BARC 

Steel Containment Vessel 

12

10_ 

'4

2

i'5rtetion Ejfecta not Considered

00 40.00 00.00 120.00 

Vertical Displacement 

Fig.No.'8 Plot of Load v/s. Displacement at ID.No.35
I BARC 

Steel Containment Vessel 

12

10 

Friction Effects not Considered 

2

0 1 1 1 1 I II I - I II 1 I l l l l llI l I MI1ll l llI l l l , 1I| I l l I I 1l III I iii 

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 

Horizontal DispLacement ( Outside ) 

Fig.No.19 Plot of Load v/s. Displacement at ID.No.36
BARC Steel Containment Vessel 

12

10 

t~t11 

00 

S~Friction Effects not Considered 

2 

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 

Horizontal Displacement ( Inside )

Fig.No.% Plot of Load v/s. Displacement at ID.No.36
BARC 

Steel Containment Vessel 

12

.10 

-4 . I,•,Io ,nn. Cnqtsidared

2

10.00 20.00 30.00 4 

Horizontal Displacement 

Fig.No.91 Plot of Load v/s. Displacement at ID.No.37

%; LF 1901.141 1 cfg not Considered 
BARC 

Steel Containment Vessel 

12

10. 

I

'4 

Friction Effects not Considered 

20 

0.00 50 10.00 15.00 20.00 25.00 30.00 35.00

Vertical Displacement 

Fig.No.%ýPtot of Load v/s. Displacement at ID.No.38
Appendix E-3.2

Bhabha Atomic Research Centre 

India

E-207
PRETEST REPORT ON THE ANALYSIS OF STEEL CONTAINMENT MODEL 

(USING COMPUTER CODES TABS/NISA) 

By 

B.KDutta, P.Swami Prasad & HLS.Kushwaha 

Reactor Safety Division, Bhabha Atomic Research Centre 

Trombay, Mumbai 400085 

MODELLING ASPECTS 

The steel containment vessel along with the contact structure is an axisymmetric 

structure, but than the presence of instrumentation hatch. Due to the presence of hatch, 

one needs to model the structure either by 3-D finite elements or by using shell bending 

elements. However, considering the presence of all types of nonlinearities in the 

structure ( geometrical, material and contact nonlinearities), one needs to have very 

small load increments in transient calculations for monotonic iterative convergence. 

However, a 3-D model, with all types of static nonlinearities in the structure and very 

small load increments, requires enormous computational time. Due to limited computer 

resources, it was felt that to complete the present analysis Within a specified time, it 

would be prudent to model the structure by using 2-D axisymmetric elements. This in 

turn means, we are neglecting the effect of hatch. Assuming the effect of hatch will be 

confined to a limited domain, analysis results are valid for the regions away from the 

hatch. However, in our standard plot set, we have not provided the plots which are near to 

the hatch area ( i.e. plot ID 1 to 6 and 39).

In the present axisymmetric model, we have used 8-noded isoparametric elements. There 

are three divisions along the thickness of the containment. There are 180 elements in the 

top head, 101 elements in the flange and top cylindrical region, 24 elements in knuckle 

region, 199 elements in the spherical shell, 426 elements in conical shell and 168 

elements in lower cylindrical shell. There are in all 1098 elements and 4041* nodes in the 

containment model. The contact structure is also modelled with the 2-D axisymmetric 

elements. There is one division in the thickness direction. There are 264 elements and 

1323 nodes in the contact-structure model. 

All the elements in the complete model are well shaped and the maximum aspect ratio is 

below 5. Beside symmetric boundary condition on the vertical plane, the bottom of the 

model is fixed to simulate its welding on the top surface of the ring support girder. The 

mesh used in the present analysis for different zones are shown in figures la to 1c. 

The model geometry is modified, as much as possible, to match with the as-built data 

prescribed in Enclosure-3 of the SNL letter No. SO-95-099 dated Dec.1, 1995. For this 

purpose, coordinates of the nodes on the outer surface of the containment were modified 

to suit the measured average thickness profile. Similarly, gap between the containment 

model outer surface and the inner surface of the contact structure was adjusted to match 

the measured average values. This gap varies from 15 mm near the top of the knuckle to 

23 mm at the end of spherical shell. The average gap in the conical shell is around 23.5 

mm.

E-209
DESCRIPTION OF THE USE OF NUPEC TENSILE DATA

In our model, the different tensile test data were used for different zones of the 

containment. Average values of Engineering Stress-Strain data were calculated using four 

sets of data provided for every zone ( Table 4 to 15 of SNL letter dated July 10, 1995). 

The plots of these data as used in our analysis for different zones are shown in figures 2a 

to 2c. As we have used Total-Lagrangian formulations for considering material and 

geometrical nonlinearities, Engineering Stress-Strain data has been used instead of True 

Stress-Strain. 

FAILURE MODEL 

As in our analysis only material flow is considered as per one dimensional stress-strain 

material curve, failure model (i.e. collapse pressure) purely depends upon the attainment 

of maximum equivalent plastic strain. We have computed average equivalent plastic strain over the thickness of the containment model at various cross sections. The collapse 

pressure is determined, when the average plastic strain exceeds the maximum equivalent 

plastic strain in stress-strain material curve. In the present analysis, weakest cross section 

has come out to be the junction between knuckle and the top head. 

MODELLING OF CONTACT BETWEEN SCV AND CS 

The contact between the SCV and CS and its progress at different elevations are 

important considerations in the present analysis. The contact between the SCV and CS at 

different regions is established once the perpendikular gap between the outer surface of 

SCV and the inner surface of CS is zero while increasing the internal pressure. Necessary 

Gap elements are employed to consider this effect in the present analysis. The Gap elements model the transfer of forces in the normal and tangential directions at those 

regions of the SCV and CS which are making contact. The tangential forces depend upon the friction factor between the surfaces. Due to the alisence of any realistic friction factor 

value, no attempt has been made in the present analysis to consider this effect. 

SAMPLE RESULTS 

We have incorporated with this report some sample results obtained through our analysis. 

Figure 3a shows the progress of deformations of the top head along with the top cylinder 

and knuckle. This figure demonstrates the large vertical deformation of the crown before 

the attainment of collapse pressure. Figure 3b shows horizontal displacement of a point 

with the increase in internal pressure. The point is on the outer surface of the top head at 

an elevation 10 cm above the junction between top head and top cylinder. This history 

shows that, this point initially deforms inward upto a pressure of 12 MPa and then starts 

deforming rapidly in the outward direction with the further increase in pressure. Figure 3c 

shows the contours of equivalent plastic strain at an internal pressure 11.5 MPa near the 

junction between the top head and the knuckle. 

E-210

V1I
A DISCUSSION ON THE POTENTIAL FOR BUCKLING OF HEAD REGION 

In the present axisymmetric model, it is not possible to obtain the buckling modes, which 

are essentially asymmetric. However, possibility of inplane axisymmetric buckling can be 

checked through the present analysis. A plot of horizontal displacement of a point 10 cm 

above the junction between the top head and the top cylinder (i.e. Fig. 3b) , shows snap through type of deformation behaviour of this point. This may indicate possibility of a 

buckling of this region at higher pressure. 

OCCURRENCE OF FIRST YIELD OF SCV AND FIRST CONTACT BETWEEN 

SCV AND CS 

It is seen from the present analysis that first point of the SCV which experiences yielding is on the inner surface of this SCV at an elevation 3360 mm at a pressure 2.0 MPa. 

Similarly the first point at which contact is established with CS is a junction point 

between knuckle and top spherical shell at an elevation 3375 mm at an internal pressure 

of 3.5 MPa. 

DISCUSSION ON EXPECTED PATTERN OF CONTACT PROPAGATION 

The contact between SCV and CS establishes at multiple points during the pressurisation 

of SCV. These points lie at various regions of the SCV. In figure 4a the SCV is divided 

into seven regions to facilitate this illustration. The following Table identifies different 

regions designated from A to G and the elevation and the pressure at which first contact is 

established in each of these regions. Figure 4b shows the propagation of these contacts as 

a function of internal pressure. 

REFERENCES 

1. NISA H, Numerically Integrated Elements for System Analysis, Ver 92.0 

2. TABS - Finite Element Code for Thermo Plastic Analyis of Bending Structures, by 

BI.KDutta, I-LS.Kushwaha.

E-211
E-212

ii

Region Description of Region First Contct in the 

Corresponding Region 

Locaton From Location To At Elev. At Pres. 

(mm) (•Pa) 

A Bottom Lower stiffener 820 9.3 

(Z = 500 mm) (Z = 921 mm) 

B Lower stiffener Material change 1380 6.1 

(Z = 921 mm) interface 

(Z - 1579 mm) 

C Material change Middle stiffener 1820 4.5 

interface (Z = 2079 mm) 

(Z = 1579 mm) 

D Middle stiffener Weld line in the 2195 5.7 

(Z = 2079 mm) upper conical shell 

(Z = 2275 mm) 

E Weld line in the Junction at 2370 4.34 

upper conical shell spherical shell and 

(Z = 2275 mm) upper conical shell 

(Z = 2694 mm) 

F Junction at Upper stiffener 2760 8.1 

spherical shell and (Z = 2893 mm) 

upper conical shell 

(Z = 2694 mm) 

G Upper stiffener Junction at knuckle 3245 6.5 

(Z = 2893 mm) and spherical head 

(Z = 3377 mm)
L 

t 

0* U 

z 

U. hi 

C U 

I.

C I

C 

g 

g.

E-213
06' 

W 

.16

E-214

rII
'0
600 I I I I I 

I I 

I I 

I I 

I I 

II 

-I- Iiii

L-----------L------------I L I I 

I I I

----------------

0.05

Lo ation- 1 

Lopation-2 - -0-4-o-Le,-tien---3-- - r 

Loation-4 

Location-5 

II 

II 

II 

I!

I I I 1 I. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 

0.10 0.15 0.20 0.25 

Strain

Stress - Strain Curves 

the Present Analysis

for Locations 1-5 Used in

550-

500 

(I)

I,.J 

i-.

450-

400 ,,, 0.00

Fig.2a

r - - - -r - -

I

I

I I 

I 

I
600

550

L

- / 

r

L

* I

"I1- .1 . I 1 I I I I I I I I I I I I I I I I I I I I I I I 1 i 

0.10 0.15 0.20 0.25 

Strain

Stress - Strain Curves 

the Present Analysis

for Locations 6-10 Used in

II I 

0

500

L. 

.4-I

r,.

450-

rn-ua-s- Lo;ation-6 

Lo ation-7 

*--Lopation-9 

Location-lO 

I

400-, 0.05 0.00 0.05

Fig.2b

I II I I I II I I

- I 

- I 

- I

I

I

I

I I 

I 

I
750, 

S700" 

0) 

(D

Strain

Stress - Strain 

the Present An

Curve for Location-1 1

alysis

Used in

L L - - -- -- - - - L - - - - - - L - - - -- 

r - - - - r - - - -I - - - - -

I ~II 

I ~II 

I ~II 

I ~II 

I ~II 

I I II 

I I II 

.I I -- ' I•1 I I II! 

I I /I I II /III ' -I 00

Fig.2c

I I

I

I I

I I I
i,,,t ,

FIGJ.A PROGRMS OF DEFORMATION OFSCV HEAD WITll PRESSURE
Uif 

0~ 

W 

(I) 

.-J 

Z 

I-Z 

Z i~i 

z 

m 

0 

0

15

10

5- -L

I I1 1 1 1 1 1 1 I I I I I I I I I 1 1 * 1 I * * 1 . 

-8 -6 -4 

HORIZONTAL DISPLACEMENT (mm)

- 2 J I I I - o -2 -0

Plot of Horizontal 

Top head Outside Displacemen 

at elevation

t of a point 

of 3842 mm

t1

I

I

rJ Ill 

-10 II II II

Fig.3b on

I 

II 

II

-- I 

-- I L I

t•
MAY/29/95 17:34:16 

ty

PIG.3C PLASTIC STRAIN C0ONTOURSflNEAR KNUCKLE-HEAD JUNCTION AT I ISMPa PRESSU1RE

rn

ROTXc 

0.0 

ROTY 

0.0 

ROM s 

0.0

EQ. MLAST. STRN. 

VIEW i 0.M09078 

RANG83 0.2160327 

0.1920 

0.1440 

0.1200 

Mot1 

7R-02 

0.0
F

4-1 

FIGURE 4v IDENTIFICATION OF RIEGIONS IN SCV TO ILLUSTRATE PROGR US OF' CONTACT
-' 14-4

"-'11 

or) 

lz 7 

0 

0

5II. I I

A

-,---------------- I

1ibbb'l I I I

S 

C

a

D

II I a I I I I a I I I I IJ I i I 1 

1500 2000 

VERTICAL ELEVATION

S

E

2500 

(mm)

F

SI II

S

* S 

_. 

*

gi l l 

3000 lIIII

Progress of Contact of SCV and CS with Pressure

15

- S 

U S 

U S 

U

,m1

Fig.4b

III 

3500

B

a

500 I
AppendIx - A 

Standard Output Plots

-224
PLOT ID = 07

III I 

III I 

III I 

III I 

III I 

I. III 

IIII 

r- r 

IIII 

II 

II 

I 

II

0.08 

0.06

-1

-- -- -

I.

6.0 

CONTAINMENT INTERNAL

-I

9.0 

PRESSURE

Plot of Maximum Principal Strain at top of the Containment

-I

z 

SO0.04

0.02 

0.00

r

0.0

-- _L I

I I I I

I

I

I

I

I

I
PLOT ID

0.000

-0.005+

-0.010-

-0.015 +

-0.020 

-0.025 , 0.0

- - - - - - -- - - - - -- - --

L

-- -- - L--------L

-~L

-~L

-LI

-LI

3.0 6.0 

CONTAINMENT INTERNAL

I 

L

9.0 12.0 

PRESSURE (MPa)

I I 

L--------I 

I I 

I I 

I I 

I I 

I I

15.0

Strain at 0.48

= 08

t1 z 

1;;

I I 

I

I

I

b I I 

I 

I 

I

I I 

I 

I 

i

I I 

I 

I

I

I

I I

I I 

I 

I 

I

I I 

I 

I 

I

I I I I

I I I

I

m

I I I I 

I

Plot of External Hoop m f rom top
PLOT ID - 09

0.020 

0.015 

z 

S0.010 

0.005 

0.000

- - - - L L - - -- L / L --------- L.......

r -I

-

6.0 

CONTAINMENT INTERNAL

9.0 12.0 

PRESSURE (MPa)

Plot of External Meridional Strain

I I 

I I 

I I 

I I 

I I 

I I

-4

0.4

I

I

I I 

I

I L

- r

!

I

I

I

at 0.48 m from top
PLOT ID

-L - - - - LL

0.05 

0.04 

0.03

L---------

--------- L -L 

I,

I I 

I I 

I I

L -_ 

I

lii 1311 1 1li t •1 I II II II I l III Iii I I 

9.0 12.0 

INTERNAL PRESSURE (MPa)

Plot of Internal Meridional Strain at 0.48 m from top

= 10

L

z 

I

(/)

-L

tz3 

00

0.02 

0.01

0.00

0.0 I I II I III Ili i Il l I |1 U I 1I I I II Il I l |[I I 3.0 6.0 

CONTAINMENT

Illl l III I I1I 

15.0 1

L L - I 

- I 

- I 

- I

I

I

I

I
0 

If 

I I I 

I I 

I I 

EL 0 

- -- - -- - - - - -- -- ( 0ý 

I I l i _I I 

----------

I- I I -

oo -j 

II I 

I a 

I I 

< 

ui 

- - - - -

Iz 0 

I I I 

00 0 

------- -j - - - --S-- -j -- - - - --

E-229
PLOT ID

I.

I I I 

I I I 

L L 

I I I 

I I I

- - - - r - -

3.0 6.0 

CONTAINMENT INTERNAL

I I 

I I 

I I 

I I 

I I 

I I 

I I 

-I 

I I 

I I 

I I 

I I 

I I 

I I 

- I

-- r9.0 12.0 1

PRESSURE (MPa)

Plot of Internal Meridional Strain at Z

= 12

0.04 

0.03

0.02 I.

w (/)

0.01 

0.00

0.0

I

I

I

I

I

I

p m :

f

I I 

I 

I

= 3.47 m
PLOT ID

0.010 -

0.005 -

0.000

JI

I

-0.005 -- I--

-0.010 0 I3I.I0III III1I l l 0.0 3.0

-I

6.0 

CONTAINMENT

I

- I 

-r - I

I I . I I I I 1 5 11 1 11 1 I 1 I I'11 

9.0 12.0 

INTERNAL PRESSURE (MPa)

15.0

Plot of External Meridional Strain at Z = 3.32 m

= 13

z 

LI, w

I I I I . . . . . . . . = •=" ,i m Hi . . . . . . . . . . . . .

I I 

I

I

I

I

I

I

I I 

'I 

I 

I 

I
0 

II I, I 

-- I I I 

I I I I I .E 

," -.---- - L.o- , . . . ..- ,.,- 

II \ I 

Iy

I_ .J . ._LL.I 

II \ I 

II I \ 

1 LL 

II II 

II II ' 

II II 

z L 

, , , , , , , , , , I,, , , , , , , )•

L- - -

I - - - - L - - - - J - - - -L - -

0 0 

0 5 0 i 0 

I I 

NIVýIIS 

B-232

1!
PLOT ID

/L

-t -

3.0 6.0 

CONTAINMENT

0.02 

0.01

INT EIRII III 

INTERNAL

I I I I 1 I I I I I I I I I 1 I "1 I I1 I1I II I I I I I 

9.0 12.0 15.0 

PRESSURE (MPa)

Strain at Z = 2.10 m

= 15

tJ w 

w

z 

(/I

0.00

-0.01

0.0l l i l i I i l l l l l i I I I I

L

-I 

- I

Plot of Externa]l Meridional
-

-

--

-

--

- -----------

Ij 

I I 

I I 

I I 

I 

I

-I a I a I I I 1 1 r I I L0 

C5

NW8~1S

5 1 1 1 1 1 I 1 1 

f

0 

C9

C 

I0

'ii 

a.c 

z 

-I

- z 

z 

6 z 

-0 

-o

5:

0

E-234

11

(0 

1

II

0 

-j

LC) 

9 0

0 

11. 

N 

cj 

.7 

0 

c 0

III

-------- --

III

IIIII

I

I

I

I

I

I

IIII

I

I

I
PLOT ID = 17 

0.03 

COTIMN INTRA PRSSR I I 

Plo of Exera StanaZ 16 Ieiioa 

I ~~IIII 

I ~~IIII 

I II II 

I I 

I I 

COT IMN INERA PRSSRE(M 

Plot of External Meridional Strain at Z = 1.60 m
PLOT ID

-

0.008 

0.006 

z 

S0.004 IU) 

0.002 

0.000

1 6.0 

CONTAINMENT INTERNAL

9.0 

PRESSURE

I

12.0 

(MPG)

15.0

Plot of Internal Meridional Strain at

= 18

t1 

'JJ 0'

I I 

I I 

-. L 

I I 

I I 

I I 

I I 

I I 

I I 

I 

I

3.1

I

I

I

I I 

I I 

I I 

I I 

I I 

I I 

I I 

-I 

I I 

I I 

I I 

I I 

I I 

I I 

L .l 

I I 

I I 

I I 

I I 

I I 

I I 

-I 

I I 

I I 

I I 

I I 

I I 

I 

I

II

I

I

I

I

II

I

I

I

I

I

I

I

I

Z = 1. 60 m
PLOT ID

I I 

I I 

I I 

I I

0.000 

-0.005 

-0.010

0.0 3.0

L 

L

51111 I 1111111I11I11I11I I 11I 1 I III I 

6.0 

CONTAINMENT INTERNAL

I I l I u.. II I I EEI I I |I 

9.0 12.0 

PRESSURE (MPa)

Strain at Z = 0.80 m

= 19

L

z 

t..) I-- w 

-J

-0.015

15.0

I I I S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . i J

L

I • I

Plot of External Meridional
PLOT ID

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I

I ~II 

I ~II 

I ~I 

I ~II 

I .I 

I ~II 

I ~II 

I ~II

0.03 

0.02 -

- L--------------L 

I I

IlllllihIllllI0 3.0 ,II1I1 uI .I i .

6.0 

CONTAINMENT

* II I IlIl III * *IIiiII III * I* *i.

INTERNAL

L

; I I I . . I. . . .I . . 

9.0 

PRESSURE

12.0 (MPa) 15.0

Plot of Internal Meridional Strain at Z = 0.80 m

= 20

--------

z 

a:: 

I. 00 C,-)

0.01

0.00 II 

0.0

I I 

I 

l 

I 

I 

i
PLOT ID = 21

I I

LL L. 

I I I

0.010 

0.008 

0.006

L--------L 

I I 

I I 

I I I I 

I I 

I I 

I I 

I I 

S I

L - I

L

--------------------------------------------------------------------------------- L

L. L

-, - --- I - I

3.0 6.0 

CONTAINMENT

9.0 12.0 15.0 

INTERNAL PRESSURE (MPo)

Plot of External Meridional Strain at Z = 2.49 m

-------------------------- - -- -

tp z 

I--

0.004 

0.002

0.000 I I 

0.0

I I 

I 

I 

I

I I 

I

L

I I 

I 

I

I

I

I

L

I I 

I 

I
PLOT ID

L ---------- L

L -I 

I I/

0.010 

0.008 

0.006 

0.004 

0.002

L-------L 

--------

S-.......L 

I ,I I

L - I

I I 

I I 

I I 

I I 

I I

-, ... ... .... . I * ***~**s . I . ... .. ... ......... I I ............... I i

.I 9 I .I . I III . .! . 1 . . vI II 1I I I I I II II1 1 51 I a I III I II I I I ) 3.0 6.0 9.0 

CONTAINMENT INTERNAL PRESSURE

Plot of Internal Meridional Strain at Z = 2.49 m

= 22

L ---------- LL ------- L

0

z

I

- I 

- I

0.000

12.0 

(MPa)

15.0

-- - - -- - - - - - -- - -- - - - - - - - - - - - - - - - - - - - - - - - - -

I I 

I 

I 

I

I I 

I 

I 

I

I I 

I 

I 

I

I I 

i 

I 

i

I I 

I 

I 

I

I I 

I 

I 

I I

I I

I I I 

I 

I 

I

I I

I

I

I

I I 

I 

J,

I I 

I 

I

I I 

I 

I

I

I I 

I 

I 

I

0.C
PLOT ID

I I I 

I I I

0.03 

0.02

---------------------------------------------- L L

I I I I I I I I I 1 I 

9.0 

PRESSURE

- I

12.0 15.0 

(MPa)

Plot of External Hoop Strain at Z = 2.49

= 23

L I

46'

z 

I

(I)=

L _ 0.01

0.00

) 3.0 SI I I I I I I I I I I I I I I I I 

6.0 

CONTAINMENT INTERNAL

m

I i

I

rI

0.(.
.PLOT ID = 24 

0.03 3. 0. .. 0. .. 0. . . . 0.. . 0 C N I EI P I 

I H I Z I III II 

I I 

I! I II 

0L.-----------

COTIMN INERA PRSSREIM 

Plot of Internal Hoop Strain at Z = 2.49 mn
PLOT ID

0.001 -------------

0.000 L - L

I I 

I I 

I I

• L 

L

SI I 

SI I

12.0 15.0 

(MPa)

-T..............I

6.0 

CONTAINMENT INTERNAL

I I I I I1 I II 

9.0 

PRESSURE

Plot of External Meridional Strain at Z = 1.45 m

= 25

L I 

z 

FL?1 

w

-0.001 

-0.002

0.0 3.0

- I 

- I

I. I ' '
PLOT ID

0.002 

0.001

0.000 -

-0.001 -

I I I 

I I I

--- L- --

-- F

-0.002 ,,,m,,,,,,,,,,r, 

0.0 3.0

Plot of Internal

LL L 

I I I

I I 

II 

II 

II 

II 

I--

III I 11 I I II 1 IIII 1I1IEE 11 E11 IjIl I I ~ I I IIII 

6.0 9.0 

CONTAINMENT INTERNAL PRESSURE

Meridional Strain at Z

12.0 

(MPo)

15.0

= 1.45 m

= 26

71

z 

I

(I)

- I 

- I

I I 

I

I
I I I

I -

- -I

I. 

---------------------------- I.........

I------------------------------------

I I

I I I I I I I I II I I I I I I I I I I I I I

C04 

0 

0

0

0

NIV81S

- U) 

-z 

cLZ 

-( z 

- I

-z 

0 

-0

0 

0 

0

6

E-245

0 

E

II 

0 n

0 

0 

L.i 

0 

04

0 

0-

rt) 

0 

0

i -

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I I

I

I

I

I I

I I

_1 I

I

I I

I
PLOT ID

0.03 - - - - - - - - - - - - - - - -

I.

-Il- - - - -l - - - - -. - .. -l.. ... ... .. .....

3.0 6.0 

CONTAINMENT

II INITINAL 

INTERNAL

*i II i II II 

9.0 

PRESSURE

#IIi III II 1111111 11i 3 1 

12.0 15.0 

(MPG)

Plot of Internal Hoop

= 28

-----

*----------

171

z 

U)

0.01

0.00

0.0

= 1. 45 m

ll l l ll ll l l lll l 1 S. . . . . . . . . . . . . . . lllL . . . . . Jill IIIJI

L - -L-_- - -

I II 

III 

III

L

Strain at Z
PLOT ID

0.015 

0.010 L 

L

" LI

L,

11I D I3.041 |1 ~3.0 6.0 

CONTAINMENT INTERNAL

~IVjii - II I I I lI ii .. .. .

I I I I a I I I I I 1I 

9.0 

PRESSURE

Plot of Internal Meridional Strain at Z

= 29

-, 

SI 

SI 

SI 

SI 

SI 

SI

rn

z 

I-(.n

0.005

0.000 12.0 

(MPa)

15.0

L

L L

I I 

I 

I 

I

I

0.{

= 3.13 m
PLOT ID = 30 

0.03 - -------------------------------------- I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

0.02--------- L.--------- ---. - -

0.01 I L -L 

0 . ilII 0 I I il I I o lII II II IV I II[ s I ip4 p llII II II 

z /iII III 

- III 

0.0 3.0 6.0 9.0 12.0 15.1 CONTAINMENT INTERNAL PRESSURE (MPI) 

Plot of Internal Hoop Strain at Z = 3.13 m
PLOT ID = 31

0.010

0.008 --------- L ---------- L-.

0.006

0.004

L

I I 

I I 

I II 

I I 

I II 

I I 

II , -I

L

0.002 -------- L j I

0.000

L---------------I 

I I

L--------

I I 

I I 

I I

L---------------I 

I I 

I I 

I I 

I I 

I I

6.0 9.0 12.0 

CONTAINMENT INTERNAL PRESSURE (MPa)

15.0

Internal Meridional Strain

Ibi

z 

i

Lfl

I I

I I

I I 

I

I

I

I

I I

I I I 

I I

I

I I

I I I 

I I

I

I I

I I I I I

"1 I 

I 

I

I I I

I I I I

I I

I I

I

Plot of at Z = 2.49 m
PLOT ID

I I I I I 

I I I I I 

I I I I I 

I I I I I 

I I I

I I 

I I I 

I I

I. 

L.

I1I111 I II I III 111111llli I ITF 

6.0 

CONTAINMENT INTERNAL

9.0 

PRESSURE

-I

IiI IlI III I I I I 11 

12.0 15.0 

(MPa)

Plot of Internal Hoop

= 32

0.03

0.02

Ibil z 

I

C,)

0.01

0.00

3.0

I I I I I E I I E I B I m g I I -- --------------

I 

L - - - - - -

I I 

L. - - - - L

L. L_

I I II 0.0 r

Strain at Z = 2.49 rn
I I - - - - - - -

-' -' F' -

U.UuU 

-0.001

-LI

L. -----

I ft 

I I' 

I I 

I I 

I I 

I I 

I I 

I I

I I I I I I I I I I I I I I I I I I I I I I I IV TI I 

3.0 6.0 

CONTAINMENT INTERNAL

I I I I II I I I 

9.0 

PRESSURE

Plot of Internal

0.001

PLOT ID = 33

z 

I

LI)

L

-0.002 C 12.0 

(MPa)

15.0

I l l 'II I l l

- - - - - - - - - -m - -m --

I

L---------------L 

I I 

I I 

I I 

I I

- I 

-I

I I 

I

I 

I.

).0

Meridional Strain at Z =" 1.25 m
I I 

I 

I 

I

I' 

I'

II ------------ I---------

I I I I a I I I I a 

0e 0

0 

NIV81S 

E-252

I I I I I I I I I I 

I

00

1'

0 LO

IE

M) 

II 

C 

0 

-J 

0

NJ 

-4--j 

(n C

0 

0 

4-& 

0 

-n-

- (I 

z 

:0 

-0 ý 

:0

6d

0 

0 0

--------------------

I I

II

III

I

II

I I 

I 

I 

I 

I I

III

I

II

I

I

II

II

I I 

I 

I 

I 

I I

IIIII
PLOT ID = 35

150 

E 100. EIO 

Iz 

50 

0~ 

C,0 5 50

0.'

L L

CONTAINMENT INTERNAL PRESSURE

Displacement at of the containment top

a L L i 

I ~~IIII 

LI 

I III

I I

I I

(MPa)

Plot of Vertical
PLOT ID

30--

.1

20- L

10--

nS| 1 | | | 1 | | 

0.0 I ll I I to I I I II I II 1 I 11II r1]r 11 I 1 1 1 

3.0 6.0 9-0 

CONTAINMENT INTERNAL PRESSURE

Plot of Horizontal Displacement at Z

4 0 T - - - - -1 1- - - -

II I. 51 1 IIII III1 

12.0 15.0 

(MPa)

= 3.57 m

= 36

tI2

E 

La 

w 

0 

(n 

0/

I I z m ,

I ... .... I

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I 

I I 

I I I 

I I I 

I I I 

L 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I I 

I I

- - - - I 

- - - - I 

---- I 

]
PLOT ID = 36 (Inside)

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I I 

I 

I

40 

30

I' I-

6.0 9.0 

CONTAINMENT INTERNAL PRESSURE

-

I

1

Displacement at 

Z

Sr 

I I 

I /. 

I

t11

E 

w 

220 

0 0

100

0.

III

I

I

I

I

I

I

I

I

I

I

I

I

I

I

II

I

I

II

I

I

I

I 

I 

I 

I I

I I I

IIII

Plot of Horizontal = 3.5 

7

m
PLOT ID = 37

IL -- L .

r

I I I I I I I I I I I I I I I I r I I I I I 

6.0 

CONTAINMENT INTERNAL

9.0 

PRESSURE

r

12.0 

(MPa)

Displacement at Z

40 -

30-

E 

Z 

w 

0~ 

(1) 

n

20+

10 

0-, 

0.0 3.0

I i . 

15.0

I 

r 71

I I 

I 

I

I

I

tp L

Plot of Horizontal = 3.352 m
PLOT ID

30- -

I I 

I I 

--------- I 

I I 

I I

L

20t- L. /

10-

I

-

I I 

- - r-- -- --- i

Plot of Vertical Displacement at Z

= 38

I.-.N 

E 

E 

z 

w 

0 

0_ 

Cl

0 , i . i i I i I i I I I I I I I I I I I I I I I 

0.0 3.0 6.0 9.0 12.0 15.0 

CONTAINMENT INTERNAL PRESSURE (MPa)

40 -r- - - - - - - - - - - -- - -

I ___L

rrl

I I I

I

I I 

I 

I 

I 

I 

t

= 3.32 .m
Appendix E-4

General Dynamics Electric Boat Division 

U.S.

E-259
ELECTRIC BOAT CORPORATION 

A aoNH ryA- r-AMJS COMPANY 

Enclosure (1) to: 

41 5:TFT/603039/3.8 

Report on Pre-Test Evaluation of the Steel Containment Vessel 

Electric Boat Corporation 

June 3, 1996

E-261
ELECTRIC BOAT CORPORATION 

A GENERAL DYNAMICS COMPANY 

NUPEC/UJSNRC STEEL CONTAINMENT VESSEL 

ROUND ROBIN ANALYSIS PROGRAM 

ELECTRIC BOAT CORPORATION 

PRE-TEST EVALUATION OF THE 

STEEL CONTAINMENT VESSEL 

K ARPIN 

A. BEACHAM 

W. MCCORMICK 

REVIEWED BY 

-MINICUCCI 

May 1996 

ABSTRACT: This report documents Electric Boat Corporation's pre-test evaluation of a steel con tainment vessel (SCV) as part of a research program sponsored b" The Nuclear Power Engineering Corporation of To/yo, Japan and the U.S. Nuclear Regulatory Commission. This program includes 

an internal pressurized test o failure of a model of a steel containment vessel enclosed by a steel 

contact structure. Round Robin pre-test and post-test analyses are being coordinated by Sandia National Laboratories. Electric Boat Corporation emploed a series offinite element models in the 

pre-test evaluation of the SCV. Material and geometric nonlinear analyses were performed using the ABA QUS/Standard Implicit Finite Element Program. Results of this evaluation include 

displacement and strain predictions for the SCV which will be compared to test data following the 

completion of the model test series.

E-263
Table of Contents

1.0 Purpose ........................................................................................................................................................... E-265 2.0 Background ........................................................................................................... ....................................... E-265 

3.0 Material Data. ................................................................................................................................................. B-266 

4.0 Finite Element Model Description ...............-................................................................................................. E-268 

4.1 Axisymmetric Shell Models ............................................................................................................... E-268 

4.2 Quarter Symmetry Shell Models..,............................................ E-272 

4.3 Axisymmetric Solid Models ............................................................................................................. E-274 

5.0 Parametric Investigation-Axisymmetric Shell Models ................................................................................. E-277 

6.0 Quarter Symmetry Shell Model Analysis Results .......................................................................................... E-280 

7.0 Axisymmetric Solid Model Results ................................................................................................................ E-283 

8.0 Head Buckling Evaluation ................................................... E-286 

9.0 SCV Standard Output Discussion .................................................................................................................. E-288 

10.0 Key Results (First Yield, First Contact, Critical Areas) ................................................................................ E-289 

11.0 Conclusions .................................................................................................................................................... E-292 

12.0 References ..................................................................................................................................................... E-293 

Appendix A .............................................................................................................................................................. E-294 

Nomenclature: 

c clearance 

C-AXSR ABAQUS S-node biquadratic, reduced integration axisymmetric solid element 

CAX6 ABAQUS 6-node quadratic, axisymmetric solid element 

CS contact structure 

E Young's modulus 

Fi allowable elastic slip fraction 

4. characteristic contact surface face dimension 

MPC ABAQUS multi point constraint 

NRC U.S. Nuclear Regulatory Commission 

NUPEC Nuclear Power Engineering Corporation 

P pressure 

PEEQ ABAQUS equivalent plastic strain, total accumulation of plastic strain 

P0 contact pressure at zero clearance 

S3R ABAQUS 3-node triangular thin or thick shell, finite membrane strain element 

S4R ABAQUS 4-node doubly curved thin or thick shell, reduced integration, hourglass control, finite 

membrane strain element 

SAX2 ABAQUS 3-node thin or thick quadratic axisymmetric shell element 

SCV steel containment vessel 

SNL Sandia National Laboratories 

strain Sengineering 

true strain 

true plastic strain 

8 o model global theta angle 

coefficient of friction 

ae engineering stress 

a', true stress 

ay yield stress, 0.2% offset

E-264
1.0 Purpose :

The purpose of this section is to describe the pretest analysis efforts performed by Electric Boat Corporation in the 

evaluation of the Steel Containment Vessel (SCV) and Contact Structure (CS) as defined in References (1-3). Results 

of this evaluation include displacement and strain predictions on the SCV which will be compared to test data follow

ing the completion of the model test series. 

2.0 Background: 

This work is part of a multi-national analysis effort in the evaluation of the Steel Containment Vessel (SCV) and its 

interaction with a Contact Structure (CS). The SCV will be internally pressurized resulting in an expansion of the 

vessel and subsequent contact between the SCV and the CS. The pressurization will continue until failure of the SCV. 

Figure 2.0.1 shows a simple schematic of the test configuration. 

SAW- Apex of Head 

Steel Containment 

02MJ Vessel (SCV) •,.20 nn Top Flange 

d "IsJ~ ,- Knucide 

IS uppr 19ra Rnun 

n€ C SGV480 

0 lemn Equipmnt 

2 AS N omin a Gap H aI~h 

I•.• Lowe 19 mm Ring 

0 

- J 2" Material Une 

u Lower 9.5 rmm 

W75 

-3.797 Contact Structure 

Lower 12.5 mrn ""(CS) SASIS GOO0 

_ R i n g Le w e r C o i a l C A n rc a l 

•'•...Shelt Interlace 

S -I. 

C 

v Storno Head Su pport Structure 

Entry Match Not Shown 

Figure 2.0.1 

SCV and CS in Test Configuration 

The Nuclear Power Engineering Corporation (NUPEC) of Tokyo, Japan and the U.S. Nuclear Regulatory 

Commission (NRC) funded all construction and test activities with Sandia National Laboratories (SNL) coordinating the "Round Robin" activitis

E-265
3.0 Material Data:

The SCV is constructed of SGV480 and SPV490 Japanese steel. The upper portion of the SCV is SGV4S0 Steel and the lower portion is constructed of SPV490 steel. The equipment hatch reinforcement plate is also constructed of SPV490 steel with the remaining equipment hatch made of SGV480. The CS is entirely SA5 16 Gr7O steel. 

Elastic material data for the Japanese steels was supplied in Reference (2). An average Young's Modulus (E) of 209,850 Mpa (30.436 ksi) was used for the SGV480 steel and an average Young's Modulus of 2 15.750 Mpa (31.292 ksi) ,as used for the SPV490 steel in all the analyses. A nominal design value of 206,844 Mpa (30.000 ksi) was assumed for the CS. A Poisson's ratio of 0.3 was assumed for all the steels. 

Tensile test data was supplied in Reference (I) for both the SGV480 and SPV490 steels. Four samples of engineering stress-strain data at twelve distinct locations relating to various material and thickness changes on the SCV were supplied. The engineering stress-strain was converted into true stress and strain up to the ultimate engineering stress 

using the following relations. 

In (l+.E,) Equation (3.0.1) 

O, = a6 (1 + Q. Equation (3.0.2) 

This was necessary since true stress, true plastic strain data is required in the ABAQUS finite element program. Reference (4). To obtain only the plastic portion of the strain data, the elastic portion of the strain was subtracted from 

the total strain using the relationship below. 

S= t - a,/E Equation (3.0.3) 

A least squares approach was utilized to determine the mean curve which would be used in subsequent nonlinear analyses. The true stress, true plastic strain data was fit with a variable knot B-spline least squares approximation (Reference 5). An interface program to the Reference (5) routines was developed and utilized to obtain the twelve 

mean material curves which would be used in all the nonlinear analyses. In operation, the test data from the four samples is read from an input file, sorted and the user prompted for the order of the spline (quadratic, cubic_.), the number of B-spline coefficients and an initial guess at the internal knot locations. The program then determines the best placement of the knots which will minimize the error in a least squares sense. Experience has shown that the use of lower order splines and a minimum number of coefficients results in the best fit without unrealistic oscillation of the splines, caused from the test data spread. Once a good fit is obtained, the splines are evaluated and a piece-wise linear true stress, true plastic strain curve calculated. The range of the material curve was limited to the ultimate engineering stress limit due to the limitations of Equations 3.0.1 and 3.0.2. This limit could well be exceeded during the numerical simulations. To extend the range of the curve, the tangent slope of the curve's end point was extrapolat ed well beyond the ultimate limit. This approximation is consistent with true stresstrue strain material behavior of 

most metals and should not be significant since the majority of the SCV response will be below the ultimate limit. Figures 3.0.1 and 3.0.2 show examples of this data fit for both the SGV480 and SPV490 steels. Location identifications from Reference (I) are shown in the figures for cross reference purposes. Table 3.0.1 presents the maximum, minimum and average true ultimate strain of the samples supplied. 

E-266

I!
Ii ke+06 

L 

7e+08 +

I I + I Test -splitm D= Le=s Sqttwes Fit

0 0.1 0.2 

Thm Plastic Strain fn/m

I

0.3

I I I I .I I " I " I " I . I . 

0 0.02 0.04 0.06 0.0M 

Tnre Plastic Stntin mhm

Figure 3.0.1 and Figure 3.0.2 - True Stress True Plastic Strain Data Fit 

S0V480 Steel 8.5 mm Thick Conical Shell 2 Location 5 

SPV490 Steel 9.0 mm Thick Cylindrical & Conical Shell Location I I 

No inelastic material properties were supplied for the SA516 steel used to construct the CS. The CS was designed to 

remain virtually elastic for the majority of the loading sequence. At higher internal pressure; the CS does, however, 

experience inelastic straining starting at the top of the CS near the SCV knuckle and proceeding throughout the 

structure at very high pressures. The SCV will most likely fail before general yielding of the CS can be achieved but 

for simulation purposes, an approximate material curve was sought. A literature search failed to produce a minimum 

material curve for 5A516 GrOO steel, however, a material curve for ASTM A36 steel was located. ASTM A36 is 

similar to SA516 steel but of lower strength. The SA516 Gr7O curve, therefore, was based on the minimum material 

properties specified in Reference (2) and the general behavior of ASTM A36 steel. While a rough approximation, this 

still represents an improvement in the simulation over treating the CS as an elastic structure. If deemed necessary, post 

test analyses may use CS material data supplied by SNL after the test series.

*Location Material 'ThICIMMS Max. Liii Mm.L Lii Avg. Etu 

(MM) M) M) M) 

I Top Head Shel SGV480 6.0 20.226 19.703 -19.961 

2 Top Head SGV480 6.0 20..I 19.480 19.944 

3 Conical Shed 3 SGV480" 7.5 21.512 20.583 21.055 

4 Spherical Shen SGV480 .0 24.468 18.795 21.616 

5 Conical Shell 2 SGV480 ILS 22.707 19.518 20.489 

6 Reinforcement Ring SGV480 9.5 22.379 20.190 21.698 

7 Reantorcrnent Ring SGV480 12.5 21.365 19.954 20.589 

8 Reido-ceme Rin SGV480 19.0 1M064 17.502 17.927 

9 Flange. Hatch Cover SGV480 20.0 20.811 17.344 19.272 

10 1nucide SGV48D 16.5 16.643 16.423 16.573 

II CyL &Conical Shell SPV490 9. 10-64 9.998 10.245 

r12 Hatch Reinforcemnent SPV490 17.5S 9.611 MM42 8.34 

"Table 3.0.1 

True Ultimate Strain Values from Four Sample Lots

E-267

Sc+0S

7e.+o 

Jc 6e+08 

Se.08 

4e+08

IF
4.0 Finite Element Model Description:

Electric Boat Corporation has developed a series of finite element models in the evaluation of the SCV and CS. 

