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ZJE - 278 1987

М. Brumovský, J. Kuchta, J. Šik, S. Štěpánek

ANALYSIS OF BRITTLE FRACTURE CONDITIONS IN WWER REACTOR PRESSURE

VESSEL UNDER THERMAL SHOCK

ŠKODA WORKS Nuclear Power Construction Division, Information Centre

PLZEŇ, CZECHOSLOVAKIA

t'f

ZJB - 278 1967

M. Впшотеку, J, Kucht», J* Šik, 3. Štěpánek

AIALYSIS 07 BRITTLE PRACTUHB COHDITI05S IN WWSR REACTOR PRESSURE VESSEL UBDBR THERMAL SHOCK

ÚVTBI 73307

ŠKODA WORKS Hucleer Power Construction Division, Information Centr*

PLZEN, CZECHOSLOVAKIA

ANALYSIS OF BRITTLE FRACTURE CONDITIONS IS WV2R REACTOR

PRESSURE VESSEL UNDER THERMAL SHOCK

1. IKTRODUCTIOJ

On* of the most important tasks for the whole lifetime

of a nuclear power station is to ensure the safety and

reliability of the reactor and, especially» the pressure

vessel* The necessity of this effort la dictated, first of

all, by the following two factors:

- The reactor pressure Tessel contains practically all

fission materials and nost of fission products (in the case

of pressure vessel failuie, a non-controlled escape of these

radioactive materials and resulting non-reversible harm to

population up to large distance can occur) |

• The reactor pressure vessel is practically not exchange­

able (damage, failure, or end of its lifetime would result in

terminating the operation of the whole nuclear power station)*

From regimes which can result in dangerous influence on

reactor pressure vessel behaviour the most important ones are

those with emergency cooling. These transient regimes mostly

•tart from full operational output, so that the core contains

fuel elements of different, mostly high buraup* After shutting*

down the reactor by emergency rods, these fuel elements must

be cooled for a long period to remove the possibility of

their melting due to a' large amount of latent heat from the

decay of fission products* In most cases these regimes are

also connected with some loss of coolant, thus a sufficient

cooling of reactor active zone becomes difficultf for this

reason special emergency cooling systems are designed end

manufactured* The main effect of this cooling system on the

rtactor pressure vessel consists in very uwev transient

conditions resulting in high temperature and stress gradients

across the pressure vessel wall*

This paper deals with some activities, necescary for as»

•teeing the potential risk of reactor pressure vessel failure

in WWER nuclear power stations*

- 2 -2. BKERGENCY COOUHG IN W/BR-TYPB REACTORS

System of emergency cooling of WWBR-type reactors, likewise in other PfR-type reactors» is put into operation by on» of the following reasons:

- decrease in water level in pressurizer - decrease of coolant pressure in pressurizer - change of coolant pressure drop in reactor core outlet - increase of pressure in boxes of hermetic sons.

As a result, besides other measures, refilling of water into primary circuit is started, using the second high-pressure filling pump (small loss of coolant). At medium and large los­ses of coolant, also the high-pressure pumps as well at pressu­rized water tanks, and (if the drop of pressure in the primary circuit reaches values below approx. 8 MPa), also the low­-pressure pumps of emergency cooling are put into operation*

A typical scheme of the system of emergency cooling In WWBH-1000 Ml reactor is shown in fig. 1*

All reactor pressure vessels for the WWER-type reactors are characteristic by their transportability ba train, which means some limitation in their diameter. Thus, design of these vessels is characterized by two nozzle rings, the upper one serving for coolant outlet, and the lower one for coolant inlet. In the latter one also nozzles for inlet of emergency cooling water from low-pressure pumps are connected, fhile the WWBR-440 KW reactor has six loops (ID of the main piping equals 500 am), the WWER-1000 ЮГ version has only four loops (ID of the main piping is equal to 850 mm), both types of reactors having four small nozzles for emergency cooling (with ID equal to 250 mm for W.7ER-440, and 293 mm for WWBR-•1000 Mff version).

