Indian Journal of Engineering & Materi als Sc iences Vol. 9, August 2002, pp. 237-249

Leak-before-break analysis of shell-nozzle junction of steam generator

Vijay G Ukadgaonkcr", Yogesh D Khairnar", Pratichi Vaidya" & P Chellapandih

"Depart ment of Mec hanical Engineering. Indian Instit ute of Tec hnology-Bombay, Powai, Mum bai 400076, Indi a hlndira Gandhi Center fo r Atomic Research, Kalpakknm 603 102, India

Received 18 Jll ly 200 I: accep fed 10 April 2002

In vestiga ti ons on leak-beFore-break an alys is of shell -nozz le juncti on of steam generator (SG) are presented here. Steam ge nerators are integral parts of the nuclear power plants. So, to prevent the catastrophic Failure of such components nowadays, leak-before-break (LBB) concept is used. There are three levels of checking LBB behav ior, namely level I, level 2 and level 3. Leve l I is inherent in the design philosophy of ASM E Sec. lJI , whi ch is normally fo ll owed in the pipe design. Thi s paper describes level 2 and level 3 LBB analysis for SG shell-nozzle juncti on.

In level 2, crack propagation analysis of surface crac k at the most critical locati ons of SG shell-nozzle junction was carried out , show ing thereby, that crack growth is insignificant during the complete one power pl ant li fe cycle. Crack propagat ion analysis was conducted as defin ed in RCC-MR code. The methodology based on Pari s law, which needs evaluati on of effecti ve 11 K (11 Kcff) taking into account effect of plasti city and crack closure coeffi cient , was used.

In level 3, th rough-wa ll leak size crac ks (LSC) were postulated at the most critical locations and crack instability analysis was carried out under max imum credible loading conditions (e.g. earthquake). For crack instability analysi . va ri ous steps namely determination of leakage area and leak size crack (LSC) using leak- rate model, elas tic-plastic frac ture mechanics an alysis (i-integral/tearing modulus approach) and limit load analysis (twice elas tic slope method) were carried out. For the evaluation of cri tical load, elastic-pl astic frac ture mechanics analysis and for the eva luation of limit load, li mit load analysis were carried out. Since no geometri cal simplifications were possible fo r SG shell-nozzle junction, compl ete three-dimensional non-linear finit e element anal ysis was performed. And , it has been proved that, because of postulated cracks, SG shell nozzle juncti on would not fa il in ductile tearing and plastic collapse under max imum credi ble load that may ac t during a safe shutdown earthquake (SSE).

LBB is an application of frac ture mechanics to pressure containment systems, such as vessel s, pipes, steam generators and pump casings, especiall y in nuclear power pl ants. Normall y, there is possibility of hav ing defects in the above-mentioned components during manufacturing stage. These defects can grow to cause fai lure by one of the several mechani sms, such as fatigue, corros ion and creep. Thi s situation becomes very serious in the ca. e of nuc lear power plant components. For such components, LBB concept can be used through frac ture mechanics analysis to demonstrate that there is neg li gi bl e chance of any catastrophic break of these com ponents without giving prior indicat ion of any leakage l

. Th is property of LB B is des irab le because leak usua ll y can be eas il y detected. Thus, inspection for the crack would not be necessary; one could simply wait fo r a leak and then repair. Indeed LBB is a desirable damage tolerance property. More work is going on pipes in the nuclear power pl ants. In thi s paper, LBB analysis of shell-nozzle junction of steam generator of 500 MWe Prototype Fas t Breeder Reactor (PFBR) being designed at Indira Gandhi Center for Atomic Research (lGCAR), India, is presented.

Over recent years, the concept of LBB has been considered in establi shing safety cases for pi ping parti cul arly for the nuclear industry. Bartholome et al. 2 have demonstrated the LBB behav ior of the coolant piping of KW U (Erlangen, Federal Republ ic of Germany) pl ants using fracture mechanics analysis and tes ting. Bartholone3 has ex plained the 'German Leak-before-break procedures, practice and appli ­cati ons' with analys is of LBB behavior. Vangderglas4

has applied LB B approach extensively to the large diameter pipi ng of a new nuclear power plant. He has also analyzed vari ous piping components such as elbows, tee and branch connections with postulated cracks. Ontari o Hydro corporation has developed LBB approach for applicati on to the large di ameter heat transport piping fo r Darlington NGSA as an altern ati ve to thc provision of pipe wh ip restraints , whi ch is ex plained by Nath wani et al. s. LBB approach is being adopted to design the PHT system pi ping of 500 MWe Indi an PHWR to be bui lt at Tarapur (Tarapur Atomic Power Plant Nos . 3 and 4). All this LBB qualification of primary heat transport piping of 500 MWe Tarapur Atomic Power Plant is explained by Ghattopadhyay el al.6 .

238 INDIAN J. ENG. MATER. SCI. . AUGUST 2002

LBB 11lethodology-The methodology of LBB consists of demonstr ring three levels of confidence. which can be explained as:

Level J-This leve l of confidence is inherent in the design philosophy of ASME Sec. III7 that is followed in nuclear pressure vessel and piping design. This design recommends (he use of ductile and tough materials because of their high resistance against catastrophic rupture. The design is done with well factor of safety code specified with 95 % exceedance probability strength. However, it does not permit the presence of any defect higher in size than specified in ASME Sec. III for girth welds.

