- 9.1 -

Aspects of Brittle Failure Assessment for RPV

H. Zecha, T. Hermann, W. Hienstorfer

TÜV SÜD Energietechnik GmbH Baden-Württemberg, 70794 Filderstadt

X. Schuler

Materialprüfungsanstalt Universität Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart

35th MPA-Seminar

October 9, 2009 in Stuttgart

- 9.2 -

Abstract

This paper describes the process of pressurized thermal shock analysis (PTS) and

brittle failure assessment for the reactor pressure vessel (RPV) of the nuclear power

plants NECKAR I/II. The thermo-hydraulic part of the assessment provides the

boundary conditions for the fracture mechanics analysis. In addition to the one di-

mensional thermo-hydraulic simulations CFD, analyses were carried out for selected

transients. An extensive evaluation of material properties is necessary to provide the

input data for a reliable fracture mechanics assessment. For the core weld and the

flange weld it has shown that brittle crack initiation can be precluded for all consid-

ered load cases. For the cold and hot leg nozzle detailed linear-elastic and elastic-

plastic Finite Element Analyses (FEA) are performed to verify the integrity of the

RPV.

1 Introduction

A nuclear power plant’s reactor pressure vessel (RPV) is one of the safety related

components of the pressure retaining boundary for the reactor coolant. Criterion 4.1

of the german safety criteria for nuclear power plants [1] principally requires that

dangerous leaks, fast growing cracks and brittle fractures must be precluded as of

the present state of science and technology.

Evaluating the plants NECKAR I and II, TÜV SÜD Energietechnik GmbH verified the

resistance to brittle fracture of the RPV via independent analysis.

The verification analysis was based on the guidelines defined in the safety standards

of the Nuclear Safety Standards Commission (KTA).

Subject of the discrete analyses was the determination of the influence of an as-

sumed loss-of-coolant accident (LOCA) on postulated defects in selected regions of

the RPV.

The considered regions were selected on the basis of KTA 3201.2 (influence of irra-

diation) [2] as well as determination of the high-stress regions due to leak position

and hot leg or cold leg Emergency Core Cooling (ECC) injection.

The following regions were selected:

Core region of the RPV

Intersection between cylindrical section and flange section (flange weld)

Cold leg nozzle

Hot leg nozzle

- 9.3 -

When the plants were built, the safety verification was based on an enveloped pres-

surized thermo shock (PTS) in the core region. Technical expertise obtained from

experiments in the Upper Plenum Test Facility (UPTF) in Mannheim (1985-1995)

helped to determine the detailed thermo-hydraulic parameters needed for brittle frac-

ture analysis. Nowadays the cold water plumes developing downwards and the water

stripes within the vapor phase are additionally taken into account.

Verification of resistance to brittle

fracture is performed using the

fracture mechanics concept de-

scribed in KTA 3201.2 [2].

For evaluation according to the

fracture mechanics concept

(Figure 1–2), we need the stress

intensity factor KI (t, T) which de-

pends on internal pressure, tem-

perature gradient etc.. Unstable

crack extension can be precluded

if the curve of KI (t, T)-values is

below the curve of static fracture

toughness KIc (T).

Crack initiation can also be pre-

cluded if, even though the load

path traverses the KIC (T)-curve,

stress intensity decreases strictly

monotonic after reaching the load path maximum and the crack tip has been exposed

to temperature within the same load case (warm pre-stress effect) (Figure 1–3).

Load paths were determined based on postulated defects, with size and shape de-

fined according to KTA 3201.2. Half-elliptic surface flaws with a depth of a=16 mm

and a=26 mm respectively and with a depth-length-ratio of a/2c=1/6 in the base ma-

terial were considered. The direction of the first principal stress in the vicinity of the

crack location defines the defect orientation (circumferential or axial). The postulated

defects in the nozzle regions are shown in Figure 1–4.

The material properties required for stress analyses and fracture mechanics assess-

ments were provided by the MPA Universität Stuttgart (MPA).

Due to the multitude of transients to be analyzed, the load path (stress intensity fac-

tor KI (t)) needed for evaluation of brittle fracture safety was determined using ana-

hot leg nozzle cold leg

nozzle knee

flange weld

core region

Figure 1–1: Selected regions

- 9.4 -

lytic calculation methods. For this purpose, the software BESIT [3] of the Fraunhofer

Institute for Mechanics of Materials in Freiburg was employed.