Axisymmetric shell models were utilized to evaluate general free field response away from the equipment hatch and 

transition regions as well as to perform various parametric evaluations. To obtain detailed response in the transition 

regions located around stiffener locations and the knuckle region, solid axisymmetric models were used. A'quarter 

symmetry shell model and subsequently refined submodels were used to obtain response data near the equipment hatch sleeve. All models were evaluated with and without friction in defining the interaction between the SCV and 

the CS. Geometric and material nonlinearities were included in all the evaluations. 

4.1 Axisymmetric Shell Models: 

A series of axisymmetric shell models was developed in order to perform parametric evaluations on variations in the 

as-built test configuration as well as to evaluate several numerical solution alternatives available in the ABAQUS finite element program. As-built conditions of the SCV and CS were supplied by SNL in Reference (3) and include 

radius. gap and thickness values which were specified at elevations on the SCV and at circumferential increments 

around the shell (either 45 or 90 degree increments). In order to evaluate the geometric variation around the 

circumference, an average value was determined. For example, a mean as-built thickness was determined by averag ing the eight samples taken around the SCV circumference. If multiple plate thickness measurements were taken for 

a given design plate thickness, these were also averaged. To evaluate the effects of plate thickness variations, an 

additional analysis was performed which utilized the minimum plate thickness specified around the circumference. 

Table 4.1.1 presents the mean and minimum plate thicknesses which were used in the axisymmetric shell models. The 

material location identifiers of Reference (1) and thickness labels of Reference (3) are used in the table for cross 

referencing purposes.

Table 4.1.1 - SCV Minimum and Mean As Built Plate Thicknesses 

In areas of significant thickness transition such as the knuckle region and lower head area, variable thickness finite 

elements were used by defining the shell thickness at nodal locations. In this way, the smooth transition from one plate thickness to another was accurately modelled. The thickness values of the CS were taken from the gap size measure

ment supplied in Reference (3). Again, the values (four at 90 degree increments) were averaged around the 

circumference. These mean values were then averaged into two sections, one for the spherical shell of the CS and one 

for the conical section of the CS. Minimum values were also determined for each section as shown in Table 4.1.2. 

E-268

11

Dsign Material T* = Minimum Mean 

s Locaton Id Label (mm) (mm) 

(MM) _MM_ (___M__ 

5.0 1 T18"i19 6.1 &.8 

6.0 2 T21 6.7 6.8 

7.5 3 TIIl,12.T13 7.2 7.5 

8.0 4 T14.T1S 7.5 7.9 

.5 5 T7. Ta, 9 82 8.7 

9.5 6 76 9.6 9.9 

12.5 7 75 13.1 13.3 

19.0 8 "10 19.2 19.5 

19.0 8 Tie 19.8 19.9 

20.0 9 T20 20.2 20.7 

18.5 10 717 16.2 16.8 

9.0 11 71.-4 8.8 9.48 

17.5 12 722 17.6 18.0 

20.0 9 T23 20.2 20.7 

20.0 9 724 20.3 20.4
Design Minimum Mean 

Thickness Thickness Thickness (mm) Section (mm) (mm) 

38.1 Spherical 43.36 44.33 

38.1 Conical 37.01 42.50

Table 4.1.2 - CS Minimum and Mean As Built Plate Thicknesses 

The gap distance values at four circumferential points at eighteen separate elevations along the CS were supplied in 

Reference (3). The four circumferential values per elevation were averaged as shown in Table 4.1.3. The location 

identifiers from Reference (3) are used in the table for cross reference purposes. For a worst case evaluation on gap 

distance sensitivity, approximate minimum, mean and maximum gap values were determined by evaluating measure

ment hole numbers 5 through 18. These locations correspond to points at which a nominal design gap of 18 mm was 

desired. The CS model was then constructed such that the normal gap clearance from the SCV was 17.0 mm for the 

minimum gap model, 21.0 mm for the mean gap model and 24.0 mm for the maximum gap model. Note that the actual 

gap was specified since ABAQUS/Standard, the implicit numerical solver in the family of ABAQUS codes. does not 

account for the thickness of the shell in the contact algorithm.

Hole Average Gap Hole Average Gap Hole Average Gap 

4 (mm) # (mm) # (mm) 

2 133.03 8 22.52 14 22.86 

3 101.69 9 23.32 15 21.45 

4 71.92 10 22.99 16 19.16 

5 19.76 11 23.08 17 17.98 

6 20.58 12 22.43 18 16.64 

7 20.88 13 21.86 19 25.91

Table 4.1.3 - Average Gap Distances 

The out of roundness values supplied in Reference (3) were not used since it is believed that as the SCV exceeds the 

yield limit of the material, the vessel will naturally conform to a cylindrical I spherical shape. Therefore, the SCV 

geometry, except for plate thicknesses, was based on the design drawings supplied with Reference (1). An average 

design half thickness value of 3.75 mm was added to all the inside radial dimensions supplied in the drawing to obtain 

an approximate mid-radius value. 

Several axisymmetric models were developed based on the permutations of model geometry and include (I) a mean 

thickness, mean gap model, (2) a mean thickness, minimum gap model, (3) a mean thickness, maximum gap model 

and (4) a mean gap, minimum thickness model. Figure 4.1.1 shows the mean gap model which is representative of all 

the axisymmetric models. 

The model shown in Figure 4.1.1 is truncated at the intersection with the support structure. The support structure, as 

shown in Figure 2.0.1, was assumed to provide fiity at this point. In addition, the lower head is present only to 

complete the pressure boundary and is not part of this evaluation. SNL has taken efforts to insure that failure will not 

occur in this area

E-269
Fixed Bouroaa, 

111ondmecs Saree Samu•

Figure 4.1.1 

SCV and CS Axisymmetric Shell Model - Mean Gap 

The finite element model was constructed of 248 ABAQUS SAX2 elements which are three-node thin or thick quadratic axisymmetric shell elements. The element allows transverse shear but becomes a discrete Kirchoff thin shell 

as the thickness decreases. Two-point integration of a quadratic interpolation function is used for the element's 

stiffness matrix and three-point integration of a quadratic interpolation function is used for the distribution of loads. The element also has the ability to account for reduction of thickness due to stretching parallel to its mid-surface. A 

full discussion of the element's theory is given in Reference (6). 

The contact definition between the SCV and the CS is simply defined in A1AQUS by creating surface definitions which specify the elements or nodes associated with a given surface. The surfaces that may contact are then paired in 

a master-slave relationship and properties of the interaction, such as friction, defined. Contact is enforced in the algorithm by ensuring that the slave surface (SCV) must conform to the master surface (CS). That is, that nodes on the slave surface cannot penetrate the master surface, but master nodes can penetrate the slave surface. Obviously, penetration of the slave surface by the master surface nodes is to be minimized and this is accomplished through mesh refinement and the use of matching meshes between the paired surfaces. Care was taken to use matching meshes on the SCV and CS by a normal projection of the SCV mesh on to the CS. Mesh refinement studies were also performed 

to assure a convergent solution. 

There are two solutions available in defining the sliding behavior of contact surfaces with nonlinear geometry. A finite sliding solution may be utilized which permits arbitrary separation, sliding and rotation of the surfaces, or small sliding may be used, in which arbitrarily large rotation of the surfaces are allowed, but it is assumed that a slave node will interact with only the same local area of the master surface. The computational savings that the small sliding solutions possess can be substantial, particularly for three dimensional interaction problems. For the axisymmetric

E-270
shell models, the savings were insignificant. however the results from both solution methods were nearly identical. This information was used to reduce the computational expense in performing the three dimensional general shell 

analyses. 

The contact behavior may also be modified in a variety of ways. Two methods which are pertinent to this evaluation 

are the default hard contact model and the softened contact model. Figure 4.1.2a illustrates the contact definition of the hard contact model. When the surfaces are in contact, any pressure stress can be transmitted between the contact

ing surfaces. 

Contact Contact 

Pressure Pressure 

..- Any pressure possible when 

In contact 

Po " /' Exponential relationship 

No pressure when no contact Po l n 

Clearance C Clearance 

Figure 4.l.2a Hard Contact Model Figure 4.1.2b Softened Contact Model 

This particular method had convergence problems for several of the parametric models which were evaluated. The softened contact model, as shown in Figure 4.1.2b, is useful when them is a thin, relatively soft coating on one or both of the surfaces. Per Reference (2), the SCV has four independent layers of primer or paint with a total paint thickness ranging from 3 nun to 5 mm. Contact occurs in this model when the gap distance decreases to a value of c. The 

pressure transmitted between the surfaces then increases exponentially with further approach. Values of c = .001 meters and P.=1.6 X l0e Pa were used which resulted in a maximum over-closure of approximately 1.7 mm. This result is entirely plausible since compression of the paint to this level is reasonable. In addition, the variation of results between the hard and softened contact models is well within the variability in the as-built gap data. The softened contact model also removed the convergence difficulties experienced with the hard contact model and reduced the number of equilibrium iterations required in the overall solution. 

Classical Coulomb theory was used to define the frictional contact between the SCV and CS. The default, stiffness methodwas used to implement the friction theory. This method permits some relative motion when the interface should be sticking. The aniount of slip permitted is controlled through the specification of an allowable elastic slip distance. The larger the slip distance, the more rapid the rate of convergence at the expense of solution accuracy. In practice, the program scans the contact surfaces and calculates "a characteristic contact surface face dimension," 4 The allowable slip distance is then kept below a small fraction F1 of 4. The default value of F1 = 0.005 was used in all analyses. The axisymmetric model was evaluated with a coefficient of friction, g = 0.0 (no friction), p = 0.4 (steel on steel in air, Reference (7)) and p = 0.2 (steel on steel lubricated, Reference (8)) to assess the effects of friction on the response of the SCV. In one of the parametric evaluations, the CS is assumed to be linearly elastic. For this case, an extension of the standard Coulomb model which permits the specification of a shear stress limit was used. With this model, regardless of the magnitude of the normal pressure stress, sliding will occur if the magnitude of the shear stress reaches the value of the specified limit. The shear stress limit was set to the minimum yield value of SAS 16 

GrOO steel (262.0 X 106 Pa). 

Internal pressure was incrementally applied to the inside surfaces of the SCV based on the automatic load stepping procedure available in ABAQUS. By default, this pressure is applied normally to the surface regardless of the rotation 

of the surface.

E-271
4.2 Quarter Symmetry Shell Model:

The SCV can be ideally represented with a half symmetry model if variations in circumferential dimensions are 

averaged. If the effects of the equipment hatch are localized, a quarter symmetry model may be used, which effective

ly models a duplicate penetration on the opposite side of the SCV. In order to reduce the model complexity and 

analysis cost, a quarter symmetry model was constructed and the free field results compared to an axisymmetric model 

(no hatch modelled). Excellent agreement between the two models was present. These findings substantiate the 

assumption that the effect of the hatch is localized and the benefits of a half symmetry model would be negligible. 

The quarter symmetry shell model, shown in Figure 4.2.1, was therefore used to evaluate the response near the equip ment hatch. The model is based on the same properties as the mean axisymmetric models. Mean as-built thickness 

data (See Table 4.1.1 and Table 4.1.2) was used as well as a mean as-built gap of 21 mm (as compared to the nominal 

gap of 18 mm). No variation in thickness or gap was supplied around the circumference of the model. The as-built 

gap data around the hatch was significantly larger than the data supplied away from the hatch. This is most likely attributed to distortions in the shell structure due to extensive welding in the area.: The mean gap around the equipment hatch was therefore increased to 25.7 mm based on data supplied in Reference (3). The gap size transition is located 

at the SPV490 hatch reinforcement plate to conical shell interface. Variable thickness shell elements were used at this transition to model the thickness transition from the thin conical shell to the thick reinforcement plate. Variable 

thickness shell elements were also used at the knuckle and lower shell sections similar to the axisymmetric models. 

The radial separation between the hatch cylinder and the CS was set at an average 25.5 mm as shown in Reference (3). The finite element model is constructed of 4724 ABAQUS S3R and S4R thin or thick, reduced integration, finite 

membrane strain elements. Default hourglass stiffness values were used to control the spurious modes which may 

occur in lower order reduced integration elements. The finite membrane strain elements allow thickness change (thinning of the element) and permit transverse shear stress outpuL Reference (6) presents a detailed discussion on the 

formulation of the S3R and S4R elements. Higher order elements such as 8-noded quadratic shell elements were not utilized since they do not account for shell thinning, which was shown to have a significant effect on results at higher internal pressures. The contact interaction between the SCV and CS utilized the small sliding solution, previously discussed, with the softened contact model shown in Figure 4.1.2b. The model was evaluated with a coefficient of 

friction of 11 = 0.0 (no friction) and ji = 0.4 (steel on steel in air, Reference (7)) as was done for the axisymme-ic 

models. 

In order to perform a more refined analysis around the equipment hatch, a submodel was constructed which effectively quadrupled the number of finite elements around the hatch vicinity. Figure 4.2.2 shows the refined submodel which 

was evaluated using the submodelling options available in the ABAQUS computer program. With this analysis option, the model shown in Figure 4.2.1 is defined as the global model. Edge displacements are then automatically interpolated from the global model onto the submodel. All other symmetric boundary conditions, pressure loads and 

contact definitions were applied to the submodel, as was done for the global model. In applying the edge displacements, only the translational values were applied to the perimeter elements since the interpolation scheme 

used in ABAQUS is inappropriate for shell rotations which are not linearly related. Rotations are therefore applied by the coupling action of the two driven nodes of a particular perimeter element. Comparison of results in the free 

field between the global model and submodel show very similar results. A detailed discussion of this submodel 

analysis option can be found in Reference (4). 

E-272

J!,
sinar v Plan

S"auy Pw*n

kiwi Plate 

d • Mode FmI 

at Uam 

Figure 4.2.1 

Quarter Symmetry Shell Model of the SCN' and CS 

(CS Showm in Phantom)

Sd

Figure 4.2.2 Submodel of Equipment Hatch Area 

CS Removed for Clarity - X Marks Location of Driven Edge Displacements

E-273
4.3 Axisymmmetric Solid Models

Three axisymmetric solid models were developed to evaluate, in detail, the localized response around several of the transition areas. These transition areas are characterized as locations around vessel stiffeners or significant changes in shell geometry which result in substantial strain concentrations. The axisymmetric models previously discussed do not possess the model detail necessary to accurately capture the steep strain gradients near these transitions. In addition, several of the required response locations are near the transition regions and it was necessary to verify that the strain gage locations were far enough from the severe strain gradient such that simple axisymmetric shell models could be used. All models were based on mean as-built thicknesses (Table 4.1.1) and mean gap data (gap = 21.0mm). The contact interaction between the SCV and CS utilized the finite sliding solution, previously discussed, with the softened contact model shown in Figure 4.1.2b. The models were evaluated with a coefficient of friction, p = 0.0 (no friction), ;i = 0.4 (steel on steel in air, Reference (7)) as was done for the axisymmetric shell models. 

Each solid model was primarily constructed using CAX8R 8-node biquadratic, reduced integration axisymmetric solid elements. Six-node quadratic CAX6 elements were used in mesh transition areas. These elements were selected over lower order elements due to their superior performance under bending loads. A detailed description of the axisymmet ric solid element formulation can be found in Reference (6). Based on comparative studies to axisymmetric shell models, a minimum of four elements through the shell's thickness was used in order to accurately capture the through thickness nonlinear strain distribution associated with the bending response. 

The first section modelled encompasses the region from the top head to just above the upper 19 mm reinforcing ring of the spherical shell. In order to evaluate the effects of variations in the contact point between the SCV and the CS at the knuckle, two models were created. For the first model, the opening at the top of the CS was governed by the design height of the CS above the support structure and the assumed 21 mm mean gap. This modelling choice resulted in a relatively large open space at the top of the contact structure with contact between the SCV and CS occurring at the bottom of the knuckle. This model is shown in Figure 4.3.1. For the second model, the CS was extended such that the open space was equal to the mean value from Reference (3) from Hole #19 or 25.91 mm. This results in contact in the thicker section of the knuckle. A close-up detail of the knuckle region of this model is shown in Figure 4.3.2. Each model consists of axisymmetric shell elements in the head area which transition to axisymnetric solid elements at the top head cylindrical shell. Multipoint Constraint Equations (MPC's) were used at the shell / solid model interface to insure continuity. Twenty SAX2 quadratic axisymmetric shell elements were used in the head area while 2494 and 2654 quadratic axisymmetric solid elements were used for the remainder of the model for the first and second models respectively. Base motion data derived from the axisymmetric shell model was applied to the lower boundary of the spherical shell. MPC's were again used to apply the single node shell response data to the multiple node solid model. 

The second section modelled, shown in Fi.ure 4.3.3, is of the lower 19 mm reinforcement ring just above the elevation of the top of the equipment hatch. The model was constructed of 1974 CAX8R elements. Base motion data derived from the axisymmetric shell model was applied to the upper and lower portions of this model. 

The third section, shown in Figure 4.3.4, models the intersection of the SPV490 conical shell with the SPV490 cylin drical shell. Two reinforcement rings are located just above the intersection. The model was constructed of 1472 CAX8R elements. Base motion data derived from the axisymmetric shell model was applied to the upper and lower 

portions of the model. 

E-274

II
Head

SCv 

Knucle.

20 mm Ring

CS

10

Figure 4.3.1 - Axisymmetic Solid Model Knuckle Region

.. 20 mm Ring

A*

scv.

CS

Figure 4.3.2 Axisymmetric Solid Model Knuckle Region Detailed View 

Based on Average Gap Distance of Reference (3) Hole 19 Measurements

E-275
Apphd Bas 

vowios.

soy

Cs

Appled 3m. 

Figure 4.3.3 Axisymmetric Solid Model Lower 19 mm Reinforcement Ring 

Apped BasM 

sov. 

"cS 

9..Mmm Pin9 

Apoed Base M• "~n 

Figur 4.3.4 Axisymmetric Solid Model Conical Shell Cylindrical Shell Interface 

E-276

|!
4.0 Parametric Investigation - Axis'mmetric Shell Models:

Axisymmetric shell models were used to economically evaluate a variety of model parameters from model geometry to 

analytical solution strategies. Table 5.01 lists the major features of the models evaluated.

Table 5.0.1 Axisymmetuic Shell Model Parametric Evaluation Reference Index 

Selected plots are presented here to illustrate the variation in response that can be expected due to variation in the SCV and CS geometry including plate thickness and gap measurement as well as unknowns such as contact friction between the SCV and CS. It is believed that these evaluations represent bounding cases with respect to the variable which is being perturbed (i.e. gap size, plate thickness, frictional constant) but not necessarily a solution for a worst case analysis with 

respect to failure. Since the major purpose of this effort is to predict response behavior, mean property finite element 

models are more appropriate. The parametric evaluations will be used to aid in the assessment of the overall accuracy of the mean solution. Numerical perturbations were also evaluated to assess the effects of finite sliding versus small sliding solutions, hard versus softened contact interaction and the effect of the use of inelastic material properties on the CS. 

Figure 5.0.1 shows the effect of gap distance on hoop strain for two internal presure levels. As expected, the gap distance has the most dramatic effect on response only in the contact region. The graph was developed by plotting nodal averaged hoop strains as a function of relative distance along the SCV surface for a selected pressure level. Table 5.0.2 presents an index table of relative distance along the SCV for key areas of interest for use with the figures presented in this report. Automatic load stepping, in which ABAQUS controls the incremental increase in load based on the previous load increment convergence rate, was used in all analyses. Therefore, discrete pressure values across the various analyses performed are not exactly equal. 

Figure 5.0.2 illustrates the effect of plate thickness on the response of the SCV. The portions of the SCV above the upper 19 mm ring. which are not in full contact with the CS at this pressure, show the most significant change in response. The load sharing nature of the thicker CS tends to mitigate the effects of the thickness variations in the shell plating below the 

19 mm ring where uniform contact is achieved at a lower pressure. 

Location Apexof Head Top 20mm ofBompof Upper 19 MM .Omr 19 mm 

S0V480Rigrudein 

Material Dicaane "ln 

SCV 0.00 0.a28 0.9a 1.00 1.644 2.483 (meters) SGV48OI Lower Concal 

Location SPV490 Lower 9.5 mm Lower 12.5 mnm ShelllLower Top of BSotom Support SPV49 ateri Ring Cytfldrical mead insert Stnict 

Materl InDistancerlace Shel roa 

SOy 2998 3.674 3.775 3.797 4.W4 _ 4.516 (meters)

Table 5.0.2 Relative Distance along SCV for Key Areas

E-277

Model NO. OMm) Gap Tl'•clness Sliding Conta Friction CS 

1 21 Mean Finite Had 0.40 Inelastic 

2 21 Mean Finite Hard 0.40 Elastic 

3 21 Mean Finite Hard 0.00 Inelastic 

4 21 Mean Finite Softened 0.00 Inelastic 

5 21 Mean Finite Softened 0.40 Inelastic 

6 21 Minimum Finite Hard 0.40 Inelastic 

7 17 Mean Finite Softened 0.40 Inelastic 

S 21 Mean Small Hard 0.40 Inelastic 

9 24 Mean Finite Softened 0.40 Inelastic 

10 21 Mean Finite Softened 0.20 Inelastic
0.04 

0.03 

12 

U .m 

0.01 

0 

-0.01

Relatve Din me

G. p 24 mum Model 9 P--.73 Mpi :--Gap 21 mu Model 5 P=5.84 Mpa 

Gip 17 mm Model 7 P=4.63 Mpa 

V

0.06 

t 0.0 

0.01 

0 

-0.01 

-0.02

4 5

Figure 5.0.1 Gap Parametric Results 

Outside Hoop Strains versus Relative Distance Along SCV

4 5

0.03 

0.02 

= 

i. 0.01 

= 

0 

-0.01

Rd-Ava Dis=ce meteui

2 3 

Reaive Dist ce metern

Figure 5.0.2 Thickness Parametric Results 

Vertical Displacement and Outside Hoop Strain versus Relative Distance Along SCV 

E-278

0 1 3 

Relative Disiwce meters

Gap 24 mm Model 9 Pc.S.601Mpa 

Ga-p 21 mm Model 5 P1`43,3 Mpa 

,- Gp 17 mm Model 7 P-4.95 Mpa 

Al

Mena Thick Model I PMMJ2 Mp 

Min. Thick Model 6 P-5.I Mpa I

0.015 

0.01 

.,1 

-0.005 

0 

-0.005

0

1!

4

0
Figure 5.0.3 shows the effects of friction on the displacement and strain response of the SCV. The mean thickness, mean 

gap models were evaluated with coefficient of friction values of p = 0.0 (no friction). p = 0.4 (steel on steel in air. Reference (7)) and p = 0.2 (steel on steel lubricated, Reference (8)). With no friction, the SCV not only has positive vertical deflections due the pressure on the top head surface, but also some negative vertical motion due to bulging of the lower SPV490 cylindrical shell into the larger gap at the base of the CS. Frictional forces effectively negate the downward 

effective pressure. A comparison of the two evaluations which utilized frictional values shows very similar response. It is therefore believed the the actual response of the tested vessel will tend toward results which assume some level of friction. The level of friction, as long as reasonable, should only have minor effects on the general response of the SCV. 

Figure 5.0.4 shows some selected results from the parametric evaluation of analysis assumptions. The comparison of hard 

contact results with the results of a softened contact model show very similar response. The use of the softened contact model was used to solve convergence problems in some of the analytical evaluations as well as, in a general sense, model the compression of the three to five millimeter thick SCV painted surface. The comparison of a finite sliding solution to the more economical small sliding solution also shows nearly identical results. This information was used in the quarter 

symmetry shell model and associated submodel to reduce computational costs. 

At approximately 8.5 Mpa (1200 psi) the SCV shell response tends to show some deviations from the inelastic versus elastic treatment of the CS. At approximately 11.2 Mpa (1600 psi) the effect of the inelastic behavior of the top portion of the CS is significant. The material properties used for the CS are only an approximation and represent a lower bound to the strength of the SA516 Gr7O steel. If pressures in the SCV exceed 8.0 to 9.0 Mpa before failure, it will be necessary to 

obtain more exact material behavior for the CS for the post test evaluation. 

0.05 F.. 0.0 Model 4 .60 0.06Fct0.0Model4 Rim .0.2 Model110 P=8.48 P 0 ... - Firct0.2OModel4 Frier 0.2 M 10 MA ode! I0 N ,A S , 

Rim0.4Model P--8.53 0.05 - fi= 0.4 Model P-2.S3 

i t 0.04 

0.03 0.03 

g0.03 

"• tt 0.0-1 ' 

0, 55.0iri a0.01 I 

--/ 0 

.0 .0 1 2 - 0 2. 

0 1 2 3 4 50 1 2 3 4 5 

Relmfe Dince nmen• Relative Distnzce meeis 

Figure 5.0.3 Coefficient of Friction Parametric Results 

Vertical Displacement and Outside Hoop Strain versus Relative Distance Along SCV

E-279
0.03 

0.01 

-0.01 

-0.01 

-00

SHard Contact Model I Pz&6'.6 Mpo 

CS MOM SEl~i. 2 P.S -. 61- MP. 

Sr- .... ,Soft Comm• Mdd $ M--AI Mps 

------- jSntl Slide Model 8 Pz.,7 Mpa

"0 1 .7 0 2 3 

Retlatve Diznec mete Res.Ive Dizsm mete 

Figure 5.0.4 Analysis Assumptions Parametric Results 

Outside Hoop Strains versus Relative Distance Along SCV 

6.0 Quarter Symmetry Shell Model Analysis Results: 

The quarter symmetry (modelled from a global theta angle. 9G, of 0.0 degrees to 90 degrees) shell model shown in Figure 4.2.1 was evaluated assuming a coefficient of friction of 0.0 and 0.4. Results for the friction evaluation are presented in this section. The model was loaded with an internal pressure load which was incrementally increased until a convergent solution could no longer be obtained for a specified minimum load increment. A minimum load increment value of 1400 Pa (0.2 psi) was used for all analyses. Maximum pressures achieved in the simulations for the frictionless and friction models were 13.51 Mpa (1959 psi) and 13.57 Mpa (1968 psi) respectively. This is consistent with the axisymmetric models evaluated. No material failure algorithm was used in any of the analyses, so these pressures do not represent a failure condition but merely the level of pressure in which a stable solution could be found for the specified default equilibrium tolerances. Figure 6.0.1 shows a displaced fringe contour plot of the SCV with friction for the hoop component of strain at an internal pressure of 8.60 Mpa (1250 psi). The effects of the equipment hatch on the uniform 

strain field ar readily apparent. 

Hoop strain versus relative distance along the SCV at a model global theta angle, Go., of 45 degrees (free field) from the shell model are compared to the axisymmetric results in Figure 6.0.2 for two pressure load levels. As can be seen, free field strain results away from the equipment hatch are very similar to the axisyrvmetric shell model. This validates the use of the economical mean parameter axisymmetric shell model results for the required free field result predictions locations. 

The contact propagation for the friction model is show in Figure 6.0.3 by plotting the gap distance versus relative distance along the SCV for various discrete pressure levels. The X-axis distance is taken relative to the lower portion of te knuckle. The path along the SCV was taken at a model global'theta angle, G0, of 45 degrees (free field) and 90 degrees (center of equipment hatch). The gap of approximately 21 mm and 25 mm around the equipment hatch is shown in the furst incremental increase in pressure. The gap distance below the lower reinforcement rings then increases dramatically based on the CS geometry. First contact takes place in the lower knuckle region at an approximate pressure of 3.5 Mpa (500 psi). The next area of contact is in the center of the upper conical shell section (conical shell 3) at a pressure of approximately 3.9 Mpa (550 psi). Contact spreads throughout the conical section and then to the spherical shell. The reinforcement rings are clearly visible in the contact plots as local peaks in the gap distance. 

Results from the submodel (Figure 4.2.2) of the hatch area are consistent with those of the quarter symnetry model but 

with a higher level of resolution in the steep strain gradient areas of the model. 

E-280

0.1 

t.3 

0. 

A 0.02

HdComwt d- Model I PI. 1.17 Mpa 

Eb.WCS ModeI21 P.1.171Mp 

SoAtCoua ModdSP•iII.40Mpa 

SmAlSlide ModeIUP8l=.2U6Mp 

S_________ / \ 

-I1!
.4LA=I-U 

.3 13m-w 

.2WdE-12 

d.234E.2 

*?Z3dE41 

4=GE4dZ 

.?An42 

Figure 6.0. 

Defored Frnge ontou Plo of te4SC 

OutideHoo Stain- Pessre= 860 pa 125 ps) Dfomed cae= .

1 2 3 

Rejative Dnwsimice mers

0.05 

0.04 

0.03

0.0 

~u0.02 

0

-0.01

.0.02 ' 4 5 0 1 2 3 

Relative Dis==t me=ci

Figure 6.0.2 Comparison of Hoop Strains 

Axisvmmetric Shell Model Versus Quarter Symmetry Shell Model at eG.-45 Degrees

E-291

0.v3 

0.02 

V. 

6. 0.02 

0

-0.01 a 

0 4 5
Cyl. Equip. 

Ring Hatch

1 

Relative Distance metms

Lower 

Ring

3

First Contact 

Second Contact

0 

0.03 

0.02 

0.01 

0

Relative Distance meters

Figure 6.0.3 Quarter Symmetry Shell Model 

Contact Propagation at Or z: 45.0 and 90.0 Degrees

E-282

Shell 

Ring

Knuckle 

Bottom 

0.03 

0.02)

U 

=

0.01

3

Pressnnen 1.4OMps lnul 

Pressure 3.16Mpt Incu15 

- - - - - -. Prssure 3.47Mpa lwc29 

Pressur - 3.S2Mpa lnca37 

------ -- Pressweu3.93Mp& Inc-42 

Prcss= w S.63Mpa lne=6E 

Prcssmm a SOMpa 1n77 

Pressalr 13MP . Inc="93
7.0 Axisvmmetric Solid Model Results :

The axisymmetric solid models were evaluated with coefficient of friction values of 0.0 and 0A. Responses from the 

friction model were compared to results from the mean property axisymmctric shell model. 

Hoop strain and inside equivalent plastic strain (PEEQ) versus relative distance along the SCV (measured from the apex of the top head) were plotted at a selected pressure for the models of the top head/knuckle region for a coefficient of friction 

of 0.4. These strains are shown in Figure 7.0.1. Strains from the mean property axisymmetric shell model are shown on 

the same plot. Note that the discrete pressure values plotted are not identical for all models due to the automatic load 

stepping scheme used by ABAQUS. The response comparisons show generally good correlation between the axisymmet

ric solid models and the axisymmetric shell models. The more detailed and refined solid models more accurately capture 

the strain gradients. Since the axisymmetric solid models included the fillet welds and the thickness of the reinforcement 

ring, the peak PEEQ strains at these stiffeners vary in magnitude and move from the ring centerline in the shell model to 

the weld toes in the solid models. Comparisons between the axisymmetric solid models show the sensitivity of the strains 

in the knuckle region to the contact structure geometry. Horizontal and vertical displacements versus relative distance 

along the SCV are shown in Figure 7.0.2. This plot shows the sensitivity of the head and knuckle displacements to the 

contact structure geometry. The mean CS opening configuration is considered more representative of the actual test 

condition. The first modelling configuration will be used to aid in the assessment of the overall sensitivity of the knuckle 

response behavior. A deformed shape of the mean opening model at a pressure of 5.68 Mpa is shown in Figure 7.0.3. Note 

that the appearance of the penetration of the SCV into the CS is from the softened contact model, which in a general sense, 

approximates the compression of the SCV painted surface. The mean opening model was also evaluated assuming no 

friction between the SCV and CS. A solution for this model without friction could not be obtained beyond 5.85 Mpa due 

to solution convergence problems in the contact algorithm. 

Ring 20 mm Knuckle 20 mm 

0.04 R K Ring Knuckle I 1 1 o.07 r

0.06 

0.03 

0.03 

.E 0.02 

S0.01 

0 /0 

-0.005 1 1.5 0.01 0.5 

Redmive Dismice meers 1.5 

aaavE n..l3JLr n.w.

Axisymmeuic Shell Model. P a 524 MPa I - AxisyMmeic Solid Model. P a 5.6 MPa 

"Axisymmetc Solid Model. Me6= CS Opentin. P a 5.6S MPa 

Figure 7.0.1 

Knuckle Region Outside Hoop Strain and Inside PEEQ Strain versus Relative Distance Along SCV

E-283
Knuckle

0.01 

o.o2 

> 0.01

I. 0 0

0.5 1 1 JS 

Reladve Diawne meters

Axisymet ic Shell Model P a 5.94 MP& 

Axisymmetrk Solid Model. P a 5.66 MPa 

I - Axisymmemc Solid Model. Mtsn CS Openin. P m 5.68 MPs

Figure 7.0.2 Knuckle Region Contact Effects 

Horizontal ani Vertical Deflection versus Relative Distance Along SCV

Figure 7.0.3 Knuckle Region Deformed Shape 

Pressure = 5.68 Mpa (824 psi) Scale = 1.0 

(overciosure at knuckle due to softened contact model)

E-284

II

0.02 

"i 0.01 

0

-0.01 & 

0

h I.

0.5 I 

Relaive Distance mers

-20 Mrn 

Ring 

%, % ,

Knuckle
Hoop strain and inside PEEQ strain versus relative distance along the SCV for a Coefficient of friction of 0.4 were plotted at a selected pressure for the model of the lower 19 mm reinforcement ring just above the equipment hatch in Figure 7.0.4. Similar plots for the model of the intersection of the SPV490 conical and cylindrical shells are shown in Figure 7.0.5. The 

response comparisons show good correlation between the solid and shell models. Some variation is shown at the ring stiffeners due to the added detail and mesh refinement of the solid models. Differences in PEEQ strains at the solid model boundaries are due to the MPC's used to apply the base motion data and clearly do not affect model response away from 

the boundaries.

0.0oS 

0.)17 

0.016 

IE 

5, 

0.03.5

19 am Ring

0.01446 

2-'$

0.04 

.~0.02

2.75 0.021

ftalte DiSlnx emi

19amm 

Ring

Re!viv Dmmewc

A....symmec SWIe Model. P. 5.34 Mpa 

-Aisyimmemc Solid Model. Pu 5.65 MN 

Figure 7.0.4 Lower 19 mm Reinforcement Ring 

Outside Hoop Strain and Inside PEEQ Strain versus Distance Along SCV

9.5 mm 12.5 mm

3.75 

Rl"Di=me=s

0.04 

0.03 

0.02 

0.01 

.1 

0

4 4D-.o

9.5n= 1235n 

Ring ping 

II 

iŽJJ 

L3 3.75 

Xalativ Distance mee

- ---. Asymmae'ic Axsymmeui Solid Stel Modck. Model. P P * a 5.9 5.34 MNa MP& 

Figure 7.0.5 SPV490 Conical/Cylindrical Shell Interface 

Outside Hoop Strain and Inside PEEQ Strain versus Distance Along SCV

E-285

0.012 

0.01 

10.00

.1 

~0.004 

0.002

0 

3.5
8.0 Head Buckling Evaluation :

As the SC%' is internally pressurized, compressive hoop strains increase in the lower head region and hence there is a possibility for buckling to occur prior to a material failure of the structure. The buckling response of a spherical shell is also known to be sensitive to imperfections in geometry. Since the type of imperfections are unknown, a typical assumption is that the imperfection in the geometry be defined by the lowest buckling eigenvalues of the structure. This is believed to be the most critical prestressed shape the structure could possess and therefore the most conservative. The maximum compressive hoop strain is at the center of the 166.7 mm radius in the lower head area on the inside surface. Figure 8.0.1. derived from the mean property axisymmetric model (Table 5.0.1 Model No. 5) shows the inside hoop strain as a function of internal pressure. The strain increases up to a pressure of II Mpa (1600 psi) and then decreases as the top head is deformed into a purely spherical shape.

*1 I

$VA I OW 0 

Figure 8.0.1 

Maximum Compressive Hoop Strain - Mean Axisymmetric Model 5 

To determine the pertinent eigenvector shape or imperfection for the inelastic buckling analysis, a three dimensional shell model of the area on the head which is in compression was developed. Only this portion was modelled, since the goal was to extract the lowest eigenvalue and associated eigenvector in the area under compression. Additions to the model would have caused this lowest buckling mode to shift to more flexible portions of the structure as investigations have proven. Figure 8.0.2 shows the shell model used in the eigenvalue buckling analysis. For these evaluations, design thickness values were used which are below the minimum as-built thicknesses. Boundary conditions are at the top and bottom edges of the shell, solely in the meridian direction. A uniform external pressure load was applied to the shell surface and the lowest buckling mode shape extracted. The mode is a fourteen wave asymmetric shape which is consistent with the results presented in Reference (9). 

The mode shape amplitude, by default, was normalized to a maximum value of one. A scaling factor of 0.003 or 50 percent of the head shell thickness was then applied to the displacement response using the Reference (10) program to obtain the perturbed mesh shape. This level of imperfection is believed io be a conservative estimate of any actual as-built geometry. Figure 8.0.3 shows the perturbed mesh model of the head area which is comprised of 2592 three or four noded finite strain elements (S3UL S4R). Pinned boundary conditions at the lower cylinder edge supply stability for the solution. The evaluation was performed up to a pressure of 12.87 Mpa (1870 psi) with no true instabilities reported by the numerical solver nor any instabilities in the displacement response. It is very unlikely that the SCV will be able to obtain such a pressure without a material failure occurring somewhere in the structure due to the high strains that are present. Based on these analyses, the head area has a minimum potential to experience a buckling failure. 

E-286

1!

o -l il l ! ! l 

0 II 

S!ii
-mm

Figure 8.0.2 

Eigenvalue Buckling Shell Model of Compression Head Area

Puinrwod uary 

ConMjon

Figure 8.0.3 

Inelastic Buckling Shell Model with Perturbed Mesh (Shown in Gray)

E-287
9.0 SCV Standard Output Discussion :

In Reference (1). SNL requested all participants to supply response predictions at 39 sensor locations for comparison to test results. The requested data consists of vertical and horizontal displacement response. as well as meridian, hoop and maximum principle strain results. The locations supplied in Reference (1), Table 16 were based on design drawings of the SCV. Notes were provided to relate the gage locations to adjacent stiffeners. welds, the knuckle. the hatch sleeve. etc. In Reference (11). the sensor locations were updated and four additional sensors were added. However, the updated locations were based on the as-bulit elevations for the SCV and the notes supplying relative locations were not updated. The new locations for sensors 11-39 were given as elevations in the global axis system, but the as-built elevations for critical locations such as the knuckle, reinforcement rings, weld joints, etc. were not supplied. The gage location with respect to the adjacent stiffener, weld joint, or knuckle is the critical parameter. Based on the above discussion and conversations with SNL. the relative locations from the Reference (1), Table 16 notes were maintained with the exception of gages I-10. The locations for these gages were based on the local hatch or head coordinate systems. Since the updated locations were shifted significantly from the Reference (1) locations, and since the locations were based on local coordinate systems, the updated data was used. The as-built data was also used for locations 40-43 since these gages were not supplied in Reference (1). Since the gage locations were estimated, differences, particularly in the transition regions, in the point to point comparisons to the test data are expected. 

Results for both the friction (pt= 0.4) and non-friction evaluations are included in the Appendix A Standard Output portion of 

Mean 

this report. Mean model geometry, based on the as-built data supplied in Reference (3), was used in all the evaluations. thickness (except for the locally thinned submodel as noted). gap, elastic modulus and plastic strain behavior values were used consistently throughout the various simulations. The softened contact model, previously discussed, was also used exclusively to mitigate solution convergence difficulties. 

Table 

models 

9.0.1 lists the finite element models which were used for each Plot ID requested. In general, the axisymmetric shell were used to evaluate free field response data, the axisymnmetric solid models were used to evaluate transition areas around stiffener locations or rapid thickness changes and the quarter symmetry shell model and associated subrmodel of the hatch area were used to evaluate response points in the hatch vicinity. 

-category Plot to oinp ouanft Nm~erical Model categoj Plat ID OU Quatittumsy Numerical Model 2Emsp. Math NUa I max. Pfta mtai 3-0 Sheal sIrmodel Free Feld 21 a* mnendcssreli armsymeftics EopL. Match, Are- 2 mPi. Strain 3-0 shoe submodel Free FWld 22 fLt,,-rld,.sran" a•,-'•-ne•t shell Ep'S Hiosh Ar 2 ad. menistrn, 32) sheal mUmodel Free Feld 22 emt o'•-p s•rain am•-n---•t shell 

EEqiLip. 

ha 

Hatch 

tch , Ama 4 in. ewldslra• 3-D shoe subtod.l Free Fied 24 inL ho-- -sr.,, a.s scca -, shea Area a e& hoop stain 3-0 9Md submodW FReeel 25 a* mendszlyaa 34) shell model CpuS. Hatch Area 6 ft. hop muai 3-0 she Ssimnoder Free Foed 26 tLi meddstmlin 3.0 she model Top emad 7 ML P am .. M..eic " Free Fmed 27 eon. hoop Stra•- 3-0 shel --- .. Top mead a e1. hoop s,0M aunsymmeft shell Free FedW 28 inL hoop s-r-, 3-D shell TOP Hea -9 e. merd.mai a ,taynrnetri, shell Free Fid 29 in. mend.tsra-a• • Wnneira solid TOP Head 10 itmendcara •mynne- shell Free FiMl 30 .it. hoop stain Amsyri,, solid Trasilion Rep"io- 11 e3t. men-,•Lraam a -r.,neul, solid Ftee Field 31 ire. meu-=.s-ah aispeneic - shell immtmonRegins 

Trar--i-p, Reg... 

12 int. mendatgai aasrmenetn solid Free Foeld 32 lin.hopm amsymetnebi s 13 an mends.• ma. at•-rmme- soud Free Field 33 ,L-. en -,smi -•. a symr .- ,,ise Trarai---n Reg=*e 14 ki men,,xtra-, a -syrnrne,, sod Free Fed 34 inL hoop st,•ai &amsrnme, shell Trsion Re-,,,, 15 Is ex ent, ana a" naetic. sold DisPtacanent 35 Vertical a-syn-ne- shea Trara-eo Region: 1If int menldsraa am•-, • nen•,- sold Diap'ae•mree 36 ho'z-t-'-•' a•---ne- s•old Trgr"s=o Reg==n 17 eat uenýsra a~rfxsymen Shea Dispacmernem 37 hortsonW isiSyiWU~ftft1 Tran--on Re-- o 18 s it a'en•d•÷sma as, . a sha Driacermere 311 Vertical a3,Ms• msolid .. Trnlio egos 19 ex nandstraan asu -snaehSolid Displacermern 39 hotisorse 34) shell model Transom Reg-n• s 20 lit mend - 0-- as•--'reu• , sold Eqp-. Had Area 40 1i1. =M.dStra-- 3-D shea sTodel" 

Euip. H Ama 41 int hoop t-rai 3-D she ,•-.-odd _________Eipuq. Match Area 42 ONlIt mehldtmh, 3-Oshee sAtmodel 

L - fto_____EU. Matci Ame 42. lit hoop m 3i20 Shea umdll 

Table 9.0.1 Standard Output Model Identification 

(C locally thinned shell submodel). 