Level 2-It consists of postulating a surface crack at critical locations on inner surface of component and then to demons trate that it will not grow through-wall during the period between two successive inspection, repai r, or if possible, during the entire life period of the reactor. It should also be shown that the final crack size at the end of evaluation period is sufficiently smaller than the critical crack size. Hence, one should perform the fatigue crack growth study of the postulated surface crack using Paris law as defined in the RCC-MR code. It is then shown that there is insignificant crack growth of this surface crack under specified power plant load collectives during the entire life period of the reactor.

Possibilities for crack growth-There are two different types of possibilities for crack growth: (i) If crack growth is significant, then one should perform crack propagation ana. lysis for unlimited power plant load collectives in order to show the fundamental tendency of the considered crack with respect to its shape development. If the crack grows rapidly in the radial direction as compared to circumferential direction and crack growth becomes asymptotic in circumferential direction, then crack growth is demonstrated as leak-before-break because crack will grow only in radial direction through the wall and it will show leakage before total failure, and (ii) If crack grows rap idly in the circumferential direction as compared to radial direction, then pipe or vessel may burst before crack grows fully in radial direction through the wall because of critical ligament without showing any leakage and this is demonstrated as break -before-leak.

Level 3-ln this level of safety assessment, It IS required to postulate a through-wall crack at critical locations . The size of crack is chosen so as to ensure the leakage that is easily detected in the plant and this crack is called as leak size crack (LSC) . Finally, it is

shown that this crack will withstand the maXl1TIUm credible loading that may act during a safe shutdown earthquake (SSE). This needs to evaluate critical load by using elastic-plastic fracture mechanics (i-integral/ tearing modulus approach) and limit load by using limit load analysis (twice elastic slope method). The load at which crack extends in an unstable manner is called as critical load . Limit load analysis is concerned with calculating the load or pressure at which flow of the structure occurs due to the yielding.

In brief, LBB level I is only design phase as per the design philosophy of ASME Sec. III . This design is input for the LBB level 2 and level 3 analysis. In this paper, LBB Level 2 and level 3 analysis of shell­nozzle junction of steam generator is presented.

LBB Methodology for Level 2 The LBB level 2 consists of postulating a surface

crack at critical locations on inner surface of component and then to demonstrate that it will not grow through-wall curing the period between two successive inspections, repair or if possible during the entire life period of the reactor.

The level 2 deals with the crack propagation analysis of surface crack postulated on the shell­nozzle jt.:nction of the steam generator as defined in RCC-MR code. This shell-nozzle junction is at colder end of steam generator; therefore for the LBB analysis, creep effect can be neglected. The geometrical details of shell-nozzle junction are shown in Fig. I. This LBB level 2 essentially consists of following steps: (i) collection of material properties, (ii) Identification of loads, (iii) Identification of critical locations, and (iv) Crack propagation analysis using Paris law.

Collection of material properties The colder end junction of the stream generator

(shown in Fig. I) is made up of modified 9Cr-J Mo steel and is subjected to the operating temperature 630 K. True stress-strain curves for modified 9Cr-1 Mo steel at various temperatures are shown in Fig. 2.

The material data for modified 9Cr-l Mo steel at 630 K is : Young's modulus, E (1.82x105 MPa) ; Poisson's ratio, V (0.3); and, Minimum yield stress, Sy (349 MPa);

The fatigue crack growth law for this material can be expressed as :

da = c.( ~K eJJ )" dN

t

UKADGAONKER el at. : ANALYSIS OF SHELL-NOZZLE JUNCTION OF STEAM GENERATOR 239

10-1120

o o M

.. o ...

184

I. 200 .1

Fig. I-Geometrical details of shell-nozzle junction

h da . ' f . k h" m/ I were, - IS atlgue crac growt 10 m cyc e; dN

t!KeJJ is effective stress intensity factor range' in

MPa"m, which takes into account the effect of plasticity and crack closure coefficient; C and n are constants having values 1.8xlO-9 log (mm/cycle) and 4, respectively.

Identification of loads The main principle for identification of mechanical

and thermal loads is that all the failure modes are identified and ruled out either by previous experience or predictability of the margins against such failure modes. The principle implies that operating conditions are known with confidence at the design stage.

For LBB level 2 analysis, particular care should be given to mechanical and thermal loads, viz. (i) High external loads of erratic natures (such as water hammer, unstable condition, etc.); (ii) Operating thermal transient loading; and, (iii) Vibrations (induced by high flow velocity, rotating machinery, etc.).

(} (Mpa)

BOO 400°C

300°C

600 91°C

25 °C

400

200

2 4 6 8 10 12 E (%)

Fig. 2-True stress-strain curve for modified 9Cr-1 Mo steel

l i Bj" -l--_'r

Fig. 3-End moment acting on SG - shell nozzle junction

These can be classified into the following levels : Level A (normal operating condition--constant load) ; Level B (upset condition-fluctuating load) ; and, Level C (emergency condition-fluctuating load) .

Magnitude of each level loading is: Internal Pressure-P (0.5 MPa for level A) ; t1P

[0.5 MPa for level B (2000 cycles)]; t1P [0 .5 MPa for level C (2000 cycles)]

End Bending moment-M (4Sx103 Nm for level A); 11M [4SxlO3 Nm for level B (2000 cycles)]; 11M [77x103 Nm level C (2000 cycles)]; where, .1 indicates fluctuating load (maximum load minus minimum load).