The system of emergency cooling is usually put into opera* tion by some type of LOCA, which may be associated with or without decrease in coolant pressure in reactor primary circuit•

The assessment of reactor pressure vessel resistance against brittle fracture during LOCA must be carried out for

- 3 -all potential nodes of LOCA, of both type», i.e. for both compensable and aon-oompensable loan of coolant (i.e. without or with decrease in primary circuit pressure after soma initial "incubation" period). FOT the VXER-type reactors the moat important types of LOCA are as follows:

- rapture of piping with IB less than approx. 30 mm (depending on reactor type), which is compensable

- rupture of piping with ID larger than 30 am (up to the main primary piping, i.e. 500 mm for VWBR-440, and 850 mm for lWBhVlOOO»)

- rupture of steam generator tube • rupture of steam lina • non-planned opening of the safety valve in pressurlser - non-closing of safety valve in steam generator • leakage in safety тайте in steam generator - leakage in quick-operating valve of turbine by-passing.

All these regimes are analysed for the initial full power reactor operation conditions. All the calculations are almo based on serere assumption that practically no water circulation (forced and/or natural) exists in the primary circuit after reactor shut-down, moreover, the following possibilities arm taken into account:

• partial mixing of primary coolant with water from high-pressure pump* and pressurised water tanks! mixing coefficient has been chosen lower than 0*5

• cold water from high pressure pumps is fully miring la reactor loops with primary coolant» then it flows in the Inlet tone of the reactor and la mixing again with primary circuit coolant (the mixing coefficient is lower than 0*5)

• cold water from high-pressure pumps and pressurised water tanks is fully mixing with primary eirouit coolant only la laftwt lone of the reactor.

Calculations have been carried out for two temperatures of water in emergency cooling systems s

- 4 -• miter temperature In water tank* for high-pressure

pump» and in pressurized water tanks is equal to +20 °C

* water temperature in water tanks for high-pressure

pumps is equal to '+55 °C, and in pressurised water trunks it is

equal to +100 °Cf

for both eases the water temperature in water tanks for

low-pressure puaps is equal to +20 °C«

In all WIER-type reactors now under operation» water

temperature in water tanks equal to +55 °C is ensured*

3* TEMPERATURE FIELDS PURIBC EMBRBMCY COOLIBg

Calculation of tenperature fields in WWBR-440 Hi reactor

pressure Teasels is divided into two parts with respect to

their configurations

• inlet noazlee

• cylindrical part.

In both cases the method of finite elements with linear

polynomial is used*

Thanks to symmetry, the computational area represents only

1/2 or 1/4 of vessel perimeter; this two-dimensional area has

been divided into 322 elements with 192 nodes (24 radial sections

with 6 elements, the first two elements cover the austenltle

cladding with a thickness of 9 mm), which gives a sufficient

accuracy in results and economy in operation time*

On the basis of experimental results it has been supposed

that oold water flows down the vessel wall in two extreme forms

of "cold tongues"In conformity with fig* 2s

- six "tongues.* with angle width of 60° on the level of

the welding joint near reactor core and with a constant tem­

perature across the width of the "tongue" (this case is charac­

terised by mutual overlapping of "tongues" - see fig* 2a)

• six "tongues" with constant angle width of 30° along the

perimeter and with a constant temperature across the width of

the "tongue"• fig* 2b.

- 5 -Tfeut temperature of water in the "tongue" in the area of the «tiding joint of interest, has been determined for both ease* from the following formula:

Г - тх +fiT4 - Ť X) (i)

Y* 0.5 - - 4 — ill - %> *** Q * 120 m*.lTX (2) 375 T r

Ym 0.5 - -~-<*í - О - 0.0033(0-120) if Q>12GsrVX Л 5 (3)

«here T - water temperature in the "tongue" in the area of welding joint,

T • water temperature in water tanks, fj, TT - initial and instantaneous temperature out of "tongue"

in the pressure Teasel inlet zone, Q - water flow rate from the emergency pumps or water tanks;

• for some regimes the ease of instantaná ms and ideal mixing of water from emergency pumps with coolant in inlet

«one of vessel was also calculated. For this case, the tempe­

rature of vessel in the area of welding joint is constant around

all ressel perimeter and can be expressed as

2L . ~9-<* . T) (4) 2t vT ' x

where T_ * volume of the inlet zone of pressure vessel*

The first case results in maximum possible temperature gra­

dient along vessel height, the seoomd one in maximum temperature

gradient around vessel perimeter, while the third one - in

gradient along vessel height. Typical distributions of tempera­

ture» in vessel perimeter is shown in fig. 3. whereas fig. 4

presents their simplified calculating scheme*

- б -Thermophysical properties of both the base and cladding

Material* «ere approximated by linear polynomials of the form as follows;

A « a • bT (5)

C T « с • dT, (6)

the coefficient of heat transfer being chosen in dependence on temperature and water flow between Mr and 10* wsf 2ť* s . Outer pressure Teasel 3urface is considered as adiabatie.