E-288

II
10.0 Key Results (First Yield, First Contact. Critical Areas)

This section discuses the predicted results associated with certain key events that occur during the pressurization of the 

SCV. as well as the identification of highly strained areas on the SCV. 

The SCV has a design pressure of 0.78 Mpa (113 psi) based on the design pressure of the full scale steel containment vessel from which the SCV is based. To determine the first yield pressure and location, all analytical models previously presented were reviewed to identify the critical areas of the SCV. The first yield pressure is based on a Von-Mises stress intensity as compared to the minimum yield limit stress specified in Reference (2) for the SGV490 (0,=265.0 Mpa) and SPV490 (a)-=490.0 Mpa) steels. As tested material properties were not used for this evaluation, therefore the estimates of yield pressure are conservative due to the use of minimum yield stress values. First yield pressure occurs at a pressure of 1.0 Mpa (145 psi) as determined by the mean gap opening axisymmetric solid model of the knuckle region (Figure 4.1.2). The maximum Von-Mises stress occurs at the bottom of the knuckle on the outside surface. Yielding also occurs at a slightly higher pressure of 1.3 Mpa (190 psi) where the material interface weld intersects the hatch reinforcement ring. This evaluation is from the mean thickness shell submodel of the equipment hatch area (Figure 4.2.2). Local thinning of the plate, as defined in the as-built conditions of Reference (3). may reduce this first yield pressure to as low as 1.1 Mpa (160 psi). 

First contact between the SCV and the CS occurs in the knuckle region at a pressure of 3.2 Mpa (470 psi) as determined from the mean gap opening axisymmetric solid model. This model is the best average estimate of the as-built conditions of the SCV and CS and therefore these results represent an average estimate and not a minimum estimate of the first contact 

pressure. The less refined, quarter symmetry shell model (Figure 4.2.1) first contact prediction was approximately 3.5 Mpa (500 psi). This small difference in results (-6.0 %) can also be attributed to the different load increments which were used in each of the respective analyses. The propagation of contact, as the internal pressure is increased, is further discussed 

and illustrated in Section 6.0. 

There are a number of critical areas in the SCV which are possible locations of failure. No material failure algorithm is readily available in the ABAQUS/Standard Finite Element Program which was used throughout this pretest evaluation. Since the loading is quasi-static, and the SCV is a complex welded structure, it is believed that such an automatic material failure model is unnecessary. Instead. the material minimum ultimate strain limit, which represents a material's point of ductile instability (necking), was chosen as an appropriate starting point for an assessment of a critical failure pressure. This ultimate limit would be subsequently reduced by a factor based on variations in analytical results derived from parametric investigations. A numerical technique which was originally intended for an objective comparison of time history data (Reference (12)) was used to derive average reduction factors for differences in response prediction over the SCV surface. For example, a comparison of mean gap versus maximum gap results data (Figure 5.0.1) results in an 

average difference of approximately 10.0% along the surface of the SCV. A reasonable reduction factor for the ultimate strain value for this parametric variation would therefore be 1.10. Similarly, reductions for thickness and friction variation would be approximately 1.10 and 1.02. The thickness reduction factor does not include the local thinning around the equipment hatch reinforcement plate since this detail was not modelled in the axisymmetric evaluations. The local thinning around the hatch was evaluated separately by a shell submodel with minimum plate thickness near the equipment hatch reinforcement plate. The friction reduction factor was derived from a comparison of the g± = 0.4 and p = 0.2 

evaluations since a zero friction case is improbable. 

Additional reductions in the ultimate strain value would be based on unknowns in the as-built structural details such as quality of construction, weld defects and surface flaws. A mean reduction factor of 1.10 was used in Reference (13) to 

account for these types of unknowns and will be used here as well. Further reductions due to material variability were not performed since mean as-tested material properties were used in the numerical simulation, but minimum ultimate strain limits were used in the evaluation of the peak equivalent plastic strains. The analytical models, in varying degrees. capture the critical geometric characteristics of the SCV and CS. Since the more refined models are used in assessing the peak plastic strains, no reductions were performed for the level of analysis detail. 

A review of plots which depict maximum equivalent plastic strains versus internal pressure would be prudent to insure that relatively stable behavior is also present at the reduced ultimate strain limit. Figure 10.0.1 illustrates the rapid increases in strain which can occur with a relatively small increase in pressure. This result was taken from the mean shell submodel.

E-289
Figure 4.2.2, near the material interface line and hatch reinforcement plate area. Figures 10.0.2 through 10.0.4 show 

critical areas of equivalent plastic strain concentration in the knuckle region, the intersection of the cylinder and conical 

shell and the equipment hatch area. Note that the appearance of the penetration of the SCV into the CS. as shown in Figure 10.0.2. is from the softened contact model, which in a general sense, approximates the compression of the SCV painted surface. Based on these evaluations, the equipment hatch area appears to be the most susceptible to failure due to the lower 

ultimate strain limit of SFV490 steel as well as the significant hoop strains which are present. In addition, Reference (3) identified local thinning of the SPV490 and SGV4S0 steel plate in the vicinity of the equipment hatch. To address the 

effects of the plate thinning, a shell submodel with the minimum plate thickness measured for the respective materials %%As 

developed. The thickness of several elements was reduced to 7.4 mnn (9.0 nim design thickness) for the SPV490 steel and 

7.6 mm (8.5 mm design thickness) for the SGV48O steel.

f14.

Ii

0 1 3 4 3 6 7 3 9 10 11 12 33 14 U5 

bnmal lI•SOW Mh

Figure 10.0.1 Representative Equivalent Plastic Strain History 

Mean Shell Submodel - Friction = 0.4- SPV490 Material 

C: . .'l4-I'. 

,20 mm fUt 

Knukl ,,,•.1S . -~ 

.1 . 

i-uce gi 

P.0 a e U00620 

c4

-I-I.. 

-4J&14.m 

Figure 10.0.2 Deformed Fringe Contour Plot of the Meani Model Knuckle Region 

PEEQ Strain - P =6.97 Mpa (1010psi) - Deformned Scale = 1.0 

E-290

11

- Iasi* 5uffw 

- Mi4d& 5afam

it T 1 Ai 

o I .7A' * • , /
.. ..

...

......... U 

C 

U .0 

lb 

.II 

U 

q. ard - 0. 

o '0 

1W 

0 

C 

ii:

Ii r- -S

I I 1' 

I 

0 0

I

CY 

U; 

I. 

iz.

0%
The local plate thinning had a significant effect on the concentrated equivalent plastic strains. While the model 

consen•atively utilized the minimum thickness value for the thinned area. it does show the sensitivity of this area to the 

as-built conditions. Figure 10.0.5 shows a comparison of equivalent plastic strains (PEEQ) between the mean thickness 

shell submodel and the locally thinned shell model for the SPV490 material in the locally thinned area identified in Figure 

10.0.4.

I 

I 

I

: 2.• I , 

- L.7h. i i~. i g I___ 

' .I I i i K 4 | 

.: I I I t I 

,it I,,, 

4 $ 4 7 I U I t~I 4 L 

, i ~ hs i !N

Figure 10.0.5 Comparison of Mean Thickness Shell Model to Locally Thinned Shell Model 

Equivalent Plastic Strain versus Internal Pressure 

SPV490 Material - Inside Surface 

11.0 Conclusions 

The response predictions at the standard output locations represent mean value data and therefore may be either conserva tive or unconservative as compared to the test response data. This is particularly true for the evaluations which include 

friction which are considered to be more representative of actual test conditions. The parametric evaluations %hich were performed using variations in gap distance, plate thickness and contact location illustrate the level of deviation between 

predicted response and test data which can be expected. 

Section 10.0 presented several critical areas in which failure of the SCV could initiate. This does not, however, preclude failure in other areas of the SCV which may be caused by unknown as-built conditions such as poor weld penetration. The 

maximum pressure level prediction for which there is a high conficence (>95%) that there is a low probability of failure 

(<1%). as requested in Reference (1), is submitted under separate cover to insure anonymity. 

E-292

iI
References:

(1) Sandia National Laboratories Submiual.l 0 July 1995. 

(2) Sandia National Laboratories Submittal. 21 September 1995. 

(3) Sandia National Laboratories Submittal, 20 February 1996, SO-96-012. 

(4) ABAQUS/Standard User's Manual, Hibbitt. Karlsson & Sorenson, Inc. Version 5.5. 1995. 

(5) Math/Library User's Manual, IMSL Version 1.0. April 1987. 

(6) ABAQUS Theory Manual. Hibbitt, Karlsson & Sorenson, Inc, Version 5.5,1995. 

(7) Avallone. E.A. and Theodore Baumeister M. Marks' Standard Handbook for Mechanical 

Engineers, 9th Ed., McGraw-Hill, Inc., New York, 1978. 

(8) ASTM D217. "Molykote Specialty Lubricants". 

(9) Wu. M.T. and Shun Cheng, "Nonlinear Asymmetric Buckling of Truncated Spherical 

Shells," Journal of Applied Mechanics, pp. 651-660, September 1970. 

(10) ABAQUS Verification Manual, Hibbitt, Karisson & Sorenson, Inc. Version 5.5, 1995. 

(11) Sandia National Laboratories Submittal, 9 May 1996, SO-96-041. 

(12) Geers, Thomas L., "An Objective Error Measure for the Comparison of Calculated and 

Measured Transient Response Histories," The Shock and Vibration Bulletin, Bulletin 54, 

Parn2, June 1984. 

(13) Sammataro. R.F., W.R. Solonick. and N.W. Edwards, "Acceptance Criteria for Steel 

Containments Under Severe Accident Loads," ASME Codes and Standards in a Global 

Environment. PVP-VoI. 259, 1993.

E-293
ELECTRIC BOAT CORPORATION 

A GENVERAL OYMAM)CS CCOMP;ANY

Enclosure (2) to: 

41 5:TFT/603039/3.8

Appendix A Standard Output Plots 

Electric Boat Corporation 

June 3, 199B 

Eý294

11
APPENDIX A 

STANDARD OUTPUT

E-295
Ouukid Merd. SimmI nmin 

0 9

. -4-

0 0 

8 a

K 

a 

U 

"a

Inside Makid. SIM"l rd/r

a 

a 

['A 

I,

S

I 

I

Imise Mal. Principle Sind" Inlm

I,. - - - -

I 

- 5-.--, 

- - I 

4%

In"d Man. Principle Strain

C 

0 

[hR 

I, 

0

rn/rn

F 

F-- 

-' - -

----- --

9. 

- I -

I 

I

I ___________ 9. ___________ 

__________ 9. __________ 

I 

S. 

U.

t%) V%

F

9m

- hA I. 

I

F

K S
Location 5 

I IV I I 

I -*ijj= I~~ If--~ 

10

Intra PleSSm7 MPS

Location 7 

a - -~V I a I - -

---I .. I L- i.[... O I I I 

~I I 1 ~I1 1 1 j jill 1 - 17 I I

5 10

Int=.'a Press=~ mps

Location 9

0O0 

0.02

=0.01 

0

kennPmetrc MNa lm=-na PIcIsUT mpa

&-297

location 6

0.12 

0.1 

1cm 

10.06 

a0.04 

0.02 

0

0.12 

0.1 

I0.06 

A0.04 

0.02 

_0 1 15

0.17 

0.15 

0.13 

A0.09 

H0.07 

0.03 

-0.01

0

is

5

. . U0.4 1 

- - - - - - - -kicdm - 0.0 1
Location 9 

14I I

0.2 

0.09 

0.0 

0.07 

10.06 

-0.03 

i0.02 

0.02 

0 

-0.01

Irnuna Pzusm mps

Location 11

~~I I* ~IJ 

-i I 

Ji ll. ~ I I I/ 

~~I -II_ I . ! 1 1 I

5 110 

bztemai Pmmwe Mh

0.1 

0.09 

0.08 

0.07 

h06 

A0.05 

10.04 

0.0 

-0.01

Location 10 

SI IFI 11 2,11I~ 

IL!imi - -1 

F-1I ! I ! f- J. 1rf

5 10 

1m~roj PrMSsum ma

Location 12

is

0.07 

0.06 

0.0 

0.04 

aO 

0.01 

0 

0.0

I I 1 T 1 11

1111111

20

lmenmal Pnjwesu Mpa

E-298

1.

5s is

0M06 

0.05 

:0.03 

am 

i0.0 

0.01

I I I I

11111 -~j

is

ftdcm a CA 

hicdm , 0.0
0.3Location 13 Loa~tion 14 

0. 3 - - * 0.'30 4 

00.0. 

0.0 

kIc . 0. 

0.013 o -* 

A I If 

0).003 

0.0 10-* is010i

kazema! Pjssm~ MP&

Ime t Mnw U

E-299
zopiaOn u l C Location IS 

I oI I 

10.01 '= -0.01 

0 0' 

0 5 10 15 0 S 10 15 

tmemai Pressurn MNn Inzm Pmusme MN 

Location 19 Location 20 

0.0125 0.012------------

40.0065 jJ A, 7 in 1[~ 

0S 10 is 0 5 30 is 

I== Presmur MPI Lua' Pressure MPS 

E-300 

II

I - - •
Loocation 21 Location 22 0.013 003' * - * . 

0.01 0.0111 e I 

0.007 ow 

I.lOM -I I I i-I 

04003 -= I ;tI..I -- iiiii:ii: 

camtion 23 Location 24

oij LL 11- .a.-

biessl Pnwsur Mpa 

E-301

0t.01. 

B M 

0 1 0 ~ is1

imerna! PIC==ur MP3

0.02 

0.01 

40
Outside I loup Sim.1, nih.

0 

[IA 

I' 

IA 

C 

0 

[IA 

I

.6 

0i

[ 

I

Wi SI 

II 

SI 

'I II 

mu 

pp

K 

U

C

[ IA 

I

Ia

Outside Maid. Sima. mion

IA

.6

40

Inside MaidL Simuah vmi 

a

I - - -

-6

-- 6- -____________ ____________ -___________ 

liz' -__ 

a 

I 

- - - -

Insa hm ~u1 Simlau WNm

F Ca 

0

F 

IF1
Locatiw, 29 -r - . - - - . - - - - a - - -

till 1W III 

*I I I V FiiiTIT 

I lii .t.1.1 I 1j1, 1111 ill 

liii ILKi -I-H-I- dKfi iLl _____ 111 I 

* -. fiiLf--I li-i-I - iEE1Et:i:i2Ef: 

I I ' I

5 10 

Internal Presur mps

L~ocation 31

5 30 

Intrna Presuu Mha

25

0.022 

0.02 

0.013 

0.016 

I0.014 

S0.012 

0.006 

0

Lecation 3V

i111 f I 

- - 1IIij 

.JT1 Ill 

- TVF1 

I 1tA-.- -

III, I I 'Ff'I' -*-f-II ]Th I I 111111 IiIiI1-

0 5 10 

lotsa Pressur MPa

Location 32

0.03 

0.015 

~0.01 

0 

0

Prtsl hsum Mha

E-303

0.028 

0.016S 

I0.014 

0.012 

0.006 

0"00 

0~0

15

0.013 

0A013 

0.009 

Ow 

0.003 

0.001 

4003

HIIj III :riri: HT

is

I i

-- Ukdon a CA 

- - - - - -friction . fl
Location 33

5 10 

Irnemza3Prmsrn MPS

---.- 0.0-" 

0.02 

- 0.018 

0.014 

S0.012 

O= 

0.016 

0.004 

0.002 

0 is

LocatIon 34 

a a - - * I I I I I I LIJ .....j....j... K JViT 

j -i-;.,.-

.LLLL]I I I I I LI

I [1fa I 111 

I tI I I I II *..I.jjJ,.

0 .LLLI 

Snn e ~

-OAJ

Location 35

5 10 

Imumd Pmsum Mpg

Location 36

0.06 

0.05 

0.04 

10.02 

0.01

.1 

is 0.01 5 10 

Imjeraw em MNA

E-304

0.002 

0.001

U I 

U I 

I

0

-0.001

4w- '*

01-25 

0.2 

0.15 

0.1 

0.05 

0 

-0.0

1.. 

I

is

i
I i

0.06 

0.05 

0.04 

S0.03 

0.02 

0 

-0.06 

0.06 

0.04 

0.03J 

0.03 

0.0 

Cu

0&03 

0.02 

U 

a0.0 

0

I

Location 38

I II III I _____________ 

........... i.......i..=...i.....* I I II 

li 

I III I II I -.-

I i I I I I 1.. II I

JilL

baaw um bipa

is

0.06 

ae 

*1 

O.oi 

0 

0

Location 37

5 10 is 

3rncril Ptuswe Mpg

Location 39

S 10 

3m=zna PremSJY MP&

is

E-305

5 10 

buaw P=LM N

U

is 0
Location 40

0.015

10.005

0 a

0 3 10 is

hmeazj Pf==M. MN

Loction 42 

- - - - - 7-i-f

03 

U0.2 

0

Location 41 

I I 

i1 ~11 -1 

S Ily II

Irntum h==sw MN 

Loation 43

03 

E0.2 

0.3

0

inmal Ntssw MPS

I I 

III 

-- I ll I-i. 

=a - - 1* 

-I -I & - 1- 000, ~ 1 1. 1 1 1. ~1

--10 -

is

Intsnia Prsw, MNa

E-306

0.015 

0.02 

0

0 5 10 is

fii.d- - 0.41 

hictim n 0.0 1

5 10 I 10

11
ELE-TRIC BOAT CORPORATION 

A GMERAL [E)YdAMI= COlANY 

Enclosure (3) to: 

415:TFT/603039/3.8 

Electric Boat Corporation Low Probability of Failure Pressure Prediction 

Electric Boat Corporation 

June 3, 1996

E-307
Low Probabiliny of Failure Pressure Prediction:

Reference (I) requested each participating organization to state what maximum pressure the SCV would obtain prior to failure. This prediction is to be defined such that there is a high confidence (>95%) that there 

is a low probability of failure (<I %) of the SCV. 

As discussed in Section 10.0 of the pre-test report. Electric Boat Corporation proposed the use of the 

minimum ultimate strain reduced by a series of reduction factors to account for variation and unknowns in the as-tested SCV as the method for determining a suitable maximum pressure. The equipment hatch area below the material interface line was identified as a possible location for failure initiation. This location 

represents a critical area due to (1) the use of the lower ultimate strain limit SPV490 steel as compared to 

SGV480 steel, (2) strain concentrations caused from the reinforcement plate and material interface line. (3) possible weld defects, and (4) local plate thinning during construction of the SCV. 

The locally thinned shell submodel of the equipment hatch region was found to possess the controlling strains of all the simulations performed. The appropriate reduction factors for this evaluation include the 1.10 factor for gap variation, the 1.02 factor for friction variation, and the 1.10 factor for as-built structural details. Combining these factors results in a total reduction factor of 1.23. Dividing the appropriate minimum ultimate strain for SPV490 steel (-... =10.0%. Reference (1)) results in the following "failure" limit strain. 

E= -£e /i.23 - 8.0% 

The maximum pressure was determined by allowing the peak equivalent plastic strain to obtain this failure limit value through the thickness of the shell. This results in a maximum pressure of 4.7 Mpa (680 psi) or approximately 6 times the design pressure. Due to the use of minimum as-built plate thickness in the evalu ation, minimum ultimate strain values with suitable reduction factors, and detailed modelling of the critical areas of the SCV. Electric Boat Corporation considers this pressure to defime a low probability of failure 

value.

E-308
Appendix E-5

Japan Atomic Energy Research Institute 

Japan

E-309
Pre-test Analysis of SCV Test by JAERI uith ABAQUS

SUGIMOTO, Jun and NIIYAMA, Kenji* 

Japan Atomic Energy Research Institute 

Tokai-mura, Ibaraki-ken, 319-11 Japan 

*Mitsubishi Research Institute. Inc. 

Otemachi 2-3-6, Cbiyda-ku, Tokyo 100 Japan 

1. Introduction 

Containment Model Tests to investigate a failure of the containment vessel has 

been initiated as a joint research program among Nuclear Power Engineering Corpo

ration(NUPEC). U.S. Nuclear Regulatory Commission(NRC)and Sandia National Labo

ratories(SNL). For the effective pre-and post test analysis of these tests, a Round Robin 

analytical activities have been organized. 

Since JAERI has done the post-test analysis of SNL's 1/6 scale RCCV test 

before(i)(2 ), JAERI expressed the intention to participate in the Round Robin analysis 

with ABAQUS code(3 ). The present paper describes the results of the pre-test analysis 

by JAERI for Steel Containment Vessel(SCV) test. 

2. FEM Modeling vith ABAQUS 

(1) FEM mesh 

A finite element code for non-linear problems, ABAQUS, was used to analyze the 

behavior of SCV and Contact Structure (CS). Both SCV and CS are modeled with shell 

elements. Most parts are modeled with 4-node shell elements. The top of the top head 

and hatch cover are modeled with 3-node shell elements. The total number of integration 

points in element section is five. Figures 1 and 2 show the FEM mesh of SCV and CS. The 

FEM Model is 180-degree symmetric, and modeled between 270 and 90 degree directions 

in the global coordinate system. The part lower than the upper surface of the ring 

support, i.e. z < 0 in the global coordinate system, is not modeled in the present FEM 

scheme, because the bottom head is much thicker than the rest of the system and the 

deformation of this part is expected to be negligible.

E-311
scheme, because the bottom head is much thicker than the rest of the system and the 

deformation of this part is expected to be negligible. 

(2) Boundary conditions and contact modeling 

The bottom of the model(z = 0) is completely fixed. Symmetric conditions are used 

as the boundary condition on the plane of the symmetry. Nodes of SCV model are 

located on the inner surface of the vessel to set clearance between SCV and CS. Contact 

between SCV and CS is modeled with small-sliding interface element. Contact model 

with friction coefficient 0 between SCV and CS are calculated. 

(3) Material properties 

The SCV is made of two materials, SGV480 and SPV490, welded into one body. 

NUPEC conducted tensile tests of the material pieces cut from SCV. The results of the 

tensile tests were used for the material properties. The tri-linear curve was used to model 

stress-strain relation of the materials. Young's moduli were measured by NUPEC. The 

hardening coefficients for two materials were evaluated by the least squares method using 

tensile tests data after yielding point. After stress reaches tensile strength, the hardening 

coefficient was set to zero. The tensile test data at loc-ll was not used to evaluate 

hardening coefficient because Young's modulus is much different from that measured 

by NUPEC. Evaluated material properties are presented in Table 1. Figures 3 and 4 

show the stress-strain relation, measured in tensile tests, used in the present analysis for 

SGV480 and SPV490, respectively. Material property of the CS made of SA516-70 is also 

presented in Table 1. The CS is assumed to be elastic in the present analysis because it 

is much thicker than the SCV. 

3. Calculated Results 

The internal pressure was loaded to the FEM model described above, and stress, 

strain, displacements and contact condition are calculated as a function of pressure. 

(1) Distribution of Plastic Strain 

Equivalent plastic strains are observed during the analysis. First yielding are seen 

around knuckle and in top head at pressure of 2.80 MPa. As pressure increases, it gives 

maximum value at just besides the hatch reinforcing plate. At pressure about 9 MPa, 

E-312

I!
the value at apex of top head overtakes that around hatch reinforcing plate. Figures 5 

and 6 show distribution of equivalent plastic strain at pressure of 9.00 MPa in top head 

and around hatch reinforcing plate, respectively. They reach about 10 % at this pressure 

level. Over this pressure level, plastic strain in top head increase rapidly, though that 

around hatch reinforcing plate does slowly. Distribution of equivalent plastic strain at 

pressure of 10.81 MPa in top head and around hatch reinforcing plate are shown in figs. 

7 and 8. Finally, calculation was terminated because of numerical instability due to 

yielding in top head region at pressure of 11.81 MPa. 

(2) Contacts between SCV and CS 

Contacts between SCV and CS are observed first at pressure of 4.00 MPa in upper 

and middle conical shells and around knuckle. Section of SCV and CS in 0 degree of 

global coordinate system at this pressure is shown in fig. 9. Contacts area propagate in 

conical shells as pressure increase. Figure 10 shows section at pressure of 7.63 MPa. In 

this figure, most of spherical and conical shells contact to with CS. Only in lower conical 

shell, area of contacts increases slowly. Section at pressure of 10.81 MPa is shown in fig. 

11. 

(3) Standard Outputs 

Standard output #35 is shown in fig. 12. It is vertical displacement at apex of top 

head. The increasing rate get small around pressure of 3 MPa, because of contact between 

SCV and CS. Finally just under pressure at which analysis terminated, it increase rapidly 

because of plastic deformation in top head. 

Standard output #36 is shown in fig. 13. It is horizontal displacement in upper 

cylindrical shell. Around this standard output point, SCV is free from CS. The increasing 

rate changes much around pressure of 7 MPa. This results shows that plastic deformation 

in top head region is getting larger over this pressure level. 

Standard outputs #5 and #6 are shown in fig. 14. They are hoop strains just besides 

hatch reinforcing plate. They are observed on inner and external surface of the vessel at 

same location, respectively. Plastic strain is maximum around this point under pressure 

of 9 MPa. A rapid increase is seen around pressure of 4 MPs- SCV begin to contact to 

CS and contacts area is propagating around this pressure level. Once SCN' contact to 

CS, these strain increase slowly until the end of the analysis.

E-313
Standard output #7 is shown in fig. 15. It is maximum principal strain at apex of 

top head. Increasing rate is very small in the beginning of loading and quickly get large 

at pressure of 5.45 MPa. The strain reaches to 12 % at the end of loading. 

4. Discussions 

Failure mode of SCV is discussed in this section. 

Plastic strain gives maximum value around hatch reinforcing plate, and local failure 

is likely to occur at material or thickness change interface around this location. But, we 

have no failure model included in this analysis. Hence structural failure mode is mainly 

discussed. 

In this analysis, calculation is terminated because of numerical instability due to 

large plastic deformation in top head. In this point of view, failure mode is expected 

to be rapture in top head. No structural failure is seen around hatch, though plastic 

strain is large in this region. The pressure at which rapture will occur in top head is 

10.81 MPa. It is detected because standard output of strains in top head show sudden 

behavior change at this pressure. We can hardly detect confidence pressure at which 

SCV is expected to be free from rapture in top head. We can say that deformation will 

be small under pressure of 6 MPa, from standard output #7 and #36.

B-314
Fig. 1 FEM mesh for the Steel Containment Vessel (SCV)

E-315
Fig. 2 FEM mesh for Contact Structure (CS) 

E-316

|,
SGV480

000 

700 

a)400 

300 

E-4 

200 

0 

0 5 10 15 .20 25 30 35 40 

True Strain [%J 

Fig. 3 Fvaluated stress-strain relation 

and experimental data in Ioc-I thru 10 (SGV480)
SPV490 

8000 

700 

600 

4'" 500 

w 400 

300 

200

O0 

0III ,I, 

0 5 10 15 20 25 30 35 40 

True Strain ItJ 

Fig. 4 Evaluated stress-strain relation 

and experimental data in Ioc-12 (SPV490)
S5. DZSPZAMCEMT IFCM'z/O FACTOR w 2.00 

Zmm CO!•TEZD IN T'S STEP .500 TOTL, AJLCCM.,JE ?ZI"2 2.50 

ABAJS VERSIZO: S.5-2 DVAT: 15-OCT-S96 TIM: 23:07:56 

STEP 3 DNCREY.MT IS5 

Fig. 5 Distribution of equivalent plastic strain 

at pressure of 9.00 MPa in top head

E-319
SECTION POINT 1

L

DISPZACDCDN YXAZFZCATZrN FACTOR a 1.00 

T?) cO2xr= ne TxIS STEP .S00 TOTAL ACCUXUrATED ZE 2.50 

A3AQS VERSZION, 3.5-1 D&TE: 15-OCT-96 TZIME: 23:07:56 

STEZP 3 INCEMET 15 

Fig. 6 Distribution of equivalent plastic strain 

at pressure of 9.00 MPa around hatch reinforcing plate:

E-320.

PDQaG VALUE 

+0.00E-00 

+1.02E-02 

+2.04E-02 

+3.06E-02 

+4.09E-02 

+5.11---02 

+6.13E-02 

+7.16E-02 

+8.18E-02 

+9.20E-02
sL-c:oMc Pox= I

PMDMG VA=ZZ 

.2 .793-C2 

-4 .26E-02 

-5 .74E-02 

-7.22K-C2 

*S.Z9-01 

.1.16K-c! 

.1.46K-c: 

-.1.4-0K4,,

DZSPL&CEV1T HAMFZCATIOI FACTO * .0 

L ?!3r C0I~P~ZwZ = TkILS S"TEP .691 T(MIL. ACC MMATED TX 2.68 

1.AMOS %rEPSZO: 5.5-1 DATE: 15-OCT-96 TIME: 23:07:56 

STECP 3 XNMRMý. 18 

Fig.. 7 Distribution of equivalent plastic strain 

at pressure of 10.81 MPa in top head

E-321
L d"DZSlACM€N': XMAUCNZFZCAT.ON ¢• FAcoR 1. 00 

TIM C -,TZD ZI THIS STEP .61 2 'OTAL A•C ,MATZD TMZ3 2.68 

A.AQtJS VERSIO•: 5.5-2 DATE: 15-OCT-96 TMMZ: 23:07:56 

STEP 3 INCREU= 28 

Fig. 8 Distribution of equivalent plastic strain 

at pressure of 10.81 MPa around hatch reinforcing plate 

E-322

S1
DZSr-ACDM~T MCN.EFICA&!ON FACTO a 1.00 

.M- COSM•,.T IN Ml5IS STEP .400 TOTAL ACCtYL7TD T• 1.40 

ASAOUS VERSION: 5.5-1 3AE: 15-OC"T-96 IP.M: 23:07:56 

STEP 2 INCREMENT 2 

Fig. 9 Section of SCV' and CS 

in 0 degree of global coordinate system at pressure of 4.00

E-323
ZMCE CCH = =IN ."Z-S SM .363 T L •,C'JH TZ,, Z' 2.36 

AM "•MR:ICI: S.S-I DATE-:.15-0CT.-9)6 Tn'D: 23:07:56 

Fig. 10 Section of SCV1 and CS 

in 0 degree of global coordinate system at pressure of 7.63

E-324
LZShEI:-. rA .'M"MON FAO,.. a 11.00 

TM COHI:2L"Ip= =) TJ STE .661 TI AC"Cr•,,,.."J TD 2.68 

AS&=• lrEM: 5.5-1 CATE: Z15-OCT-S6 TZ3": 23:07:56 

S"M 3 7NDEMET It 

Fig. 11 Section of SC\" and CS 

in 0 degree of global coordinate system at pressure of 10.81

E-325
Standard Output #35

120 

100 

800 

60 

40 

20 

0 2 4 6 8 10 12 

Pressure [MPaJ 

Fig. 12 Standard output #35 

vertical displacenment at apex or top head.
Standard Output #36

2 4 6 8 10 12 

Pressure [MPaj

Fig. 13 Standard output #36 ; 

horizontal displacement in upper cylindrical shell.

50 

45 

40

4J 

U) 

.,-4 

.6-I

1t1

35 

30 

25 

20 

15 

10 

5 

0

0
Standard Output #5,6

0.08 

#6 

0.07 

0.06 

• 2 0.05 

U 

0.04 

k 0.03 

0.02 +++ 

0.01 

"0 W" -4 I I - I 

0 2 4 6 8 10 12 

Pressure [MPa] 

Fig. 14 Standard outputs 115 and #6 ; 

hoop) strains just besides hatch reinrorcing plate
Standard OutDut #7

0.12 &--

0.1 

0.08 

0 

VJ 

0.06 

0.04 

0.02 

0 4m• _ m A m I 

0 2 4 6 8 10 12 

Pressure [MPaJ 

Fig. 15 Standard output #7 

maximum principal strain at apex or top head.
Standard Output #1 

0.02 

1) 0.015 

0 0.01 

0.005 

0 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #2 

0.025 , ' 

0.02 

U 0.015 

J1 

ii 0.01 

41 

C4 

0.005 

0 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #3,4

2 4 6 8 10 Pressure [MPaJ

0.035 

0.03 

0.025

0.02 

0.015

wp

4-i 

U)

0.01 

0.005 

0

0 12
Standard Output #5,6

2 4 6 8 10 12 

Pressure [MPaJ

I,, 

b) 

qj

4., 

g41 

In)

0.08 

0.07 

0.06 

0.05 

0.04 

0.03 

0.02 

0.01 

0

0
Standard Output #7 

0.12 

0.1 

0.08 

10 4 0.06 

0.04 

0.02 

0 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #8 

0.01 

0.005 

0 -0.005 

-0.01

-0.015 

0 2 4 6 8 10 12

Pressure [MPal
Standard Output #9,10 

0.07 

*9 #10 a 

0.06 

0.05 

0.041 

0.03 

jJ 

0.02. 

1+3 

~~3II 

0.015 

08 

•, 004 2 4 01

Pressure [MPa]
Standard Output #11,12 

0.06 

0.05 

0 -4 0.04 

0.)03 

Sk 0.02 

4J 0.03 

4w 0.0 

w 0 

-0.01 

0 2 4 6 8

Pressure [MPa]

10 12
Standard Output #13,14

0 2 4 6 8 10 

Pressure [MPa]

0.01 

0.008

w

on 

0 

.1-I 

4J 

o 

-4J 

-'4 

(a

0.006 

0.004 

0.002 

0

-0.002 

-0.004

12
Standard Output #15,16

2 4 6 8 10 12 

Pressure [MPa]

w

om 

0 

141

0.007 

0.006 

0.005 

0.004 

0.003 

0.002 

0.001 

0 

-0.001 

-0.002

0
0.0015 

0.001 

0.0005 

0 

-0.0005 

-0.001 

-0.0015 

-0.002

Standard Output #17,18

0 2 4 6 8 10 

Pressure [MPa]

-,4 M 

0 

-H 

4.1 

43 

to

12
Standard Output #19,20

2 4 6 8 10 12 

Pressure [MPa]

0 

.-ri 

-1 

m 

4.1 *rt 

ji 

*r 

JJ

0.014 

0.012 

0.01 

0.008 

0.006 

0.004 

0.002 

0 

-0.002 

-0.004 

-0.006

0
Standard Output #21,22 

0.007 

#21 

#22 

0.006 

0.005 

.1-I 0.004 

"•m• ~ 0.003 " , 

a, 

0.003 

0.001 

I 

I 

0 A 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #23,24 

0.02 

0.018 #24 

0.016 

0.014 

44 0.012 

-$4 0.01 44 

0.008 

.6-I 

43 0.006 

0.004 

0.002 

0i 

0 2 4 10 12 0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #25,26 

0.0012 

0.001 ' 

0.0008 1 

0.0006 

44 0.0004 

S0.0002 

%..I 

Im ~ ~ 0 ~ ..................... ~ ~ ~ ~ ..... °°°'°•°°°°°° ..... .............. °°".......................... °.................... 

4 -0.0002 

-0.0004 

-0.0006 

-0.0008 

0 2 4 6 8 10

Pressure [MPa]

12
Standard Output #27,28

0 2 4 6 8 10 12 

Pressure [MPa]

w 

LA

g44 

4-

In 

4-,

*rI

0.018 

0.016 

0.014 

0.012 

0.01 

0.008 

0.006 

0.004 

0.002 

0
Standard Output #29 

0.008 

0.007 

0.006 

0.005 44 

Np 0.004 "4I 

0.003 

4J 

0.002 

0.001 

0 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #30 

0.03 

0.025 

H 0.02 

I.• 14 0.015 

44 

h4 0.01 

0.005 

0 1 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #31 

0.007 

0.006 

0.005 

H 

w 

4 0.004 

0.003' 

4.J 

t 0.002 

0.001 

0 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #32

2 4 6 8 10 

Pressure [MPa]

.0-% 

44I 

a) 

N 

%-I 

-ti 

4J

m)

0.02 

0.018 

0.016 

0.014 

0.012 

0.01 

0.008 

0.006 

0.004 

0.002 

0

0 12
Standard Output #33 

0.0012 

0.001 

0.0008 

.• 0.0006" 

w 

$4 0.0004

.. 0.0002 

'4

0 .. .. .. . .. .... . ..... . . . . . . . . .... . . .. 0° ° , ° ° ...° ..°° ...° ....° .0 . . .. . . . . . . . ...... ..... . . . . . .. . 0 . 0. . . . . . . . . .. .0 . .0 ...° 0 . 0 °. . ..0... . 

-0.0002 

-0.0004 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #34

2 4 6 8 10 

Pressure [MPa]

171 

w 

I-

*44 

44I 

41 

4-I

0.018 

0.016 

0.014 

0.012 

0.01 

0.008 

0.006 

0.004 

0.002 

0

0 12
Standard Output #35 

120 p 

100 

80 

60 

"r40 

20 

0 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #36

2 4 6 8 10 12 

Pressure [MPal

tIn

9-I 

IJ 

U 

H 

p. U) 

.f4

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

0.

0
Standard Output #37 

25 

20 

4;b-, 

10 

5 

0 

0 2 4- 6 8 10

Pressure [MPa]

12
Standard Output #38 

12 

10 

8 

6 

.4 4 

2 

0 2 4 8 I 0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #39 

25 

20 

I

15 

10 

.1-0 

5 

0 2 4 6 8 10 12

Pressure [MPa]
Standard Output #40

-0.0005 

-0.001 

-0.0015

0 2 4 6 8 

Pressure [MPa]

'I) 

-4

0.002 

0.0015 

0.001 

0.0005 

0

14 

J-P 

to]

10 12
Standard Output #41

2 4 6 8 10 

Pressure [MPa]

0.025 

0.02

00

U 

4J 

co

0.015 

0.01

0.005 

0

0 12
Appendix E-6

Nuclear Power Engineering Corporation 

Japan

E-359
Pretest Analysis of a 1:10-Scale Steel 

Containment Model Subject to Static 

Internal Pressurization 

July ,1996 

Nuclear Power Engineering Corporation

E-361
Contents 

Abstract ........................................................................................................................ E-363 

1. Introduction ........................................................................................................... E-363 

2. Analysis M ethod and Outline of Analysis Series .................................................. E-364 

3. Analytical Conditions ........................................................................................... E-365 

3.1. Adopted Analysis Options ..... o ........................ E-365 

3.2. M aterial Properties ................................................................................. E-365 

4. Global Shell M odel Analyses ................................................................................ E-367 

4.1. Analysis M odel and Analytical Conditions .............................................. E-367 

4.2. Parameter Study Analysis ......................................................................... E-370 

4.2.1. Effect of Gap Size ........................................................................ E-370 

4.2.2. Effect of Friction Coefficient ....................................................... E-371 

4.3. Global 2-D Shell M odel Analysis ............................................................ E-374 

4.4. Global 3-D Shell M odel Analysis ............................................................ E-375 

4.5. Comparison of 2-D and 3-D Analysis ...................................................... E-375 

5. Local 3-D Submodel Analyses .............................................. * ............................... E-383 

5.1 Submodel Analysis of Local 3-D Top Head Section ............................... E-383 

5.2 Submodel Analysis of Local 3-D E/H Area ............................................. E-383 

5.3 Buckling Analysis of Local 3-D Top Head Section ................................. E-384 

6. Investigation of Critical Area ................................................................................ E-390 

7. Pretest Prediction Summ ary and Conclusions ...................................................... E-390 

8. References ............................................................................................................. E-392 

Appendix: Standard Output ........................................................................................ E-393 

E-362
Pretest Analysis of a 1:1 0-Scale Steel Containment Model Subject to Static 

Internal Pressurization 

K. Komine*, M. Konno** and T. Matsumoto* 

*Nuclear Power Engineering Corporation 

Fujita Kanko Toranomon Bldg.5F 

17-1, 3-Chome Toranomon, Minato-ku. 

Tokyo 105 Japan 

**Htachi Engineering Corporation 

2-1, Saiwai-cho 3-Chome, Hitachi-shi, 

Ibaraki-ken, 317 Japan 

Abstract 

This report summarizes the results of a review, on the basis of pretest analysis, about deformation 

behavior, failure pressure and failure mode of Steel Containment Vessel (SCV) test model, which is 1/10 

scale model (1/4 thickness) of actual SCV, under pressure beyond design conditions. 

The reviewed items and evaluation method are as follows: 

(1) Global behavior, failure pressure and failure mode of the SCV test model 2-D axisymmetric elasto 

plastic/large displacement/contact analysis. 

a. parameter study 

b. global behavior prediction of SCV test model based on the results of the parameter study. (2) Global and local behavior, failure pressure and failure mode of the SCV test model 3-D elasto-plastic 

/large displacement/contact analysis. 

a. global behavior evaluation of SCV test model 

b. top head submodel 

c. equipment hatch submodel 

d. top head buckling model 

Based on the above results, a predictive study of the pressure test on SCV test model was conducted. 

1. Introduction 

The nuclear reactor containment vessel is an important equipment which prevents release of radioactive 

materials outside of the system at accidents. Since Chernobyl accident, many research programs on the 

containment vessel under severe accident conditions, especially in the U.S. and European countries, have 

been conducted. Relating such research programs, the NUPEC and the USNRC are carrying out a 

cooperative research program on structural integrity of various containments. One of the cooperative research programs is a pneumatic pressurization test for the SCV test model. This test will be done at 

Sandia National Laboratories (SNL), Albuquerque, New Mexico, USA. Regarding this test. a multi

national analysis effort in the evaluation of the SCV model test, Round-Robin activity, is sponsored by 

the NUPEC and the USNRC and is coordinated by the SNL. 

We NUPEC conducted a pretest analysis of the SCV model test for the Round-Robin activity. This 

paper describes the results of the pretest analysis.