The nature of end bending moment (M) acting at the extreme end of the nozzle is shown in Fig. 3.

As level Band C loading are having same number of cycles and load C is more in magnitude than load B, crack propagation analysis has been done for combination of loading level A and C.

Identification of critical locations The critical location is the location of maximum

principal stress under combination of loading level A and C. This location of maximum principal stress is critical because there is possibility of crack growth is

240 INDIAN J. ENG. MATER. SCI., AUGUST 2002

more if it opens in the first mode of defect. Therefore, for crack propagation analys is, semi-ellipti ca l surface crack is postulated at the criti ca l location such that crack plane is perpendicular to the direction of maximum principal stress. For the determination of maximum principal stresses and criti ca l locati ons, the elast ic stress analysis without considering any defect has been carried out.

Owing to practi cal limitations, analytical problems in fracture mechanics are generall y solved by simplifying geometry and boundary conditions (e.g. plane stress/s trai n condition). But, because of nature of load ing and three-dimensional geometri c nature, no geometri c si mplificati on was poss ible for SG shell-nozzle juncti on; therefore, full y three­dimensional model was used for the elast ic stress analysis. The junction was modeled using shell element SHELL93 hav ing 8-nodes, which is ava ilable in A l SYS. The fini te element model for shell-nozzle j unction used 562 elements and 4000 nodes, as shown in Fig. 4. The analysis was carried out under loading level 'A', i.e. internal pressure of 0.5 MPa and bending moment of 45x l03 Nm. From the analysis, it has been concluded th at there are two crit ical locati ons namely 'A ' and 'B '. The stress concen­tration factors is 3. 1 at criti ca l locati on 'A' with reference to hoop stress in the nominal secti on of shell and 2.289 at criti cal locati on 'B' with reference to hoop stress in the nominal secti on of curricul ar cy I i ndrical portion of nozz le. These stress concentration factors were calculated w ith reference to the hoop stress of conical porti on of the SG shell ­nozzle juncti on. These criti ca l locati ons are shown in Fig. 5.

Crack propagation analysis

In the L BB level 2 demonstrati on, crack

I I !"-~ \ le-i-

-1= 1"- ". A-i

"'~: ~ ! - c- --- -I I

i lih q:, ~. - -

- - - .

Ii tf±i-t- - .. - -

I! IT - ..

~ - , - )r - -- -

. - . -

------ -- 1-+ - e-- ~,Y)~. / --- ~

j i/ /71

Fig. 4- Finite element mesh or she ll - nozzle junction

propagation analysis is the main step. After locating critical locations, postu late the surface flaw at critical locations. The surface fl aw is of semi-ell iptical shape with minor and major dimension as a and c, respectively as shown in Fig. 6. In the present case, crack length c=6 IT and crack depth a=O. 125 /z is assumed as per ASME Sec. Ill. The maj or axis of the semi-elliptical crack is along circumferentia l direction and minor is along the rad ial direction. The wa ll thi ckness (h) of shell-nozzle juncti on i. 18 mm. Only mode I is assumed to be predominant. Accordingly, the crack plane should be perpend icular to maximum

Fi g. S- Cri tica l locations on she ll -nozzle j unc tion

Elli tical Crack

~ - Crack angle c - Crack length a - Crack depth

Fig. 6- Semi -ellipt ical crack

+

UKADGAONKER et al. : ANALYSIS OF SHELL-NOZZLE JUNCTION OF STEAM GENERATOR 241

principal stress direction. For the crack propagation analysis loading level A and C were used.

Crack growth analyses of both crack length c and depth a were performed using Paris law. These crack propagation laws are:

~ = Cr!lK 1, dN ~ eff J

da r 1, and, - = C l!lK eff J

dN

where C is material constant, c and a are crack length and depth respectively, ,1Keff is effective stress intensity factor range, which takes into account effect of plasticity and crack closure coefficient. The step­by-step procedure for determining stress intensity factor range (,1KejJ) is:

(i) To determine the range of i-integral (,11) over the cycle-i-integral is the parameter, which takes into account the effect of plasticity. Following equation is used for the determination of M:

where, M e range of i-integral (1) due to only elastic

contribution, which can be calculated from stress intensity factor (KJ) and KI can be calculated from standard Handbook solutions. K t>.I is amplification

factor for taking into account the effect plasticity.

K t>.I can be calculated by using:

and, 'P = O.sl(!lcr ref Y + (Sy Y J

where, Sy yield stress, !lcr ref is stress range, which is

difference of equivalent stresses for minimum and maximum load for specified cycle. !lE ref is strain

range corresponding to !lcr ref' which can be

determined from true stress-strain curve of the material.

(ii) To determine an effective stress intensity factor range (,1Keff)- It can be determined by:

where, E * =E for pl ane stress condition and E*=E( 1-V) for plane strain and v is poisson' s ratio. q is crack closure coefficient, which is calculated in terms of stress ratio R=Kmi,IKmox as:

[l-O.SR] s: R 0 q = [ ] lor <

I-R

1 and, q = [ ] for R > 0

I-O.SR

For crack propagation analysis, a computer code was written in FORTRAN language, which follows all the steps mentioned above8

. This computer code requires initial crack dimensions, stress and strain range for load cycle specified and Handbook formulae for calculation of effective stress intensity factor range. For each load cycle crack propagation was done using the Paris law and after the crack exceeds 10% of its initial value, the crack dimensions are updated. Calculation for effective stress intensity factor range (,1Keff) has been carried out, whenever crack dimensions are updated.