The input for all calculations, i.e. time dependencies of coolant pressure and temperature, пате been receired from thermophysical calculations of the whole primary circuit or the whole plant.

4. ?Tftg?g f7IR№? ffWP ^TOERCY COOLIBg Calculations of stress fields in the cylindrical part of

the pressure vessel at the presence of cold "tongues" are carried out using formulas for "Jump" changes in temperature distribution, in analytical and/or integral forme*

According to fig. 2, two different pictures of cold "tongues" can be obtained! the first case (fig* 2a) is repre­sented by the maximum temperature gradient along vessel height, the second one (fig. 2b) by maximum temperature gradient across pressure ressel perimeter. Thus, for the first case (fig. 2a), a contribution of axial temperature gradient (along vaaael height) must also be taken into account, because the mean temperature of vessel wall along vessel height is also chan­ged i in the upper part of cylinder between the nozzle and the Intersection of two "tongues" it assumes a linear form, then it is practically constant (or slightly changed but with another slope)| therefore these additional stresses <Sj and 4r must also be added to the summary stresses given in equations (7) to (10), even if their magnitudes are not high (epprox. 10 HPa).

- 7 -Resulting atreaaea in the point "i" of the veaael «all

can be expraesed aa: - "A" - cold section ("tongue")»

«U»<o - «? • <& •'/* «)

- *B" - bot «action:

whore tha indazea meant s - axial (maridlal) direction P - tangential (circumferential) direction p - membrane etreaa from pressure p

0,i - temperature streaa from radial gradient through mail thickness in point "i"

о 2 a - temperature etreaa from circumferential distribution of temperature* in cold auction (A) or hot section (B) temperature stress from axial gradient of •aaaal mall mean temperature,

to be on the more conservative aide, substitution of terms into eqs* (7) to (10) are made in such a amy that for atreaaas, resulting from temperature gradient along vesael height, results from the first caae (figt 2a) era used, and for atreaaes resulting from circumferential atreas distribution* reeulte from the aaeond ease (fig* 2b) are used. In addition* stresses resul­ting from temperature gradient through Tassel thickness (radial gradient) and from preaaure are included.

Typical reeulte, received for the case of rupture of piping with ID equal to 20 mm and temperature of cooling water equal to •55 °C are shown in fig, 5 far different tine intervals from the beginning of the emergency oooling* Fig* 5 presents the «tress and temperature fields through vessel wall thickness in the area of weld joint.

- 8 -Computations of temperature and stress fields in the

inlet nozzles of the primary circuit (500 or 850 mm) and of emergency cooling (250 or 295 mm) are carried out using finite element method as «ell as boundary integral equations method»

5. tFVlffl? 9? BRITTLE FRACTURE CCMSITIONS Analysing brittle fracture conditions of IfSR-type reactor

pressure vessels is carried out in accordance with the standard of the International Economic Corporation "IHTEBATOMBIKHBO*. Within the activities of this corporation the full «cope of standards for all steps of WSBR type reactors, i.e. from design to operation* are in progress, most of them finished and approved*

This analysis is based on the linear elastic fracture meehm» nice approach and the main principles can be presented ass

• only i n i t i a t i o n approach is used* i.e. the material is characterised by static fracture toughness* K-Q| during all operation regimes no crack initiation is permitted*

- no austenitic cladding is taken into account in calculations of brittle fracture conditions* but they are taken into conside­ration in calculating the stress and temperature fields.

• calculation is carried out for a "calculated defect" * a surface semielliptical defect with the ratio- of sen!axes equal to 2:3.

- the material is characterized by critical temperature of brittleness (transition critioal temperature), Tfc| It serves for determining the allowable fracture toughness values, LlCli v a l C B involves *l*o safety factors.

• the calculation is carried out for all normal (i * 1) and the upset regimes end hydrostatic tests (i * 2), and for all emergency conditions (i • 3).