Figure 1–2: Fracture mechanics concept

Figure 1–3: Warm pre-stress effect

a.) b.)

Figure 1–4: Postulated defects (a.) cold leg nozzle knee, b.) hot leg nozzle)

- 9.5 -

For the leading transients (maximum stress intensity factor and lowest allowable ref-

erence temperature RTNDT, respectively), Finite Element Analyses were performed to

determine the J-integral considering an elasto-plastic material model.

2 Thermohydraulics

2.1 Method for determination of thermal loads

The assessment of the integrity of the Reactor Pressure Vessel (RPV) requires the

analysis of many different transients. Loss-of-Coolant Accidents (LOCA) have to be

investigated as well as nonLOCAs. The size of leak openings due to LOCAs can vary

within a wide range (from 5 cm2 up to 2F). Depending on the leak/break location (hot

leg or cold leg) and its size, in the analysis the high-pressure injection can be as-

sumed in the cold leg or hot leg. Furthermore, the assumption of a single failure as

well as a simultaneously occurring repair leads to different numbers of high-pressure

injecting pumps. In order to account for all these possible configurations engineering

models are used to simulate physical effects in the downcomer of the RPV and mix-

ing phenomena in the cold leg due to Emergency Core Cooling System (ECCS) in-

jection. 1D system code predictions are used as boundary conditions for the regional

mixing models. The PTS (Pressurized Thermal Shock) evaluation for NECKAR I / II

was done with the system code ATHLET 2.1 A [4] and the regional mixing model

‘GRSMIX’ [5]. GRSMIX can be described as a set of correlations and equations de-

duced from the UPTF-TRAM experiments. This model yields results with high accu-

racy for NPPs with similar geometrical conditions as the UPTF test facility. The re-

quired similarity is given for NECKAR I and NECKAR II.

The following physical quantities are determined by the mixing model GRSMIX:

Temperature of the cold-leg emergency coolant

Temperature in the center of the cold water plume and/or in the stripe

Local heat transfer coefficients determining the heat transfer between the cold

water plume/stripe and the wall of the RPV

The following boundary conditions for GRSMIX are determined from thermal-

hydraulic computer code ATHLET:

Temperature of the hot fluid layer in the cold-leg nozzle

Pressure history

Global temperature in RPV downcomer outside the plume/stripe

A similar procedure is developed by AREVA NP. AREVA NP uses its regional mixing

code ‘KWUMIX’ together with the system code S-RELAP5. Thus the assessment of

PTS analysis for NECKAR I / II is based on different computer codes. This ensures

- 9.6 -

and highlights the independence of the chosen approach as a special feature of the

assessment of PTS for the NPPs NECKAR I and NECKAR II.

2.2 Table of Transients for Neckar I / II

In NECKAR II the ECC water is injected into the hot leg via a scoop flow device

(‘Hutze’) that directs the injected water towards the Upper Plenum. Depending on

pressure differences between the hot leg and the cold leg a high pressure ECC injec-

tion into a cold leg is possible. Assuming leaks smaller than 40 – 50 cm2 and intact

three-way valves, a cold water injection can only take place in the hot leg. Neverthe-

less cold-leg high pressure injection due to small leaks (<= 40 – 50 cm2) in the main

coolant pipe is also analyzed, Table 2-1.

The design of NECKAR I prefers cold leg injection, Table 2-2. For NECKAR II small

leaks in the cold leg of the main coolant pipe in connection with a hot-leg injection are

considered, Table 2-1. During these transients a thermal stratification will establish

with saturated liquid above sub-cooled ECC water. A superposition of high pressure

leads to significant thermo-mechanical loads and corresponding structure-

mechanical impacts.

2.3 Engineering model simulations

2.3.1 Model description and assumptions

The mixing model GRSMIX is capable of describing the most significant physical ef-

fects occurring in the mixing zone of the coolant injection point and the RPV down-

comer (DC) during a LOCA [5]:

Mixing of injected cold water with surrounding hot water near injection point

Condensation of steam at the cold water injection jet when the water level in

the RPV DC has fallen below the ECCS injection pipe

Mass and heat transfer exchange between the plume and the surrounding

warm water in the DC by admixture

Condensation of steam at the cold water stripe in the DC when the water level

in the RPV DC has fallen below the cold-leg nozzle.