Results and Discussion (Level 2 LBB) As discussed earlier, the crack propagation analysis

using Paris law is carried out for combination of loading level A and C. Tables I and 2 list some of the steps of variation of crack dimensions with number of fatigue cycles. Figs 7-10 show the variation of the crack length (c) and crack depth (a) with number of cycles (N) for both critical locations ' A' and 'B' , respectively.

There are 2000 cycles of loading level C along with operating loading level A during one power plant life. This combination of loading level A and C results in the stresses well below the yield limit in SG shell­nozzle junction. So, at the end of 2000 cycles, we can see from Tables 1 and 2 that crack depth growth is less than 1 % of wall thickness, which is negligible. Even after 40000 cycles (20 power plant life cycle), crack depth growth is less than 1 %. Also, from Tables 1 and 2 and Figs 8 and 10, it can be said that crack length growth is becoming asymptotic. Thus,

242 INDIAN J. ENG. MATER. SCI. , AUGUST 2002

Table I- Variation of crack dimensions with the number of fatigue cycles at critica l location ' A'

N (cycles) (/ (mm) c (mm ) t1K,.'1 for (/ (M Pa VIIl) t1K .. '1 for c (M Pa VII1 )

10 4.500 108.000 6.6 17 8.052 100 4 .500 108.00 1 6.617 8.053 500 4.501 108.002 6.6 18 8.054 1000 4.502 108.004 6.619 8.055 2000 4 .504 108.007 6.62 1 8.058 5000 4.510 108.01 8 6.627 8.068 10000 4.520 108.036 6.638 8.083 20000 4 .540 108.071 6.660 8.1 13 30000 4.561 108.109 6.682 8. 144 40000 4 .571 108. 130 6.694 8.162 40500 4.573 108.13 1 6.695 8. 163

Table 2- Varia ti on of crack dimensions wi th the number of fa tigue cycles at critical location ' 8 '

N (cycles) (/ (mm) c (mm)

10 4.500 108.000 100 4.500 108.001 500 4.50 1 108.002 1000 4.50 1 108.003 2000 4 .503 108.006 5000 4.507 108.0 15 10000 4.515 108.031 20000 4 .529 108.062 30000 4.544 108.093 40000 4.559 108.124 40500 4.560 108 .1 26

4.58 E 4.57 E 4.56 :; 4.55 i 4.54 ~ 4.53 :il 4.52 U 4.51

4.50 0 10000 20000 30000 40000 50000

No. of Cycles

Fig. 7- Variati on of crack depth {/ with Ilumber of cyc les at location ' A'

108.14

E 108. 12 .s 108. 10

~ 108.08 §i 108.06 ~ 108.04 u (Q ... 108.02 u

108.00 0 10000 20000 30000 40000 50000

No. of cycles

Fig. 8-Variati on of crack length c with number of cycles at locati oll 'A'

t1Keq for a (MPa V,n) t1K .. q for c (MPa VII1 )

5.938 7.636 5.93 8 7.637 5.939 7.638 5.939 7.639 5.940 7.641 5.944 7. 647 5.950 7 .657 5.963 7.677 5.975 7.697 5.988 7.71 8 6.0 13 7.749

4.57

E 4.56 .§. 4.55 .z:. 454 a. . .g 4.53 ~ :il 4.52 ...

4.51 u 4.50

0 10000 20000 30000 40000 50000

No . of cycles

Fi g. 9- Variat ion of crac k depth a with nu mber of cyc les at locati on ' 8 '

108.14

E 108.12 .§. 108.10

~ 108.08 ~ 108.06 ~ 108.04 u (Q

U 108.02

108.00 0 10000 20000 30000 40000 50000

No. of Cycles

Fi g. 10- Vari ati on of crack length c with number of cycles at locat ion' 8'

UKADGAONKER et 01.: ANALYSIS OF SHELL-NOZZLE JUNCTION OF STEAM GENERATOR 243

both the cracks are showing leak-beFore-break behavior.

LBB Methodology for Level 3 In LB B level 3 of safety of assess ment, it is

req uired to postulate a through-wall crack at critical locations. The size of crack is chosen so as to ensure the leakage that is eas il y detected in the plant and thi s crack is called as leak size crack (LSC). Finally it is shown that thi s crack will withstand the maximum credible load ing that may act during a safe shutdown earthquake (SSE).

The level 3 deals with non-li near finite element analys is of SG shell-nozzle junction for crack instability anal ysis. This needs to evaluate critical load by usi ng elastic-plastic fracture mechani cs (J-integral/tearing modulus approach) and limit load by using limit load analysis (tw ice elastic slope method). Critical load is the load at which unstable ductile tearing of the structure occurs and limit load is the load at wh ich structu re fails in the plastic co llapse. Safety assessment of a structure with crack can be performed by using the i-integral-tearing mod ulus (J-D concept9 and limit load analysis 10. [t req uires the evaluat ion of i-integral and also the limit load at the plastic coll apse. Critical load and limit load can be compared with each other to predict whether plastic coll apse precedes the onset of unstable ductil e tearing or not. For the eva lu ati on of i-integral for elas tic­plast ic fracture mechani cs analysis and end face rotat ion of SG shell-nozzle junction for limit load analysis, elastic-plastic finite element ana lysi s (EPFEA) is adopted.