E-363
2. Analysis Method and Outline of Analysis Series During pressurization, SCV test model is predicted to show non-linear behavior, due to material yield and contact with CS, as well as large displacement effects as deformation progresses. ABAQUS (version 5.4 and 5.5) has been used to perform the analysis, because this general structural analysis 

materials, 

programn with finite element method possesses good non-linear analytic capabilities for such geometry (structure) and boundaries, and is also widely used for a number of analyses. [8.1][8.2] 

Table 2-1 shows the list of calculations conducted in this analysis. This analysis program consists of two parts, i.e. 2-D analysis to grasp the global behavior of SCV test model and 3-D analysis to grasp local behaviors. 

cases, 

For the 2-D analysis concerning the global behavior of SCV test model, analysis performed a study on 5 case-AX I to 5, from which the most appropriate case is to be selected, after having performed elasto-plasticlarge displacement/contact analysis with such parameters as gap and friction coefficient, to realize the effects of the parameters on deformation behavior of SCV test model. For the 3-D analysis, case-3D! has been performed elasto-plastic/large displacement/contact analysis, aiming at the deformation of the equipment hatch and its vicinity, which can not be modeled in 2-D analysis. 

expected 

Case-3D2 and case-3D3 study top head, knuckle and equipment hatch regions which ame 

whole model 

to be under the most severe conditions in terms of strength. These regions are separated from the to create a submodel with fine meshes, which has been examined meticulously. Case-3D4 has been conducted on an analytical model to study buckling of top head region and linear buckling eigenvalue analysis has also been performed. 

Table 2-1 Outline of Analysis Series 

case descri~dto 

AX I Parameter study using Global Axisymmetric Shell Model Analysis. SCV-CS Gap size = 18.0 mmn (Friction Coefficient = 0.2) AX2 Parameter study using Global Axisymmetric Shell Model Analysis. SCV-CS Gap size = 14.4 mm (Friction Coefficient = 0.2) AX3 Parameter study using Global Axisymmetric Shell Model Analysis. SCV-CS Gap size = 21.6 mm (Friction Coefficient = 0.2) AX4 Parameter study using Global Axis)ymnetric Shell Model Analysis. SCV-CS Friction Coefficient = 0.0 mm (Gap Size = 18.0 mm) AX5 Parameter study using Global Axisymmetric Shell Model Analysis. SCV-CS Friction Coefficient = 0.4 mm (Gap Size = 18.0 mmn) 3D! Global 3-D Shell Model Analysis. Gap Size = 18.0 mm/ SCV - CS Friction Coefficient = 0.2 3D2 Local Top Head 3-D Shell Submodel Analysis. Gap Size = 18.0 mnu/ SCV - CS Friction Coefficient = 0.2 3D3 Local E/H 3-D Shell Submodel Analysis. Gap Size = 18.0 mn / SCV - CS Friction Coefficient = 0.2 3D4 Local Top Head 3-D Shell model Buckling Eigenvalue Analysis.

E-364
3. Analytical Conditions 

3.1 Adopted Analysis Options 

ABAQUS (version 5.4 and 5.5) has been used for the pretest analysis. The adopted analysis options are as follows. 

As for material model, an isotropic elasto-plastic material model has been selected with *ELASTIC and -*PLASTIC, which are options about materials provided by ABAQUS. Then, TYPE, optional parameter of *ELASTIC, has been determined as TYPE= ISOTROPIC and HARDENING, that of *ELASTIC. as HARDENING=- ISOTROPIC. And large deformation effects have been introduced by declaring NLGEOM parameter for *STEP option of ABAQUS. Contacts have been determined by such options like *SURFACE DEFINITION, *CONTACT PAIR and *SURFACE INTERACTION, and friction coefficients by *FRICTION, which is *SURFACE INTERACTION's option. Coulomb friction has been adopted for friction model with stiffness method for the treatment. Also, analysis has been used for automatic incrementation scheme. 

3.2 Material Properties 

Material properties figure on Table 3.2-1, Table 3.2-2 and Table 3.2-3 shows the typical cases for SGV480 and SPV490 of stress-strain curves applied on each parts of analytic model at elasto-plastic analysis. 

These stress-strain curves have been drawn based on the stress-strain curves provided by SNL from the tensile test results. That is, stress-strain curves obtained by the material tensile test have been classified according material and thickness, then is represented, for each of SGV480 and SPV490, by 2 theoretical hardening curves, namely inverse hyperbolic sine hardening and power law hardening. 

- Inverse hyperbolic sine hardening : a - a ys = A [asinh 1B ( P - L) 

Power law hardening : u V- ys= A (cP-cL) n 

For each pan of the model the stress-strain curves have been applied to each corresponding component tested, and for the parts where no experimental results are available, such as lower spherical shell and support ring, substitution has been made with values of the same material and the most approximate thickness.

E-365
Table 3.2-1 Material Proer'ties

ITEM 

Young's Modulus 

Poisson's Ratio 

Density

SGV480 

209800 MPa 

(21400 kg/mm2) 

0.3 

7.7 X 101 N/m 3 

(7.9 X 10-' kg/mm3 )

SPV490 

216000 MPa 

(22000 kg/mm2) 

0.3 

7.7X 104 N/m3 

(7.9 X 10-6 kg/mm3)

Table 3.2-2 

Material Properties for Upper Cylindrical Shell (SGV480)

True Stress True Plastic Strain 

(Mpa) (Crm/rm) 

404.9 0.00 

404.9 0.01 

428.4 0.02 

473.4 0.04 

513.6 0.06 

548.4 0.08 

578.2 0.10 

636.8 0.15 

Young's modulus = 209800 Ma 

Poisson's ratio = 0.3 

Yield Strength = 404.92 MPa 

thickness = 6.0 (mm)

[rue Stress 

(MPa) 

680.4 

714.7 

742.9 

766.9 

787.6 

806.0 

822.3

True Plastic Strain 

(mm/tm) 

0.20 

0.25 

0.30 

0.35 

0.40 

0.45 

0.50

(21400 kg/mm2) 

(41.3 k-gmm 2)

Table 3.2-3 

Material Properties for Lower Conical Shell and Lower Cylindrical Shell (SPV490)

True Stress True Plastic Strain 

(MPa) (mmnmm) 

656.0 0.00 

656.0 0.015 

672.8 0.0155 

688.6 0.018 

695.1 0.02 

709.1 0.025 

727.1 0.035 

734.2 0.40

True Stress True Plastic Strain 

(Mna) (mminn m) 

756.6 0.06 

774.0 0.08 

788.6 0.10 

818.4 0.15 

842.5 0.20 

863.3 0.25 

881.7 0.30

Young's modulus = 216000 MPa (22000 kg/mm2) 

Poisson's ratio = 0.3 

Yield Strength = 656.OMPa (67.3 kg/mm2) 

thickness = 9.0 (nun) 

E-366

I!
4. Global Shell Model Analyses 

4.1 Analysis Model and Analytical Conditions 

(1) Global 2-D Shell Model 

Most of SCV test model are symmetrical to the axis. Except for the equipment hatch and its surrounding 

areas, 2-D model (axisymmetric) elasto-plastic/large displacement/contact analyses were performed to 

review the deformation behavior of SCV test model effect from friction coefficient and a gap size between 

the SCV test model and the CS. 

Figure 4. 1-1 shows the 2-D analysis model created. 

This analysis model simulated the shell wall of the SCV test model, reinforcement ring, support girder and CS in axisvmmetric shell element (SAX I) from each part shape and dimensions, the top head flange in axisymmetric solid element (CAX4), and ribs of the ring support girder in plane stress element 

(CPS4R). This model has 914 nodes and 857 elements. 

As shown on Figure 4. 1-1, the analysis model was given gravity acceleration in the vertical downward 

direction so that internal pressure as well as weight of the test model and CS may apply to the model. For the boundary condition, the node of the top head apex and symmetrical axis of the lower spherical shell 

has been given the symmetrical condition and the vertical displacement of the node the bottom surface of 

the ring support girder has been fixed. 

The internal pressure applied to the model is 14.7 MPa (150Lkgcm 2). This pressure gives allowance for 

the estimated pressure analyzed from ABAQUS due to excessive strain on the SCV test model. 

Three models with gaps of 18.0 mm, 14.4 mm and 21.6 nmm are available for 2-D analysis model to 

review the effect of the gap size between the SCV test model and the CS. 

(2) Global 3-D Shell Model 

Most of SCV test model are symmetrical to the axis. However, the equipment hatch is non-axisymmetric. To review the deformation behavior of the SCV test model, elasto-plastic/large displacement/contact analysis have been performed for 3-D model. Displacement or amount of rotation obtained from the 3-D 

model is used as the load for elasto-plastic/large displacement/contact analysis for the top head submodel 

and equipment hatch submodel separately analyzed. 

Figure 4.1-2 shows 3-D analysis model created. 

This analysis model has simulated all components in 3-D shell element (S4R) for one side of symmetric surface (180 deg.) through the center of SCV test model, CS and equipment hatch. 

This model has 7812 nodes and 7640 elements. 

Similar to the 2-D model, the analysis model was given gravity acceleration in the vertical downward 

direction so that internal pressure as well as weight of the test model and CS may apply to the model. 

For the boundary condition, the node on symmetrical surface of the SCV test model and CS has been 

given the symmetrical condition and the vertical displacement of the joint of the bottom surface of the ring support girder has been fixed. The gap between SCV test model and the CS is 18.0 umm and the friction 

coefficient is 0.2.

E-367
Top Read Flan 

(Axisym. solid CS (Axisym. 

shell elem.)

Xnuckl region

(Axisym. shell slem.)

SCV Shell Wall 

and Reinforcement Ring 

(Axisym. shell elem..) -

Gravity 

Internal 

Pressure

Detail of Knuckle region 

CS (Axisym. shell slem.) 

Support Ring 

(Axisym. shell elem.) 

Inside/Outside Rib 

(Plans stress elem.)

0/

Pqgus4.1.1 Global 2-DShcll Model and Analytical Conditions

E-368

4

I
Symmetry about 2-3

* CS (Oeneral shell 

sCV

no verticeal disp. 

(bottom surface of ring support girder) Load a Internal Pressure end Ore 

Modal Outside View I 

Figtum 4.1.2 Global 3-D hilf Shell Model and Analytical Conditions

vity

[ Model Inside View I

LI

1" 2
4.2 Parameter Study Analysis While the gap between SCV test model and CS is not constant as some allowable tolerance occurs during fabrication of the actual SCV test model and CS, the friction coefficients between SCV test model and CS are not constant either and can not be determined easily. Therefore, prior to perform the analysis on SCV test model, an analytical study has been conducted with such parameters as gap quantity and friction coefficient, in order to identify their effects on deformation behavior of SCV test model. 

4.2.1 Effect of Gap Size 

To understand the effect of gap size between SCV test model and CS, analyses were performed for three gap size of 18.0 mm, 14.4 mm and 21.6 nun (cases-AXI to AX3) respectively with a constant friction coefficient of 0.2. Typical points of SCV test model and CS were checked for history of deformation, stress, and plastic strain for comparison. 

(1) Radial displacement Figure 4.2.1-1 shows the history of radial displacement at the knuckle region and middle conical shell section 

points 

which are typical points on the SCV test model. The relation between displacements of these and the internal pressure indicates that each part of the SCV test model initially expands slowly due to its elastic deformation, followed by a rapid increase of displacement due to yielding, then again expands slowly once it comes in contact with CS. Considering the relation between the gap size and the radial displacement of SCV test model the initial contact pressure between the CS and SCV test model that has been expanded by internal pressure becomes smaller for smaller gap size, and further deformation is restrained by CS. Therefore, once in contact, the radial displacement of the SCV test model becomes smaller for smaller gap size. 

(2) Vertical displacement Figure 4.2.1-2 shows the history of vertical displacement at top head apex and knuckle region. The vertical displacement of knuckle region at the pressure level in contact with CS tends to be smaller for smaller gap sizes due to similar reasons to that of the radial displacement. On the other hand, vertical displacement 

model 

at top head apex seems to differ among gap sizes at the initial contact between SCV test and CS, but the final displacement are almost identical in all cases. This is considered that because the top head region is not covered with CS and because the vertical displacement of the top head region is effected by the deformation of the lower part, the vertical displacement fluctuates under the effect of the contact between SCV test model and CS, but then displacement increases rapidly due to plastic deformation of the top head region itself resulting in relatively smaller displacement caused by the gap size at the initial contact. 

(3) Plastic strain 

Figure 

model. 

4.2.1-3 shows the history of plastic strain at top head apex and knuckle region of the SCV test The histories of plastic strain at these typical positions on the SCV test model shows similar characteristics as the above description on displacement. The plastic deformation below the knuckle region differ among the amount of expansion before the SCV test model contacts CS. However, at top head apex where the largest plastic strain occurs, the amount of plastic strain is almost identical to any gap size because it is not covered with CS. 

Based on the above (1) - (3) results, the difference in gap between SCV test model and CS gives an effect in such a behavior that, below the knuckle region where the SCV test model is covered with CS, the smaller the gap, the lower is the pressure at which it starts contacting with CS, slightly reducing plastic strain. The amount of plastic strain there is, however, extremely small when compared with that at the top head where such strain becomes the largest and, therefore, from an ultimate plastic strain's point of view, the effect of the difference in gap on the SCV test model's deformation behavior is negligible. 

E-370

1!
4.2.2 Effect of Friction Coefficient 

To understand the effect due to the difference in friction coefficient between SCV test model and CS, three cases (case-AXl, AX4, AX5)were analyzed with friction coefficient of 0.2, 0.0 and 0.4 

respectively, while setting the gap at 18.0 mim for all cases, for the comparison among noticeably representative SCV test model and CS points in terms of history in displacement, stress, and plastic strain. 

(1) Radial displacement Figure 4.2.2-1 shows the history of radial displacements at the knuckle region and lower cylindrical shell 

section as representative points of the SCV test model. 

The radial displacement with friction coefficient of 0.2 and 0.4 are almost the same but only the case with the friction coefficient of 0.0 tends to give a larger amount of displacement than in other cases. 

(2) Vertical displacement Figure 4.2.2-2 shows the history of vertical displacements at the knuckle region and lower cylindrical shell section as representative points of the SCV test model. 

The vertical displacement with friction coefficient of 0.2 and 0.4 are almost the same like in radial displacement however, when the friction coefficient is 0.0, the deformation tends to move downward 

after developing to a certain extent. 

For the above different behavior due to the difference in friction coefficient, it is important to take notice of the lower cylindrical shell section of SCV test model. This section swells due to the internal pressure by an extremely large amount, as shown in Figure 4.2.2- 1, since the gap with CS is greater than at the 

upper section. Possibly the section draws the upper parts downward, when it swells. On the other hand, the difference in friction coefficient affects the friction force acting on the SCV test model when it slides over the CS. A smaller friction coefficient, therefore, allows the parts above the lower cylindrical shell section to be drawn downward due to a smaller friction force the rest model receives from CS. While, if the friction coefficient and, therefore, friction force are larger, the behavior to draw the parts above the lower cylindrical shell section downward seems to be restricted, justifying the judgment that this appeared as the above difference in deformation behavior observed. 

(3) Plastic strain 

Figure 4.2.2-3 shows the history of plastic strains at top head apex and knuckle region of the SCV test model. It is clear from the plastic strain history at knuckle region of CS that the strain is a little larger for the friction coefficient of 0.0 than the case for 0.2 or 0.4. because of the above different deformation behavior resulting from the difference in friction coefficient. On the other hand, at top head apex causing the large plastic strain throughout the SCV test model, which is almost the regardless of the difference in friction coefficient as top head region is not covered with CS. 

Based on the mentioned (1) - (3) results, the difference in friction coefficient between SCV test model and CS affects the deformation (sliding) behavior of the SCV test model against CS, causing a larger amount of plastic strain at the knuckle region and upper spherical shell section for the friction coefficient of 0.0 than in other cases. The amount of plastic strain is, however, extremely small when compared with that at top head apex having the largest plastic strain and, from an ultimate plastic strain's point of view, the effect of the difference in friction coefficient on the SCV test model's deformation behavior is 

negligible.

E-371
4 £ 0 sO 

Internal Pressure (MPa)

IN. 

S120 

0.

13 Is

Figun: 4.2.1-1 Effect or Gap size for Radial Displacement

4 0 a to is ,4 

Internal Pressure (MPA)

igoum 4.2.1-2 Effect of Gap size for Vertical Displacement

0.50 

-' 0.11 

.0 

": 0.2) 

0.21 

SI.I 

"055 

g•.m II

0 4 a r 0 is 

Intcrzial Pressure (MNA)

Apex 

Knuckle region

Middle Conical Shell section

L as 14

j o a .I t L o a I

Figure 4.2.1;3 Effect of Cap size for Plastic Stn

E-372

In

S0* 

U 

a U 50 

0.

8

Top Head Apex

mL

4 

Kwce region

-- Gap = 18.0 (mm)
Boo 

- -- Friction -=0.0I Lower Cylindrical 

---- Friction ,0.4 Shell section ,. 

C. 30 I fS 

6.4 

I/ O 

0 0 / 2 4 , 0 6 I6 1 3 3 4 

Internal Pressure (MPa) 

Fliture 4.2-2-1 Effec of Friction for Radial Displacemnent

ion -0.20 --- Friction "-F -0.0 - -ricition -0.4 

S- " ..~ ........... . E 

"" LweCylindrick! 

~ 32 

Internal Pmsu (M•) 

Figun: 4.2.2-2 Effect of Frictio for Verica Displacement

2 4 6 0 to 12 

Internul Frsts o (MPa) 

Figure 4.22-3 Effec of Friction for Plastic Strain

Top Head Apex 

) Knuckle region

Middle Conical Shell 

, Lower Cylindrical Shell

L 34

I si L ±t . i

E-373

6.30 

0." 

SII 

U 

S.0i 

"630 

C.l

0
4.3 Global 2-D Shell Model Analysis 

As an achievement of parameter studies in the preceding 4.2, it has been confirmed that the effect of the 

differences in the gap between SCV test model and CS and in friction coefficient on the SCV test model's 

deformation behavior is negligible. It was, therefore, decided that case-AXI with the nominal gap of 18.0 

mm and the friction coefficient of 0.2 be adopted as a case for the analysis to predict the SCV test model's behavior under pressure using a 2-D model. Followings are the detailed results of this analysis. " 

Figure 4.3-1 shows the deformed shape of the SCV test model at representative pressure obtained 

through analysis. And, Figure 4.3-2 - Figure 4.3-5 shows the histories of displacement, equivalent stresses and plastic strains at each section of the SCV test model. 

Figure 4.3-6 shows the profile of plastic membrane strains and inside/outside surface plastic strain along the meridional direction from top head apex to the around of the ring support guarder of the SCV test 

model at representative levels of pressure. From these figures concerning the deformed shape, history and profile, the SCV test model's behavior is 

judged as follows: 

(1) Deformation due to gravity (before pressure loaded) As seen from the deformed shape of Figure 4.3-1, the SCV test model sinks downward due to its gravity, allowing the gap between SCV test model and CS to increase only slightly at knuckle region. The displacement due to the gravity of SCV test model is, however, as smaller 0.015 mm or less at best (occurring to top head apex). It can, therefore, be judged that the gravity gives almost no effect on the 

deformation behavior of SCV test model. 

(2) First yielding (at the internal pressure of 2.09MPa=21.3kg/cm 2) 

As seen from the plastic strain history of Figure 4.3-5, when the internal pressure is 2.09MPa 

(21.3kg/cm2

), the first plastic strain occurred at the knuckle region of SCV test model. The history of 

radial displacement shows the identical pressure at which displacement sharply increases and plastic strain 

occurred. 

(3) First contacting (at the internal pressure of 3.52MPa=35.9 kg/cm2) The SCV test model caused its first contact with CS at the knuckle region when the internal pressure was about 3.52MPa (35.9 kg/cm2). At this pressure, the gap at the upper conical shell section also decreases. 

This justifies the judgment that this section' is expected to make contact next and the upper and middle 

conical sections also is started to yield allowing the radial displacement to sharply increase. 

(4) After contacting (at the internal pressure of 3.52MPa-7.59MPa) After the SCV test model and CS contacting for the first time at the knuckle region, it is shown by the 

history of radial displacement that, between the internal pressures of 3.52MPa to 7.59MPa, the upper conical, middle conical, lower conical and upper spherical shell section contacted in that order. 

(5) After contacting (at the internal pressure of 7.59MPa=77.4 kg/cm2) 

The internal pressure of 7.59MPa (77.4 kg/cm2) is a pressure almost equal to the middle of the pressures 

at which the knuckle region of SCV test model makes its first contact with CS and that reaches the final 

increment. At the pressure of around 7.59MPa, almost all the CS covered section of SCV test model 

comes to contact with CS. Deformation, however, still continues to develop at the large gap lower cylindrical shell section and top head section not covered with CS, which causes the largest plastic strain. 

of about 4.9 % to occur near top head apex. 

(6) Final increment (at the internal pressure of 12.5MPa= 127.5 kg/cm2) At this pressure, the SCV test model comes to contact with CS at its knuckle region through lower 

cylindrical section except for knuckle and upper spherical shell section junction. 

B-374

11
The junction between knuckle and upper spherical shell section did not contact even at this pressure because the knuckle region, with its plate thickness of as much as 16.5 mm, still deformed so that it fitted 

the shape of CS. 

The largest plastic membrane strain at the SCV test model was about 40 %, causing at top head apex. Figure 4.3-6 of plastic strain profile shows that the SCV test model has a largest value at the knuckle 

region at lower pressure. As the pressure rises, the plastic strain of top head without CS cover and lower 

cylindrical shell, which has large gap between SCV test model and CS, gets larger. Therefore, top head 

section without CS cover needs a detailed investigation. 

4.4 Global 3-D Shell Model Analysis 

3-D model analysis (case-3D1) is performed under the condition that gap is nominal 18.0 mm and 

friction coefficient is 0.2. This condition is same as last analysis on 2-D model (case-AXI). 

Followings are the detailed results of this analysis. 

Figure4.4-1 shows deformed shape under representative pressure for global SCV test model. 

Figure4.4-2 "-Figure4.4-4 show history of displacement at SCV shell wall and plastic membrane 

strain. The above mentioned result of 2-D model analysis, deformed shape obtained from above 3-D 

model analysis, and various history of free field, values are almost same. Therefore, from standpoint of global deformation behavior of SCV test model, 3;D model with harsh mesh is as effective as 2-D 

model with more fine mesh. 

Figure4.4-5 show history of horizontal displacement at representative points near equipment hatch 

area, obtained from 3-D model analysis. Figure4.4-6 and Figure4.4-7 show plastic strain history at 

each point equipment hatch area of SCV test model and inside/outside surface. 

Judging from history of horizontal displacement at each region near equipment hatch area and plastic strain, the point farthest from equipment hatch contacts with CS at about 4.1 MPa pressure. 

The points near equipment hatch contacts with CS at about 5.2 MPa pressure. The equipment hatch area is surrounded by thick insert plate with high material intensity (SPV490/t17.smm), thinner lower conical shell section of same material (SPV49O/t9.Omm) and 

thinner middle conical shell section with relatively low material intensity (SGV480/t8.Smm). Therefore, the different expansion rate of each material against internal pressure brings about large plastic at region near to material change interface (MCI) between upper and lower conical shell section 

and insert plate joint region. 

Comparison of plastic strain history between equipment hatch area and SCV shell wall shows that the 

plastic strain at equipment hatch area is the largest when the internal pressure is between 4 - 8MPa. 

Therefore, equipment hatch area needs a detailed investigation. 

4.5 Comparison of 2-D and 3-D Analyses 

Figure4.5-1 -Figure4.5-3 show comparison of history of radial displacement, vertical displacement and plastic membrane strain at representative points, obtained from above mentioned global 2-D and 

3-D analyses. 

From these figures, contact starting pressure of SCV test model and CS and deformation behavior are 

almost same in 2-D and 3-D analyses. 

The history of radial displacement of 2-D and 3-D analyses may seem to show difference, but this 

difference is brought about because the range of vertical axis is narrow.

E-375
=defc= d

defc=ed

(Disp. Mag.-3000) 

mr-ravity -1y ( o HPA )

(Disp. Maq.-I) (Disp. mag.-I) 

(2)At 3.5PPa (35.9kg/cm^2) (3)ft 5.6mpa (56.6 kg/cm-2) 

deto=ed 

undefo=cd 

maq.-I) (Disp. Mag.-I) 

(5)A-- 20-SHPA (106.7 kg/cm^2) (6)At 22-511P& (127.Skg/cm'2)

(Disp. Xag.-I) 

(4)At 7.6MP& (77.4 kg/cm-2)

Figure 4-3-1 Deformed Shape of Global Axisy=n=ic Sýcll Model 

B-376

I ý,
Top Head Apex 

- Knuckle region

Upper Conical Shell

Middle Conical Shell

L

I 10o Itl o tn

1E

r... 

0,,N

S 3

ntem Prnssure (mPs)

Figure 43-2 Radial Displacement of SCV She

a'

Xe.

a mcrn-L Premssur ( s) I 

Figure: 4.34 Equivalent S =•f SCV Shell Wall

I

a

A]. 

.5-

It so * be . $ as 

"Internsi Pessur: (MPA) 

IWall Figure 4.3-3 Vertical Displacement of SCv Shell Wall

a.

•Top Head Apex " -nuckle region 

---- Upper Spherical Shell 

Upper Conical Shell 

S ---Mdfle Conical Shell - Lovwr Conical Shell o.. l-ou C'/h'•Lic•Shell 

* ,-LowerCylinticaj Shell 

'3. 

a 

S 

- .... 

Fiure4-35 Equivak-enb.t Pac Scain of SCV Shell Wall 

E37-

.20
0.4! 

0.41 

0.3 

0.30 

0.2! 

0.20 

0.15 

0.1x 

0.05 

0.00

•SShel 

0" 

7.4 3w.( T7. tlJl|. ol4.Vk~a-. 

5 

Membrane Strain . . S. 6 3W. 1 $4.6 m ~~2 :. - o ...... 2.5 3.. ,o.. 

0 100o[ 500 2000 :2500 3000 3500 4000 4500 

V.-teie Position (i- C .m , Top Head Apix 0 ,m

500 100Q 1500 

Vertici•. Position

2000 2500 3000 3500 4060 

:1 Top Head Apix - 0 nu

0 500 1000 1500 2000 2500 3000 • 3500 4000 

Vez-±cal Position I : m e ) Top Head Apex - 0 urn 

F3:= 4.3-6 Eqfivcntp matic Sumin Profil 

E-378

I!

Top Head Apex

c 

ro 

.,, 

0r 

.1 

C

0i 

U

Ou e1Su6 liat( 7S.trai-- Outside Surface Strain,. .au sm,-i 

4 i • 

*-•,. c 0.45 

S0.40 

0.35 u "'-- 0.30 

0.25 ~.£0.20 

- 0.15 

0.10 

-0.05 

law 0.00 

=- 0.45 

" 0.40 

0.35 U "- 0.30 

! 0.20 

- 0.15 

0.10 

0.05 g o.oo

4500

""*d" 1e. uC rf.4 I•S n Inside Surface Strain-- :se.tls e-I

4500
11 1 .%% m I I I I 1 11 

(Disp. X&q.-I) 

(I)At 4.411P& (44.4kg/cm-2) (2)At 5.4HP& (55.2kg/cm-2) 

dcfO=ed 

Uudefo=ed 

eo 

de:Eo=ed 

?h F"I I /M 111 aTTFT) 

(Disp. Kag.-I) \ -", 

(3)At 9.2HP& (93.6kg/cm-2) (4)At 22.4HPa (126.6kg/cm-2) 

Fig=4.4-1 Dcfmr-d Shape of Global 3-D HajfShdl 'Model

B-379
me

2 4 a I I. 13 

Internal Pressure (Mat ) 

Figur 4.4-2 Radial Displacement of SCV Shell Wall

5

ntmnal P=ssur (MNa)

U.e 

,0. 

• 4 

=o

14 0 , : 4 : , l 

ln=nal P=ssu (MPa)

Figure 4.4-3 Vertcal Displacement of SCV Shell Wall

L is 14

Fiur= 4.4-4 Equivalent Plastic Swain of SCV Shell Wall

Top Head Ap=x 

Knuckle region 

Upper Spherical Shell 

Upv€cr Conical Shell 

Midd Conical Shell 

.- Lower Conical Shell 

Lower Cylindrical Shell 

Le Lt~ I

E-380

II

4. 

E 

30

-Top Head Apex 

Knuckle region 

Upper Spherical Shell 

Upper Conical Shell 

-Lower Conical Shell 

-Lower Cylindrical Shel:

22 14

-Top Head Apex 

--- nuckle region 

Upper Spherical Shell 

--- Upper Conical Shell 

-Mddle Conical Shell 

Lower Conical Shell i 0.30 -Lower Cylindrical Shell

"OIO

0."

0

i

a !

I9e

----------- - - -------

: .... ....... ................
N4397T N4025 

. 6 6 to U 4 

Internal Pressu= (mpa) 

Figure 4.4-5 3-D Global Horizontal Displacement (near EJH) 

E 

-E247(Mid)j 

• 0.2 

"" --- E-)..46 EM) . 

.6 C- 0.64 

/ .2 

S 2 4 6 i 1 I 12 94 

Internal Pr•ssurc (1h) 

Figure 4.4-6 Equivalent Plastic Mebmne Stain (near EH)

I ro s0 itl on a

6 4 a Is La 14 

Internal Pressure (MPa) 

Figure 4.4-7 Equivalent Plastic Surface Strain (near EJ)

E-381

E2446

44

2O

E 

E 

CS 

Eo 0. 

Z2 

Z,
so

ho

-30 

U 

20 Middle Conical Shell 

V 

-------

- Knuckle rgo 

0 a S 5 4 0 I IO 33 

Internal pressure (Mpa) 

FIgure 4-5-1 2.D/3-D Comparison (Radial Displacem~ent)

0.43 

-0.35 

5.3 

a. . " 

0 4 0 to 

Internal Pressure (MN)

S - - - D-D Model 

3--DDModelI Top Head Apex 

Knukl region 240 

'Int! Pre.ss= (MPI) 

Agur 4.-5-2 2-0/3-D Comparison (Venca l:)Lpacemeno)

Top Head Apex

Knuckde region

Upper Conical Shell

-Lower Conical Shell

Lower Cylindrical Shell

S|L 

to all4

Figunt 4.5-3 2-D/3-D Comparison (Equivalent Plastic Strain)

E-382

1!
5. Local 3-D Submodel Analyses 

5.1 Submodel Analysis of Local 3-D Top Head section 

The results of prior analysis of 2-D model and 3-D model show that the plastic strain at pressurization 

on SCV test model is larger at top head region and knuckle region. Thus to perform detailed 

investigation on these regions, top head region submodel was prepared. Figure5.1-1 shows the prepared top head region submodel. This analysis model is to simulate the 

circumference of 30 deg. for each direction from top head region to upper spherical shell section and 

CS. This model consists of 3-D shell element (S4R) and has 4545 nodes and 4290 elements. 

This analysis model uses internal pressure, displacement and rotation obtained from prior 3-D global shell model analysis. The boundary condition is given to the SCV test model and CS nodes on symmetric surface. The internal pressure applied to the model is same as the pressure applied to the 3-D global model analysis which has been conducted in previous section. 

Figure5.1-2 -FigureS.1-5 show history of plastic membrane strain and plastic surface strain at top head apex, above and below of top head flange joint, and above and below of knuckle joinL The plastic membrane strain history at each point shows that the largest plastic strain occurs at above 

or below of knuckle joint when the internal pressure is below about 7.3MPa. When internal pressure rises, the larger plastic strain occurs at top head apex. Also, plastic strain at the below of top head flange joint is larger than that at knuckle joint, when the internal pressure rises above about 10.8 MPa. This is because the deformation of knuckle region is controlled when the region contact with CS, while other parts are free from such control. 

On the other hand, history of plastic surface strain shows that the plastic strain of inside surface below of top head flange joint or below of knuckle joint is the largest when the pressure is below about I 1.8MPa. When the pressure rises, the plastic strain of top head apex becomes larger. The plastic surface strain at below of top head flange joint or below of knuckle joint is larger than the plastic membrane strain up to higher pressure. This is because these regions are effected by bending deformation, but top head apex is free from such deformation. 

Therefore, top head apex and below of top head flange joint and below of knuckle joint are the place that attention should be paid on the strength of these parts. 

5.2 Submodel Analysis of Local 3-D E/H area 

The analysis results from the previously performed 3-D analysis model show that the ultimate plastic strain of SCV test model under the higher level pressure occurs at top head apex, but the largest plastic strain occurs near equipment hatch under the lower pressure level. For further review on this part, a 3 D submodel for the equipment hatch and the adjacent areas has been prepared. Figure5.2-1 shows a submodel of the prepared equipment hatch area. This analysis model is to simulate the equipment hatch insert plate, its surrounding conical shell and reinforce=et ring, and CS which 

covers them 3-D shell elements (S4R). This model has 4816 nodes and 4572 elements. This analysis model uses internal pressure, displacement and rotation obtained from prior 3-D global shell model analysis. The boundary condition is given to the SCV test model and CS nodes on symmetric surface. The internal pressure applied to the model is same as the pressure applied to the 3-D global model analysis which has been conducted in previous section. Figure5.2-2 shows the horizontal displacement history of the representative points near equipment hatch given from analysis. Figure5.2-3 and Figure5.2-4 also show the plastic membrane strain history and plastic surface strain near equipment hatch. 

Judging from the history of the horizontal displacement and plastic strain of the parts near the equipment hatch, contact is made with CS at approximate 4.1MPa on the points distant from the 

equipment hatch and contact is made at approximate 5.2MPa near the equipment hatch points. Therefore, the contact pressure with CS near equipment hatch proves to be dose to the former 3-D global model. However, for the horizontal displacement at the point near the contact part of the

E-383
material change interface (MCI) of the upper and lower conical shell and the insert plate, which gives the largest plastic strain near the equipment hatch by the former 3-D global analysis, the detailed 

submodel clearly gives lager values compared to the global model. Similar result is obtained also on 

the plastic strain near the contact part. The strain of the submodel is higher than that of the global model by approximael3% on the plastic membrane strain and approximate 28% on the plastic surface 

strain at 1 IMPa. 

Though the strain of the equipment hatch does not rise higher compared to those of the top head apex and joint of top head flange and knuckle because the contact with CS control the deformation, attention 

should be paid on the strength of this part. 

5.3 Buckling Analysis of Local 3-D Top Head section 

As the top head region of the SCV test model consists of two spherical shells with different 

curvatures, the rigidity difference could cause buckling under pressure. Thus, a 3-D model for the top head region of SCV test model was prepared to perform a linear buckling eigenvalue analysis. Figure5.3-1 shows a model for the buckling eigenvalue analysis on the top head region. This analysis model is to simulate the half side (I 80deg.) of the SCV test model symmetric section 

from the top head to the upper spherical shell, with 3-D shell elements (S4R) completely. This model 

has 2233 nodes and 2150 elements. 

For analysis model, 9.8MPa (100kg/cm 2) intemal pressure was given, and the bottom end of the 

upper spherical shell was completely fixed. Tbe analysis is a linear buckling eigenvalue analysis, and 

the buckling eigenvalue and their buckling modes were found from 1st to 10th modes. 

Figure5.3-2 shows the original model and a representative buckling mode given by the analysis. Table5.3 shows the buckling eigenvalue given by dhe analysis. It has been proven that the buckling near top head of the SCV test model occurs at the upper cylindrical shell from 1st to 6th modes, and near the top head apex from 7th to 10h modes. 

Table5.3 shows the buckling load calculated from the corresponding buckling eigenvalues, and the 

buckling eigenvalues were all negative. An internal pressure was given to the model, so the top head 

of the SCV test model could buckle under external pressure. However, the model is unlikely to buckle 

under internal pressure in this test. 

This analysis is linear buckling eigenvalue analysis and one of evaluations for the buckling of the top head section. Furthermore, we will investigate the potential of nonlinear buckling too. 

Table 5.3 Buclding Analysis Result ( Ei~envalue 

Mode No. Eigenvalue Buckling Load 

MPa (kg/cm2) 

1 -0.9344 -9.2 (-93.4) 

2 -0.9606 -9.4 (-96.1) 

3 -0.9661 -9.5 (-96.6) 

4 -1.0377 -10.2 (-103.8) 

5 -1.0730 -10.5 (-107.3) 

6 -1.1515 -11.3 (-115.2) 

7 -1.1697 -11.5 (-117.0) 

8 -1.2778 -12.5 (-127.8) 

9 -1.2911 -12.7 (-129.1) 

10 -1.2966 -12.7 (-129.7) 

Notel; 'I "TLOAD= 9.8MPa (IOOkg/cm2) 

Note2; Negative value means buckling by external pressure. 

E-384

J!
IN

Submodel area in Global Hodel 

CS (General shell elem.)

Symietric Boundary Conditions 

(both side edge of SCV and CS) 

SC. Shell Wall 

(General shell elem.) 

Load t Internal Pressure 

(SCV Shell Wall) 

Top Head Flange 

.(General shell elem.) 

Load I Disp./Rot. from Global 3D shell analysis 

(bottom edge of SCV and CS)

I Model Outside View I

M~

Figu 5.1-1 Local 3-D Top Head section Submoel and Analytical Conditions

I Model Inside View I
I Top Head Apex

Above Knuckle

Knuckle rcZioi 7"

I Po r it leon

C# 

2h 8.83

Internal Pressure (MPa) 

Figun: 5.1-2 3-D Top Head Submodcl Equivalent Plastic 

Mtnbrane Strain

,_ Above Top Flangle 

-Below Top Flange 

-- Below Knuckle

Internal Pressue ( a) 

FigunS 5.1-3 3-DTop Hcad Submodel Equivalent Plastic 

Strain (Top Head Apex)

C 83 

C: 

8, .33 

U)

* lo~ Presure(MPa) 

Figum S.1-4 3-D Top Head Submodel Equivalent Plastic 

Strain (Top•Head Flange)

-o .1 .... |~ 

Fimum 5.1-5

Internal Pressure (Mfa) 

3-D Top Head Submodel Equivalent Plastic 

Strain (Knuckle Region)

E-386

1!

ugw

- Top Head Apex 

- -- Above Top Flange 

------ Below Top Flange 

---- Above Knuckle 

---.--.Below Knuckle )

Ij

-Top Head Apex (inside) I ----. Top Hea Ape (Outsi=)l I

m !.

J
Symme•ric Boundary Condcitions Reinforcement Rling

(ContCe UU9

wr

Subtodel area In Global Model )

SCP Shell Wall 

(General shell elem.)

1,nod s Internal Presaa're (SCV Shell wall) 

and Iisap./Itot. from Global 3D shell neslysls (edge of SCV and CS)

M Model Outside View I I Model Inside View I

Figure .2-1 Local 3-._) mIeaSubmodcl and Analytical Conditlons

Q-I
N2740

SGV4800(tS. -5mN) 

Material. Chanige 1atS~A- t 

I 

SPV490(t3.oin)

MC

I * 4 9 ** "

Figwm 5.2-2 3-D Submodd Ha~onzala Displacecmcn (nwv EM) 

* 1

9667 Mid 

2 

,a 

( s 1 Urso Ima 

Fion 5233DSbofEuvam? t mSri 

(narFI

1.

I V o 1 %i 0a I

----- E974 (In~side) 

--- E974 Otie 

........... 

-C. .. , 

Fix= 5.2-4 3-D Subct=&I Eouivalent Plastic Swufam Strain 

tnear EM) 

388

29 

a

I--N19961 

--N22_01 

i--N23501 

-N 374

i

I I
2 Fix (bottom edge Of SCV) 

Miodel Outside View I M ?odel irside View 

Figurc 5.3-1 Local 3.D Top Head section Bucklin:- Model and Ana%-ivczi Conditions 

(ijiodi sIa~e(ZjBucklift o'~-a Kode shape (mode no.1) 

(3)DUckling Mode. shape (vmxde nto.5) 44)Buckling Node shape (mode no.10) 

Fi.-u m 5.3-' ucklin.- Mode Shape of Local 3-D Too Head section Suckling Model

E-389
6. Investigation of Critical Area 

The failure place of the test model is termed of critical area. From the results of the previous two submodel analyses, the critical area of the test model is investigated. Figure 6-1 shows the plastic membrane strains vs. the internal pressure at the typical points from the two submodel analyses. And, Figure 6-2 shows the maximum plastic surface strains at the same points. Until the internal pressure reaches to 7.3 MPa, the outside surface plastic strain near the E/H insert plate describes the maximum value. However, beyond the 7.3 MPa and until about 11.8 MPa, the inside surface plastic strains at the below of the knuckle joint and at the below of the top head flange joint describe the maximum value. Beyond the 11.8 MPa, the outside surface plastic strain at the top head apex of the model describes the maximum value. Generally speaking, the larger the surface strain value, the larger the failure probability of the model. Therefore, it seems that these points are those in the critical area of the model for the failure initiation. However, such a behavior as in the Figure 6-2, the point that gives the maximum surface plastic strain moves depend on the internal pressure level. Therefore, it is possible to say that the critical area is one of these areas, however, it is difficult to prescribe the exact critical area. In other words, attenstion shoud be peyed to these areas in the test and have to be measured the strains at some points in those 

areas. 

According to the references [8.3] and [8.4] concerning 1:8-scale steel containment model test like this SCV model test, the strain at failure position is expected 15%. Hence, an attempt to operate this failure criteria as a preliminary evaluation allows the occurrence of failure on the inside surface below of knuckle joint at the pressure of about IOMPa to be expected. It is, however, not physical to apply the failure mode in the references [8.3] and [8.4] to the failure position expected here. This should, therefore, be taken into account for any future post-test analysis. 

7. Pretest Prediction Summary and Conclusions 

As a pretest analysis, elasto-plastic/large displacement/contact analyses were conducted using global 2 D and 3-D models for the purpose of understanding the deformation behavior and failure position / pressure of SCV test model at the tests under pressure. Similar analysis was also made using separate submodel to review in detail the top head and equipment hatch area expected to cause high strain through the analysis of the global shell model. A linear buckling eigenvalue analysis was further applied on the top head region to confirm whether or not such a part is likely to suffer from buckling when pressurized. Table 7-1 summarizes the results of the above analyses and the main phenomena involved at each 

pressure level of SCV test model given by the above analyses. The deformation behavior of SCV test model when pressurized starts with the initial yield occurring at the SCV test model knuckle region around 2.1 MPa and then allows the deformation there to rapidly develop. As a result, when the internal 

pressure becomes around 3.5MPa, the first contact with CS occurs to the knuckle region. On the other hand, the strain at each region of the SCV test model becomes maximum near the equipment hatch until the internal pressure reaches around 7.3MPa. At higher pressure, the knuckle region's lower joint yields the maximum value and, when the internal pressure exceeds around 1I .SMPa, the largest value is reached at the top head apex. Based on the parameter study concerning the effect of friction coefficient and/or gap distance between SCV and CS, these parameters will not be significant. And little probability of top head buckling has been found from our study. But, this analysis is linear buckling eigenvalue analysis and one of evaluations for the buckling of top head section. Futhermore, we will investigate the potential of nonlinear buckling too. 