Especially for small leaks the thermal loads strongly depend on the assumptions

concerning the circulation of water in the main coolant pipes:

The mixing calculations in the cold leg are carried out under the assumption

that the injected cold water does not mix with the circulating loop mass flow.

The global water temperature in RPV downcomer is taken from an ATHLET

system analysis. Thus the warm water temperature depends on the calculated

loop mass flow (natural circulation or stagnation).

- 9.7 -

Table 2-1: Table of transients, NECKAR II

5 10 20 25 40 100 200 300 5 10 25

4

2

4

2

legend:: simulated transients (TÜV)

hot leghigh pressure

injection

leak size (cold

leg) / cm2

PTS GKN II

leak size (hot leg) / cm2 HP

pumpsECCS Injection

location

cold leghigh pressure

injection

Table 2-2: Table of transients, NECKAR I

20 50 100 200 20 50 100 200

1

3

4

cold leg high pressure injection

PTS GKN I

ECCS Injectionlocation

HPpumps

leak size (hot leg) / cm² leak size (cold leg) / cm²

To account for thermal loads in the cold leg and hot leg nozzle the program was de-

veloped further within the framework of actual assessment of NPP’s NECKAR I/II:

To include the influence of a stratified flow in the cold leg on the heat transfer

between the pipe wall and the cold water, an appropriate Nußelt-correlation

was implemented [6]

The theory of critical depth was used to implement an expression for the cold

water depth in the cold and hot leg [7].

2.3.2 Simulation results

In the following section two different LOCAs in NECKAR I and NECKAR II are dis-

cussed with respect to PTS in DC, the cold leg nozzle and the hot leg nozzle.

The first LOCA describes the thermo-hydraulic process of a 100 cm2 leak in a hot leg

of the NPP NECKAR I. One high pressure injection pump, injecting into the cold leg,

and one low pressure pump are available. The loss of coolant leads to a fast pres-

- 9.8 -

sure and temperature decrease, Figure 2–1. The temperature drops by approx.

250°C within 1500 seconds in the downcomer. 500 seconds after leak opening, the

collapsed level in the downcomer falls below the flange weld. As a consequence, the

developing cold water stripe leads to a higher heat transfer coefficient between 500

and 1000 seconds, Figure 2–1. The heat transfer coefficient (HTC) for the cold leg

nozzle is of the same order of magnitude as the HTC’s in the DC.

Figure 2–1: NECKAR I, LOCA 100 cm2, cold leg high pressure injection

The second LOCA describes the thermo-hydraulic process of a 5 cm2 leak in a cold

leg of the NPP NECKAR II. Two high pressure pumps, injecting into the hot legs, and

4 low pressure pumps are available. As described above for NECKAR I LOCA, the

pressure decreases quickly after leak opening and stabilizes between 90 and 100

bar, Figure 2–2. In the hot leg nozzle a thermal stratified flow is assumed, i.e. the

cold injected water and the counter flowing hot water do not mix. This leads to a huge

difference in temperature between the cold and the hot fluid layer. Together with the

high inner pressure, strong thermal loads in the hot leg nozzle are possible. Figure

2–2 shows that the cold water layer only covers the bottom of the main coolant pipe.

The HTC for the cold water layer ranges between ~ 5000 and 15000 W/(m2 K).

Pressure Temperature in downcomer

Heat transfer in downcomer Heat transfer in cold leg nozzle

- 9.9 -

Figure 2–2: NECKAR II, LOCA 5 cm2, hot leg high pressure injection

2.4 CFD simulations

In addition to the one dimensional simulations, CFD analysis were carried out for se-

lected transients. These CFD simulations serve as verification for the local 1D mixing

calculations. Furthermore, with these three dimensional simulations local physical

quantities were determined that cannot be obtained by other methods.

2.4.1 CFD model

For CFD simulations, the software ANSYS CFX-11 was employed [8]. For verification

as well as simulation of LOCAs the SST turbulence model is used. The reactor core

is modeled as a porous body. Due to existing temperature differences in the fluid, the

CFD model also accounts for buoyancy effects. The simulation is transient and is

based on one phase flow.