Leve l 3 essent ia ll y consis ts of the fo ll owing steps : (i) col lec ti on of the material properties, (ii ) identi­fica ti on of loads, (iii ) identifi cation of criti cal 10cati oil S, (iv) determin ati on of LSC that ensures detectable leakage, and (v) sa fety assessment of the components to determin e the criti cal loads(' .

Collec tion or elastic-plastic material I)f'Opcl' tics

The shell-nozzle juncti on of stream generator IS

made up of modifi ed 9Cr- 1 Mo stee l. The elastie­plastic material data for modi fied 9Cr- 1 Mo steel at 630 K is:

Young's mod ulus, E ( 1. 82 x 105 MPa) ; Poisson's ratio, v (0.3) ; Allowab le stress , Sill ( 180 MPa); Minimum yield stress, Sy (349 MPa); Minimum tensil e stress, SII (490 MPa).

The true stress-strain curves for 9Cr-1 Mo steel at various temperatures are shown in Fig. 2. For the non-

linear finite element analysis, true stress-strain curve at temperature 630 K was used .

Tearing modulus (D can be defined as rate of change of i -integral with increase in crack length. The material properties for elastic-plas ti c fracture mechanics , which are enough to represent i-integral­Tearing mod ulus (J-D curve for material , are:

i lc for d=0.2 mm-70 /mm for parent meta l; 70 N/mm for welds

dilcld (Do) for d=0.2 mm-270 N/mm2 for paren t metal ; 200 N/mm2 for welds

where, i lC' is criti ca l value of the i-integral for material , when crack just starts to propagate. But for determining the va lue of i lc experimentall y, crack is allowed to extend by di stance d=2.0 mm. dilcld(&/ ) is value of tearing modulus (D , when crack propagates by di stance d= 0.2mm. For critical load evaluation, material properties of weld have been used, because weld material has less fracture toughness than the parent material

Identification or loads

The main principle for i c.~n tifi catio n of mechani cal and thermal loads is th at all the fai lure models are identified and rul ed out either by previous experience or predictability of the margins against such fai lure modes . The principle implies that operating co nditi ons are known with confidence at the des ign stage

SG is . ubjected to in ternal press ure and bending moment during normal service cond iti on. Bendi ng moment is introduced on the nozzle because of offset fluid tl ow force acting on the nozzle. But duri ng the fau lty conditi on such as earthquake, extra in ternal press ure and bendi ng moment act.

The loads which arc to be considered for LBB leve l 3 analysis, can be class ifi ed into:

Level A for normal operating condit ion Level D for faulted condition [maximum credibl e

loading (e.g. earthquake)]

Magnitude of each load ing is shown below: In ternal Pressure (P)-0.5 MPa for level A: 6.0 MPa for level D End moment (M)- 45 x 103 Nm for level A; 135 x 103 N m for level D

The direction of end bending moment is shown in the Fi g. 3. Level A and level D load ing are monotonic

244 INDIAN 1. ENG. MATER. SC I. , AUGUST 2002

in nature. As magnitude of loading level 0 is more than level A, only level 0 is considered for checking LBB leve l 3 assessment.

Identification of critical tocation

For the determination of critical location, e lastic finite element analysis of the shell-nozzle junction under loading level A without considering any defec t was carried out as for LBB level 2 assessment. The element used was 20 noded solid brick element SOU095, which is available in ANSYS . This model is shown in Fi g. 11 and consists of 838 elements and 84 12 nodes. Critical locations with reference to this finite element analysis for combined loading level A and C were identified as shown in Figs 12 and 13 as A and B, respectively.

Determination of leakage size crack (LSC)

As mentioned earlier, Level 3 safety assessment in LBB study consists of postulating a through-wall crack that will ensure detectable leakage and then to

11 i'." 1": '--I--

I', " ~

~ , ,

I/ll ru: ~

1/ \/ • v V I TT

Fig. II-Finite element mesh of Shell-nozzle junction

Crack 'A'

( (1 ---.------

Fig. 12-Steam Generator shell - nozzle junction with crack ' A'

demonstrate that the crack wi II be stab le under the severest loading. The minimum leakage that can be detected depends on the accuracy and sensitivity of the leak detecting instruments avai lable in the power plants. For the present work , minimum detectable leak rate Q lllill given is 100 g/h . United States of Nuclear Regulatory Commission (USNRC) reco mmends a fac tor of safety equal to lOon thi s6

. I-lence, it is assumed that the crack, whi ch ensures 1 kg/h leakage under normal operating condition, is known as leakage size crack (LSC). It is to be established that the LSC will be stable under the maximum credible loading (level D) . Therefore, there is need to develop a thermo-hydraulic model which correlates internal pressure, properties of the fluid flowin g through SG, operating temperature and leak rate with the crack size. To accomplish this a computer code "CRACK LENGTH" has been deve loped in computer language c++. For the determination of the LSC, code "CRACKLENGTH ' requires membrane and bending stresses of the location of the interest.

There are two critical locations as shown in Figs 12 and 13. Table 3 lists the values of membrane stress, bending stress and crack length at the critical locations ' A ' and 'B' .