E-390

]I
Above Knuckle \

Knuckle region

ITý Top Head Apex 

SI 

Above Top Flange 

Below Top Fange 

_ Below Knuckle

13

4 0 0 36 Inte-nal Pnessure (MPa)

6.66 

6.3S 

E 0.30 

C 

-IS 

6.0.32 

,O 8U. 6.211111111 O

It 14

Fig= 6-1 3-D Shell Submodel Membrane Plastic Strain

6 4 6 6 so 

Internal Pressure (MPa)

Figure 6-2 3-D Shell Submodcl Surface Plastc Strain

E-391

I P o8 it i on I

6.46 

0.30 

0.3 

Ig, *

0

-Top Head Apex (Outside) 

---- Above Top Flange ;Inside) ----.- Below Top Flange (Inside) 

-----.Above Knuckle (Outside) 

- -- Below Knuckle (Inside) 

--- EM Ins. Plate (Outside)

'I

7-,,-

J 31t 34
Table 7-1 Analysis Results Summary

Analytical Methods 

Constitutive Models 

Model Geometies

nonlinear axisymmeric finite element shell and general 

shell models; plastic, large displacement and contact 

analysis. [8.1][8.2] 

ABAQUS nonlinear isotropic material with stress-strain 

curves as provided by SNL. [8.2] 

Global 2-D model : axisymmertic shell, axisymmeric solid 

and plane stress element 

Global 3-D model and Local 3-D submodel: 

general shell element

Event

- 2.1 MPa First yield occurs at below of knuckle - 2.2 MPa Yield occurs at near equipment hatch insert plate 

-" 3.2 MPa Yields occur at upper and middle conical shell section 

"- 3.5 MPa First contact initiates at knuckle region "- 3.9 MPa Contact initiates at upper conical shell section - 4.2 M:a Contact initiates at middle conical shell section - 4.4 MPa Yields occur at lower conical shell section 

and contact initiates at near equipment hatch 

"- 4.8 Mh Yields occur at lower cylindrical shell section 

"- 5.2 MPa Contact initiates at lower conical shell section - 5.3 MPa Yields occur at upper spherical shell section 

"- 7.6 MPa Contact initiates at upper spherical shell section 

"- 4 Ma Maximum equivalent plastic surface strain occurs 

at knuckle region 

4 - 7.3 MPa Maximum equivalent plastic surface strain occurs 

at near equipment hatch insert plate 7.3 - 11.8 MPa Maximum equivalent plastic surface strain occurs 

at below of knuckle region 11.8-- MPa Maximum equivalent plastic surface strain occurs at top head apex

8. References 

[8.1] "ABAQUS/Standard User's Manual Volume I", HIBBITT, KARLSON & SORENSEN, Inc. [8.2] "ABAQUS/Standard User's Manual Volume II", HIBBITT, KARLSON & SORENSEN, Inc. [8.3] "Pretest Predictions for the Response of a 1:8-Scale Steel LWR Containment Building Model 

to Static Overpressurization", D.B.Clauss, 1985, NUREG/CR-4137, SAND85-0175 

[8.4] "Comparison of Analytical Predictions and Experimental Results for a 1:8-Scale Steel Containment Model Pressurized to Failure", D.B. Clauss, 1985, NUREG/CR-4209, 

SAND85-0679 

E-392

4

1!
Appendix

Pretest Analysis of a 1:10-Scale Steel Containment 

Model Subject to Static Internal Pressurization 

Standard Output 

July ,1996 

Nuclear Power Engineering Corporation

E-393
Figures and Tables

Table

Standard Output 

Standard Output 

Standard Output 

Standard Output 

Standard Output 

Standard Output 

Standard Output

(Plot ID 1-6) .................................................................................................... E-395 

(Plot ID 7-14) .................................................................................................. E-396 

(Plot ID 15-22) .......................................................................................... E-397 

(Plot ID 23-30) ................................................................................................ E-398 

(Plot ID 31-38) ................................................................................................ E-399 

(Plot ID 39) ..................................................................................................... E-400 

(Plot ID 40-43) .......................................................................................... E-401

Figure

Strain History (Plot ID 1-6) ................ 

Strain History (Plot ID 7-10) .............. 

Strain History (Plot ID 11-16) ............ 

Strain History (Plot ID 17-20) ............ 

Strain History (Plot ID 21-24) ............. 

Strain History (Plot ID 25-28) ............. 

Strain History (Plot ID 29-34) ............. 

Displacement History (Plot ID 35-38). 

Displacement History (Plot ID 39) ....... 

Strain History (Plot ID 40-43) .............

E-394

1!

1-1 

1-2 

1-3 

1-4 

1-5 

1-6 

1-7

1-1 

1-2 

1-3 

1-4 

1-5 

1-6 

1-7 

1-8 

1-9 

1-10

.E-402 

.E-402 

.E-403 

.E-403 

V AAA

.........................................

e-4049 

.........................................

E -1405 

.........................................

E-405 

.........................................

E-406

,4W6

...............-........................................................................ 

........................................................ *..... 

.................................... °................. 

..............................................................

........................................................................................
Tab. 1-1 Standard Output ( Plot ID 1 - 6 ) 

Results of Local 3-D Shell El/ Submodel Analysis 

Itl&in 

IntenalProsare Plot3 IV lo0t ID2 Platot333 Plot Oll PlotI~ 1 1o5Plt ID (kg/cm2) I C J•a ( Pd I ) ( C ) I 1.510.14710209 0.10859242 1.21Z-04 1,.00-04 5.443-OS 3.81-O05 6 5.47E-0S |1.03Z-04 31 0.29420413 0.37738494 2,!3!-!4 2.00Z-04 3.338-44 7.66Z-03 1.301-04 2.093-04 .5.1483732 0.00734 4.1 -0 3.42--04 2.24Z-04 I 1.35Z-04 I 2.26Z-04 j 3.43E-, M.32 10.943563701 1.084406 4 '°4.84-04 5.49r-04 3.47,-04 2.233-04 I 3.77,-04 3.-7t-04 13.687511.3423054 11.033-03 8.99z-04 5.79?-04 3.57r-04 6 021-04I 9.443-04 21.283212."3708444 2. 66E1.41-03 1•1.39Z-03 8.93Z-04 3.42E-04 9.41X-04 1.461-03 32.673T 

35.52 33.48337,746 

3.2041777g 4.1079201365.85Z-03 

4.465 st 12.30Z-02 3.321-03 1.3@Z-03 3.323-04 8 T 1.433-03 s 5.473-03 33.3•7 2.74257723 4.923816961 2.30E-02 6.43Z-03 2..7n-04 1.41.-03 8.02z-03 1.303-02 1 3.0-03 1 Z.932-04 I 4.46r-03 I 1.323-02 

41.3,205 42.214 4.04177699 

,.95,238011 5.131276381 .2041313 3.39Z-02 

3.47Z-02 1 2.193-02 

2.25-02 [ 3.171-03 1 3.493-03 1.49Z-02 2.43Z-02 B 3.30-03_ 3.723-03 . 4.Z,-02 2.,,-02 42.?82q,.o,,o8• .34,2241 .,,-0=, 33n-2 ;J ,•-• *1.,,3-02 2.43.,-02 

4 1. 5 l701, 4. 7•59903 5.2 26337221 3. 833-02 2.32Z-02 8.33-03- 3.94Z-03 I 1.623-02 2.33•-02 .;43. ii4.09415003 5.248923241 3.02Z-02 2.3n-02 f 9.15Z-03 4.201-03 1.48Z-02 2.603-02 42.01311 4.12!3442213.28249339j 3.71-02 T 2.453-02 9.40-03 1 4.3553-03 1.07-02 2.48,-02 42.415451 4.159-20481 5.33234475 34.33-03 1 2..-02 1 3-02 1 5.110-03 3.37Z-02 I 3-o0-2 43.01645 4.21333435 5.499317i3 4.003-02 723Z-02 1 1.2 1 5.933-03 N2.02-02 02 .23-02 0; I 43.24171 4.2406295 2.3- 02 5.435704611 4.06Z-02 2.773-02 2.16Z-@,I 0 .321-01 2.032-02 ! 31 OO-02 42.8S758J 4.3273775175.41448 • 4.152-02 I 2.852-02 1.243-02 5.333-03 I 2.130-02 3.053-02 43.704335 4.2341134 q3.49312439 4.183-02 j 2.•3 -02 2- 2 | .3"-01 3.3Z-02 3.933-02 43.8394051 4.30483323 5.51019451 4.322-02 2.93*-02 . 2.3%-92 i7.31-02 2 *.23Z-02 3.13-25. 44.22.5551 4.31270935 3.53432707 4.30?-02 2.97Z302 j 1.37E-02 7 .3U300 I 2.303-02 3.19Z-02 44.464705 4.340743481 5.590022381 4.30..2 1 2.98Z-02 1 2.423-02 a -03 236-02 3.242-C. 44.537571 4.3"7732s33 .24.1 47-023-0 1 2- 2171-C2 t 3.231=-C 44.56471 4.32037364 5.5030413 2..38-02 I 1.433-02 08.353-03 2.37Z-02 3.273-02 44.60479514.374305461 5.0830421 4.36Z-02 I 2.,99-02 2.43•-•2 3 3.38Z-03 I 2"339-22 3.283-12 44.644931 4.43020313 5.415"437 4.31M-02 I 2.93r-02 1.43E-02 3.4=1-C3 2.439-01 .2720@2 44.7332414.3490497214 .52 4486221 4.3U0-02 2 .83-02 1.423-03 3.443-03 .. 403-02 1 2.308-22 44.890441 4.402316331 5.o64432"9 4.331-02 2.,8-02 1.423-02 1 .47--0 2.41z-02 I 3.21Z-02 45.093341 4.42222124 5.54o514411 4.403-02 1 23. -02 2 1.422-02 9.32Z-03 i .40,-02 23.303-C2 435354J 4.45203297 5.7077935 71 4.411-02 1 2.91•-02 2 5.t-03 I 2.453-02 I 3.323-02 45.54491 

46.5335414.3640,423, 4.4904024 5.745206211 4.423-02 T 2.9n02 2.411-02 1 3.501-03 1 2.503-02 I 2_.31-02 5.0533437i5 4.44303 2.9n3-02 2 .41Z-02 8 .433-031 2.571-e2 3.411Z.02 '7.567041 4.56443731 5.160522271 4.432-02 j2.993-02 1.40Z-921 3.703-03 2 .69Z-02 3 .303-C2 47.1322914.70257821 4.02897.715 4.43Z-02 f 3.993-02 1.392-C2 I 0.71Z-03 I 2.73Z-02 i 3.54-_2 48.5303414.73927621 4.101423i 3 4.433-02 2.9a8-02 1.393-02 M I .733-031 2.233 -02 I 3.43-0: 49.3•27341 4.944102271 4.22042,13 4.71-i2 3.,1 73-02 - 2.38-02 8.i74-83 3.02-02 I 3.78Z-02 50.497691 4.97182407?1.374133421 4.70r-02 2.953-02 1.36Z-02 8 3.73Z-03 I 3.233-02 3 3.993-02 I 51.022741 5.02?70o0el 6.41500241 4.709-032 53-Z-02 11.363-02 8.746-03 i 3.243-02 I 4.053-02 51.347791,5.03•5781 ,.43538 4.70-02 .37 2.3 1.25-02 8 .761-03 3.2-U-02 ,.03-02 51.335441 5.833401 4.317137? 4.713-02 I 3.95Z-02 j 1.33•3-02 i 3-C-03 3 3 .36Z-02 I 4.091-02 52.5"-415.1.5127,30 6.409123434 4.712-02 1 2.93z-02 1.34Z-02 I I 5 3.771-02 .441-02 F 4.121-02 32.554011 3.2527331541.74702379 4.733-02 -2.94302 1.33--02 8.302-03 3.531-02 3 1 4.14$-02 5,.75 134.370323331 .885049151 4.733-02 1 2.94"-0o' 1.533-02 I 8.832-03 | 3.356-02 1 4.273-02 35.351951 

54.--58413 

S.47794351 7.02300451 4.74Z-02 I 2.94F-02 1 1.333-02 8.902-03 1 3.58Z3-02 4.171-02 5.5235489 7.2109,831 4.743-02 1 2.94-03" 1.3U-02 3.933-01 j 3.4o0-02 1 4.171-02 50.053091 5.43153871 -. 292913221 4 .74 -02 2.943-02 1.33Z-02 2 3.98Z-03 I 3.42t-02 4.28Z-02 59.150341 5.30075O051 7.430703714.733-03 2 3.343-02 1.333-02 1 .20Z-03 3.543-02 1 4.189-.02 40.24739 5.108344221 7.37482M31 4.733-02 I 3.33-02 1.311-02 9.443-03 j 3.443-02 I 4.13-02 51.333091 5.45973221 7.781711521 4.773-03 I 2.933-02 I 1.27Z-02 1 2.12"-02 3.53-02 "54.342091 6.3186525j 8.0,212441 4.712-02 2.93L-02 2 13ý.22. 3-C2 1 1.35Z-02 I 3.70Z-02 I 4.233-02 46.83209; 16.539,5211 8.402358071 4.793-02 1 2.93Z-52 1 1.2 02 I - 3z--2 ---. 3.722-02 I 4.263-02 S4 5.731:533 7.300081 2.71:921191 4.813002 2.932-02 21.24Z-021 1.37E-02 I 3.743-02 4.29Z-02 73.3038q9 7.1393"2029 9.17351531 4.94Z-02 I 2.93•--2j 1.303-02 2 1.43Z-0. I 3.78@-02 I 4.33E-02 73.558091 7.70403942 1.874173621 4.90Z-02 I 3.00Z-02 1.43-03Z 1.533-0 3.31-02 I 4.42Z-02 84-112391 3.24758446 10.57533141 4.943-02 I 3.043-02 2.093-02 1 2.14-302 1 2 .49-02 .,.,,70, 8.7134774, 31.2739893 3.0.-.02 1 3.15.-02 2.53t-02 2.35t-02 1 3.93Z-02 . $7.11959j 9.53012941 22.321321 5.693-02 3.29Z-02 3.043-02 3.216-02 I 4.433-0e2 4.655-02 101.12403 9.917043251 12.71423D1 3.123-02 i 3.34i-02 I 3.-1-02 3.333--02 J 4.07Z-02 4.61X-02 105.2009 10.3 7455021 13.3033207 5.171-02 3.46E-032 3.43342 3.41C-02 4.233-02 . 

112.840311 11.05505771 34.11723340 3.24Z-02 1 3.44i-02 J -3843-02 4.02r-021 4.24Z-02 4.323-02 121.3*333 12.1 002333 15.513058,1 5 .35Z-02 3.368-02 4.27Z-02 I 4.42Z-02 4. 4.4-2 23.21039 1 3.65211241 17.50270 321 5.27-02_ 3.9.3Z-02 I 4.3 7Z-02 I 4.SIZ5 4.98Z-02 

SOML~rs inta". "tXmeri. inat . ext. opit. boo p ri..lfl.333 prin.Utlaj 3tZAj traain &train 

I ( 3 2 10.97 C k9C1h -2 

1 (Pd 2 * 0.73 C3Ma 2

E-395
Tab. 1-2 Standard Output ( Plot 11D 7 - 14 

Results of Global xxisy=nmetric Shell model Analysis 

strain xateral Prssure plot X0 7 iplot 0 a plost ID 9 1plot IS I0 Plot ID It Plost ID-12 Plot XD 13 !Plot ID 14 Mra C rd sktd2 

:lI• ~••-i• ~~o~~ - I.O -. -i_ •- 7.g -O-- ) 

0.000 3.35P-07 -1.20"07 -2.372-4 0.000 -3.24Z-07 -2.402-07 -6.042-07 1.50.47120 

30.29420418 0.2 

0.37718434 1242 4.392-S -46553c 0 22-" 7*861-0- 2-a.59z- -4.943-05 9.532-04 o .352. -0 9.763..03 -1.312-04 4.433..05 1.S72-04 5.12Z-05 -1.36..-05 2.932-051 4.762-051 5.25 0.32485731 0.6600734, 1.70-•-04 -2.2$Z04 7.713-05 2.743-04 8.94Z-O05-2.322.-05 3.372-C5 1.192-04 

13.075, 

3.523 0.04333701 

1.3423045C 

1.02440642 2.77Z-04: -1.71"t-04 1.292-04 4.472-04' 1.443-041 -3.67---05 5.223-C51 1.#S1-04 .720905 . - - 4 2. 060-004 .022-04 21.28212.01708444 -5.2-05. - 2.673749261 6.632-ga -8.83.3-041 3.23Z-04 1.089-03 3.51Z-04-o 3.o .3-4 4020 

32.673 3.S20417 4.107920131 1.002-0. -1.332-•0 S3.20-04 1.622-03 -1.74Z-03 -1.742-041 -2.592-02 2.771-03 35.63805 3.5.2 3.40337749 

3.5008334S 4.445534354 

4.825446 1.092-03 

1.0Z03 -11.472P-03 5.86W-04 2.79Z-031 -2.612-03w -5.112-041 -3.302-031 3.433-03 .IAZ.Oj - 1.312-03 -2.4663031 -4.232-041 -3.562-03 3.322-03 

36.1431'3.54442347 

35.8761 3.313393 4.3106403 1 1.1024-3 -1.492-03 3.o22-04 1.83Z-03 -2.722-03 -5.342-04 -3.60Z-03 3.55s-03 4.54 2 0981 210" -1.32-031 5.982-04 1.862-03 -. 0 -0 -.5 522-04 -3.60-2-031 3.56T-03 

37.14435 

3.5.436 3.59375993 

3.642-743 

4.59455401 IZ12-03 -1.532-031 6.052-04 2.392-02 -2.92Z-033 -6.422-04!-.020 3.542-03 .-. IU ---___._ o .. 3. -2.4fZ-,ii - 7 .23z 4 -3. 31.0454 3.73103354 4.73302741 1.1 -i - 031 42-04 2.072-03 -2..42-.4 -7.352-04 -3.52.03 3.57r-03 3•.7399 3.8535775322-031 

40.7434. 4.7n-04 2.222-03 -2.Z-303 0-.42-04 -3.5SZ.3i 3.-S 0' 3.9952135 .12322•2• 1 1.24-.03 -1.831-03 7.4n2-04 2.442-03 -2.511-03 -9.142-04 -2.532-03 3.342-03 

43.441 

42.0999 

4.219447 

4.12 5491 3.2931801 

40 

1.282-03 -1.99-03 8.3U2-041 2.68r-03, -2.443-03 -9.701-04 -3.512-03 3.512-03 1.322-03 -2.290-03 9.392-04 3.032-034 -2.381-03 -1.032-031 ;- 41C.00291 4.30373345 5.4321991 2.33Z-03 -2.429-03 E1.20=2-043 3.4492-03 -2.312-03 -. 9 -0 3-3.32-03 3.452-07 46.2309 

46.0589 

4.59251343 

4.7914973 6.24294531 

5.88799856 1.412-03 -2.39-0 1.5203 4.33Z-03 -2.20Z-031 -1.:79-031 -3.382-C31 3.4-t-03 1.472-03 -3.452-03 1.592-03 S.312-031 -2.32-0 -1.24Z-031 -3.2n-03 3.382-03 50.8849 4.91037t52 

".39792247 1.532-03 -4.152-03 2.2-03 4.512-03 1. N0 -1.312-031 -3.143-03 3.372-03 $1.64711 5.05493035 -6.493501121 2.553-031 -4.452-031 2.341-03 7.002-03 -1.8,2-031 -1.352-031 -3.072-031 3-332-0: !2.40731 

53.1475 

5.12394e221 4.53S9079741 2-1.52-03 -4.74CZ-031 2.55Z-83 7.492-031 -1.853-3 -.-03 03 -992-031 3.342-C3 

53.9277 

5.224C335414.6$401383 1.62Z-03 -5.032-031 2.752-03 7.182-031 -1.322-03 -1.420 -2.902.03 3.342-03 

S4.4979 

5.23$55418 4.78022702 1.7 -01 -. 322-031 2.952-03 8.442-031 -1.772-031 -1.421-031 -2.801-037 3.32.2-03 

3554431TS.4374367$61 

3. 34313422 4.37523544 1.792.03 -5.402-031 3.172-03 8.952-03 -1.731-031 -1.441-03 -2.3 o0; 331 -0 

36.52841 5.54952456T7.12476226 

6.9713943 1.SS32.sj -3.88-31-o 3.238-03 i*3m3 -. 8-01 .7-3 -5403. 3292-03 

33.2934 

3.552-03 -. 322-03 3.71r-032, - -1.592-03 -2.52z-03- -2.27z-o31 1.242-03 5.71721094 7.32975762 6.982-03 -4.992-• 31 4.2$M-03 1.13O-021 -1.442-03 - 72-03l -,1.72Z-031 3.222-C3 50.0034 

1.7134 

5.33490-331 7.54475211 9.-22-03 -7.66Z-031 4.32-031 1.2.86020 -1.253-03 -1.341-03 -. 132-03 3.0o2-03 9.0525"371 7.759748U 1.s"-0 -3.322-03 5.472-03' 1.3,Z-02 -2.082-031-1.7-03 64.28491 5.3042953018.08242999 -5.07-04o 2.,1-.03 1.43r-02 -9.292-03 4.452-03 1.322-021 -7.172-041 -1.322-031 4.392-04i 2.323-03 ""4.9263 4.35719O23i 3.130721 1.502-12 --. 512-O3 6.73r-03 3.352-02 -6.0121•-1.092-04 5.502-04 2.792-03 45.56771 

66.529*1 

6.4300970913.2437142o 

6.5244493719.36467739 2.53Z-82- -9.7,-031 7.0,3-03 1.,02-02 -4.83Z-04 -2.932-03 .C12-041 2.792-03 2.991-021 -1.01Z-02 7.37r-031 3.563-02 -3.012-041 -1.00-031 1.202-04 2.712-03 47.9731 

59.4154 6.80733.6310.72760445 

5.6653913.34614102 1. 31-02 -1-.0Z-521 7.90V-031 1.7412-02 -1.0n2-031 -2.1- 0 1.0-2-03 2..4--03, 

70.9397 1.963-024 -21.2-02 9.442-03: 1.322-021 2.97t-041 -2.212-03 1.272-031 2.562-03 '.94907,326) 8.9030624 2 2.112-•-•-'-- 2- ' '.2- -0 -9.321-03; 1.48Z-03 2.492-03 73.0242 7.16134157 9.13220714, 2.332-02 -1.221-02 9.792-03 2.0212-0 1.0 -0 I34181 331 1 2320 75.1337 

77.3512 

7.3736098,I 

7.5"537l2 

9.45334601 2.552-02 -3.232-02 1.052-02 ._2.120 1.5930 -2.-03 03 2141-03 2.242-03 9.72543407 2.79t-02 -1.322-02 ".142-02 2.212-021 2.232-03 -2.5'2-03 2.502-03 2.o09-03 79.5177 

t1.4322 

7.79314551 9.99742374 3.02t-02 -1.382-021 2.212-02 2.30Z-021 2.772-031 -2.682-03 2.362-03 1.94"-3 3.01041403 20._2972i 135-2-021 -1.42Z-02 1.-il-021 2.331-02 3.311-03 -2.702-03 3.212-033 1.02-03 33.3467 

87.09421 

$.22683314 

O.. 

10.54210153 3.322-02 -1.462-021 1.332-02 2.452-02 3.24Z-03 -2.692-03 3.522-03 1.47Z-031 

91.947 

21 3 -0 -. 502-01 1.40-02 2.2-02 4.70-03 -2.502-03 4.042-03 1.472-031 90• 17Oi65 11.3425535 4.382-02 -1.32-03 1.502-0.1 2.701-621 4.012-031 -2.2n-03 4.34-03 1.132-03 

101.70571 

19.93521 1.416440213 

9.97408041212.78722381 

12.17412321 5.303-02 -1.55-021 1:.539-021 2.812-021 7.44Z-017-1.652-03, &.52Z-03 9.31F3-04 4.112-02 -1.572-02 1.372-02r 2.951-02 1 .032-031 9.072-04 6.34Z-03 5 .022-04 106•57421 

11.3927 

10.431.7212 13.3995424 1 -'..52-0• 3.52-021 2.162-021 1.44Z-02 5.222-031 7.32.22-03 2.292-04 11.6354 1 3 27 3.75Z-021 -1.432-021 t.:-21 3.312-02 2.24-,•"21 1.202-01 1 O.2i-031i 2.9Os 124.,,17 22.229933.,,.. N 1 1.4 •"-"M 2.;-.! 125.52475 

2.74-04 •0. - . 98r O-O2 3.94Z-021 2.91Z-02 9.73•-03 5.352-04 12.3,01,41113.73222•2,1:.50-cl :..30 03 .- 4.393-02 .32 -02 4.012-02 2.•3--02 ,.772-037-9.%z-04 Isa 12.3773453 11.,-331271 1.592-03 4.972-031 4.79Z-021 6.73r-02 4.5-021 2.o32-02 9.322-03 9..o4 

127.335431 

127.2393 12.4731212131.99757835 

12.4875581 

1.312-01 1.242-024 5.613-02 7.59Z-02 4.512z021 3.26-021o 9.322-03 1.132-03 12.0096399 1.332-01 1.26o-02! 4.752-C' 7.743-02D 4.592-02 3.302-02 9.932-03 1.152-03 127.4_0125 

127.493572 

12.50_72341 .0275'7 1.99- S I.-02i 9.36Z-021 8.192-0o 4.679-02 3.37r-021 o.92-03 .19-03 1 33.3030549115.02959021 2.023-021 1.702-021 4.232-021 1.243-021 4.433-02 .9-2 9.172-33 1.192-03 127.4170591 

_____0.,i_ 

12.50333911 2;; 121 M0041 14.021983 2.03Z-03 2.04r-02 2 1.521 .722-021 6.282-02 8.292-021 4.592-02. 3.392-02 9.97r-03 1.202-03 1127.5046 12.033 603501.5-1 11.7-23.3-2*.3-2 6._2Z-0210.33r0 127.50041 12.503212 1 4.69r-021 3.402-02 9.972-031 1.202-03 6 *020 04

lO 2.04-07 1.772-03 5.312-02 13.332-021 4.6n2-02 3.402-02 9.97Z-03 1.0-3 127.5036441122.5040.1541 16.030739 2.0 4 -olj 1.S01-02~ 5.372-021 9.382-02~ 4 .7 0 Z-0 2 227-5356961 t 3.41t-02 9.972-03 1.020 12.55-11-1136.032072,.I 2.0S2r01I 1.302-02j 6.372-021 1.382-021 4.702-02j 3.412Z-02 .9.72-031 1.202-031 

Remrk ext.2Me., 1 ext. hoop ext. natrid. int. eMnjd 1

eut. m in.jt. meid. ext. Manu, int. zaend. J7

1a.atram Strain strain I trai strain .-trin Stia train 

"114a ) 20. 197 C kq/82-2 

Pd 0.73 ( HP& 

B-396

1I
Tab. 1-3 Standard Output ( Plot XD 15 - 22 ) 

Results of Global Amisymmetric Shell Miodel Analysis

1-.--.. Stimin _

ot,. XD 15

0.2424110.3771 84j2i0.1 -.

5.25 0.5140 

s.6254 0.6453

_____ 1.112306541 

2122208704441

35.521 3.433377461 4.4653115M 

35.679305 12"

33. 14_1:_

4--67120131

I-7.69C-04

1 -6.31 

L-g.<7s2 2.~5 4

44397I!!334 932o

S) 20 Plot 17 P hun lot It20_lot Is;19 Pot azol 20 10~

I I .... ] .. I I

II

fi -7. - .. 3.312-07

. . 4 .52-4 .02Z-05 207

2. A&-051 .372 7*77Zs -2.51Z 1I.2Z0 Fiizo 7.M3z051 7.3i2-05 4.?-4 1.3&Z-04j 1.32g-04J -4 .052-041I r .972-041r 1.222-0.0 '.212._4, 6.39E-041 2.17z-04J 3.042t04J -4.272-0415203 .3.411920 3.3~4 .2!.39E4 3.172-04 -9.3n2-041 3.382-031 3.042 04 132.0

7.12-0 3.12-51 2.27Z-051 -7.27Z-01 1.752-04

3.442-02i a 6.3-0 3.302. 

2.54r-031 6.312-041 3.632.

5. . . Z-041

2430 -3.-659-3 4.3z61

-1.412-031 3.682-031 5.je&ii_ 12 4 -1.34Z-031 4.06X-631 1.652-039 .2F ,..

-1.53Z-03 4. 10-0!31

37.144351 3.46742 3 .~ot. 1 .332-03 4.39r-041 _ 1.632-031 -*~ -2-8..-311 ~ .8-3 .e-3 IZ 'l2O~31201.7..

33.0454 1.31a34 .isi.*i T713371 _. - - ~- SI-3 4.25t-03 2.432-831 3.152-o

3.9937663.5772521 4.35330452 1.62 2- 3 4.79Z-031 2.312-03 1.92 6076 .3 155.32236323 -1.-932-03 S.732-031 2.132-03 1.732 42.4109334.2269554,15S.293346001 -1.83r-03 3.832-03 2.682-03 1.712 43.45141 4.261124471 5.46306087 -162-3 6.052-03 3.322-03 1.532Z 44.6023 4.313733451 1.93209141 63334.5293481435.38794156 -1.320 6.07t-03 3.302-03 1. .0.312-0,1 6002-031 4.620 1.302 433614.7324975I 4.14294521 -3I.561204 3.37Z-03 S.292-031 1.412 50.3363 4.19027152 6.337922471 1.63E-04 5 .732"3 5.13Z-031 2.12 5'.6473 5.06663036 '.433 -02211 2.772---o, 72.01 2*...S

S2.40731 5.1 3943221 6.589079741 6.632-C4 53.1675 5.214033541 6.634538341 7.152-0. 

53.337 5.3533 .700237021 3.612-04 

34.6873115.363239221 6.975311661 14-03 

5.2!841 .7-.72-1041 7.32137921 1 fift02.

5.632-03~ -.-3920 3.03.3Z-31-2 31 _.1-3 _.520 32-0 -3 26-031 3I.p .329-03 2.642-03 2.6)2.03 13.532-03 4.32-ft031 3.692-03 -3.752-03 1.020 3.2-03 2.611Z-03 5.3-4V 4.352-03 2.97E-03 -4.152-03 1 20 2.722-03 3.672-03 ,5.462-03 4.33Z-03 6.002-03 -4.532Z-03 1.20 2742-031 3.702-03 542Z-03 4.32ý2-3 4.132-03 -4.34Z-031 1.45-037 2.772-03 :.73Z-02 5.36-03 4.332-C03 4.26Z-03 -5.502z-031 1.64Z-021 3.302-03 2.772-02

P. IU2-031 4.342-031 3.7oz-031 64832.04 

03 _-2.722-031 4.51t-031 3.132:-031 3.32o-0* 031 -1.772.03f 4.632-031 3.15Z-031 1.042..03

031 -1.913-039 .6-39332 3.032-021 1.3*1.1

0 31 -2JU1-7031 3.31 03 2.5329 S .212-0

. . -U '2 s . 3 1 2-472-03 

-2.22Z-03 7.82Z-03 2.572-031 2.54m-a3 

-3.05Z 03 8.532-C31 2.10Z-03 

-2 2 * i 2L ! 

03Z-03 1 2412-03

;7 . 

. - . -3 40.00*413.89490733 1.9or-021 z.2'r-03 2.832-03 

6.0326037117.75974234 

7.S4475210 2.491-03 5.25t_031 . r_ 4.4tt-031 -7.11Z-011 2.2or-62 2.962-03 2..92T_03 

64m2849 

2.882-031 SAIU-03 4.S42-0A 4ift-03 -7.9GZ-C3 2.45z-021 3.052-03 3.41SE-03 

64a,243 4.367194231 

6.304293381 2.03242991 3.642-031 4.96z-03 4.7412-03 4.902-03 -8.922-031 2.742-02 3.-242-03 2 32Z-61 

4 

8.16-30721. 3.922-031 4.922-03 4.74?,-03 4.842-031 -I.I.Z-031 2-.91.2-02 3.292 3.342-03 3.5477 &-43oe97oTs_.24371423 3.9v--031- SA12-03 4.71M-03, __±.#9X_03L_ -9.362-03 2.1192-11# 2 24IX-03 3.23z-oj Em 47.9731 1 

6.3244403711.36 6.6659919.34414302 9' ', 7391 4.22Z-a3l 4.24Z-03 4.11412-83 -9.442-011 2.*tZ-*21 3.23T-0 3.182-03 4.6iTC-033 4.832-03 4.91Z-03 S.14Z-03 -I.OIZ-021 3.13Z-031 3.212-03 3.241-03 

.. 'j 70.1397 

$0.4164 4.60 

6.941673291 

531631 6.721F.E1.144., 

2.909"228 

]E lr-03 4.71FE-031 5.142-03 3.312-03 23:-C2 3_342-031 3 - It-03 

73.0242 7.142342571 

13.77 -03 4.7sr-931 5.312-03, 5.512-03 -2.§&X 1.21 '! 321-02 3.392-031 375-4 V-03 

75.1827 

9.28120724 9-322-03 4.76r-o3i s.s3ro3 S.972-C3 -!.SEX 4SE-02 3.118Z_2ý43.4;121-03 7.373601191 *.43334601 

17 1919 1_51113117821 9.72SAR437 

- - 3 4.7sr-o3i cm-o3 s.zAz-D3 .372-02 3.40.2-8, 3 mft--_o3 4.7sr-031 _6.34Z-031 6.112-03 -1.092-02 3.69z-02 3.6$Z-031 2.62V-0; 

711-01 4 4or-03 6 0 1 

79.S177 7.7912-965112.1974237 1 8.772-03 4 .9-03 7."-3. 7.59Zu 1.1-03 1.tt2 3.792-02 3.77Z-031 3.702-03 _22122 .0844211026764 _,--03 4.802-031 3.252-03 3.472-03 -2.29E-021 3.8111-02 2.24z-03 3.77Z-03 

17.01431 

93.8467 3.22263314110.54130151 

6.114115926 13.350320421 

9.9920 .4-3 33212-031 a.1-d- -. 020 3.942-021 3.902-03 3.332-03 :.osz-o:I 4.832-203113S 1 .-

.1 - I

.. . . . -. 

10.74"0. 45172 12

11.6563543 1.142-03 - ~4.oSz-02 333-0 3.302-03 4.872-031 1.462-02 1.462-021 -1.04:C-02 4.19Z-021 4.052-03 3.372-03 12.1742332 1.322-02 4.33203 1.-03 03 .7-02 -1.062-021 4.32-0 4.102-03 4.012Z-03 1.71-2325 1.272-09 .323 2.1.3392- 1.372-02 -2.142..021 .620 4.112-03 4.02Z-03 13.3936424 1.332-0 472-03 2.032-02 2.0SZ62-0 -1.242.42 4.91--021 4.13Z-03 4.63r-413

2137.58927 12.071 14.030412 1.462-02 . 623 23.0X-02 2.421-021 -1.242-02 5.16Z-021 4.302-03 4.092-03 125.012467 

127.20116 

12.32013 

12.-3.503013.11.330273 

0251.7302242 1.442-031 4.31z-02 2.502-021 2.462-03 -2.202-021 5.13Z-02 4.29-3 40E0 1.442-02 4.562-03 2.59t0210 2.46M=021 -1.32@-021 5.142-02 4.32*-03 4.01-32 

127.505367 12.5023651116.0314071 1.44t--021 4.532-03 3.502-0 2.462-02 -1.202-0235.16Z-02 4.02@-031 4.032-03 

12.47591.53811.1.2181 .4Z8 4.59Z-3~ *2.*-2u 3.44ai0 -1.2Z-0 5.26r-0 4.292-03 attai 

2 7 .5 0 6 ) 12 .0 3 7 217 1 4 0 0 4 3 2 . 4 - 2 4 5 9 - 3 q i- . 6 - 2 -1 2 2 0 .2 r 0 . 0 -0 . 9 - 3

1(1 .3(4 ) 

E-397

Internal 1Zos30zo

(k9/ea-2) 

0 

1.5

3

91 944719.43 96.9352 5.49444013 

20. _'.q -1 . -v__

ý000_5ý08Z C

E2 =74.2 -4.22Z3.7310365414.7833927.-r 3.

031 -- r-o" 4.742-031 _.

C21 -2-012-11% 5.23' 2.332

aw-G.

. 69 -3

1

, 2.03Z-CS _ 2.0

1 .6.2ir-a'

912-04

47432 4,9700932211 112 03
Tab. 1-4 Standard Outpft ( Plot ID 23 - 30 ) 

Results of Global Axisyoetric Shell Model Analysis 

Strain 

Intrnal Presur P 23 1Plot ID 24 1, Plot 23 Plot ; D 26,1 Plot 27 Plo. 2 28 PO3 29 

(kC-2)-) (- (-) 2 (- (. ) ! (.

01 0 S.6SZ-08 5.71z-02 0.000 -6.942-47 1.972-074 1.97-071 0.000o 2.65r0 

1.5 0.1473020,96 13.59242 3.872-O5 1.372-O5 1.932-03 2.142-05 8.602-o0 9.412-ol 2.25z-o, 3.3Os 3 0.2942041. 0.377184,41 1.77r-04 1.772-04 3.92.-05 4.32.-05 1.722-04 1.72Z-04 ,.33,-0- , .562-Os 5.25 0.53433753 0.460073481 3.20Z-04 32.02-04 6.92r-C5 7.722-05 3.012-04 3.022-04 2.112-04 1.152-04 

13.1875 1.24230545 1.720905331 3.08-04 @.032-04 2.922Z-04 *.02-04 2.62-04 7.342-04 2.92X-04 2.932-04 21.232 2.0670$444 2.973740281 1.2-07 1.292-03 2.32-04 .0 1.22Z-0 4.352-04 4.42--04 32.6731 3.2041777 4.107920131 2.24Z-03 2.252-03 ,.372-0d1. 3.742-04 1.90-03 7.022-04 .8.12-04 

33.5213.48337744 4.434593541 7.242-03 7.262-03 1.932-04 7.692-041 2.11__-03 2.10t-03 1.012r-04 7.292-04 35.,930313.500,334o 4.48232446 7.722-03 7.7Z-03 1.342-04 7.3.-04, 2.12Z-07 2.122-031 8.072-04 7.312-04 3S.97411 3.3122995 4.510440381 .212-03 3.242-03 1.722-04 2.131-03 1.012-04 2.132-031 3.1r42-04 7.352- 4 

39.1413 .54442343 77 4o$9320043 8.903*2 .02 132-03 I.C-04.32 .5-04 2.920 2.7423-03 8.1 1Z0 .742 40.743413.5879934155.13224502 1.072-02 1.372-02] -3.22-04 9.432..03 2.19Z-031 2.272-031 8.522Z-04 7.642-04 372.994.24351. 49643 4.27014308 1.192-021 1.262-02 -3.92Z-S 932-04 2.262-03j 2-s .23j-031 8.32-041 .1.02-03 43.0454143.2411544.75.3093387 13.5Z-214 1.402-021 -3.922-04, 2.6-3 2320123Z0 1.442-04. 81.02-03, 4.2343357324 C.22913345 1.542.02 1.402-031 -3.802-04 1.252-03 24.762-031 2.742.03 8 .542-041 8.122-04 4!.;3!!! Y4.224143 5.82322432 1.372-03 1.472-021 -7.32Z-04 7.432-03 34.32-031 3.372-03~ 8520 1 .222-04 43.83391 4.712S4973 .42943140 1.402-02 1.302-02 -7.0282-04 13.412-04 3.z81-r31 3.941-031 8.53Z-041 1.3a-22.o 40.831414.290394521 ..39792247 1.593-02~ 1.402-02 -8.892Z-04 -3.92-0 1 3.120 1.12sx02 1.042-03 1.092-03 1.41 3.0730345 5.63933131 1.402-02 I .0 -03 S.002-041 . X~-5!.4-4 1.22-02 1.82--03 -1.102-031 1.32E-03 .342 5247 .580797854 1.402-021 1.402-02 -.4.34204]1 -. 742-041 1.232-032 91.33-03 1.142-03 .4420 33.34581 5.214093514 .13423311 1.402-02 1.411-02i -7.328-041 -6.0=-04 1.352-02 1.332-03 1.792-04 1.232-03 33.9277 4.2333343314.73027022 1417 0 1.1-7 -. 3-0 -. 1- .362-02 1.372-02 2.392-0312.452-03 £ ."713.34313422 64.173S1541 I.10 .420 -4.712-041 32Z0 _34Z0 

.1.2-021 1.102-03 1 .232-03 

52.4031 3.43137542 4.58719743 1.412-021 1.402-02 -4.3724 -a.742-041 1.352-02 1.342-02 1.442-03 3.322-07 534.5415.93.214024 7.11475824 1.602-02! 1.412-02 -3.89Z-041 -4.382-041 1.35T-02 1.35Z-02 2.232-0314.732-03 

7.237212 .3.127715.28544 1.41X-0 1.412-02 -4.68"4 -4.3%Z-041 1.372-02 2.372-02,1.32-03 2.432-03 40.0017 5.33432322 6.7.544 1 2.412-02 1.12-03 -4.712-04 -4.042-041 1.362-02 1.36Z-02 3.55-03 2.63Z-03 41.71 .4371 7.97433 1.62Z-02 1.422-02 -4.172-04 -5.5n-041 1.332-02 1.36Z-02 4.622-03 3.32Z-03 

4.5864913.3042953454 3.032427422 1.42-02612-02 -4.242-04~ -2.3-4 1.32-07 1.322-02 3.472-03 1.732-03 

7.32175762 1.6z02 -.. 521-o4 -, ,H 

54.29241S.371742310 7.5407"218 3.421-02! !.'12-02 ;392-4 a2820 1:792-02 1.372-02 2.422-03 1.432-03 '40.00WS.8430087093.23 12 z.2-; 1 ;.422-0 -3.77n-04 -2.*71-04I 1.371-02 1.392-02' 3.752-01 1.22Z-02 611.791" "47.71'.'4* 1.052444371ZL 7.4447721 1.42Z-021 3.41-021 -3.642-04 -3.5n-041 1.39Z-02 1.382-02 3.201-03 2.42n-03 3.,4.14102 1.42.-021 3.6! o- -0- 21 - 1. -02 1.392-02 4.212-03 1.592-02 4 9. 4 20.1471 1 ?4 4.14033.90e4323 4 . 130 7 3 2 2 .3. 07 0 740 4 1 1 1.X632-02 . 4 . 32 -0 2 1 . 4 3 2- 0 2 -2 . 9 2- 043 - 3. 7 4 0 --4 1 1 . 4 0 2- 0 2 1 1 .4 0 2 -0 2 4 .7 3 2 -0 3 1. 7 2- 0 2 .432-02 -2.272-04 -1.2151-041 1.402-022 1.341-02 .2-03 1.702-0 5.5771 6.43009702.2131071421 1.42Z-021 1. 2-021 -3.72 ,. -4. -0,1 1.41Z-02 1.12- . -023 1.02-02 74A19-1 7%37340939457311 1.42Z-02 3.622-021 -3.32-03-o 2482-031 3.422-02 1.352-02 4.91Z-03 1.701-03 7.157321 ".426 o" 7.977299 

0-841407331 8.342541202 

0.243 1.43r-02! 1.441-02 -2. 4 12-5 30.2-045 1.392-02 1.329-02 4.21Z-02 1.67.02 2 1.43-023-021 1.4,1.-02 -0.0.0 _2.!92_0;7 _. 1--4 1 11.0-0o210 .,M-2,1 6.78Z-03 1.7=2-02 *710 2.571.15071 6.9010340294 1.432-02 1.432-02 -2.122-04 -32.52-041 13.402-0211.40t-02 4.03 1.702-02 71.0244| 3.03379.,11.021343 3.31 9 4411-7-223 1.442-02 - 1.442-02 -3.10Z-04 -2.38-041 ,.32-02 1.41Z-02 7.02Z-03 1.702-02 -10022-01 0" 

73.19717.734029 9.33462 A -1.2--1 ý.4;1-.!! 2.42t-026o:03 27r0 

77.032 7.19403041 1.725202713 1.47-02 1.42"-021 -. 2-04 0 5 2-041 . -02 1.2-02 7.032 1.702-02 

706.52772 10.7f17211 .1.99742341 1.432-02 2.432-02 3.302-041 1.542-041 1.4-0 .442-02 7.052-03 1.702-02 

.133.184 27 14.31 32741 1.631-02 1.4.n-021 2.430-04 7 3.42-02 1.42-02 7.302-03 1.70Z-0 2.047 2.21172132 15.24 1.702-02 1.702-021 2.734-04 35.3t01 .2-02 2.4Z-02 7.22-03 1.702-02 

12.5247319.02.3710 3 11.73242S43 1.7&Z02 0 1 .662-021 7.oz0 40 .3=-0jj. '.422-02 2.348-02 7.022-03 2.702-02. 