Critical temperature of brlttleness, ?к, during operation is determined as the sua ofi

Tk " *ko * 4 T* * *TT • &Tf (11)

- 9 -where T f o « initial critical teaperature at the start of

•eseel operation Jfg - critical temperature incraaae caused by

cyclic damage,

JTff * 20.A (12) «bare A - total coefficient of fatigue damage

4ff - critical temperature increase cauaed by tempera-tare ageing I for component* from steels of 15Kh2MFA, 18ВЪ2КА, 15sb2mVA, 15Di2n*FAA gradea and their «aid joint* at operating temperature (up to 330 °c) it is put equal to «его

dtp - critioal temperature increase, cauaed by neutron irradiation (-irradiation amUrittlement) which is given aa

« » - Ay • (F x 10" 2 2 ) 1 / 3 (13) «hare kj - coefficient of irradiation embrittlement

F - fast neutron fluence «1th E *0.5 HeY in n.m , corrected to attenuation by reaael mall material. For typical steel of IWBR reactor pressure vassal, i.e. 15Kh2KFA grade» this coefficient A» is put equal to:

.3 for base material A, » ' (14) ' 13 for «eld metal.

The allowable raluee of fracture toughness hare been chosen as a lover boundary for 999» probability fron large sets of tests carried out in different countries of steels of аооте mentioned grades and their joints (i.e. for materials with guae reateed yield strength not larger than 600 HPa) as followst • for normal operational regimes

řidl ш 13 • Ю-*)Ж»(Ь.<й<Мк)] *•* (T-Ťk) С 80 °C a (X5) • 100 for (T-Tk) г 80 °C

- 10 -

- for upaet regimes and hydrostatic test*

[KI0J2 * 1 7 + 2*-exp[°'°lb^-Tk)j for (T-Tk) < 80 °C

120 for ÍT-Tj г 80 °C (16)

(17)

- for emergency regimes

(^IcL * 2 б * Зб.ехр[р.02(Т-Тк)] for (Т-'Г̂ ) < 80 °C » 200 for (T-Tk) ̂ 80 °C

Relatione (15) - (17) include also safety factore with respect to a lower boundary curre which is identical with

• for normal conditions

Bg - 2 and á \ « +30 °C (18)

- for hydrostatic teste

Oj » 1.5 and ЛТк - +30 °C (IS)

- for emergency conditions

Bj • 1 and л?к » 0 (20)

for surface semielliptical cracks is the main parame­ter, the stres* intensity factor (Kj), determined using the following formula

qr . 1/2 h - *<ÍA + ̂ •"b)-<-jr-> (21)

where ť « 1 • 4.6Í-5--) (22) 2c

M - 1 + 0.12(1 - -2-) (23) ш с

M^ « 1 - 0,64(-«~) (24)

h being that part of vessel wall thickness for which C^O.

In addition - 11 -

В

<4i--|-/^dB> <25)

0 В denoting Teasel wall thickness, aad index i denoting axial or circumferential stress, "thet <k - «k - < * w>

Bqs. (21) - (24) are valid, with a good accuracy, for cracks with a é 0.25 В and а/с 2 2/3.

Coefficient fr represents the influence of stress gradient on Kj value, and is equal tot • cylindrical part:

7 - 1 (27> • nozzles (crack in area of minimum stress)i

1/2

%• fl + 10*exp(-0.86-|-).5-~i JforB/R^O.8; (28)

7« jl + 4-|. . ™ - i | for B/R ?0.8 (29) For WWER-type reactor pressure vessel configuration

and only for emergency cooling conditions the following appro­ximative .formula can be used:

ОДО g- + 0.50)'

Af , SlSB / • ! + Д.5 (30)

Resistance against brittle fracture is ensured if the following in-equalities ere satisfied}

KjU ш 0.25 В) -С [к 1 с] х (31) Kj(a • 0.25 В) < [К 1 0] 2 (32) Kj(a é 0.25 В) £ [KjC]3 (33)

Similarly to ASHE CODE, Case III and XI, all potential regimes must be taken into account, and the conditions of safe operational)-(33), must be fulfilled.

- 12 -The most severe emergency cooling conditions are the

•compensable" ones, because besides quick cooling of pressure veesel wall the coolant pressure (after some short period) returns to its normal (operational) value, or in certain casea even to somewhat increased values caused by the operation of emergency high-pressure pumps.

Thus, one of the most important regimes is a failure of a piping with ID • 20 mm, for which case some results from computations are shown in figs. 6 and 7.

Pig. 6 presents several situation** for different time periods up to 3600 s from the 3tart of this emergency regime. Computed values of Kj for different crack depths are compared with allowable values of fracture toughness. In fig. 7 there are shown summary diagrams: fig, 7a shows the time dependencies of K, values for chosen crack depth (between 5 and 35 • a 0.25 B) while fig. 7b compares calculated K, values with allowable frac­ture toughness values.