But these crack lengths are less than the shell and nozzle wall thickness, which is not possible practically. Therefore, for the LBB analysis, crack

Location

A B

Table 3 - Crack lengths at critical locations

Membrane stress am

(MPa)

49.592 69.38

Bending stress a b (MPa)

69.607 20.769

Crack length (mm)

9.68 9.52

{~-------------~. (Q

Fig. 13-Stearn Generator shell - nozzle junction with crack 'B'

UKADGAONKER el al. : ANALYS IS OF SHELL-NOZZLE JUNCTION OF STEAM GENERATOR 245

length for both locations ' A' and ' B' were taken equal to 100 mm. The crack length of 100 mm is equivalent to angle ( ~ ) of close to 30 degree as shown in Fi g. 6. This is the most preferred angle (~) used for pipes for crack instability analysis in nuclear power pl ants. For the LBB qualification of primary heat transport piping of 500 MWe Tarapur Atomic Power Plant crack representing the same ang le (~) has been used6

.

Elastic-plastic fracture mechanics analysis

Stability analysis of the crack involves the determination of the critical load at which the crack will extend in an unstable manner and limit load at which plasti c collapse of the structure occurs. This is caITi ed out by performing the elastic-plastic fracture mechanics analys is of the component with postulated through-wall cracks under maximum cred ible load ing level D and this load is high in magnitude, which introduces non- linearity. The type of elast ic-plasti c fracture mechanics analysis for the determination of the critical load is known as l-integral-tearing modulus (lIT) approach8

. [n this approach, both "applied" and "material" l-integral and tearing modulus curves are determined. The "applied" curve is calculated by using fin ite element analysis . The intersection point of both the curves determines the crack instability .

The conditions, which decide instability of the crack, are:

l app 2? l i (necessary condition for crack initiation) l app 2.IJ//n/ (necessary condition for crack instability) T al'l'2?TJ//(1/ (sufficient condition for crack instabi lity)

For the evaluation of the limit load twice elasti c slope method is used.

Non-linear tinite element analys is

Simple analyti cal so lutions for the evaluation of l ­integral for cracks in strai ght pipe and elbow are readily availab le in the literature. However same types of analytical solutions for tee pipe are limi ted in the open literature. SG shell-nozzle junction is analogous to tee pipe joint. Therefore, one has to carry out non-linear finite element analysi s to evalu ate the applied l-integral and limit load . Consequently, the general purpose finite element code' ANSYS 5.6' is used for the determination of the aforesaid values.

Finite elemellt rnode/ing- Figs 12 and 13 show the location of the postulated cracks on the shell-nozzle junction. Since no geometrical simplification is

possible, fully three-dimensional model s fo und essenti al. It is sufficient to model half of the structure because of sy mmetric geometry and boundary conditions. Figs 14 and 15 show typical finite element mesh of the model having crack ' A' and ' B' respecti vely.

For finite element modeling, 20 noded solid brick element SOLID95, which is available in A SYS, is used. Only one element is taken across the thickness. The finite element model of shell-nozzle junction having crack 'A' and 'B' consists of 1916 and 1824 twenty nodded so lid elements and 13875 and 132 1 I nodes respecti ve ly. Aspect rati o for all the solid elements is within ANSYS package's default va lues for so lid elements . The crack is simulated on the junction by creati ng add iti onal nodes of the same co­ord inates along the length of the crack. Appropriate boundary conditions are applied on the fi nite element models.

Fig. 14- Finite element mesh of Steam Generator she ll - nozz le uncti on with crack 'A'

Fi g. IS- Finite e lement mesh of Steam Generator shell - nozzle unction with crack ' 8 '

246 INDIAN J. ENG. MATER. SCI. , AUGUST 2002

Evaluation of i-integral and tearing modulus by FEM- i-integral means energy release rate. This concept used to determine the amount of work (change in energy) associated with a crack opening or closure. One method to calculate the energy release rate is the virtual crack extension method, outlined below. In the virtual crack extension method, one has to perform the finite element analysis twice, one with crack length ' a ' and the other with crack length 'a+ila '. If the pote tial energy U (strain energy) for both cases is stored, the energy release rate can be calculated from:

1 = _ U {/ +t.a - U {/ M

where, L\A is the increase in crack area of the fracture model. ila is equal to 1 % of a.

Tearing modulus can be defined as rate of change of 1-integral with respect to crack length . It is a dimensionless quantity. Tearing modulus (n and 1-integral can be related to each other by:

where, T is the 'tearing modulus', E is the Young's modulus, CYJ is the ' flow stress' (generally taken as average of yield stress and ultimate stress), and a is the ' crack length' .

Since virtual crack extension method is used for the calculation of i-integral, so it is necessary to model the junction for each location two times, with crack length 'a' and 'a+& '. Thus for the finite element analysis, SG shell-nozzle junction was modeled 4 times as given in the Table 4. In this table, a=lOO mm.

Material non-linearity is considered in the finite element analysis by using true stress-true strain curve.