!2.,315 1.71744.3 12.174232 1.67Z.02 2.61 -02F 0 .,00 -04 2 1.50r-02 7.03r-03 1.7=.-0

12.3 4 0002637 1 22.70943259 2.972-021 1.702-02l 4 .752-04 3.8-4 .:-2 152C 7.04r-03 1.702-03 

1074012110.2.0172214 1.0295247 1.78-021 1.02-02 5.•2Z-04 6.7&Z-041 2.57Z-02 1.534-02 7.23243 1.702-02 127!43472 12.15030349 10.35402 1.702-02 1.702-0217.42-04 7.202-04 1.572-02 2.542-02 7.232-03 1.70Z-02 

,,.,,!!,.!I 11, 5. -• ,--;: - -.,2-° 

127.49703 1,2.2421213 .94.3231 4 1.702-02 1.70 2 .4- 0 4 8.7.-" Z-02 I.S.Z- -. 2 2-03 .7 27.5004312.3212 3.04221201 1 .702-02 7.7-. 0 9.202-04 1.572-02 1.SZ-021 7.259-03 1.702-02 126.2042 12.770463413.0307 1.702 0 1.702.21 7.52r-04 9.202-04 1.57z-02 1.572-02 7.232-03 1.702-02 127.2314 22.4701112 341.30400 2.702-02 2.70Z-021 2.752-04 9.202-04 1.372-02 1.100 7.23-03 1.7•02-02 

127.500295 12.5072" 22.3033iL 227.493472 2,0"0 14.03715 1.702-02 N~rl~l !* 7.72-04 9.202-04 ,..-702.-.02 1.572-021 1.57T-02 ,57 7.23f-03 1.702-02 1.75Z-0 5.2Z-04• 2.57Z-02 . 57-2 72-3 17 0 227.9705 1 2 2.70 .2.30322o1 , o.70op _1.i. 7.7 0 2 -4. 57t. 2oo-0 7.2,Z-0t 1.70Zi02 

1 ! 7 P 2 , 0.77 (- 

E-395

1!
C.-All Lit-at . wag T

002SIVI ito-URS-1 110'XFSVC CO-aUL -t to-Zlglt Ico-zfd*t !to-260-; T0+XSTVt lt**ZLIS*t ItO*ZZGL'c gozV- I I -9t F 17,

towaawt ito-ZLIS'l !to-zawc go.2891-1 

-ZLSsT Ito-wwc gozsL-1 

.1:1 F-1,01"2f SO- f I TA-SO - r

I MIN guato-vt 

z0vt to-366,1P footoca,91

.co-Itf, t 

--- - P- __ -

aggsto-'t l i --- __ I"ZgtL*t t9#2986*1 to*zsgL.c 90-UCL*t 10-315*1 co-2641t to-ZOL, I Ito-ago-v la-ntL't too=zs*t 10*2114*9 go-mv.1 go-116.1 to-2661t to-zovt Ice-260.0, to*aLot*l to.XGL51t toý2169-1- TO-.zsPP-j 70--=St T-9:74-6.1 40-IOL-t it*-Uo-V 

ra t Tao 1-9 -I i-OMES-9 In.-321vt TF-ITS, co-ZL6*t a-zovt Ica-uo-$, to-ZLIP*T 10436PS"I to*=tt.g 10.265P.t go-UL-1 Ito-JIG-Op to+atp*z tO-=PS*t tW.SLC'g go-ZPTP-T go:iim! to-aovt Ito-aso-P to-3469*1 10.2ectIt to.atzs I co.16091 . -2607% to-28'.1 Ito-iro-p 

10*ZLCI*z to.296clt 10*2101.t t "Uts.8 go-up't to-ars-t Ito-xvvt ito-m-r -0-2201-t TM-Cut Do-Sz3VL 1042909*. lCOP29. Ito-=P-t ite-up., lco-azoTo#xc8ct to*nlc*t 00.2aws to.zow' Ito T"219VT 10*ZLK-t 00.3CLO. ! Vt S to-20gug I co-. 129-215-c 

Qf fwo 90-20vt 

Fo-.-z6cc-t ro--atcc - t wo.at ,, , -to-alrv"s Igo-ZIP-1 Ice-zto-l

66

tt$Lv-tz It4 vut 

PULUZZ JITT-9911 

Otatc-at IsLocc-scy

RR!,!; N! Rar.; !I;,! -

o+zsct*t 10.29cf-I i-s..-cwt To-ZICV9 _j co-alp*tto-zof*t loxesvol 7's UcIGFLSý 120-2dr-t lbM-W.-. .1- .... ......... -----------

to.utct 110*219t.t oQ+zt9V9 Ito-ILOM f5-F.M IN-iii-i to*=Ot*t it"Zete-I -------- --- ----- T__xZ7t - -

ispiteivi rL-Lts-SL

ast. I lia-avo-S ýro--Z" ýjý89*1 6.3toc'T 00-agai=z 

0-21,6vt a 0 72 -P- t a c 

a-umc-I

0-awst

4-9 j16CVQL -- ---- -- -----

a z -Cc - t --------

60-Utt*t toý.Zcl 

100=99*1 lt"xgPx-T 00-ampt-I TQ+zrrT.c go-acut

------ --- --- -

O*t !Ica-zzs-z rG711: -ttI 

[XIS 9 IVSL&tgr-g flawsr 

ISSLelt jugett'vc Iftes- PC

0-awc

Do-ZILL-9 I 0-70-cs to*zMall Igo-259.1 1.

to-all't RO Vt 

FO--201- t C'. c go-zo,-l

ITS L --I t c 9

00-2064*9 looaSIG-5 51-6 Ito-zcw t Ifto-urt i 100-att P ---- ----

------ --------

6crt.,

-- ------ --

.7_;!;! . 00*2111'L 1.2.!:Ul. . Ito -2tSt-0 lto.zgg,-l lco-act-c Ito-290-9

00+3Z as I b to-agotlt t0*2969'T to-z9vt "-ZCL*g go-awt Ico-zpo*t 

PO-269, 9 90-2vs*t "_Zoc*4 zo-21 _ Ic - I 00-29GLet tO-3199*t I 0-as K, 1 to-26VC vo-asp's -co-alt't 

0002SIt'L 0**3GC&'V ZO-SLU-t 10421CSIT to-avclc touc*f to-MIT to-act's 70--ifet-I 04*Zlsg*v to-Mvc 10*20cs-I to-zove to-aws co-Zlelt to-ut * v oo#a*L,-t go-ZOOVC 10+Z195"t 70--ist - c to-zovi - _=916 

P 110-XLLPIC O-Zlt*c Pf-mple, *o_=W*t a -- L ;0--am-t to-acwt PS-act's tozrl*4 to-aoc*t 70--a-M-1 ;70_,x,,v , - Ito-avve VO-219-9 ICO-219-L Ito-itg*c 

**+IS Its' a -to-Ittv't Itoozory'r

I v tsocem-c Itcro, 

cttLzt,-c ISCIPI.Lc 

F-P 0clwvvs*t tcvt*lc 

Fv 1-66cezvc 191.8-st 

't otstgooslc 90069*9t 

`0 IULCEWC &C'St

to-ust-5 Ito-zrta-Z 0. N.......

TO p-iOl - at - t !!ý R 

5-3028-, to-ZOWT o+ a clz plo-atc-9 vo-uo-z 1"-2 a-$ 03-ati-I 

WGzTcIt Ito-zol

COSOWT

tLOO19-0, ItCLSSOTC-0 199-r.

ri-OFE Pal'a - 6 IsFairc us-i ISO-uo-c 

ZIL'S ILO-2809- I@ a is

,=Lw'g- is a -0-076-

66E-3

Irmt wo - Pd t

.d"p -49ý. -d-P ITZOD"ZOR TJMUOBT-ý TROTZZOA doaq --AUT

e zzc*t I te-266 1 t tea-2641t

'ZOL'T to-ase'r 95-91 6SOL6wLgT

1 u'L t co.aPSL I ea

;t its -cl 

t8s9LlP*9t etscelLct

mto-* "V,6*tg

l
Tab. 1-6 Standard Output ( Plot ID 39 ) 

Results of Global 3-D Shell Nodel Amnalysis 

|Displacm• 

Intuzaal 133813= Plot =5 33 

*1 0 -3.002-03 

1.5jj 410.12020 0.28859242 9.232-02 

0.29420413 0.37718484 1.863-01 

' 5.25 0.3148573 SS04~ 0.96007348 .472Z-01 3.27Z-01 0.6231o0.353701 1.o.o644 =I 5.=0 

13.8?751 1.34230654 1.720nS80 8.Sr-01 

21.2321 2.08706444 2.07574220 2 

32.473 3.2041777 4.107120112.3213.00 

35.•2 3.40337746 4.4658683454 3.Zo00 

36.2319 3.35315212 4.55537431 3.372+00 

36.453• 3.57937•42 4.3$34394 3.4124•00 

36.8904 3.6136S254 4.43929113 3.46Z*00 

37.04355 3.43337746 4.45317624 3.722*00 "'727"13.6554722 4.350"232 3.8400 

37.91:01 3.6383143 4.7238"269 4.o84400 

38.1132513.73132009 4.7?271307 4.3*4800 

33.2 3.31237143 -3 4.88324671 4.331403 

48.0207S 3..2673424 5.93153773 1.342#00 

41.73035 4.0392342 .246"0031 8.822.00 

4.60164 4.3440853 5.369341M 1.593201 50.3145-1 a.338117| 6.389502129 2.2%3*01 

44.457351 4.37533692 S.306016721 1.224z01 

45.84365 4.3S353 J 6.439,12691 1.232-01 

45.12271 .142341S S.68326,420 1.23Z-01 

43.7235 14.4,50 8452 3 5.76333207r 1.292401 

46.3571 4.5.734623 6.48557351 1.372+01 

47.9524 4.08621371 4.008479126 1.422i01 

4.51 5.0830 4035 6.213051481 1.782*01 

SO.SNM 12256.$1f8 6.0611 1.631+01 50.55430 4.1581354 !.547152301 2.73E401 

52.32135 5.1310734 6.423219371 1.797+01 

31.14227515.0154237 3 4.530038031 1.49Z001 

51.22314513 .0243038 6.44024823 1.70X-01 

561.3454 15.635348632 7.410335172 1.7201 

573232 15.6027 7223 1.742401 

63.q !67 _!! 2834 5 11 *47.544 4 553 1 .3 2 

63.31 2 ;.1 .5 12331 7.513037 14 1.733201 

732.7254.1 071 3.325 0 526543"720 1.313*81l 

72.3313 .51310794 S.70,37•92) 1.372401 

31.87525I 3.02334437 61.2340344 3.032401 

53.75" 3.1718 4.75479406. 2.8013402 

... 217581 1.4011467281 4.03332131 1.182201 54.334531 5.344233,6 7.107,,1791 1.,0=001 

10.92725 3 .6804207231 7.28253051 1.1•3-01 

8040.375 15.$8474341 7.544535 2.01 1.44 

13.131275 11.271M71144023 2.zm2*61 

2,3.0375 1,.1,153,1,15.M23733394 32*01 

2,.01725 12.367410,1 0.35,4,271 1.4=+01 

!72.52032 .2102330217.35 s1e7VII 3.4724o1 

17.?225 1. 74133 14.7034367 .7 2.472401 

91.27.3375 2.40502 15.0324.1 2.432401 

816.51351211.48013727 10.31,721 2.04Z701 

(1.5)175 9.17836128 11.77 7 2902 2.13Z02 

94.22173 P .d) 6944702 ý1.30733 2.150*01 |'100.280703 ,.824727301 12.39,520S1 2.2n+6Ol 

225.e02275 ZI.27,?7,2 21..6SO2,o 2.333901 

123.900,73 12.2313927• 15.s378939 2.432o0 126.134231 12.3497411• 15.K8534241 2.40+01 

226.34273• 12.3902883• 15.284236o2 2.46201 

726.420143• 22.3078547• 25.8246881 2.47Z-01 

M0.S8 2 *4S 12.0301J 15.901436 2.472.01 

72-.S.12|III ;7t40,021 23.900%4246 2.47Z+01 

122.5412051 12.40•1727 13. o,,e"S 2.472+01 

ctisp. 

I Me )•0. 2', 197 kq/cx-2 

I ( Pd 0.71 (?Wml )

F.-00

1!
Tab. 1-7 Standard Output ( Plct ID 40 - 43 ) 

Results of Local 3-D Shell E/! Subnodel Analysis 

Strain 

Iuternv. PZ688=6 Plot ID 40 PI0 ID 41 Plot 1D 42 Plot ZD 43 

(k9/cW*2) ( ,n6 ) I ( Pd ) (-I ( ) c 1.5 0.14710200J1 0.288592422 1.99Z-05 i. 2.011-05 8.451-0O 

3 0.2942041781 0.377134843 3.9"1-I5 2.05Z-04 4.021-05 1.682-04 

5.25 0.514357311 0.66007i476 6.7-05 3. -04 j 7.042-05 1.91 -- 04 1.425 0.845837011 2.084406424 5.3-04 1.19Z-04 r .74Z-04 

13.675 1.5342304561 1.720.05,47 2.92-04 1. 05Z-04 7.431.44 2.77;7 2.8Z H.IM0 .4210 1 4 

21.232 2.0870944372 1.421- .1 01-044 1.14Z-03 

32.6731 3.204177611 4.107920127 3.84Z-04 2.522-03 5.23Z-04 1.76z-03 35.521 3.4833774641 4.4653868544 3.29-04 3.171-03 7.322-04 1.717-43 3.1.347 3.7625772291 4.2381456 -7.2Z-03 1.091-02 j 5.501-04 2.31Z-03 41.214 4.041779931 5.111755376 -1.141-03 2.372-02 1.581-04 6.602-03 41.31920• 4.058233011 5.204159126 -1.20Z-03 2.431-02 '1.43 -04 9.151-03 

42.5701 4.07199029 5.226537217 -1.23"-03 2.41M-02 1.311-04 4 3.721-03 41.2.7415 4.641600471 5.249923137 -1.352-03 2.542-02 4 1.--2704 1.23r-02 42.015151 4.120344211 5.232412583 -1.452-03 2.622-02 8.81-O j 1.Ol1-02 

42.41545 4.153420477 5.33284.67•51 -. 53-03 2.741-42 4 •.41-OS 4 1.141-02 43.014 4.213534343 5.40337303 -1.7.-03 2.312-02 4 -1•HI-M! H.275-02 

43.2417 4.2404215,71 5.433704411 -1.31-031 2.171-02 I -3.44Z-05 2 1.321-02 43.57945 4.7 13 5.479194434 -1.111-03 2.051-02 1 -4.0Z-05S 1.381-02 43.704355 4.2841974211 5.4;51248891 -1.14t-03 3.038-02 1 --. 41--0S 1.41Z-02 43.1440513 4.304335244 5.51,0215441 -2.001-03 4 2.121-02 1 --. 222-05 | 1.452-02 44.1115551 4.222791534 5.554370915 1 0 3.201-02 I -1.111-04 1.52t-02 44.4•5705 4.34,0743,1 .-. 0722304 -2.171-03 3.251-02 I -1.37,--04 ,.53--02 44.53717 4.347752281 5.5191!242 -2.1 -03 3 .246-02 1 -1.441-04 1 1.591-02 44.54471 4.3703736311 5.6020431271 -2.20-03 3.271-02 1 -1.471-04 4 1.51Z-02 44.4047195 4.3743054781 5.030834203 -2.211-03 3.231-02 -. 512Z-04 1 1.402-02 

44.6",13 4.380203001 S.41544873 -2.231-03 3.21M-02 1 -1.58Z-04 1.414-02 44.75514 4.39,0417211 5.626334321 -2.25Z-03 .1-2- 162 1.1-2 1 44.01044 4.4023183291 5.4439173515 -2.271-02 3.31l-02 --1.101-04 1.41F-02 

45.01331 4.Z222212421 5.6465144121 -2.31C-03 1 3.331-02 I -2.012-04 1.64r-02 45.3197319 .4520829441 5.7077184741 -2.37Z-0312 3.37-2-02 I -2.31•-04 l 1.54-02 45.8U41 4.416B608421 5.745206207 -2.441-02 3.421-02 j -2.321-04 T 1.419-02 46.53"54 4.5S40423651 5.131331436 -2.601-03 3.501-02 -3.53.-04 - 1.7,41-02 47."6704 4.6648072161 .32217M -2.4-0 3 -4.-4 7.5-02 1.87Z-02 47.15239 4.7025178231 4.028171541 -2.97Z-03 3.751-02 -5.22Z-04 1.93Z-02 48.S30341 4.7276281 .01636228 -3.202-03 2.93Z-02 -6.05-04 2.132-02 41.31734 4.3443012451 4.2106426414 -. 551-02 4 •.23E-02 I -7.483-04 4 2.411€-02 

50.69741 4.971324046 4.374133418 4 4-1-2 4 -0.73--04 2.74Z-02 53.02274 S.0037010391 4.415001384 -4.22--03 4 4.74.-02 -1.021-03N 2.821-02 51.34771 5.0355711121 4.4550513731 -4.34Z-03 4.371-02 -31.07Z-03 2.11Z-02 51.23544 5.334021 4.51718077 -4.342-03 4.3E--02 4 -1.001-02 i 3.04Z-07 52.64684 5.7551271791 6.6012384341 -4.342-03 5.03Z-02 4 -3.122-04 4 25--02 

53.4,401 5.262732157( ,.74703791 -4.40E-43 .1731.-2 C 2242-04 -. 3 3.52Z-02 54.74134 5.370333235 4.8350491471 0.151004 - 5.142-02 I -. 1 2 .4 11-02 

55.38853 53.4779415134 7.230045041 -4.31n-03 5.141-02 -7.912-04 I 3.652-02 56.155384 5.5355484111 7.'1419511 -4.171-03 5.132-02 4 -7.72Z-04 I 3.671-02 53.053091 5.4131538311 7.2981152141 -4.3641-03 5.13Z-02 4 -7.32--04 3.7Z11-02 

51.350341 5.5007590471 7.4343705731 -4.351-03 4 5.13Z-02 -7.341-04 D 3.75Z-02 60.247391 5.9o08342251 7.5748253291 -4.351-03 1 5.131-02 -7.13--04 1 3.7K-02 

61.813031 4.9351752142 7.7817118141 -4.341-0- 0 5.131-02 1 -5.311-04 4 3.352-02 44.362031 4.3113652541 3.0121349421 -4.351-03 I 5.13Z-02 1 -4.5Z1-04 1 3.931-02 4".310 . "53152-3: .40255003-41I 4-,.071,-04 5. -02 1 3.,9--02 

69.3000o, 6.7941253331 2.7129131241 -4.312-03 1 5.25•-02 i -5.424-04 4.05_-02 73.003591 7.159326338 1.176153322 -4.241-031 3.353-02 -3.961-04 4.14Z-02 

78.3 701 7.704031423 1.87197362 -4.131-03 I 5.522-02 I -2.00G-04 I 4.30Z-02 34.112531 9.247534530 10.575331341 -4.081--03 1 5.48Z-02 1 -4.T17-06 I 4.42n-02 1.144701 3.793477453 11.273681091 S4.0 Z-103 I 5.93r-02 1 1.80Z-04 1 4.541-02 

17.91539 9.410629517 22.321321 -3.211-03 1 4.04Z-02 1 4.121-04 - 4.721-02 301.12409 .,173043241 -3.7245 I .38-13 4.15z-02 I 4.921-04 ± 4.30z-02 335.310014 2112. 841051 10.371017 11.0 6410 37 66 24.',7251'142 01.303320744 .7175-03 I 6.30E-02 4 4. 121-04 4 V.9-02 . 8315 -0 3t 6.51 "- 2 I 80 3Z-04. "H GE1 02. 123.3-559 32.100153515 23.511058141 -3.833-063 .791-02 1.0'1-03 5.41r-02 

131.21059 13.452112391 17.502703191 -3.822-03 6.841-02 1.032-03 4 5.451-02 

Rom="int. we . int, boop Iint. icrid. Ant. 

@=&in I strain I trainn 

I.(zaG ) 10.1974 k4/0'2 ) 

ILPt) - 0.7 (MP& )

E-401
2 4 6 a 10 12 14 

Internal Pressure ( MPa )

Strain History ( Plot ID 1/2/3/4/5/6 )

2 4 6 a 10 

Internal Pressure ( MP& ) 

Strain History ( Plot ID 7/8/9/10 

E-402

12 14

1I!

0.090

0.080 

0.070 

0.060 

0.050 

.= 0.040 

14 

w 0.030 

0.020 

0.010 

0.000

0 

Fig. 1-1

0.250 

0.200 

0.150

-4 

U 

'4J

0.100 

0.050

0.000 

-0.050

0 

Fig. 1-2
D 11 

12 

3 1 

314 I 

D 16/ 

is. is/

4 6 8 10 

Internal Pressure ( MPa )

12 14

Strain History ( Plot ID 11112/13/14/15/16 )

2 4 6 a 10 

Internal Pressure ( MPa )

12 14

Strain Eistory ( Plot ID 17/18/19/20 )

E-403

0.050

0.040 

0.030

Plot Ir 

fPlat m 

-Plat 2

0.020 

0.010

14 

Si

0.000 

-0.010

0 2

Fig. 1-3

0.060 

0.050 

0.040 

0.030 

0.020 

0.010 

0.000 

-0.010 

-0.020

-.4 

14 

Si 

£0

0 

Tig. 1-4

SsOI
2 4 6 8 10 12 14 

Internal Pressure ( MPa ) 

Strain History ( Plot ID 21/22/23/24

0 2 4 6 8 10 

Internal Pressure ( MPa 

rig. 1-6 Strain History ( Plot ID 25/26/27/28 

E-404

12 14

0.018 

0.016 

0.014 

0.012 

0.010 

= 0.008 

,.Jj 

00.006 

0.004 

0.002 

0.000

0 

rig. 1-5

0.016 

0.014 

0.012 

0.010 

0.008 

. 0.006 

t 0.004 

0.002 

0.000 

-0.002

I
0.040

0.035 

0.030 

0.025

-4 

SJ 

a.'

0.020 

0.015 

0.010

0.005 

0.000 

-0.005

0 2 

Pig. 1-7

200.0 

175.0 

150.0 

125.0 

100.0 

U 

75.0 

50.0 

25.0 

0.0

4 6 8 10 12 14 

Internal Pressure ( MPa 

Strain History ( Plot ID 29/30/31/32/33/34

2 4 6 8 10 

Internal Pressure ( KPa )

12 14

Displacement History ( Plot ID 35/36/37/38 ) 

E.4W

flat I.D 29 

-~.D Plot ZD 32 

--o- Zt 34 

-- ?m=3 - - - -

= !3 

ri = / 

--------------

0 

Fig. 1-8
30.00

25.00 Plat I 

20.00 

15.00 

,-4 

0.10.00 

*,4 

5.00 

0.00 

0 2 4 6 8 10 12 14 

Internal Pressure ( MPa 

Fig. 1-9 Displacement Bistory ( Plot ID 39 

0.100 

0.090 __- lat X_ 4_ 

0.090 Plot 3M 41 

----------- Plot XD 42 

0.070 ------ Plot -D 43 

"0.060 -- " " -

S0.050 0.050 •----------- --- '" .... 

-I f 

z 0.040 

,. 0.030 i 00 

0.020 I 

0.010 

-0.010 

0 2 4 6 a 10 12 14 

Internal Pressure ( MPa ) 

Fig. 1-10 Strain Ristory ( Plot ID 40/41/42/43 

E-406

1I
Appendix E-7

Sandia National Laboratories 

U.S.

E-407
Sandia National Laboratories

SCV Round Robin Submittal 

1. INTRODUCTION 

The authors of this section are Paul Carter and Samuel Key. This work was supported by the U.S. 

Nuclear Regulatory Commission and performed at Sandia National Laboratories, which is 

operated by the U.S. Department of Energy under contract number DE-AC04-94-ALS5000. 

This section summarizes the pretest structural analyses of a scale model of a Steel Containment 

Vessel (SCV) to be tested at Sandia National Laboratories. A complete description of the test is 

provided elsewhere. This section includes a summary of material modeling details, finite element 

model descriptions, results, and a failure prediction.. 

The structural analysis effort consisted of four basic finite element models with some analyses repeated with slight modifications. The ABAQUS general purpose finite element code was used 

for all structural analyses [1]. The first finite element model was a global axisymmetric shell 

element model. This model was run with two different gap dimensions (the nominal distance 

between the SCV and contact structure): 18 mm (the as-designed gap), designated the GAX18 

model, and 34 mm (a worst case scenario gap), model GAX34. All remaining analyses used the as

designed 18 mm gap dimension. The second model was a 3-dimensional global shell element 

model, designated G3DS, whose only non-axisymmetric detail was the addition of the equipment hatch. Results from this model called for further study in two areas: 1) the area near the junction of the material change interface and the equipment hatch insert plate; 2) the top head including the 

knuckle. The third model was a locally refined shell element submodel of a cut-out of the material 

change interface/equipment hatch insert plate junction from the 3-dimensional shell element 

model. This model, referred to as the LEHS model, was also rerun later with some as-built shell 

thicknesses incorporated into the model, the LEHSTh model. The last model was a local 

axisymmetric continuum element model of the top head area, model LTHAXC, including the 

contact structure from the apex extending down to the upper 19 mm stiffener. 

2. MATERIAL MODELS 

2.1 Introduction 

Each of the analyses used material models based on tensile test data provided by Hitachi [2]. The 

true stress-true strain data were used to fit a theoretical hardening curve such as a power law or 

inverse hyperbolic sine law. In addition to capturing the measured behavior up to maximum load, prediction of the behavior of the SCV up to failure requires reasonable extrapolations of the true 

stress-true strain data beyond maximum load. The tensile test were recreated using a finite element 

model to verify the behavior after maximum load. This section describes the procedure used to fit 

the material models to the tensile test data and to obtain reasonable extrapolations beyond 

maximum load.

E-409
2.2 Background 

In a tensile test, the engineering strain, e, is written in Equation 2.1:

e 1-10 

10

(EQ 2.1)

where 1o represents the initial gage length of the test specimen and I represents the current gage 

length of the test specimen. The engineering stress, s, is calculated from Equation 2.2:

F 

Ao (EQ2.2)

where F is the axial load on the tensile test specimen and Ao is the original cross-sectional area. 

The true strain, e, is defined as

£ = In-L 

0o (EQ 2.3)

which is only valid for a homogeneous deformation, and the true stress, a, is defined as

(EQ 2.4)

lo/2

j Slmoedi Displacement 

Figure 2.1 Axisymmetric finite element 

model of typical tensile test specimen show

ing boundary conditions and loading.

Radius r 

E-410

fI

ýT
where A is the instantaneous cross-sectional area. By rearranging Equation 2.1 and combining with 

Equation 2.3, the true strain may be written in terms of the engineering strain: 

E= In(1 +e). (EQ2.5) 

By using the constant volume relationship, AOL, = AL, and combining Equation 2.2 and Equation 

2.4, the true stress may be written in terms of the engineering stress: 

a= s(1 + e). (EQ 2.6) 

Equation 2.5 and Equation 2.6 assume that the volume is constant, the stress is uniform through 

the cross-section, and the deformation is homogeneous throughout the gage length. However, at 

the point of maximum load, defined as the load corresponding to the highest stress on the 

engineering stress-strain curve, the deformation localizes and necking occurs. Thus, the 

assumption of homogeneous deformation throughout the gage length is violated and the stress 

distribution is no longer uniform through the cross-section. So, Equation 2.5 and Equation 2.6 are 

not valid beyond maximum load. Although the engineering stress decreases after necking because 

less load is carried, the true stress continues to increase [3]. 

In geometries which are more complex than that of a tensile test specimen, local stresses may reach 

values higher than the true stress in a tensile test specimen at maximum load. Also, true stress-true 

strain data will be required beyond maximum load to assess localized material failure. Therefore, 

it is necessary to extrapolate the true stress-true strain data supplied by Hitachi beyond maximum 

load. 

2.3 Procedure 

The following procedure was used to obtain the necessary data. First, two different hardening 

plasticity models were fit to the experimental true stress-true strain data, which is only available 

up to maximum load, using a MATLAB [4] curve fitting routine. These two models were chosen 

for their ability to accurately capture the hardening behavior of most steels. The first model is the 

power law hardening model shown in Equation 2.7 [5]: 

S n 

Fe-0 = A(e-E/ , (EQ2.7) 

where A and n are the constants calculated from the curve fit, a, is the effective stress, ey, is the 

yield stress, ep is the equivalent plastic strain, and eL is the Luder's strain or yield plateau. The use 

of the brackets, <, denotes the Heaviside function where the expression enclosed in the brackets 

takes the value of the enclosed expression when positive and is zero when the enclosed expression 

is negative. The second model uses the inverse hyperbolic sine function and is shown in Equation 

2.8: 

re-ays - Asinh' (B(EP-te) (EQ2.8) 

where A and B are the constants calculated from the curve fit.

E-411
After determining which of the two hardening models provided the best fit to the data from each 

set of tensile tests, the next step was to simulate each set of tensile tests computationally using the 

appropriate constitutive relation in the SANTOS finite element program [6]. Figure 2.1 shows the 

axisymmetric finite element model used. Only half of the length of the round bar was modeled 

since it is symmetric about the plane normal to the axis of the specimen. To ensure that the 

localized deformation occurs at the center of the gage length, the diameter was reduced by 0.5

1.0% at the plane of symmetry to provide an initial geometric imperfection. The specimen is 

restrained in the y-direction at the plane of symmetry, and displacements were imposed in the y

direction at the free end. 

As shown above in Equation 2.1, the engineering strain is obtained by dividing the change in the 

gage length or displacement by the original gage length. The load on the specimen can be 

converted to engineering stress by dividing by the original cross-sectional area as in Equation 2.2. 

The load-displacement data from the finite element analysis was converted to engineering stress

Table 2.1: Summary of Material Parameters - SGV480 

crys, Yield A. 

Batch Thickness elHardening B, Strain Luder's EL, 

Designation Location Material Strength Constant, Constant Strai 

(Wa) W(MPa) 

RT12/ Top Head, 

RT34 Top Head SGV480 6.0 404.9 153.7 15.36 0.01 

Shell 

RT56 er Coi SGV480 7.5 404.2 147.5 15.36 0.01 cal Shell 

RT78 pper Spheri- SGV480 8.0 386.5 148.0 16.70 0.01 cal Shell 

RT910 ddle Coan- SGV480 8.5 399.8 145.0 17.03 0.01 cal Shell 

RTRl12 Siening SGV480 9.5 409.6 139.2 17.71 0.01 ________Ring 

RT1314 Stiffening 

RT1314 Ring SGV480 12.5 383.6 142.1 18.25 0.01 

RT1516 Stiffening SGV480 19.0 378.7 126.0 23.83 0.01 

______ Rings (2) ____ 

Top Flange, Hatch Coy

RT1718 ers(2), Hatch SGV480 20.0 379.8 122.0 25.43 0.02 

Sleeve 

RT1920 Knuckle SGV480 28.0 371.6 110.9 33.20 0.01

E-412

1;
strain data and compared to the engineering stress-strain data supplied by Hitachi in an attempt to 

verify the post-peak behavior. If the data from the finite element analysis did not correlate well 

with the Hitachi data, a new curve fit was tried and a new finite element analysis performed. This 

iterative process was repeated until reasonable post-peak behavior was obtained. 

Hitachi performed a set of four tensile tests for each of the 11 different material/thickness 

combinations (two in the rolling direction and two in the transverse direction) for a total of 48 tests 

(one batch of tests was repeated). Table 2.1 summarizes the results of the curve fitting for the 9 

different SGV480 thicknesses; Table 2.2 summarizes the results of the curve fitting for the SPV490 

thicknesses. For the SGV480 materials, the inverse hyperbolic sine law model worked best, while 

the power law worked best for the SPV490 materials. Figure 2.2 shows a typical true stress-true 

strain tensile test data set with a typical corresponding curve fit. Figure 2.3 shows the engineering 

stress-engineering strain data with the output of the finite element analysis of the tensile test. These 

material models do not address material failure. 

2.4 Implementation into ABAQUS 

The ABAQUS input deck requires two options to specify an elastic-plastic material model: 

*ELASTIC, where the user specifies the elastic modulus and Poisson's ratio; and *PLASTIC, 

which specifies a metal plasticity model with a von Mises or Hill yield surface. For this option, the 

user must specify the yield stress as a function of plastic strain, using true stress and log plastic 

strain values. The above data was converted by a simple FORTRAN program to a format 

compatible with ABAQUS. 

Table 2.2: Summary of Material Parameters - SGV 490 

lays, A, 

Batch Thickness Yield Hardening n, Strain EL' Locaion MateialLuder's 

Designation (mm) Strength Constant, Exponent 

_(M:a) (MPa) Strain 

Cylindrical 

RT2122 Wet Well, SPV490 9.0 660.0 390.0 0.45 0.015 Lower Coni

cal Shell 

Bottom 

Flange, Bot

tom Head, 

RT-2324 S Rening SPV490 17.5 598.9 450.0 0.48 0.01 

Rig, Ring 

Support 

Girder, Gusset 

Plates

E-413
8oo

700 

SSoo 

400 

0 

2 300 

1

100 

0

20 

True Strain,(%

Figure 2.2 True Stress - True Strain curves for RT78; Material 

SGV480; Thickness - 8.0 rmm; Location - Upper Spherical Shell

S4ool 

400 

300 

200 

100 

0 20 30 

Engineering Strain, (%)

40

Figure 2.3 Engineering Stress - Engineering Strain curves for RT78; Material - SGV480; Thickness - 8.0 mm; Location - Upper Spherical Shell

E-414
3. GLOBAL AXISYMMETRIC ANALYSES (GAXIS / GAkX) 

The first part of the analysis effort assumed the containment was axisymmetric. The effects of the 

non-axisymmetric features such as the equipment hatch were ignored since the primary purpose of 

these analyses was to study the global behavior of the SCV and its interaction with the contact 

structure. Two analyses were performed with different gap dimensions. The first model (GAX 18) 

used the as-designed gap of 18 mm between the SCV and the contact structure. Table 3.1 

summarizes the yielding and contact events for the 18 mm case. The second model (GAX34) used 

a worst-case scenario gap of 34 mm. The results for this case are presented briefly in Section 3.3. 

3.1 Finite Element Model Description 

The basic finite element model of the SCV and contact structure for the axisymmetric analyses 

appears in Figure 3.1. Two-node axisymmetric shell elements were used for the shell walls, ring 

stiffeners, and rings of the support girder. Four node axisymmetric quadrilaterals were used for the 

flanges, gusset plates, and the contact structure. Two-node axisymmetric contact elements were 

superimposed on the shell elements on the wall of the SCV to model the contact between the SCV 

and the contact structure. The total number of elements used was approximately 1600 for both the 

18 mm case and the 34 mm case. Axisymmetric boundary conditions were imposed on the node at 

the top of the hemispherical dome of the SCV as well as at the bottom hatch cover. The model is 

also constrained in the vertical direction at the bottom outside comer of the ring support girder. The 

loading consisted of pressure on the interior of the SCV and self-weight of the entire structure and 

the analysis was arbitrarily terminated at 8 MPa internal pressure or roughly 10 times the scaled 

design pressure (1 Pd = 0.78 MPa = 113 psi). All computations for these two models were 

performed with the commercial finite element code ABAQUS/Standard, Version 5.3. 

Table 3.1: Summary of Yielding/Contact Events for GAX18 

Internal 

PresEvent 

0- 2.2 MPa Elastic behavior 

2.2 MPa Yielding in knuckle (see Figure 3.1) 

2.5 MPa Yielding in wet well/lower conical section 

2.8 MPa Yielding in torus of top head 

2.8 MPa Yielding in spherical section 

3.1 MPa Yielding in middle/upper conical sections 

4.0 MPa Contact initiates in knuckle/upper conical section 

4.1 MPa Contact initiates in middle conical section 

5.5 MPa Contact initiates in lower conical section 

5.6 MPa Yielding in hemispherical dome in top head 

6.0 MPa Yielding in contact structure 

6.7 MPa Contact initiates in spherical section 

6.7 MPa Yielding in top flange 

8.0 MPa Analysis arbitrarily terminated

E-415
No Radial 

Displacement 

Boundary Condition

,,.--Top Head

Lower Conical 

Section

Wet 

Wen

Head

Bottom (SAX1)

No Radial 'Displacement 

Boundary Condition

Figure 3.1 Axisymmetric finite element model (GAX18/GAX34) showing knuckle and ring support girder details. 

F-416

L
Gusset plates are welded between the upper and lower rings of the ring support girder to provide 

it with significant shear and bending resistance. In order to include the effect of the 32 gusset plates 

in the axisymmetric finite element model, they were modeled as a solid ring with an orthotropic 

material model and a reduced Young's modulus. The ring representing the gusset plate is assumed 

to have no stiffness in the hoop direction. The reduced stiffness in the axial and radial directions is 

obtained by multiplying Young's modulus of the actual material by the ratio of the actual area of 

the gusset plates to the area of the solid ring in the axisymmetric finite element analyses. 

ABAQUS/Standard Version 5.3, unlike newer versions of ABAQUS, requires the user to explicitly 

input contact elements. For both axisymmetric models two-node axisymmetric contact elements 

(ABAQUS type ISL21A) were superimposed on the wall of the SCV to model the contact between 

the SCV and the contact structure. These elements are capable of modeling finite sliding between 

two deformable bodies. Contact interaction takes place along a "slide line" which the user defines 

as a collection of nodes on the opposite surface of the contact elements. Based on an earlier 

parametric study, the coefficient of friction used for these analyses was gt-=0.2 (see Section 5.2 for 

a discussion of the friction coefficient). 

Because of recent changes in the design of the contact structure, there are two important differences 

between the as-modeled contact structure and the as-designed contact structure. The first design 

change is that the contact structure will be composed of SA516 Grade 70 steel rather than A36 

steel. The SA516 has a slightly higher yield (258 MPa (38 ksi) compared to 245 MPa (36 ksi) for 

the A36) and also a slightly higher ultimate strength (476 MPa (70 ksi) compared to 408 MPa (60 

ksi) for A36) [7]. Since the contact structure is expected to remain elastic until sometime after 10 

multiples of the design pressure, it is unlikely that this difference will significantly affect the 

results. The other important difference lies in the geometry of the contact structure near the knuckle 

of the SCV. Figure 3.2 details the differences between the as-modeled and the as-designed 

geometry for the part of the contact structure adjacent to the knuckle. Note the gap at the top of the

As-Modeled 

i----Top Flange

As-Designed 

.- Top Flange

Figure 3.2 Comparison of as-modeled and as-designed details in contact structure near the 

SCV knuckle.

E-417
knuckle in the as-designed structure is nearly twice that of the as-modeled: 38 mm compared to 18 

mm. The last finite element model, which covers the top head and knuckle region, includes the 

latest design information discussed above. It appears in Section 4.3. 

3.2 Results - 18 mm case (GAX18) 

For the 18 mm case, yielding is observed first in the knuckle at 2.2 MPa. The wet well, lower, 

middle and upper conical sections, as well as the transition in the top head all yield prior to contact. 

Contact initiates in the knuckle and upper conical section first at 4.0 MPa. By 6.7 MPa, the 

spherical section, the hemispherical dome, the top flange, and the contact structure have all 

yielded. 

3.3 Results - 34 mm case (GAX34) 

The axisymmetric model with a 34 mm gap was performed as a check on the worst 

case, as-built condition of the contact structure. With a larger gap, the contact 

structure will not be effective in slowing plastic flow until a higher internal pressure 

and may even be useless if the SCV accumulates too much plastic strain prior to 

contact. Since this analysis was only intended as a worst case scenario, it will only 

be presented as a tabulated summary. Yielding and contact events are shown in 

Table 3.2. 

Table 3.2: Summary of Yielding/Contact Events for GAX34 

Internal 

Pressure Event 

0 - 2.2 MPa Elastic behavior 

2.2 MPa Yielding in knuckle (see Figure 3.1) 

2.5 MPa Yielding in wet well/lower conical section 

2.8 MPa. Yielding in torus of top head 

2.8 MPa Yielding in spherical section 

3.1 MPa Yielding in middle/upper conical sections 

4.3 MPa Contact initiates in upper conical section 

4A MPa Contact initiates in middle conical section 

4.5 MPa Yielding in top flange 

4.8 MPa Contact initiates in knuckle 

5.6 MPa Yielding in hemispherical dome in top head 

5.8 MPa Contact initiates in lower conical section 

6.3 MPa Yielding in contact structure 

7.1 MPa Contact initiates in spherical section 

8.0 MPa Analysis arbitrarily terminated

&-418
:4. 3D ANALYSES

4.1 Global 3-D Shell Model (G3DS) 

The next analysis performed to characterize the global behavior of the SCV and its interaction with 

the contact structure used a 3-dimensional shell element model. Table 4.1 summarizes the yielding 

and contact events. 