Experimental results .-«how that the standard reference temperatures for both approaches (i.e. according to IAE and ASME) are practically identical, i.e.

М Ю Т ^ T k o <34>

so that it is possible to compare also the allowable fracture toughness values, i.e. [ K I C ] 3 with K * ^ and K J R ^ » а я U

is shown in fig. 6 and 7b. It can be ooncluded that there is only a small difference between both static values; for higher reference temperatures, TR = T - Tk, with the value of [K^QJ, being a slightly more conservative than the K*„ ' curve. Similarly, as it is seen in figs. 4 and 5» the values of K», after come local increase after about 500 e, are monotonioally decreasing practically to their initial values, but at sub­stantially lower temperatures. For calculated case, i.e. for the '.7WER-440 MW pressure vessel, which is characterized by steel 15Kh2MPA with Tko » +20 °C (weld metal)

Ay «13 A i O P i 1.6xl024 n.ra"2

- 1 3 -it is clearly seen that resistance against brittle failure is fully ensured for all allowable fracture toughness values.

Moreover, a comparison of both approaches can be madet only initiation approach which characterises the USA standard, is more strict than that of the ASHE, beoauses

- no Initiation is allowed (i.e. the conditions for crack-arrest are not necessary to assess)|

• allowable fracture toughness values K ™ * are for larger part of temperature region lower (i.e. more conservative) than Kj^1?

A similar analysis can be carried out for nozsle ring of these reactor pressure vessels. Because of substantially higher resistance of the material of this part against brittle failure (the base material has ?ko< -10°C for WWBR-440 ЮГ, and 4z -25 °C for WWER-1000 ЩГ), and taking into account that the only degra­ding factor is cyclic damage with coefficient A - 0.1, i.e. dry * +2°C, for the reference temperature it may be written: TR • T - *k £ 65 *C (for WWBR-WO MW) and T R £ 480 °C (for WWER-1000 lif). In addition, because the minimum water tempera­ture during emergency cooling is +55 °C, the allowable fracture toughness values are close to upper shelf, i.e. 200 MPa.m ' • Consequently, there can occur no conditions for brittle frac­ture in the nozzle region even in the most severe' emergency cooling regimes.

14 -6. C03CLPSI03S

The paper shows the principal steps during computational assessment of HWER reactor pressure yeseel resistance against brittle failure during transient regimes during thermal shock at emergency cooling*

On the example of one of the most severe types of failure (piping with 3D«20 mm) it has been shown that typical 1"П21-440 reactor pressure Teasel is always safe fror. the point of view of a potential brittle failure.

Even tho4|hthe computational methods are of high level of confidencef there are some more questions which must be solved in the near future ала which are included in the theoretical and experimental programmes of the ŠKODA Concern:

- experimental validation of chosen approach to reactor

pressure vessel assessment during thermal shock; this programme

represents tests of plates and ribgs with simulated tempera­

ture and stress fields similar to those of thermal shock;

- studying the degree of beneficial influence of auatenitic

cladding on the resistance against crack initiation and propaga­

tion during thermal shock transient conditions;

- studying the effect of warm pre-stressing on subsequent

behaviour of the material during normal operation as well as

during thermal shock conditions; ч

- study of the application of elaeto-plaetio fracture mechanics on material behaviour under thermal shock conditions.

- 1 5 -

1 - pressurised water tank 2 - steam generator 3 - oaln circulating pump 4 - nitrogen input piping 5 " nitrogen output piping 6 - piping for filling ana discharge of pressurized water tank 7.13.15 - high-pressure рдар of emergency cooling 8.12.16 - low-pressure pump of emergency cooling 9 - tanks with emergency supply of oorio «old 10 - inserted cooling circuit 11 - piping of cooling (technical) water 14 * beat-exchangers for heat output from ooolant

SCHEKB OP ЕМВШНС* С 0 0 1 Ш SYSTEM OP REACTOR ACTIVE ZOHE IB WWER-1000 1ЛГ

ЯЯЯ-т

9\ I

CALCULATING CAS£S OP «COLO TONGUES'» DURING EMERGENCY COOLING IN WWBR-TYPE REACTORS

a - overlapping "tongues" Ъ - "tongue»" with constant width

- 17 -

Я?* <9

TYPICAL DI3TRIBUTI0H 07 TEMPERATURES АХОВО PRBSSUKE VESSEL PERIMETER

- 1 8 -

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