------------------------------------------Table 4---Different crack models

Model name Locatlon Crack length Cracked area (mm) (m2

)

Crack_AI A A 9.52845 I 282e-4

Crack_A2 A 1.0 I *a 9.62373583ge-4

Crack_BI B A 1.282946434e-3

Crack_B2 B 1.01 *a 1.295725307e-3

Limit load analysis--The limit load of the piping components containing a flaw is an important parameter in its safety assessment. No c lose form solutions are available for limit load of through-wall cracked shell-nozzle junction. Therefore , elastic­plastic finite element analysis was carried out to evaluate the limit load. In the evaluation of the limit loads, the internal pressure was kept constant and bending moment was monotonically incremented. The twice-elastic slope method 10 was adopted to determine the limit moment from moment versus end­rotation curves . This procedure gives conservative estimation of limit loads.

Results and Discussion (Level 3 LBB) The results of the LBB analysis of SG shell-nozzle

junction are discussed here. The resul ts are split into four subsections, namely, evaluation of leak size crack, load steps, stability analysis by 1fT approach and evaluation of limit loads.

Evaluation of leak size crack (LSC) Membrane and bending stresses of the critical

element under loading level A, thermo-hydraulic properties of the liquid sodium flowing through SG are the input needed for the computer code "CRACKLENGTH". It gave following results.

Length of crack 'A' Length of crack 'B'

9.68mm 9.52mm

But, thickness of shell and nozzle is more than 18mm. So, above-mentioned crack lengths are not possible. Therefore for further analysis , crack length equal to 100 mm is assumed for both the cracks 'A ' and 'B' on the basis of literature survel.

Table 5- Load steps

Load step I nternal pressure Bending moment number (Mpa) (kN-m)

I 6.0 45 2 6.0 90 3 6.0 135

4 6.0 180

5 6.0 225

6 6.0 270

7 6.0 315

8 6.0 360

9 6.0 405

10 6.0 450

" 6.0 540

UKADGAONKER el at.: ANALYSIS OF SHELL-NOZZLE JUNCTION OF STEAM GENERATOR 247

Load steps

Elastic-plastic finite element analysis is carried out on all 4 models. Internal pressure is kept constant and moment is increased in small steps. Table 5 lists the loading details as:

Evaluation of applied J-integral and tearing modulus The i-integral is calculated by using virtual crack

extension method and tearing modulus can be calculated by using numerical method. For the calculation of i-integral and tearing modulus, equations as given earlier, have been used. Tables 6 and 7 list i-integral and tearing modulus

Table 6--i-integral and tearing modulus values for crack 'A'

Load i-integral for i-integral for Tearing step Crack Al Crack A2 modulus for

number (kJ/~2) (kJ/~2) crack 'A'

168.968 173.033 3. 174 2 338.234 348.808 5.886 3 505.854 521 .668 12.489 4 673.848 692.457 15.175 5 929.848 956.191 21.834 6 1694.927 1749.652 47.697 7 3209.343 3325.325 87.071

3500

~:mJ ...... 2500 i2(llJ '! 1500 , 10XI c

""T' 500 ~

0 0 100 200 300 400

End bending moment (kN-m)

Fig. 16--Typical variation of applied i-integral with end bending moment fo r model Crack_A I

3500

N 3JOO .E2500 i2000 '! 1500 CI

! 1000 ~ ~ 500

0 0 100 200 300 400

End bending moment (kN-m)

Fig. 17-Typical variation of applied i -integral with end bending moment for model Crack_A2

values for crack ' A' and 'B ' respectively for load steps 1 to 7 as listed in Table 5. '

i-integral versus bending moment curves are shown in Figs 16 and 17 for crack 'A' and in Figs 18 and 19 for crack ' B' . Figs 20 and 21 show i-T approach for cracks 'A ' and 'B ', respectively, which contains both "applied" (lapp versus T app) and "material" (lmat versus T mat) curves. Intersection point of these both the curves gives the instability point. The corresponding load of i-integral of this unstable point is the critical load. Thus from Figs 20 and 21, we have:

Table 7 - i-integral and tearing modulus values for crack ' B'

Load i-integral for i-integral for Tearing step Crack BI Crack B2 modulus for

number (kJ/~2) (kJ/~2) crack 'B '

52.430 56.082 0.734 2 79.819 88.116 1.253 3 11 8.601 124.183 1.524 4 164.333 170.920 2.108 5 245.717 250.623 3.202 6 467.695 476.229 6.115 7 903.051 917.108 11 .807

HID

~ fO)

i 600 ~ ... 400 Ii' .. c 200 :::;

0 0 100 200 DJ 400

End bending moment (kN-m)

Fig. 18-Typical variation of applied i-integral with end bending moment for model Crack_B 1

1000

~ 800

~ 600 «i ... 400 f c 200 ~

0 0 100 200 300 400

End bending moment (kN-m)

Fig. 19-Typical variation of applied i -integral with end bending moment for model Crack_B2

248 IND IAN J. ENG. MATER. SC I. , AUGUST 2002

3500

300U

r-.. 2500 N e g 2000 ':;

~ 1500

.5 LOoo I h

500

0

0 SO 100 150 100 150

Tearing modulus

Fi g. 20- J-T approJch for shell -nozzle junction with CJ'Jc k ' A'

2000

I ..... ISOO

~ . Applied

a } 1000 .

\

c ''0 ...