4.1.1 Finite Element Model Description 

The finite element model of the SCV and contact structure for the G3DS Model appears in Figure 

4.1. The half-symmetry model used approximately 4800 four-node reduced integration shell 

elements with finite membrane strain capability (ABAQUS S4R elements). The only non

axisymmetric detail included in this model is the equipment hatch. Symmetric boundary conditions 

were imposed on all nodes lying in the vertical (x-y) plane passing through the centerline of the 

equipment hatch, and vertical displacements were constrained at the support locations on the 

underside of the ring support girder. The loading consisted of gravity and internal pressure and the 

analysis ran until it failed to converge at approximately 12.7 MPa internal pressure or slightly over 

16.3 Pd. The nominal gap between the SCV and the contact structure was 18 mm. Computations 

for this model were performed with the ABAQUS/Standard, Version 5.4. 

Table 4.1: Summary of Yielding/Contact Events for Global 3-D Shell Model 

Internal Event 

Pressure 

0- 2.3 MPa Elastic behavior 

2.3 MPa Local yielding in top/bottom of E/H sleeve at attachment to insert plate 

2.3 MPa Local yielding at middle conical section attachment to E/H insert plate 

2.7 MPa Yielding in knuckle 

2.8 MPa Local yielding at bottom of E/H insert plate 

3.0 MPa Local yielding in upper conical section above E/H 

3.1 MPa Yielding in middle conical section around circumference 

3.4 MPa Yielding in upper conical section around circumference 

3.7 MPa Yielding in lower conical section near insert plate 

3.9 MPa Yielding in lower conical section around circumference 

4.1 MPa Contact initiates in the SCV in the upper conical section and knuckle 

4.1 MPa Circumferential contact in upper conical section 

4.3 MPa Circumferential contact in middle conical section 

4.7 MPa Yielding in cylindrical wet well around circumference 

5.1 MPa Yielding in dome of top head 

5.3 MPa Circumferential contact in lower conical section 

5.5 MPa Yielding in spherical section (away from knuckle) 

6.6 MPa Contact initiates in spherical section 

11.3 MPa Circumferential contact in wet well

E-419
The contact definition in versions of ABAQUS after 

Version 5.3 is much simpler. The newer versions use 

the contact pair approach in which the user can 

simply specify two element sets that are candidates 

for eventual contact. One additional specification 

required for structural elements, such as the shell 

elements used for this model, is that the surface be 

specified. For this model, a small sliding 

formulation was used since the relative sliding of the 

SCV and contact structure was assumed to be small. 

The friction coefficient, discussed previously in 

Section 3.1, was p,=0.2. 

The thickened equipment hatch insert plate was 

constructed such that it is flush with the inside 

surface of the SCV. The thickness eccentricity poses 

a problem when using shell elements in ABAQUS 

since there are no means of explicitly modeling a I 

shell with uneven material distribution about a 

reference line. A simple elastic test case showed that 

using the *SHELL SECTION, COMPOSITE y 

option in ABAQUS is an accurate way of implicitly 

modeling the eccentricity at the equipment hatch 

insert plate [8]. The equipment hatch insert plate X 

was modeled as a composite shell with 3 layers. The 

eccentricity was introduced by making the middle Figure 4.1 Global 3-D Shell (G3DS) 

layer the same thickness as the adjacent material and model mesh. Note: contact structure ap

then placing two shells with the same thickness on pears behind SCV. 

either side. The middle and outside layers were given the modulus of elasticity for the equipment 

hatch insert plate (measured from the Hitachi tensile tests), Epl.- 216 x 109 Pa, while the inner 

composite layer was given a dummy modulus of Edummy - 1 Pa. This formulation makes the 

stiffness of the inner layer of the composite shell negligible with respect to the outer layer. 

Because of the eccentricity at the insert plate shown in Figure 4.2, the gap between the insert plate 

and the contact structure is reduced considerably to approximately 9 mm. The eccentricity 

formulation described above does not account for the smaller gap since the contact algorithm uses 

the centerline of both the composite shells in the SCV insert plate and the regular shells in the 

contact structure as the reference. So, the gap between the insert plate and the SCV in the finite 

element model is 18 mrm. 

As with the axisymmetric model described in Section 3.1, there were two important changes in the 

design of the contact structure which were also not incorporated into this model. The contact 

structure material and its geometry near the knuckle of the SCV were the same as in the 

axisymmetric model (see Figure 3.2 for knuckle details). It is unlikely that the difference in 

materials will significantly affect the results. However, the geometry near the knuckle is especially 

important and is modeled more accurately and completely in the LTHAXC model in Section 4.3. 

E-420
4.1.2 Results 

Results presented for this model include deformed shape plots, contact history plots, and a brief 

discussion of the high strain or critical areas. 

4.1.2.1 Deformed Shape 

Figure 4.3 shows the deformed shape of the SCV at 8 different pressure levels. The contact 

structure, ring support girders, and gusset plates are not shown for clarity. At 3 MPa, when only 

localized yielding has occurred, very little deformation is discernible. At 4.1 MPa, when contact 

first occurs, there is noticeable deformation in the upper and middle conical sections. The effect of 

the stiffeners is evident in the upper conical section as it tries to expand outward but is restrained 

by two 19 mm stiffeners. The knuckle shows deformation in both the outward (radial) and vertical 

directions, while the top head and top head flange appear to be deforming exclusively in the 

vertical direction. The equipment hatch also appears to be rotating outward and downward at this 

pressure. By 6 MPa, most of the upper and middle conical sections are contacting the SCV. The 

outward expansion of the cylindrical wet well is now apparent. At 8 MPa it is clear that the contact 

structure is arresting further radial expansion of most of the SCV. The apex of the top head and the 

cylindrical portion of the top head, which are not shielded by the contact structure, are showing 

excessive amounts of deformation. At 10 MPa, which is nearly 13 multiples of the design pressure, 

the only locations where further deformations are clear are the top head and the cylindrical wet 

well. 

4.1.2.2 Contact Hstory 

Figure 4.4 shows the progression of contact. Only that part of the SCV which is shielded by the 

contact structure is displayed. Dark areas indicate contact while light areas indicate no contact. The 

first plot shows contact initiating in the upper conical section and the knuckle. The area of contact 

has increased considerably at 5 MPa to include the middle conical section and by 6 MPa includes 

the lower conical section. By 8 MPa, the spherical section, the last area to make contact not 

including the cylindrical wet well where the gap is considerably larger, has made uniform 

Gap 9 •r¢ .mrAs-designed 

G Gap =18 mm geometry 

"• Interior \ Contact 

Thcee Surface / Structure 

rtPl - -As-modeled 

7p Gap= 18 mm (shell) geometry 

F22222Z ý ý////// ,4j-/// \ •Interor 

q/\• Surface Reference line 5%' Dummy material elements used for contact algorithm 

Figure 4.2 Cut-out of thickened equipment hatch insert plate and attached conical section 

showing as-designed geometry (top) and as-modeled geometry (bottom) using shell elements. 

Reference line shown at lower right is used for contact algorithm which makes the gap a uni

form 18 mm even over insert plate

E-421
Stiffeners

P=3MPa Top

P=6MPa

P = 4.1 Ma 

(first contact) P=5 MPa

P=8MPa

Figure 4.3 Deformed shape of G3DS at 6 pressure levels. Contact structure, ring support girders, and gusset plates are not shown. Displacements are magnified by a factor of 5. 

E-422

1I
circumferential contact except near the upper 19 mm stiffener, which is still arresting the radial 

growth of the SCV. At 10 MPa, the only area of the SCV that has not contacted the contact 

structure yet is the cylindrical wet well where the initial gap is well over 100 mm. 

4.1.2.3 Critical Areas 

Contour plots of equivalent plastic strain indicated three locations with high strains that dictated 

further study. Figure 4.5 compares the three locations which consistently displayed the highest 

plastic strains throughout the history: 1)the junction of the equipment hatch insert plate and the 

material change interface; 2) the apex of the top head; 3)the knuckle region. The element at the 

knuckle and at the material change interface near the insert plate both yield at roughly the same 

time but the element at the knuckle contacts first and so the plastic strain for this element levels out

* Contact

P=4.1 MPa 

(contact 

initiates) 

Li

M No Contact 

P=5MPa

P=6MPa 

L 

P=8MPa 

L,

P=7MPa

L,

P= IOMPa

Figure 4A Plots showing contact evolution

E-423

L

41
earlier in the loading. Both elements are eventually shielded by the contact structure and so do not 

accumulate nearly as much plastic strain as the apex of the top head. The apex yields at 5.1 MPa, 

compared to 2.5 MPa for the other two locations, but the amount of plastic strain quickly surpasses 

that accumulated at the other two locations and reaches a value of nearly 40% before the analysis 

fails to converge at just over 12.7 MPa. To assess the importance of these critical areas, refined 

models for both the top head, including the knuckle, and the area near the equipment hatch insert 

plate were created and are discussed in Section 4.2, Section 4.3, and Section 4.4. 

4.2 Local Equipment Hatch Submodel (LEHS) 

This section covers the model created to study the junction of the equipment hatch insert plate and 

the material interface. 

4.2.1 Finite Element Model Description 

Shown in Figure 4.6, the model used 4800 four-node reduced integration shell elements with finite 

membrane strain capability (ABAQUS S4R elements). The boundary conditions were imposed 

using the * SUBMODEL option. Submodeling in ABAQUS is used to study a local part of a model 

with a refined mesh based on interpolation of the solution from an initial, global model, onto the 

nodes on the appropriate parts of the boundary of the submodel. Figure 4.7 compares the G3DS 

model mesh and the LEHS model mesh. For this particular analysis all nodes on the boundary of 

the submodel were "driven" by the results from the G3DS model as indicated in Figure 4.6. The 

loading consisted of gravity and internal pressure. The coefficient of friction used for this model is 

the same as in previous models, g--=0.2. The eccentricity of the equipment hatch insert plate was 

also modeled as described in Section 4.1.1. Since this model uses results from the previous G3DS 

model, the model was only allowed to run up to 12.7 MPa, the point where the global model failed 

to converge. Computations for this model were performed with ABAQUS, Version 5.4. 

0.20 

0-O- Knuckle 

0-0 Near insert PlateMaterial Interface 

I i1 -- Apex of Top Head 0.12 

0.12 

L. 0.08 

0.00 2 4 8 a 10 12 

Internal Pressure, (MPa) 

Figure 4-5 Equivalent plastic membrane strain for three critical locations in the Global 3-D 

Shell Model as a function of internal pressure. Locations of strains are shown at left. 

E-424

It
4.2.2 Results 

The contact history is presented for this model with a comparison of critical areas between this 

model and the G3DS model. 

4.2.2.1 Contact History 

Figure 4.8 shows the evolution of contact for the Equipment Hatch Submodel. As before, black 

areas indicate contact, white areas indicate no contact. The elements on the border of the model are 

gray because they are "driven" nodes and so are not included in the contact algorithm. Contact first

inse 

Mat 

Thic

Boundary conditions 

from Global 3-D Shell 

Model applied on all 

boundaries

Y

z x

;rt Plate 

erial: SGV490 

,kness: 17.5 mm 

Material: SGV480 

Thickness: 8.5 mm 

•Material: SGV490 

Thickness: 9.0 mm

Figure 4.6 LEHS model mesh (contact structure not shown). 

z x 

Figure 4.7 Comparison of Global 3-D mesh at left and Equipment Hatch Submodel at right. 

The increase in mesh density between the two models roughly a factor of 10.

E-425
occurs at 4.2 MPa in the middle conical section. It propagates towards the insert plate at 5 MPa and 

by 6 MPa has contacted a large part of the insert plate and has spread to the lower conical section 

(below the material interface). At 8 MPa the contact is widespread throughout the model. 

4.2.2.2 Critical Area 

This model was intended to study the junction of the equipment hatch insert plate and the material 

interface subsequent to the G3DS model which indicated potentially high strains in this area. 

Figure 4.9 compares the equivalent plastic membrane strains from the two models at the same 

location: the element in the 8.5 mm wall (middle conical section) that is adjacent to the equipment 

hatch insert plate and adjacent to the 9.0 mm wall (lower conical section). These elements are 

indicated in the figure. In the G3DS model this element is approximately 60 mm by 30 mm in size 

while in the LEHS model the element in the corresponding location is I 1 mm by 11 mm. 

Qualitatively the behavior of the two elements is similar. Quantitatively the element in the LEHS

I Contact [- No Contact

P=4.2 M 

(contact 

initiates) 

P=6MPa 

V 

LiA

P=5MPa 

P=8MPa 

FT

Figure 4.8 Evolution of contact for Equipment Hatch Submodel. Black areas indicate con

tact, white areas indicate no contact. 

E-426

B
submodel reaches strains nearly 50% higher than the G3DS mrdel: 9% in the submodel compared 

to approximately 6.5% in the global model. The difference is best explained by the submodel's 

ability to more accurately measure the strain concentration due to its finer mesh. 

4.3 Top Head Submodel (LTHAXC) 

The second critical area requiring further study as indicated by the G3DS model was the top head 

region including the knuckle. For this area a local axisymmetric continuum model was created 

which includes the most recent as-designed geometry of both the SCV and the contact structure 

from the top head apex down to the upper 19 mm stiffener. 

4.3.1 Finite Element Model Description 

Figure 4.10 shows the finite element model for the Top Head Submodel. The model used 7200 

four-node reduced integration, axisymmetric continuum elements (ABAQUS CAX4R elements) 

and 5 two-node thin or thick linear shell elements (ABAQUS SAXI elements). Axisymnnetric 

boundary conditions were imposed at the apex of the top head. At the lower bound of the model, 

rotations and displacements from the G3DS model were applied to the shell nodes in a manner 

similar to the * SUBMODEL option in ABAQUS. However, ABAQUS does not allow the submodel 

option to be used when changing from a 3-dimensional model to an axisymmetric model, so the 

same process was carried out manually. The displacement and rotation histories from the 

appropriate nodes on the G3DS model were applied "manually" with the *USER SUBROUTINE 

option, which provides the user with a means of prescribing the magnitude of any degree of 

freedom using FORTRAN code. Multi-point constraints were used to transition from the shell 

elements to the continuum elements. As with the other models, the loading consisted of internal 

0.10 

*-49 Global3-D Shell Model 

0.09 [h.. Local 01 Shen SubmodelI 

0.08 

_W 

•0.06 

S~E 

E 0.04 

i •. . "E 0.04

0 2 4 6 8 10 12 

Internal Pressure, (MPa) 

Figure 4.9 Comparison of critical area elements from G3DS 

and LEHS models with element locations indicated at left.

E-427
pressure and gravity. The contact definition for this model was basically the same as the previous 

models (the coefficient of friction was gt = 0.2) except that the small sliding formulation was not 

specified. For this case, ABAQUS defaults to a finite sliding formulation, which allows for 

arbitrary separation, sliding, and rotation of the surfaces. 

As mentioned in Section 3.1 and shown in Figure 3.2, the design of the contact structure was 

changed considerably after the GAX18/GAX34 and G3DS models were completed. This model 

includes those design modifications. Since continuum elements were used throughout the model, 

this model also more accurately models the geometry, especially near the top head flange and the 

knuckle. 

4.3.2 Results 

Results presented for this model consist of deformed shape plots and a discussion of the critical 

areas. 

4.3.2.1 Deformed Shape 

Figure 4.11 shows the deformed shape plots for the Top Head Submodel. The first three plots are 

the deformed shape of the entire model at 3 different internal pressures, while the last six are a 

close-up of the knuckle/top head flange region as in Figure 4.10 with some additional pressure 

steps included. The displacements are not magnified. First contact occurs at 3.2 MPa at the knuckle 

as it expands radially outward to meet the comer of the contact structure. At 6 MPa, the bending 

of the cylindrical section of the top head from the bottom of the top head flange is apparent and at 

8 MPa bending around the top of the top head flange is now beginning. The vertical growth of the 

dome is also significant at 8 MPa. Note that the top head flange shows almost no radial expansion 

0 r

Figure 4.10 Local Top Head Axisymmetric Continuum Model with close-up of knuckle/ 

top head flange.

E-428
at 8 MPa. The overly stiff behavior of the top head flange and the rapid radial expansion of the 

knuckle create bending locations with significant plastic strains as will be shown in the next 

section.

P = 3.2 MPa 

(contact 

initiates)

P = 5 MPa "P 8MPa

P = 3.2 MPa 

(contact 

initiates)

P=6MPa

P=4MPa

P= 8MPa

P=5MPa

P= 1OMPa

Figure 4.11 Deformed shape plots of Local Top Head Axisymmetric Continuum Model with close-up of knuckle/top head flange. The displacements are not magnified.

E-429
4.3.2.2 Critical Areas 

Figure 4.12 plots the strains from the critical locations from the top head submodel as a function 

of internal pressure. The 5 locations can be broken down into 3 areas: the apex of the top head, the 

top head flange, and the knuckle. After 8 MPa, all of the locations show very similar strain histories 

except for the element below the knuckle. The main differences in the strain histories appear early 

in the loading. 

The exterior surface of the apex of the top head yields late in the history compared to the other 

elements at about 5 MPa. Since this location is not protected by the contact structure, the growth 

of plastic strain is rapid up to a maximum of over 34% at an internal pressure of over 12 MPa. 

The overly stiff behavior of the top head flange can probably be attributed to the mixed scaling of 

the SCV: 1:4 ratio thickness; 1:10 ratio on size. This causes large bending strains in the elements 

just below and just above the top flange on the interior surface, since they are both in tension due 

to bending. The element just above the top flange behaves similarly to the apex of the top head 

except that it yields sooner. The element just below the top flange accumulates more plastic strain 

early in the loading but otherwise behaves similarly to the first two elements. 

The element at the interface between the top of the knuckle and the cylindrical section of the top 

head on the exterior surface accumulates still more plastic strain early in the loading but then 

appears to be temporarily affected by the contact structure at just over 3 MPa. The last location 

under consideration is the element at the interface between the bottom of the knuckle and the 

spherical section on the exterior surface. It accumulates more plastic strain than all of the other 

elements until it contacts the contact structure at just over 3 MPa. The effect of the contact structure 

on this element is much more apparent as this element reaches a maximum strain of only 12% 

compared to nearly 34% for the apex and 24% for the other elements. 

*--Apex of Top Head(Ext) 

k-AAbove Top Flange (Int) 0.M2 

- Below Top Flange (Int) i 

$--Above Knuckle (Ext) 

O-OBelow Knuckle (Ext) 024 . 

.02 

0.16 

0.12

S0 2 4 6 8 10 12 

Intrd al Presure (MPa) 

Figure 4.12 Comparison of critical high strain areas 

from the LTHAXC model. Four of the locations are indi

cated at left; the other one is the apex of the top head.

E-430
4.4 Equipment Hatch Submodel with Thinned area (LEHSth) 

The last analysis performed to characterize the global behavior of the SCV and its interaction with 

the contact structure was used to study the effects of thinned areas near the junction of the 

equipment hatch insert plate and material change interface. 

4.4.1 Finite Element Model Description 

Figure 4.13 shows the basic finite element model used to study the effects of thinning. The model 

is essentially the same as the previous Equipment Hatch Submodel except that the measured 

thicknesses near the junction of the equipment hatch insert plate and the material interface were 

input explicitly using the *NODAL THICKNESS option in ABAQUS, Version 5.5. This model is 

only intended to study the thinned area near the equipment hatch insert plate and so does not 

include any other as-built information. 

The input data for the thinned area appeared in the February 20, 1996 memorandum from Sandia 

[9] regarding as-built properties of the SCV model and contact structure. The as-built 

measurements indicate that the nominal thicknesses of the as-built SCV are 5-10% thicker than the 

designed configuration of the SCV, while two locations on either side of the equipment hatch insert 

plate are up to 22% thinner than the designed configuration, on which all of the finite element 

models are based. To accommodate for this in the finite element model, the measured thickness

o 100% of nominal thickness * 89% of nominal thickness 

N 96% of nominal thickness 03 91% of nominal thickness

A 84% of nominal thickness A 78% of nominal thickness

Figure 4.13 Diagram showing the equipment hatch submodel at right (contact structure not 

shown) with a detail of the thinned area at left. Values for thickness reduction are shown as per

centages and superimposed on the appropriate nodes.

E-431
from the thinned areas from the SCV were converted to a percentage of the nominal measured 

thickness. Then, these percentages were used to calculate the input thicknesses for the thinned 

locations in the finite element model. Simply changing the nominal thickness in the finite element 

model was not an option since that model uses boundary conditions from a global model (G3DS) 

which uses the original, as-designed thicknesses. 

4.4.2 Contact History 

The contact behavior for this model is nearly the same as for the LEHS model (see Figure 4.8). 

4.4.3 Critical Areas 

Figure 4.14 compares the critical strain area from this model to the G3DS and the LEHS model 

with the locations indicated in the diagram at the left. This is the same figure as Figure 4.9 with the 

data from the LEHSTh model added. Qualitatively each curve represents the same behavior: the 

element yields at between 3 and 4 MPa, accumulates plastic strain very quickly until it reaches the 

contact structure between 5 and 6 MPa. The main difference between each curve is the amount of 

plastic strain accumulated prior to contact. The effect of the thinned section is apparent, as the 

slightly thicker and higher yield SPV490 material now shows the greatest accumulation of plastic 

strain. This issue will be discussed in more detail later. 

5. MISCELLANEOUS CALCULATIONS 

This section covers additional calculations which supported the finite element analyses presented 

above. Buckling is presented in Section 5.1 while a discussion of the determination of the friction 

coefficient is presented in Section 5.2. 

020 

9-9 G3DS (8.5 mm wall) 

A-- LEHS (8.5 mm wall) 0.18 

*-u LEHSTh (9.0 mm wall) .o16 

- LEHSTh (8.5 mm wall) 0.14 

I 0. 121 

I i -SGV480 0. 

8.5 mmn 0.08 

S 0.06 ...... • ,// 3 ..

0.04 

0.02 

SPV490 0.00 

9.0mm 0 2 4 8 10 12 Internal Pressure, (MPa) 

Figure 4.14 Comparison of high strain locations from the 

G3DS model, the LEHS model and the LEHSTh model. Lo

cations from the LEHSTh model are shown at left. See Figure 4.9 for locations from other models. 

E-432

II
5.1 Buckling 

The G3DS model did show compressive strains in the torispherical head but they were not 

sufficient to cause buckling. To further investigate the potential for buckling simple closed-form 

solutions were used [10]. Equation 5.1 may be used to estimate the elastic buckling pressure of a 

torispherical head subjected to internal pressure, 

PB 251 1.5 11°stt"O3'"' 

F=285 ( 115f(L) 094 ( (EQ 5.1) 

while the plastic collapse pressure can be estimated by Equation 5.2: 

P= 12.6(1 + 2400 OO) . (EQ 5.2) 

For these equations, 

PB = elastic buckling pressure, 

Pc = plastic collapse pressure, 

Y = yield strength (SGV480, 6 mm) = 405 MPa 

E = elastic modulus (SGV480, 6mm) = 210 GPa, 

D = inner diameter of adjoining cylinder = 965 rmm, 

L =inside radius at crown = 873 num, 

r= inside radius of knuckle = 166.7 mrm, 

t= thickness of head = 6 mm. 

Both of these equations are valid in the ranges: 

.000667 < tMD < .002, 

.06 < rMD <.018, and 

.75 < L/D < 1.0. 

For the SCY scale model: 

/D = .0062 (out of the range), 

rMD = 0.17 (near the upper limit), and 

LID = 0.9. 

The t/D ratio is out of the specified range, but values for PB and PC can be calculated by using a 

thickness that falls within the range: 

LID =.002; t =.002D = 1.93 m. 

Now, 

PB = 1.65 MPa 

PC = 1.46 MPa.

E-433
Since the actual thickness of the top head in the SCV scale model is more than three times the 

thickness used for these calculations it is reasonable to assume that the buckling pressure for the 

SCV will be significantly higher. Also, should buckling occur, it will most likely be a cosmetic 

failure only, since torispherical heads subjected to internal pressure can typically carry loads 

significantly higher than their critical buckling load. 

5.2 Parameter Study - Coefficient of Friction 

A parameter study was performed in which the frictional coefficient between the SCV and a rigid 

contact structure was varied from 0.0 (frictionless) to 0.5 in 0.1 increments [11]. Several 

axisymmetric finite element models were run and the displacements at the apex of the top head and 

at the elevation of the equipment hatch were studied. It was found that for all of the different cases 

with non-zero friction, the vertical displacement at the apex of the SCV did not vary significantly. 

The vertical displacement at the equipment hatch elevation also did not vary significantly with 

different values of J.1 The only significant differences in vertical displacement at either location 

were evident when comparing the frictionless case to a non-frictionless case. For this reason, the 

nominal value of the friction coefficient used for all finite element analyses described here was 

taken to be ;L = 0.2. 

6. CRITICAL LOCATIONS / FAILURE PREDICTIONS 

Figure 6.1 shows a comparison of the critical areas from the finite element analyses. Only the 

results from two local models, the LEHSTh and LTHAXC models are shown. Also, in order to 

compare locations with differing material properties, the strains for each location were normalized 

by their true strain at maximum load from the Hitachi tensile tests. Therefore, a y-value of 1.0 

corresponds to the strain at necking from that material's uniaxial tensile test. The raw data appeared 

(unnormalized) in Figure 4.12 and Figure 4.14. 

Apex of Top Head 2-oo 

(E) - LTHAXC 1.75 

Above Top Flange'! 

S(Int) - LTHAXC • tso --

Below Top Flange •I _ _"

(Int) - LTHAXC . 

Above Knuckle ,.oo -2 

Below Knuckle •. 0 

9.0 mm wall 

(Ext) - LEHSTh oM - -

8.5 mm wall 00 

"(Int) - LEHSTh 0 2 4 a a 10 12 

Internal Pressure. (MPa) 

Figure 6.1 Normalized equivalent plastic strain from critical areas. Only critical areas from 

the local models are included since they are the most accurate. Strains have been normalized by each material's true strain at maximum load. 

E-434

I!
When the strains are normalized the primary candidate for failure location becomes clear, the 9.0 

mm wall section just below the material interface and near the equipment hatch insert plate shown 

by the long dashes in Figure 6.1. The main reason that this particular location stands out is the 

difference in the ductility between the SPV490 steel and the SGV480 steel. The true strain at 

maximum load for the SPV490 material is approximately 10%; the true strain at maximum load 

for the SGV480 material is approximately 20%. Thus, the SPV490 material in the thinned section 

(9.0 mm nominal thickness, lower conical section) at an internal pressure of 5 MPa has reached a 

plastic strain that in the uniaxial-stress tensile test led to necking. 

Continued deformation in the thinned section is "displacement controlled." That is, the boundary 

around the plastic domain in the thinned section appears to the adjacent thicker stiffer elastic 

sections as a "cut out" or opening with a nominally fixed membrane load. Further increases in 

internal pressure cause the boundary around the thin section to expand similarly to the way an 

unreinforced cut out or opening in a pressure vessel expands. The expansion of the opening 

imposes additional strain on the yielding thinned section. 

While the shell element mesh used in the LEHSTh model has some ability to represent locally 

accelerated thinning, it does not have the refinement necessary to track the strain localization on 

the length scale exhibited in the tensile test. The nature of the strain state, biaxial tension, is also 

important for failure prediction. The analysis indicates that the total strain in the thinned section is 

very nearly equal in two directions (circumferential and radial directions with respect to the edge 

of the equipment hatch insert plate edge). Although a forming limit diagram for this material is not 

available, examination of a typical forming limit diagram in Figure 6.2 shows the differences 

between the load path for a tensile test and the load path for the area under consideration (equal 

biaxial strain). In a typical tensile test, necking occurs at "2n", where n is the strain-hardening 

exponent, while equal biaxial extension produces a -neck at "1.3n". Thus, one can expect that 

¢', "" 

NoOccure) 

Minor Strain, e2 n 

Fiure 6.2 Typical forming limit diagram for low carbon steels. The strains below the curve 

are acceptable while those above the curve correspond to regions affected by local necking. Note the differences in major strain values between a tensile test load path and a biaxial strain 

load path [12].

E-435
significant localization of plastic flow with attendant tearing will occur in the thinned section when 

the normalized value of effective plastic strain in reaches (1.3/2.0) = 0.65 or 65% of the necking 

strain from the tensile test. In Figure 6.1 this corresponds to approximately 4.5 MPa internal 

pressure. 

6.1 FAILURE LOCATION 

Given the early and rapid occurrence of plastic flow compared to other locations within the 

pressure vessel, and the strains attained relative to the material's ductility, it is expected that failure 

of the pressure vessel will occur in the thinned section next to the equipment hatch insert plate. 

6.2 FAILURE PRESSURE 

Given the biaxial tension strain state , the strain localization characteristics exhibited by the plate 

material, and the involvement of weld and heat affected zone (HAZ) material, it is expected that 

ductile rupture of the pressure vessel will occur at or shortly after reaching an internal pressure of 

4.5 MPa. 

An early failure at this or another location due to the presence of welding flaws or inclusions cannot 

be ruled out since there are at the same time states of stress producing plastic flow in at least 4 other 

locations in the pressure vessel (primarily the top head and knuckle regions). The weld metal and 

HAZ near the thinned areas introduce additional uncertainty. The yield strength and ductility of the 

weld metal is typically higher than the parent material, while the same properties in the HAZ are 

typically lower than the parent material. Brittle failure modes have not been considered in this 

analysis effort. 

7. ANALYSIS SUMMARY & CONCLUSIONS 

Five different finite element analyses have been performed in an effort to characterize the 

structural behavior of a steel containment model subjected to static overpressurization. The models 

are summarized in Table 7.1. 

7.1 First Yield / First Contact Prediction 

Comparing the results of all analyses indicates that first yield will occur at 2.0 MPa in the knuckle. 

The analyses results also show that first contact will occur at 3.2 MPa in the knuckle. 

7.2 Failure Prediction 

The G3DS model, a global model which included the equipment hatch, showed two areas which 

dictated further study: 1) the area near the equipment hatch insert plate/material change interface 

junction; 2) the top head region, including the knuckle. Two additional local models were created 

to study these locations. 

The first model, a local model which takes advantage of the new * SUBMODEL option in ABAQUS, 

modeled only the equipment hatch insert plate, parts of the middle and lower conical sections, and 

the contact structure. The results of this model, which are shown with the results of the G3DS 

model for the same location in Figure 4.9, indicate an increase in strain as much as 50% from the 

G3DS model to the LEHS model. The element shown for both models is in the middle conical 

section (8.5 mm thick nominally) adjacent to both the equipment hatch insert plate and the lower 

conical section (9.0 mm thick nominally). 

E-436

ii
The second model, an axisymmetric continuum model, included he top head from the apex down 

the upper 19 mm stiffener. This model, which was originally intended to study the behavior of the 

knuckle and the apex of the top head, also suggested other potential failure areas immediately 

above and below the top head flange. The results for this model, shown in Figure 4.12, indicate 5 

competing areas for failure: the apex of the top head; the interior surface of the top head 

immediately above and below the top head flange; and at the exterior surface immediately above 

and below the knuckle. 

After reviewing thickness measurements of the SCV in the area near the equipment hatch insert 

plate/material change interface, it was decided that one additional analysis would be performed. 

This analysis was a modification of the LEHS model where the measured thicknesses, which 

Table 7.1: Summary of Pre-test Analyses 

First Yield First Contact 

Model Purpose Analysis type/ Location Pressure Location Pressure Elements 

Axisymmetric/ Knuckle/ 

GAXI8 Study global behavior 1500 shell/con- Knuckle 2.2 MPa conical upper 4.0 MPa 

tinuum elements con section 

Study global behavior Axisymmetric/ Knuckle/ 

GAX34 with worst case gap 1500 shell / con- Knuckle 2.2 MPa upper conical 4.0 MPa 

dimension of 34 mm tinuum elements , section 

E/H 

sleeve at Knuckle/ 

G3DS Study global behavior 3-Dimensionhlee attach- 2.3 Ml upper 4.1 Ma with equipment hatch 4800 shell ele- nent to conical insert section 

plate 

Study local behavior 3-Dimensional/ MCS Middle 

LEHS near equipment hatch 4800 shell ele- adjacent 2.6 MPa Conical 4.2 Ma 

insert plate and mate- ments to insert Section 

rial change interface plate 

Study local behavior at Ammetric/ 

LTHAXC top head and knuckle; 7200 continuum Knuckle 2.0 MN Knuckle 3.2 MN include latest contact elements 

structure design elements 

Above 

Study effect of thinned Aboved 

area near equipment 3-Dimensional/ setion 2Middle 

LEHSTh hatch insert plate and 4800 shell ele- adjcent 2.2 MPa Conical 4.2 Ma 

material change inter- ments Section 

face to insert 

I I plate

E-437
ranged from 5% increase in the nominal thickness to 22% thinner near the weld at the material 

change interface near the insert plate, were incorporated into the finite element model using the 

ABAQUS *NODAL THICKNESS option. 

Results of this analysis, when compared with the previous submodel for this area (LEHS) and the 

global model (G3DS) indicate a significant increase in strain and also suggest that the critical 

location has shifted from the 8.5 mm nominal thickness middle conical section to the 9.0 mm 

nominal thickness lower conical section. In Figure 6.1, the ductility of each different material is 

taken into account by normalizing each material's equivalent plastic strain by the true strain at 

maximum load from its corresponding tensile test. The forming limit diagram in Figure 6.2 

indicates that the material under consideration may neck prior to the strain at which necking 

occurred in the uniaxial tensile test. When taking all of this into consideration, it is expected that 

ductile rupture of the pressure vessel will occur at or shortly after reaching an internal pressure of 

4.5 MPa in the area just below the weld line in the lower conical section at the material change 

interface adjacent to the equipment hatch insert plate (the location is indicated by the small square 

in the SPV490/9.0 mm material in Figure 4.14). 

8. ACKNOWLEDGMENT 

The authors would like to thank Vicki Porter, Gerald Wellman, and Harold Morgan for their 

technical assistance. 

9. REFERENCES 

[E] ABAQUS, Version 5.5, Hibbitt, Karlsson, and Sorenson, Inc., Pawtucket, RI, 1994. 

[2] Branstetter, L. J., Attachment to Round Robin Letter, July 10, 1995. 

(3] Dieter, (. E., Mechanical Metallurgy, Third Edition, McGraw-Hill Book Co., New York, 

N.Y., 1986. 

[4] MATLAB Reference Guide, Version 4.2, The Mathworks, Inc., Natick, MA, 1992. 

[5] Stone, C. M., Wellman, G. W., Krieg, R. D., A Vectorized Elastic/Plastic Power Law Harden

ing Material Model Including Luders Strain, SAND90-0153, 1990. 

(6] Stone, C. M., SANTOS: A Two Dimensional Finite Element Program for the Quasistatic, 

Large Deformation, Inelastic Response of Solids, SAND90-0543, 1997. 

[7] Structural Alloys Handbook, ed. by Hucek, H. J., Volume I, Batelle's Columbus Laborato

ries, Columbus, OH, 1985. 

[8] Carter, P. A., "Eccentricity Test Case", Sandia memorandum to V. K. Luk and M. F. Hesshe

imer, July 17, 1995. 

(9] Hessheimer, M. F, Letter to Round Robin Participants dated February 20, 1996. 

(10] Kalnins, A., Updike D. P., "New Design Curves for Torispherical Heads," Welding Research 

Council Bulletin, Bulletin 364, New York, June 1991. 

E-438

11
[11] Porter, V. L., "Further Investigation of Friction Effects for Shielded SCV Model," Sandia 

memorandum to V. K. Luk, May 4,1994. 

[12] Hosford, W. F., Caddell, R. M., METAL FORMING: Mechanics and Metallurgy, Prentice

Hall Inc. Englewood Cliffs, N. J., 1983.

E-439
10. APPENDIX OF STANDARD PLOTS 

These plots are provided for comparison to results obtained by other investigators. The prescribed 

analysis parameters and locations are described in the original Round Robin package dated July 

10, 1995 issued by the International Nuclear Safety Department at Sandia National Laboratories. 

Some output locations were updated later in a memorandum dated May 9, 1996. The results 

presented here were obtained from three models: the G3DS model, the LEHSTh model, and the 

LTHAXC modeL Results from the local models, LEHSTh and LTHAXC, were used for locations 

that were contained within the domain of these models since the local models provided the most 

accurate results in these areas. For requested, output locations outside the boundaries of the local 

models, the global G3DS model was used. 

E-440

I i
0.08

0.07 

0.06 

0.05 

• 0.04 

E 

"0.03 

0.02 

0.01 

0.004

0.0 6.0 8.0 

Internal Pressure, (MPa)

14.0

Plot 1: Maximum principal strain versus internal pressure for an element located near the 

equipment hatch insert plate at (67.5 degrees, 0.36 m) in the equipment hatch coordinate sys

tem (Model: LEHSTh).

0.06 

0.05 

C 

, 0.04 

•. 0.03 

E 

0 .02 

0.01 

0.00

6 8 

Internal Pressure, (MPa)

14

Plot 2: Maximum principal strain versus internal pressure for an element located near the 

equipment hatch insert plate at (45 degrees, 0.36 m) in the equipment hatch coordinate system (Model: LEHSTh).

E-441
0.06

0.05 

S0.04 

C. 0.03 

" 0.02 

0.01 

0.00 , 0 2 4 a 8 10 12 14 

Internal Pressure, (MPa) 

Plot 1: Maximum principal strain versus internal pressure for an element located near the 

equipment hatch insert plate at (67.5 degrees, 0.36 m) in the equipment hatch coordinate sys

tem (Modeh LEHSTh).

0.06 

0.05 

j0. 04 

0.03 

S0.02 

0.01

0.00

0 2 4 6 8 10 12 14 

Internal Pressure, (MPa) 

Plot 2: Maximum principal strain versus internal pressure for an element located near the 

equipment hatch insert plate at (45 degrees, 0.36 m) in the equipment hatch coordinate system (Model: LEHSTh). 

E-442

ii
S C) 

S t 

(0 

'I, 

'5 

0

0.014 

0.012 

0.010 

0.008 

0.006 

0.004

0.000 

2 4 6 8 10 12 14 

Interr• Pressure, (MPa) 

Plot 3: Exterior surface meridional strain versus internal pressuze for an element located near 

the equipment hatch insert plate at (0 degrees, 0.36 m) in the equipment hatch coordinate sys

tem (Model: LEHSTh).

0.010

TS 

0.008 

0.006 

0.004 

0.002

0.000

6 8 

fntoral Pressure, (MPa)

14

Plot 4: Interior srface meridional strain versus internal pressure for an element located near 

the equipment hatch insert plate at (0 degrees,. 0.36 m) in the equipment hatch coordinate sys

tem (Model: LEHSTh).

E-443
0.040

0.035 

0.030 

". 0.025 

S0.020 

w 0.015 

0.010 

0.005 

0.000 0 2 4 a 8 10 12 14 

Internal Pressure, (MPa) 

Plot 5: Exterior surface hoop strain versus internal pressure for an element located near the 

equipment hatch insert plate at (90 degrees, 0.36 m) in the equipment hatch coordinate system (Model: LEHS'I).

-20

0.040 

0.035 

0.030 

0.025 

0.020 

0.015 

0.010 

0.005 

0.000

a 8 

Internal Pressure, (MPa)

Plot 6: Interior surface hoop strain versus internal pressure for an element located near the 

equipment hatch insert plate at (90 degrees, 0.36 m) in the equipment hatch coordinate system (Model: LEHSTh). 

E-44

Ii
0.16 

0.12 

i 0.08 

0.04 

0.00

14

Plot 7: Maximum principal strain versus internal pressure for an element located at top head 

apex (Model: LTHAXC).

0 2 4 6 8 

Internal Pressure, (MPa)

10 12 14

Plot 8: Exterior surface hoop strain versus internal pressure for an element located at (270 de

grees, 0.48 m) in the top head coordinate system (Model: LTHAXC).

E-445

020

6 8 

Intemnal Pressure, (MPa)

I 0

0.040 

0.030 

0.020 

0.010 

0.00 

-0.010
0.10

0.09 

0.08 

*Q 0.07 

0.06 

_1 0.05 

• 0.04 

10.03 

0.02 

0.01 

0.00 0 2 4 6 8 10 12 14 

Internal Pressure, (MPa) 

Plot 9: Exterior surface meridional strain versus internal pressure for an element located at 

(270 degrees. 0.48 m) in the top head coordinate system (ModeL LTHAXC). 

0.14 

0.12 

I0.10 

O0.08 

• 0.06 

0.04 

0.02 

0.00 0 2 4 a 8 10 12, 14 

internal Pressure, (MPa) 

Plot 10: Interior surface meridional strain versus internal pressure for an element located at 

(270 degrees, 0.48 m) in the top head coordinate system (Model: LTHAXC). 

E-446

11
0.03 

0.02

C!

0.01 

0.00 

-0.01

-0.02 

-0.03 

0 2 4 6 $ 10 12 14 

Internal Pressure, (MPa) 

Plot 11: Exterior surface meridional strain versus internal pressure for an element located just below the top flange at (0 degrees, 3.47 m) in the global coordinate system (Model: LTHAXC).

0.12 

0.10 

S0.06 

" 0.04 

0.02 

0.00

6 8 

Internal Pressure. (MPa)

14

Plot 12: Interior surface meridional strain versus internal pressure for an element located just below the top flange at (0 degrees, 3.47 m) in the global coordinate system (Modeh LTHAXC).

E-447
a 8 

Internal Pressure, (MPa)

Plot 13: Exterior surface meridional strain versus internal pressure for an element located just below the knuckle at (0 degrees, 3.32 m) in the global coordinate system (Model: LTHAXC). 

0.08 

0.07 

* 0.08 

a 0 .05 

10.03 

2 0.02 

0.01 

0.Pe meiIona r i s a u o n n

Plowt 14: Interior surface meridional strain versus internal pressure for an element located just below the knuckle at (0 degrees, 3.32 m) in the global coordinate system (Model: LTHAXC). 

E-448

6 8 Internal Pressure, (MPa)

0.05

0.04

S 

0 

0 

I 

0

0.03 

0.02 

0.01

0.00 

-0.01

14
0.008

O0.0

to 

CO

0.004 

0.002 

0.000

-0.002 

-0.004

6 8 

Internal Pressure, (UPa)

14

Plot 15: Exterior surface meridional strain versus internal pressure for an element located just above the middle stiffener at (0 degrees, 2.10 m) in the global coordinate system (Model: G3DS).

