

4 . At the shel l p la te surfaces surrounding ra-

dia l nozzles , the meridion al s t re sses , which are

normally considered to decrease as the nozzle

wall is approached, have been shown to increase

near the weld toe to a value approaching the cir-

cumferent i a l s t re ss . This confi rms indicat ions

obtained dur ing reactor vessel proof tes ts ,

although it is not shown by simple thin shell

theor ies .

5 . The mea sure men ts of nozzle t i l t conf i rm

exis t ing information obtained f rom exper imental

and reactor vessel s . Al though t i l t i s smal l a t

design pre ssu res , i .e . , less than 10 minutes of

arc , i t s d i rect ion cannot be predic ted.

ACKNOWLEDGEMENT

This paper is publ ished by permi ss io n of the

Centra l El ectr ic i ty Generat ing Board.

R E F E R E N C E S

[1] A. Grindrod and E. Pro cte r, CEGB Report R D/B/

M.424 (1965).

[2] A. Grindrod and R. P. Fearnle y, CEGB Report RD/

B/M.428 (1965).

[3] K. G Mantle and E. Proc te r, The Eng ineer 209 (1960)

527.

[4] P. H. R. Lane, The Engi neer 204 (1957) 812.

[5] J M. O'Connell and E.J. Chubb, CEGB Report RD/

B/R.585 (1966).

experimental elastic stress analysis of partial penetration welded nozzle

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