500 Material

oL-~--~==~==~-J o 50 100 150 200 250

Tearing modulus

Fig. 2 1- J-T JPproach for shel l-nozzle juncti on with crack '13 '

Crit ica l load for crack 'A ' 180 kN-1ll (under internal pressure 6 MPa)

Critica l load for crack '13' 3 15 k -m (undcr interna l pressu re 6 MPa )

Evaluation of limit load by tinite clement method

In the evaluation of the limit loads, the internal pressure (6 MPa) was kept constant and bending moment was monotonically incremented. The twice­el<uic slope method was adopted to determine the limit moment form moment versus end rotation curves. Table 8 li sts the edge rotation angles for shell ­nozz le junction with crack configurations' A ' and' B' for load steps I to 11 as li sted in Table 5. The edge rotation angle is the angle though which end face of the nozzle rotates in the plane of bending moment after application of load from its initial position when there is no load acting on the nozzle,

700

8' 600

~ 500

ii 400 § 8 300

~ 'eI 200 ii ~ 100

0

0 0.5 1.5 2 25 3

End rotation (deg. )

Fi g. 22- Typic::Ii vu riation of be nding moment vs. end rotation for shell -nozz le juncti on with cruck 'A'

700

8' 600

~ 500

ii 400 § 8 300 gp

'eI 200 5 ~ 100

0 0 0.5 t 1.5 2 25 3

End rotation (deg.)

Fig. 23-Typi ca l vari ati on of bending moment vs. end rota ti on for shell -nozz le juncti on with crack ' 8 '

Table 8-End rotation angles for crack' A' and '8 '

Load step End rotati on for End ro tati on for number crack ' A' crack '8'

(Dc:g) (Deg)

I 0. 111 0.104

2 0.206 0.198 3 0.307 0.296

4 0.4 14 0.399

.:l 0.529 0.509

6 0.652 0.630

7 0.796 0.777

8 0.980 0.967

9 1.246 1.203

10 1.592 1.522

II 2.853 2.599

Twice elasti c slope methods for cracks' A' and '8 ' are shown in Figs 22 and 23. These figures contain straight l ine and curve, If the slope of the curve at the

UKADGAONKER el al.: ANALYS IS OF SHELL-NOZZLE JUNCT ION OF STEAM GENERATOR 249

origin is angle y with respect to x-ax is, then straight line is drawn at an angle y/2 with respect to x-ax is from the origin . The intersection point of these curves gives limit load. Thus, from Figs 22 and 23, we have:

Limit load for crack . A'

Limit load for crack 'B '

Conclusions

498 kN-m (under internal pressure = 6 MPa) 516 kN -m (under intern al pressure = 6 MPa)

In this paper LBB level 2 and 3 analysis of the shell-nozzle junction of steam generator are presented. Critical locati ons were identified by using elastic finite element analysis for combination of loading level A and C. Crack propagation analysis for LBB level 2 assessment and crack instability analysis for LBB level 3 assess ment were carried out.

The conclusions drawn from the LBB level 2 analysis of steam generator shell-nozzle junction are: (i ) The crack propagation analysis for combined loading level A and C may be carried out at critical locations with initial crack dimensions as crack length c and crack depth a equal to 108 mm and 4 .5 mm, respectively; (ii) There are 2000 cycles of loading level C along with operating loading level A during one power plant life. This combination of loading level A and C results in the stress well below the yield limit in SG shell-nozzle junction. So, at the end of 2000 cycles, we can see from Tables I and 2 that crack depth growth is less than 1 % of wall thickness, which is negligible; (iii) Even after 40000 cycles (20 power plant life cycle), crack depth growth is less than 1 %. And crack length growth is becoming asymptotic at 40000 cycles. Thus, both the cracks are showing leak-before-break behavior; and, (iv) This shell-nozzle junction of the steam generator is qualified for LBB level 2-safety assessment.

The conclusions drawn from the LBB level 3 analysis of steam generator shell-nozzle junction are: (i) The leakage size cracks (LSC) corresponding to 1 kg/h leak rate under normal operating load is approximately 10 mm. But, this LSC is less than the wall thickness of shell and nozzle, which is not practically possible. So, for the further analysis LSC equal to 100 mm is assumed on the basis of literature survey; (ii) The critical bending moments obtained by i-integral-tearing modulus (J-D approach are 180 kN-m for crack 'A' and 315 kN-m for crack 'B'. These critical bending moments are higher than

spec ifi ed max imum credible load (Level D - P=6 .0 Mpa, and M=135 x 103 Nm) . Thus, SG shell-nozzle junction would not fail in ductile tearing under specified max imum credible load; (i ii ) The limit moments at plastic collapse of SG shell-nozzle junction with pos tulated through-wall cracks are evaluated from the moment-end rotation curve by elastic slope method . Bending moment versus end rotation curves were generated from the outpu t of finite element analysis. The limit load varies from 498 to 516 kN-m. These limit load values are higher than accidental loading (Level D - P=6.0 MPa and M= 135x 103 Nm). Thus, SG shell-nozzle junction would not fail in plastic collapse under specified maximum credible load level; (iv) It can be noted that critical moment values are less than the limit moment for both cracks 'A' and 'B' and hence it governs the design. It indicates that there is more chance that structure would fail in ductile tearing prior to the onset of plastic collapse for LSC. This indicates low toughness of the material ; and, (v) As limit moments and critical moments are more than specified maximum credible load, structure would not fail in ductile tearing as well as in plastic collapse under specified maximum credible load for LSC equal to 100 mm at critical locations ' A' and ' B'. Thus, we can say that SG shell-nozzle junction is qualified for LBB level 3-safety assessment.

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