0.008 

0.007

0.006 

0.005 

.E 0.004 

10.003 

2 0.002

0.001 

0.000

6 8 

Intemal Pressure, (MPa)

Plot 16: Interior surface meridional strain versus internal pressure for an element located just above the middle stiffener at (0 degrees, 2.10 m) in the global coordinate system (Model: 

G3DS).

E-449
0.030

0.025 

j 

co 0.020 

00 

0.015 

0.010

0.005 [ 

0.000 0 2 4 6 a10 12 14 

Internal Pressure, (MPa) 

Plot 17: Exterior surface meridional strain versus internal pressure for an element located just above the material change interface at (0 degrees, 1.60 m) in the global coordinate system 

(Model: G3DS).

j I

0.030 

0.025 

0.020 

0.015 

0.010 

0.005 

0.000

6 8 

Internal Pressure. (MPa)

Plot 18: Interior surface meridional strain versus intenal pressure for an element located just above the material change interface at (0 degrees, 1.60 m) in the global coordinate system (Model: G3DS). 

E-450

11
U 

CO 

"1V '5

0.004 

0.003 

0.002 

0.001 

0.000 

-0.001 

-0.002

-0.003 

0 2 4 6 8 10 12 14 Internal Pressure, (M~a) 

Plot 19: Exterior surface meridional strain versus internal pressure for an element located just below the lower pair of stiffeners at (0 degrees, 0.80 m) in the global coordinate system (Mod el: G3DS).

0.020

S 

U 

*1 

.5 

0, 

I

0.016 

0.012 

0.008 

0.004

0.000

6 8 

Internal Pressure. (MPa)

Plot 20: Interior surface meridional strain versus internal pressure for an element located just below the lower pair of stiffeners at (0 degrees, 0.80 m) in the global coordinate system (Mod el: G3DS).

E-451
0.008

0.007

0.006 

0.005 

- 0.004 

0O.003 

• 0.002

0.004 0.000 , , , , I , 0 2 4 a 10 12 14 

Internal Pressure, (MPa) 

Plot 21: Exterior surface meridional strain versus internal pressure for an element located at 

the mid-height of the upper conical shell at (45 degrees, 2.49 m) in the global coordinate sys

tem (Model: G3DS).

2 4 6 8 

Internal Pressure. (MPa)

10 12 14

Plot 22: Interior surface meridional strain versus internal pressure for an element located at the 

mid-height of the upper conical shell at (45 degrees, 2.49 m) in the global coordinate system (Model: G3DS). 

E-452

J!

0.008 

0.007 

0.008 

0.005 

0.004 

0.003 

0.002 

0.001

j 

I:

0.000 L. 

0
0.020

0.016 

S 

Ca 0.012 

O.5D 

0.004 

0.000 0 2 4 6 B 10 12 14 

Intenal Pressure, (MPa) 

Plot 23: Exterior surface hoop strain versus internal pressure for an element located at the mid

height of the upper conical shell at (45 degrees, 2.49 m) in the global coordinate system (Mod

el: G3DS).

0.020 

0.016 

0.012 

0 

0.004 

0.000

0 2 4 6 6 10 12 14 

Inte•al Pressure. (MPa)

Plot 24: Interior surface hoop strain versus intermal pressure for an element located at the mid

height of the upper conical shell at (45 degrees, 2.49 m) in the global coordinate system (Mod

el: G3DS).

E-453
0.002

0 

Co 

I 

C 

I 

I

0.001 

0.000

-0.001 a 8 

Int=al Pressure. (MPa)

14

Plot 25: Exterior surface meridional strain versus internal pressure for an element located 0.126 meters below the material change interface at (45 degrees, 1.45 m) in the global coordi

nate system (Model: G3DS). 

0.002 

0.001 

0.000 0 2 4 8 8 10 12 14 

Internal Pressure, (MPa) 

Plot 26: Interior surface meridional strain versus internal pressure for an element located 0.126 

meters below the material change interface at (45 degrees, 1.45 m) in the global coordinate sys tem (Modelk G3DS). 

E-454

11
0.016

0.014 

0.012 0 0.010 

0 c• 0.008 

10.006 

0.004 

0.002 

0.000 0 2 4 6 8 10 12 14 

Internal Pressure, (MPa) 

Plot 27: Exterior surface hoop strain versus internal pressure for an element located 0.126 

meters below the material change interface at (45 degrees, 1.45 m) in the global coordinate sys

tem (Model: G3DS).

0.020 

0.016

I 

-S

0.012 

0.008

0.004 

0.000

6 8 

Internal Pressure, (MPa)

Plot 28: Interior surface hoop strain versus internal pressure for an element located 0.126 

meters below the material change interface at (45 degrees, 1.45 m) in the global coordinate sys

tem (Model: G3DS).

E-455
0.030

0.025 

S0.020 I 

- 0.015 

0.010

0.000, I , I , I 

0 2 4 a a 10 12 14 

Intemral Presur, (MPa 

Plot 29: Interior surface meridional strain versus internal pressure for an element located at the 

mid-height of the spherical shell at (45 degrees, 3.13 m) in the global coordinate system (Mod el: LTHAX). 

0.020 

0.016 

• 0.012 0 

0.004 

0.000

6 8 

Internal Pressure. (•Pa)

Plot 30: Interior surface hoop strain versus internal pressure for an element located at the mid

height of the spherical shell at (45 degrees, 3.13 m) in the global coordinate system (Model: 

LTHAXC). 

E-456

I !
0.020

S 

I 

h. 

I 

I

0.016 

0.012 

0.008

0.000 

002[ 2 10 12 14 

Internal Pressure, (MPa) 

Plot 31: Interior surface meridional strain versus internal pressure for an element located at the 

mid-height of the upper conical shell at (270 degrees, 2.49 m) in the global coordinate system (Model: G3DS).

0 2 4 6 6 

Intemal Pressure, (MPa)

10 12 14

Plot 32: Interior surface hoop strain versus internal pressure for an element located at the mid

height of the upper conical shell at (270 degrees, 2.49 m) in the global coordinate system 

(Model: G3DS).

F-457

0.008 

0.007 

0.006 

0.005 

S0.004 

S0.003 

0.002 

0.001 

0.000
0 

U 

0 

Co 

I 

S 

S 

Co 

I 

0

0.016 

0.014 

0.012 

0.010 

0.008 

0.008 

0.004

0.002 0.000, , , , I , 

0 2 4 6 8 10 12 14 

Intemal Pressure, (MPa) 

Plot 33: Interior surface meridional strain versus internal pressure for an element located mid

way between the material change interface and the top of the lower pair of stiffeners at (270 de

grees, 1.25 m) in the global coordinate system (Model: G3DS).

0.003 

0.02 

2: 0.001 

0.000 I 

0 2 4 a 8 10 12 14 

Internal Pressure. (MPa)

Plot 34: Interior surface hoop strain versus internal pressure for an element located midway between the material change interface and the top of the lower pair of stiffeners at (270 de

grees, 1.25 m) in the global coordinate system (Model: G3DS). 

E-458

11
240

210 

180 

150 

60

30 

S 10 io 12 14 

Intemr! Pressure, (MPa) 

Plot 35: Vertical displacement versus internal pressure for the apex of the top head at (- de

grees, 0 m) in the top head coordinate system (Model: LTHAXC).

60 

50 

~40 

30. 

20 

10 

0

6 6 

Internal Pressure, (MPa)

14

Plot 36: Horizontal displacements versus internal pressure for the interior and exterior surface 

4 cm above the top surface of the top flange at (45 degrees, 3.57 m) in the global coordinate 

system (Model: LTHAXC).

E-459
40

35 

-3 

25 2

0 

15 

~10 

5 

0 0 2 4 6 8 10 12 14 

Internal Pressure, (MPa) 

Plot 37: Horizontal displacement versus internal pressure for a location 4 cm below the bottom 

of the knuckle at (0 degrees, 3.32 m) in the global coordinate system (Model: LTHAXC).

40 

35 

30

25 

_20 

10 

5 

0 a 8 

Internal Pressure, (MPa)

Plot 38: Vertical displacement versus internal pressure for a location 4 cm, below the bottom of 

the knuckle at (0 degrees, 3.32 m) in the global coordinate system (Model: LTHAXC).

E-460
30

25 

20 

10 

5 

0 2 6 10 12 14 

Internal Pressure, (MPa) 

Plot 39: Horizontal displacement versus internal pressure at the apex of the equipment hatch at 

(- degrees, 0.0 m) in the global coordinate system (Model: G3DS).

0.07 

0.06

V

0.05 

0.04 

0.03 

0.02 

0.01

0.00 

-0.01

6 6 

Internal Pressure, (MPa)

14

Plot 40: Interior surface meridional strain versus internal pressure for an element located at the 

thinned area near the equipment hatch insert plate at (74.8 degrees, 1.569 m) in the equipment 

hatch coordinate system (Model: LEHSTh).

E-461
0.05

0.05 

*t 0.04 

S0.03 

•"0.02 

0.01 

0.00 --- 0 2 4 a 810 12 14 

Intemal Pressure, (MPa) 

Plot 41: Interior surface hoop strain versus internal pressure for an element located at the thinned area near the equipment hatch insert plate at (74.8 degrees, 1.569 m) in the equipment hatch coordinate system (Model: LEHSTh).

0.08 

0.07

S I :1 

S I 

.1 

I

0.06 

0.05 

0.04 

0.03 

0.02 

0.01

0.00 

-0.01

6 8 

Internal Pressure, (MPa)

14

Plot 42: Interior surface meridional strain versus internal pressure for an element located at the thinned area near the equipment hatch insert plate at (105.4 degrees, 1.569 m) in the equipment hatch coordinate system (Model: LEHSTh). 

E-462

1.
0.08

0.07 

0.06 

S0.05 

S0.04 

0.03 

0.02 

0.01 

0.00 0 2 4 6 8 10 12 14 

Intemal Pressure, (MPa) 

Plot 43: Interior surface hoop stain versus internal pressure for an element located at the thinned area near the equipment hatch insert plate at (74.8 degrees, 1.569 m) in the equipment hatch coordinate system (Model: LEHS•h).

E-463
Page intentionally left blank.

E-464

I i
Appendix E-8

Staatliche Material priifungsanstalt, Universitfit Stuttgart 

Germany

E-465
Staatliche 

Materialprhimfugsanstaft 

UnIversItit Stuttgart 

swaat Mwwlexmsn 

UWnsfI Smpgart Posftah 801140. D-TWI 1 SM•aPt 

Dr. Vincent Luk 

Sandia National Laboratories 

Department 6403, Mail Stop 0744 

1515 Eubank SE 

Albuquerque, NM 87123 

USA

MPA 

STUTTGART

MM. Zchd. Ine NacdhW mn Wmmre Zai-hen vmer NachchZ v=i 

Dr.StklEf

Diathwatl 6&5

3041 October 16, 1996

Sublect: Steel Containment Vessel Round Robin 

Dear Dr. Luk, 

Enclosed please find the pretest report of our round robin analysis in printed form. Also 

enclosed are the plots # 1 to # 43 in printed form and on diskette. 

Sincerely yours 

MPA STUTIGART

/5 I r/') 

Encl.: Pre test report 

Plot #Ito #43 

Diskette

0.7WS6 •sg EVaigen) Ptaflenwa~rngO S 

WW6;-LULJ.S.USO( InJ

Tolefon (07 11)6 8.5.1 

Telefax (07 11) 6 85-26 35

Tleogt-wn. 

Kuzanschrift: 

MPA S'UTrGART

Wftrersndungen BaftfndM 

S-tgaVst-Vab n BW-8aa Sumrt, Kwo-Nr. 1054 611 700 

Shz. 1293 (BLZ 6O 200 230)

E-467
MPA STUTTGART

STEEL CONTAINMAENT VESSEL (SCV) ROUND ROBIN 

Section 4 Pro-Test Analysis Report 

4.1 Idealization 

The analyses within the SCV round robin were performed using the finite element 

program ABAQUS, release 5.5 /HKS 19951. Pre- and postprocessing of the finite 

element data was done with CAE-software MSCIPATRAN, release 1.4.2 IMSC 

1995/. 

For the geometric idealization of the steel containment vessel we used shell 

elements from the ABAQUS element library with 5 degrees of freedom per node and reduced integration scheme. Usually 8-noded quadrilateral elements with quadratic interpolation of geometry and displacements, called SSR5, were used. Some 

triangular elements with six nodes, called STRI65, were inserted for mesh refinement. The missing sixth degree of freedom, which designates the "torsion" of 

the shell, is essential for boundary conditions only and will be introduced 

automatically if necessary. The stiffeners are also idealized with shell elements and directly connected with the nodes of the vessel. A look on the total model is given in 

fioure 4.1. 

A failure criterion does not exist within ABAQUS for this kind of analysis..Therefore 

no failure analysis can be performed. Also no buckling analysis was done, because 

a combination of eigenvalue determination together with unilateral boundary conditions is not possible. 

The coordinates of the nodes, which give the location of the mid surface of a shell 

were chosen so that the inner surface of the vessel was continuous. Therefore at the 

transition between the different regions of the vessel additional geometric constraints have to be applied to make sure continuity of the unknown displacements and rotations. This is done with the multiple point constraint option (MPC) of ABAQUS. In our case the type BEAM was chosen. 

The symmetry of the vessel can be used to mesh only one half of the vessel. The 

symmetry plane is located at 0 = 900 in the global coordinate system. The mesh 

starts just above the ring support girder, i.e. z=0 in the global coordinate system. The 

forces resulting from internal pressure on the lower head of the vessel are applied as external tensile forces acting tangential to the wall. Axial displacement and bending is suppressed there via boundary conditions. In the symmetry plane, displacements perpendicular to this plane are suppressed, as well as rotations around the global r and z-axis. The loading is applied as surface loading on the inner surface of all shell 

elements. The maximum loading applied is 50 bar or 5 MPa. 

The contact between the vessel and the contact shell is simulated with the ABAOUS 

surface interaction option. There one have to define two surfaces, which may contact. ABAQUS automatically calculates the initial distance of relevant nodes 

MPA STUTTGART Steel Containment Vessel Round Robin 1114 

E-468

J!
before loading and subsquently for every load increment which is applied. The 

contact shell was defined as rigid spherical shell and as rigid conical shell for 0.816 

m< z < 3.359 m. Our first analysis of the vessel without contact shell showed, that 

only In the region around the equipment hatch relevant displacements may occur. 

The Initial gap size was 18 mm /SNL 1995L. 

4.2 Material properties 

Based on the provided tensile test data we defined three stress-strain curves. The 

first one describes the behaviour of the SGV480 material, the second one describes 

the behaviour of the SPV490 material with wall thickness of 9 mm and the third one 

describes the behaviour of the SPV490 material with wall thickness of 17.5 mm. The 

different yield strength of these materials is given in table 4.1. 

Material/wal| thickness Yield strength [MPa] 

SGV480/- 400. 

SPV490/9 mm 680 

SPV490/1 7.5 mm 610 

Table 4.1: Yield strength of the SCV materials used for FE analysis 

The strength of specimens from the 9 mm blanks is quite higher than from the 17.5 

mm blanks. The input stress-strain curves are given in figure 4.2. Isotropic kinematic 

harding model due to von Mises is used. 

Young's modulus is kept constant to 200 000 MPa. 

4.3 Description of the analysis 

The internal pressure is applied up to a maximum load of 50 bar, i.e. 5 MPa. The 

automatic time incrementation algorithm of ABAQUS is used. Beginning with an 

initial load increment, ABAQUS enlarges the load increment with a factor of 1.5. if 

convergence seems to be good. For bad convergence, the load increment is 

reduced to a factor of 0.25 of the previous increment. The first and second load 

increment of the present analysis are 15 bar, each. The next increment is 3.75 bar. 

Subsequent increments are again smaller. It can be easily seen, that for special points In the time history, the convergence becomes much worse, and the load 

increments decrease rapidly. Subsequent the load increment is again Increased. 

These events coincide with beginning of contact or with beginning of yielding of the 

material. 

4.4 Discussion of selected results 

MPA STUTFGART Steel Containment Vessel Round Robin 2/14

E-469
As it can be seen from different evaluation points, first yield appears for different 

pressure loads. 

Near the equipment hatch, yielding starts for a pressure load of about 25 bar, see 

figure 4.3. where the meridional strain on the inner surface is given. In the same 

figure, one may see that full contact between vessel and contact shell is readched 

for about 35 bar, for beyond this pressure load, the strains decrease (plot id # 4). 

Looking at the max principal strain on the apex of the vessel, we can see that yield 

starts for a preesure load of about 35 bar, together with contact between vessel and 

contact shell. Only for higher pressure loading, the strain inrease again, figure 4.4 

(plot id # 7). 

In the upper conical shell, first yield is reached for a pressure load of about 33 bar 

and full contact in this region is reached for a slightly higher pressure load of about 

35 bar, see figure 4.5 (plot id # 21). Due to the contact the meridional strains are 

reduced for higher pressur loads. 

The performance ot the strains near the material interface are quite different. 

Looking on the meridional strain component, we find a strong unloading on the outer 

surface for pressure loads higher than 35 bar, while on the inner surface the 

meridional strains are increasing rather monotonic, with some steps at 35 bar and at 

43 bar. These steps may be observed also on the outer surface, see figure 4.6 and 

4.Z (plot Id # 25 and 26). 

Looking on the vertical displacement of the upper head, we find that there is a rather 

linear elastic behaviour up to about 33 bar, followed by a region of nearly constant 

displacement from 35 to 40 bar and a subsequent strong increase, see figure 4.8 

(plot id # 35). This is due to a missing contact shell in our model around the upper 

head of the vessel. 

From these evaluations we can estimate the pressure load for starting of yield near 

the equipment hatch to about 25 bar. 

The location of first contact between vessel and contact shell is given in figure 4,9. 

For simulation of friction we used a friction coefficient of 0.3. No sticking as 

assumed. An analysis without friction was not performed. We think that friction will 

reduce th stresses and strains in the vessel, due to the induced friction forces, which 

act again the relative motion due to the internal pressure. 

Summary 

The vessel was analyzed with the ABAQUS finite element code using release 5.4.1. 

The idealization of the vessel started just above the ring support girder. Using 

symmetry properties of the vessel, one half of thestructure has been modelled We 

used standard shell elements with 8 nodes per element and 5 degrees of freedom 

MPA STUTTGART Steel Containment Vessel Round Robin 3/14 

E-470

1'
per node with reduced integration scheme. The different wall thicknesses have been 

taken Into account. The contact shell was simulated as rigid body with a prescribed initial gap of 18 mm between SCV and CS. For the material description we used best 

fit stress-strain-curves based on the supplied tensile test data. The loading was 

applied as internal pressure on all shell elements. To simulate the influence of the 

lower head of the vessel, forces acting in the wall are applied at the ring support girder. Friction was assumed to be constant with a friction coefficient of 0.3. 

The load was raised from 0 to 50 bar using the automatic time incrementation schem 

of ABAQUS. 

First yield will occur for a pressure load of about 25 bar near equipment hatch. 

First contact between SCV and CS will occur for a pressure of about 35 bar. 

References 

HKS 1995: Hibbitt, Karlsson ans Sorensen, ABAQUS Users manual, Rel 5.5, 1995. 

MSC 1995: McNeal-SchwendlerCorp.: MSC/PATRAN Users manual Rel 

1.4.2,1995. 

SNL 1995: Sandia National Laboratories, SCV Design Package, July 10,1995. 

Ust of figures 

Figure 4.1: Finite element mesh of SCV 

Figure 4.2: Stress strain curves used in FEM analysis Figure 4.3: Meridional strain on the inner surface near equipment hatch 

Figure 4.4: First principal strain on the apex, outside 

Figure 4.5: Meridional strain on the outer surface in midheight of upper conical shell 

Figure 4.6: Meridional strain on the outer surface below material change interface 

Figure 4.7: Meridional strain on the inner surface below material change interface 

Figure 4.8: Vertical displacement of upper head 

Figure 4.9: Location of first contact between SCV and CS 

List of tables: 

Table 4.1: Yield strength of the SCV materials used for FEM analysis 

MPA STUTTGART Steel Containment Vessel Round Robin 4/14.

E-471
0 

E. 

z 

Figure 4.1: Finite element mesh of SCV
-u800 - -- ------------ -- --- --------- -

500 600

00 

400

Cf 

S~300 

•- 200 

a 1 S0V48O0 100- - .. sPv49o0,mm .. S PV490117.5mm 

0I I I 

0.0 0.05 0.1 0.15 0.2 

$traln / m/r

Figure 4.2: Stress strain curves used in FEM analysis
0.3

"* 0.2-

0 5 10 15 20 25 30 35 40 45 50 

pressure lb MPA /bar MPA

Figure 4.3: Meridlonal strain on the inner surface near equipment hatch

Ch

!tI

0 

OD 

3" R 

'2

i I

I| ,1
0.14

0.12 ... m ax. prin. strain ............... ....... ".. ......................... 

3. . 2... .. . . . . . . . . . . . .. 0.1 ................... 

0.0_ 8 .. ......-.-.. 

=-"1-• 0 .0 6 .. .. ... . ... .. ......... ................................ ... . .... ................ ...... 

.. .. .... .... .. .. ~~~~0 .0 4 . ... ..... .. .• . ...... . . . .. . .. . . . ...... ... ........... ............ ................... ................. I... ... ...... ........... .... . . . ... .. ....... .., . ..... .... . .. 

0.0 ' 

0 5 10 15 20 25 30 35 40 45 50 

pressure / bar SUTA

Figure 4.4: First principal strain on the apex, outside
--- I

Cid :0! 0.2 ........... ................. ............ ... ........ ......... . .......... 

- 0.1 .. .. ..................... 

CO) 

0 .0 - . .....-----

II 

-0 .1 I . . . . .

-02- - iI1 1 - I 

0 5 10 15 20 25 30 3 

pressure /bar 

Figure 4.5: Merldional strain on the outer surface in midheight of upper conical shell

5 40 45 50 

MPA 

BTUTTGART

-u

S2 

5.
0 5 10 15 20 25 30 35 40 

pressure /bar 

Rgure 4.6: Merldlonal strain on the outer surface below material change Interface

45 50 

MPA 

STUTJ1An'

CU M

0X 

V)

0 

0 

I S. 

0 

I. 

2 

0 05.
• G 0.1 ... ...... ..................... .... ....... . ... . .. ..................... ....... 

1 T1- 

0 .0 5 . . ....... .. ..... . . . . ... .... ...... .. ............ ............. ..... .. . .. . .. . . . .. 

-0.05- | 

0 5 10 15 20 25 30 

pressure /bar 

Figure 4.7: Meridional strain on the Inner surface below material change Interface

35 40 45 50 

MPA 

STUTTGART

-u I

00

S 

2. 

I 

I 

S 

2 a 

8
4 I I U U U

-U I

1 1 

5 10

I Is 20 25 30 

pressure /bar

35 40 45 50 

MPA 

8TUTTOAnT

Figure 4.8: Vertical displacement of upper head

(D vertical displacement 

0 ... ...... ..... .... ..... I. ....... .... ... ...... .... . ...... .......... ..... ...... ........ ... ............................. 2 

.I0 .... .......... .. .......... ... .... ...... ........... .... . ... ........ .... . ...... ... ...... .. I• 0 0 

(D( 

I0 - ... - .. . .-. -. . ... ...-. .. ...... . ..-.........-..-.-......-----.... .. .................. 

0 I 

0O 

)C

In-

(D 

(D 

5. 

0 

0 

a. 

0

E 

E 

E. 

CU 

"0

10 

8 

6 

4

2

0
FRINGE PLOT LC=2.7 RES-4.1(VEC-MAG) MSCIPATRAN R-5.0 ABAOUS 16-Oct-96 10:27:50 

DEFORMATION PLOT LC=2.7 RES=4.1 MSCWPATRAN R-5.0 ABAQUS 16-Oc-96 10:27:49

z 

X)--y

.4

Figure 4.9: Location of first contact between SCV and CS

-U a 

-1

00 0

0 

I 

0)

'first contact

19.88 

18.54 

17.23 

15.92 

14.61 

13.29 

11.98 

10.67 

9.356 

8.043 

6.731 

5.418 

4.106 

2.793 

1.481 

len4

111M 163A4J

. 77TIlrlýý
Notes:

MPA STtJ'IGART Steel Containment Vessel Round Robin 

E-481

14/14
Plot id No 1

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

GTUTTQA"I

00 C1

4-0 Cfo
Plot id No 2

0 5 10 15 20 25 30 35 40 

pressure/bar

45 50 

MPA 

STUTTGART

w 0 a 0.-
Plot id No 3

CO)

0 5 10 15 20 25 30 35 40

pressure / bar

45 50 

MPA 

STUTTGART
AlU vPIJ.Le 

Vd Wl 

09 911 ot?

jeq/enssaid 

I I I

9L 

I - a - I - U - I - U - a * - a - . - ii

*+4+.-+V +. ............. 

F- uleils -pliew -Jul + 

apisul

- I i - I - b I i

t7 ON P!101~d

0I 9 0

- L'0

-3. 

2.* *1*

..... .....

ý' ............. + ............ ..... 

-ý++ +4
Plot id No 5

0.0-

-0.2 -. ............................

-0.6-

SI ]1 I I-I 1 I -II 

+

outside 

+ ext. hoop strain

•i==I - - p - p -= ,. = -. • I - =

0

1 

5 10

i 0 

15 20

i 

25 30 35

I 

40

pressure /bar

I 

45 5 

MPA 

8TUTTGART

'0

T 

St

:0E 

C-O Ci=)

-U.'

i I

0.;

++",i.'H-+

v
Plot id No 6

0 5 .10 15 20 25 30 35 40

pressure /bar

I

45 50 

MPA 

STUTTQAfT

o0

TJ • • -0.4, 

cO
Plot id No 7

m. 

00 

00 N

ON 

4-'

0 5 10 15 20 25 30 35 40

pressure / bar

45 50 

MPA 

STUTTQAIRT
VdW 09 91,

e nssead 

SO• 03 Ot?

- -I ~~~ A

+ 

-t

+.............

+ 

.... .......... ...... 

..

r-ir

- i - U - II i~a

uieais dooq "Ixe + 

eplslno S... .. .. .....I ....... - -.. ... .... . .. .

8 ON P! 1Old

OL 9 0

0

CO) 

-0I.

K1

.. I .. ........ . I.............

.............................

E E J

..... ........... ....... 

... ....... ........ .

... .... ..... ... .... I....
Plot id No 9

on - -- I --- I - i M I

-2

".3-

-4- r -

Outside 

+ ext. merid.strain

-I

+

+

4 

±

t-

-b -i.jin i j-, - m - m a

0

I 5 I 

10

I 

15

I 20 25

I 

30

I 

35

4 40

pressure /bar

1

....... IK .....

I 

45 

MPA 

8TUTTGAflT

.4-Z

A

TIo" | I •--.,•

•0

.............................

.... ........... -
Plot id No 10

inside 

+ int. merid.strain

1.0 - ..........................................................-

I uI II I -

- - Y I -l -- I - - I I -no-w

5

I I I 

10 15 20

2.(

1.5-

til 4'. 

'0

4._ 

ci)

0.5

0.0-

+ 

+ 

*

-I ........ +AZ +1 

+.....

0

+

25 30

3 

35

pressure /bar

40 45

1 

50

MPA 

8TUTTGART

•11 i -4 .... ............ ...... ... .. .. ............

|

A

V

P

v -0.,
Plot id No 11

0 5 10 15 20 25 30 35 40 45 50 

pressure/barMPA presur /br8TUTT~GAR•T

'D CO
Plot id No 12

0 5 10 15 20 25 30 35 40 

pressure /bar

45 50 

MPA 

STUTTGART

w

,0ý--
Plot id No 13

0.2 3 5 S I I

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

-1.2-

20 25 30 

pressure /bar

.. +...........

.. .....

.. ... .... 

+ 

-H .-4 .....

+ 

+ 

+# ........... 

+ ............

i 

15

I 

35 40

I 1 

45 50 

MPA 

STUTTQART

I - I I - I I - .I - I - S - I -

Ct

+

Outside 

ext. merid.strain

I 

0

1 

5

I 

10

..... .....

...............................

I 

I

.............. .. ....

. ........... 

................... 

iw+++"41

..... .............. ..... 

......... ..... I
Plot id No 14

i 1! ! ! m

+ 

+ 

+f v

.................................................... .............

+ 

+ 

............-..-- +

t . .. .... .... .j. j. .............. ..... ....... ..... . 4........ .... . . . ............. . i.......... *....... *-- ..------- .------- I - .................

Inside 

+ int. merid, strain

+

+

.- Ij - I ----- -' - - -

pressure /bar

i 1 

45 5 

MPA 

STUTTOART

0

1Ii

0.5-

0.0- ........

-1

:0ý 

Co

+

-1.0-

-1

0

I 

5

1 10 g 

is 20 25 30 35

i 

40

... ........... ...... ...

I

A

.v
Plot id No 15

0 5 10 15 20 25 30 35 40 45

pressure/bar MPA 

STUTTGART

50

CO)
Plot id No 16

ý00 

4a . -- ,

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART
Plot id No 17

T 

%0 

00

0_C 

CO

0 5 10 15 20 25 30 35 40

pressure/bar

45 50 

MPA 

STUTTQART
Plot id No 18

-• I - I I- III - II-. I .

a . h

inside 

+ int. merid.strain

-+

+

-t

+

-I4-

rJl- _ I - u i -

I 

5

I I 

10 15 20

5 25 0 30 I 

35

4 

40

pressure /bar

45 50 

MPA 

STUTTGART

0.1

0.0-

C 

I

4-. 

Co -0.1-

-0.2-

-0.:I.,

0

A

N

S.... .. . ........... . ..

......... ......... + ...
Plot id No 19

outside 

+ ext. merid.straln

0 .05 -1 ... I " . ---.- ...-.................... .............................. . . . . .

- I - P - I - - - U -

_ I I

20 25 30 

pressure /bar

...A ..

I 

5 10

I 

15

I 

35 40

I 1 

45 50 

MPA 

STUTTGART

0.1-

Lft 

8 Cl: 

ca 0.0-

-0.05-

-U.1

0

1'•4

A A--

|.... ..................... ........ ...........
Plot id No 20

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART

0

:0E 

Cl)
Plot id No 21

!I mm mu -.

outside 

+ ext. merld.strain

... ................

+

- 1 - I - i J mm r s mm m

10 15 20 25 30 

pressure /bar

35 40 45 50 

MPA 

STUTTGART

0.4

0.3-

0.2-I ......... ._c:

0.1

0.0

-0.1-

-U.

0 5

w

........... ... ...
Plot id No 22

CI-I - p m I I I II- I l II

inside 

+ int. merid.strain

.!.--

" .... .................. I...................... . ............................... 

+

.................. t .. ........ . . .. ................ ................... ................... ...... .................................... ........................ f............................ ................................. .. ...................

... +......

04++

+

- - -- aI -n• -

5 5 10

I 

15 20

I 

25 30

i 

35 40

pressure /bar

0.'

0.3 a

0.2-

C 

4-' 

Cl)

0.1

0.0

-0.1-

0 45 50 

MPA 

STUTTGART

i f 

! !

..........
Plot id No 23

"Z.U - , I I

1.5-

m

zo! 1.0-

C/3

0.5-"

outside 

x ext. hoop strain

c

i

x

XXX)> 

S ....... .........

:w= x

u.u - p--i-i - I - I - I - - -

0

5 

5 10

1 

15 20

i 

25 30

I 

35 40

pressure/bar

1 

45 

MPA 

STUTTGART

I l= 

!

I i 

!

•0

.w W*0
Plot id No 24

.a1 

,4) Eg

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART

t'zi
Plot id No 25

- I i mm

outside 

+ ext. merld.straln

+

+-t

+

b - t Iii mj - i - mi - I - I - I 

5

I 

10

1 

15

0 

20 25 30

I 35 I 

40

pressure /bar

I 

45 , 

MPA 

STUTTGAIT

0.

0.05-

0.0-I.

.O

-0.05-

-0.1-

-U. 1

0

+I

50

.... .. .. ...... .
Plot id No 26

inside 

+ int. merid.strain - . -

mm ml ml mumi - m

. +............ ...

.L+ 

-I5 ~ A~ A jy i5 10

5 

15 20

I 

25

0 30 35

I 

40

pressure /bar

45 50

MPA 8TUTTOART

FM~1

:0E 

CO)

0.15

0.05-

0.0-

-0.0

0

................................

ii 

!

0.- ...............

.4-"
Plot id No 27

b II I- in n Ii ,U I

N. 1 

outside 

x ext. hoop strain

- .- S -

- I' i - i-rn - - i-rn - I 

0 5

OJ

0.4-

0 

00

0.3

0.2

0.1

0.0-i

.c 

CO

x

x x

-U.1 I I 

10 15 20

1 

25 30

i 

35

pressure /bar

i 

40

I 

45 50

MPA 

STUTTGART

............ .. ......... ....

! !

.................... 

4ý Ar XX ................ 

x )

S.. ... .... ...........

.. .........

. . .... ........ . . . . 
Plot id No 28

:0ý 

4- C,)

-0.1

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART
Plot id No 29

- mm mmmi mp m q mimi mmmi m

iinside 

+ int. merid.strain

- I * f m j m m j m m i m i

I 

10 15

I 

20 30 35

pressure/bar

0.1 0.5 

0.05-

,A 

0 CI 

E. 

CO)

0.0-

++-HiH-It-H-+

-0.05-

-U. 1

0

I 

5 25

I 

40

I 

45 50

MPA 

STUTTGART

u

+.ý H+ +++,
Plot id No 30

pressure /bar

45 50 

MPA 

STUTTGART

V1

0X

0 5 10 15 20 25 30 35 40
Plot id No 31

.5- -, - ,~ - - ,

-Pt i.5

inside 

x int. merid, strain

- N - N -

5 

5

I 

0 10 15 20 25

x

xk

30 35 40

pressure /bar

45 50 

MPA 

9TUTTGART

fli1

N-.

1.5

1.0

0.5-

ISC, 

,Cl) .O) 

0.0-

i= I 

Z

I ! 

I

C.. U N X X>) ..... ," -

................. ....
Plot id No 32

- - urn q rn m;

inside 

+ int. hoop strain

+

I-

-I

,tj Y -| ~ I - - -

5

I 

10 15 20

2 

25 30 35

1 

40

pressure /bar

45 50 

MPA 

STUTTOART

0.

0.2-

0.0-

wt C 

1

C', -0.2-

-0.4-

0

.... .I. ........ ,

S....... .................
juq/ einsseid

09 Ci v ot, 9 ý 0 L 9

0X0

iLuvoiAniLe 

VFdUV

60 ON P! 101d
Plot id No 34

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART

Lu1

C,)
Plot id No 35

111111 I S U m i .

0 vertical displacement - I - II I 

-

I 5

C

I 

10

!)

15 20

2 

25

0

3 

30

3 

35

/ 

0 0

40

pressure /bar

( 

0.... 

I

1 

45 5 

MPA 

STUTTGART

*0

O%

1-.. 

C 

ai) E 

CO

80

60

40

20-

U-L

I 0

gVV

I

t. . .... ......... ... 

..

()

a

.... ........ ........
Plot id No 36

0 5 10 15 20 25 30 35 40 45 50 MPA 

pressure /bar STUTTQIAnT

171 

-,,

E 

E 

E 

ca 0 

"(U
Plot id No 37

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART

00s

E 

E 

(1) 

E c) 

-ocoI 
Plot id No 38

0 5 10 15 20 25 30 35 40 

pressure /bar

45 50 

MPA 

9TUTTGART

'0

E 

E4

CD 

0 Cui 

CL 

U)
Plot id No 39

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART

t91 E 

cri c) 

-o
Plot id No 40

I I I I

inside 

E0 int. merd, strain

"*10 

1.0

0.8

0.6

S0.4 

i 0.2

0.0

-0.2

-0.4

0

S.. ...... ..... ..... ..

I I I'

5

I 

10

15 -I 1 

20 25 30 

pressure /bar

....... ... (. 

. .. . . . ... . .. . .. 

...................... .. .... .

....... . . .. .. . 

.. ......

... ... 

.... . ........ . . . .

......................... 

[90 

10 .I ........ ...... 

........ .. ... ... ...... 

.. ... .... . 

............

35

.. ........ 

.. . .................. 

.... ] ...... 

i........................... 

S.........................

....................

0 

40

'i'

0 

C 

I. 

4

C, ( 

| .. ........ ....... . . 

i......... ...... ........ ..

45 50 

MPA 

STUTTOART

.. .................. | 

.. . ...... ...... ........... .. .

S. .. . . ... ... .... ...| 

... ............. .... .. . . 

..... ..... ...... ....... .

.. . . .. . .....

" III "

I
Plot id No 41

* 10

0 5 10 15 20 25 30 35 40

pressure /bar

45 50 

MPA 

STUTTGART

tr

:0C 

Co
Plot id No 42

* 10.' 

1.0

0.8 

0.6 

0.4 

0 0.2 

0.0 

-0.2 

-0.4 

0

iI .......................... 

S.............................

......................... ... 

........ .......

.. ................ 1 . 

inside 

int. merd, strain 

.. ......... ..

. .. . . .. . .. ... |.. ... . .. .....

I I I 

I . L

20 25 30 

pressure /bar

... ....... .... | 

... ..... . . ........ . ..... 

! . .................. .

....... .... I... ....

I 

35 40 45 50 

MPA 

BTUTTrGAIRT

El

LA

| ............ ........ ....... 

I

cf.

5 10 15

........................ 

............ .. ..... ......

E

t .. .. .. ..... ..... .

.... ...... 

......... ..... ......
JLuviJ.nls 

Vduv 

09 9tr 

I I

oi0 

I - - It

jeq/ einsseid 

I I I

9'. 

I

O0 

I ! I - I - linE

K........................... 

.... ........ .... 1....... ..... 

S................. . ...-...

I. 

.. ........ 

.......... .. 

... .......

S... .... ........... .. ..... 

. .. ..

I i n I - III n IIi li

8t ON P! 1Old

9 0 

-91'0

9"0 

-8"0 

•ol rotI.

-9. 

D

A

i i I I I

.... ... . .. ... ... 

.... .. .....

.... ...... . 

.......... ....... 

.. ........... .. 

I ..... ......... 

................................ 

....................... .......

UlaIu s dooq lul 1v [ episul

.......... .. .... .. .......

................ 

....... ...... .

......... . ..... .... . ........ .

.... ....... ......
NRC sOpm 332 U.S. NUCLEAR REGULATORY COMMISSION 1. REPOR! NU\V5E R "1.Es |4Assign by NRC. AC Vol.. S.C:.. Re. . 

%Rcm 1$C.. and A@cnoum Nwrmm.,. Io .f 

3701.37^: BIBLIOGRAPHIC DATA SHEET NUREG/CR-6517 

2 LfM ins:,-,:ufWlJ on the, reverse)I S D96-2899 

2. TITLE AN?.S:J6TITLE 

Round Robin Pretest Analyses of a Steel Containment Vessel 

Model and Contact Structure Assembly Subject to Static 3. DATE REPORT PUS.HSi4ED MONT H • IV East 

Internal Pressurization hmOst 1j 9 

4. FIN OR GRANT NUMBER Al40 

S. AUTHORIS 6. TYPE OF REPORT 

Vincent K. Luk/SNL 

Eric W. Klamerus/SNL 7. PERIOD COVERED rsn:,,.,.. O:,.o' 

June 1994 to November 

_ 1 QQ•

6. PERFORMING ORGANIZATION - NAME AND ADDRESS 1114WR. proide Dir,,in. Offscro rlevion. U.1 Naclea Regu•latr onvni, o adm inakn aret:0 Cot e,•ra, ,1W a~V #Ad amAý addim). 

Sandia National Laboratories 

P.O. Box 5800 

Albuquerque, NM 87185-0744

9. SPONSORING ORGANIZATION-- NA-UE AND ADDRESS ft NRC tvpe "e awo,,e" ftemigcr.9ewaeie NRC Di,,io.,. Offeor-Ae,.on. U.S ivduce- f,,wtutor Cwm,,,•.s. 

and m0ansM astacJ "Division of Engineering Techrioogy Systems Safety Department 

Office of Nuclear Regulatory Research Nuclear Power Engineering Corporation 

U.S. Nuclear Regulatory Commission Fujita-Kanko...-Buil di ng 

Washington, D. C. 20555 17-1, 3-Chome, Toranomon, Minato-ku 

Tokyo 105, Japan

10. SUPPLEMENTARY NOTES 

3. F. Costello, NRC Poject Manager

13. ABSTRACT OXw . or rsfj 

The Nuclear Power Engineering Corporation (NUPEC) and the U.S. Nuclear Regulatory Commission 

(NRC) are co-sponsoring and jointly funding a research project at Sandia National Laboratories (SNL) to 

conduct a failure test of a steel containment vessel (SCV) model and contact structure assembly. The SCV 

model, representative of an improved Mark-H Boiling Water Reactor (BWR) containment vessel, is scaled 

1:10 in geometry and 1:4 in shell thicknesses. The contact structure, a thick bell-shaped steel shell, 

provides a simplified representation of a concrete reactor shield building in the actual plant. The failure 

test will be conducted in December 1996 to provide data on the response of the composite structure up to 

its failure in order to validate analytical modeling, to find the pressure capacity of the model, and to 

observe the failure mechanisms.. 

Eight international organizations performed model analyses and provided predictions of the model 

behavior at 43 specified locations and the failure pressure and mechanisms. This report describes the 

analysis models and tabulates the pretest predictions submitted by each organization. A pretest meeting of 

all participants will be held on October 1-2, 1996, to discuss modeling approaches and analysis results.

12. KEY WORDS.')ESCR!PTORS ike wes- mwemur met -wri fvteovM in worn tme nroot.1 13. AVAILABILIT V STA"M-EN7 

Unlimited 

%4. SECURI-TV LSI~lt 

ITAiM PAeW 

Steel Containment Vessel, Failure Test, Model Analysis, International Participants, Unclassified 

Failure Pressure and Mechanisms. 17*4 o.m,., 

Unclassified 

15. NUMBER OF PAGES 

16. PRICE

flap anatn....,
Federal Recycling Program
A

UNITED STATES 

NUCLEAR REGULATORY COMMISSION 

WASHINGTON, DC 20555-0001 

OFFICIAL BUSINESS 

PENALTY FOR PRIVATE USE, $300

SPECIAL STANDARD MAIL 

POSTAGE AND FEES PAID 

USNRC 

PERMIT NO. G-67