2.4.2 Validation

The validation of the CFD model was realized by simulating an experiment that was

carried out at the Upper Plenum Test Facility. Figure 2–3 shows the geometry that

was utilized for the simulation of the UPTF-TRAM experiment C1, RUN3b1. During

the experiment cold water with a temperature of 32 – 36 °C is injected into the main

Pressure Temperature in hot leg nozzle

Cold water depth in hot leg nozzle Heat transfer in hot leg nozzle

- 9.10 -

coolant pipe with hot water of 190 °C. The injection rate is approx. 70 kg/s. During

the validation process selected experimental temperature profiles in the DC and main

coolant pipe are compared with corresponding simulation results. Figure 2–3 displays

the location of the temperature gauge points.

Figure 2–3: UPTF geometry (left); UPTF measurement points (right)

In the measurement plane ID 21 (flange weld) the fluid flow shows a radial tempera-

ture gradient, Figure 2-4 (left hand side). The lowest temperature is observed in the

middle of the RPV DC (gauge 1A21TF075). In the CFD simulation the cold water

plume comes into contact with the wall of the RPV, i.e. the temperature is lower than

in the experiment (1A21TF073). Close to the wall of the core vessel the simulated

temperature is higher than in the experiment (1A21TF077). Thus the comparison in-

dicates that the temperature profile in plane ID 21 is somewhat overestimated by the

CFD simulation. In the measurement plane ID 14 (core weld), experimental data and

simulation results are quite similar, Figure 2-4 (right hand side).

Figure 2-5 shows the quantitative comparison of measured and simulated tempera-

tures in the main coolant pipe. Z denotes the distance of the measurement point from

the bottom of the main coolant pipe. The direct comparison reveals a good match

concerning the cold water temperature (JEC02CT034/6) and the hot water tempera-

ture (JEC02CT031/2). The observed differences concerning measurement point

JEC02CT033 can be explained by the location of JEC02CT033, being situated in the

transition layer between the cold and the hot water. This transition layer is character-

ized by a strong thermal gradient. Hence differences between measured data and

simulation results are likely.

- 9.11 -

Figure 2–4: UPTF DC. Experimental data compared to simulation data (Left

hand side: flange weld; Right hand side: core weld)

- 9.12 -

Figure 2–5: UPTF cold leg nozzle - Experimental data compared to simulation

data

2.4.3 CFD simulation results

Due to uncertainties regarding the azimuthal expansion of the cold water plumes in

the RPV downcomer a LOCA simulation with a leak size of 100 cm2 was carried out.

Due to symmetry, only a section of the RPV was modeled, Figure 2-6. The wall of the

RPV is modeled to account for heat transfer between the fluid and the wall. The

boundary conditions are taken from an ATHLET system analysis.

To analyze the flow in the DC the temperature profile was evaluated in specified

planes. For example, Figure 2-7 displays the temperature distribution for a specified

DC level and time. Each point represents the temperature in a control volume. The

so called “plume width” is defined by T2/T1 = 1/e, where e denotes the Euler number.

Figure 2-7 illustrates the application of this definition.

- 9.13 -

a.) b.)

Figure 2–6: a.) geometry; b.) mesh

Figure 2–7: Plume width definition

A systematic data evaluation yields time dependent values for the plume width, Fig-

ure 2-8. Based on these results a critical survey and revision of the existing formula

for the plume width was possible.

Another aspect concerns the heat transfer coefficient at the edge of the cold leg noz-

zle. A section cut through the cold leg nozzle and the upper part of the downcomer

reveals an increase of flow velocity at the nozzle edge, exactly in the location of the

postulated crack, Figure 2-9.

Central angle / °

Tem

pera

ture

/ °C

- 9.14 -

Figure 2–8: Simulated plume width

A higher flow velocity gives rise to a better heat transfer between the fluid and the

wall, i.e. a higher heat transfer coefficient. The CFD results lead to a relationship be-

tween the time dependent HTC at the Nozzle Edge (αNE) and the reactor coolant line.

In terms of a conservative assessment the maximum between two different heat

transfer coefficients was applied at the edge of the cold leg nozzle: αmaxNE :=

max(αNE, αFL). In this case αFL denotes the HTC at the flange weld.

Figure 2–9: Velocity field (scalar) at the cold leg nozzle

- 9.15 -

3 Material characteristics

3.1 Material properties for finite-element analyses

3.1.1 Linear elastic material characteristics

To perform transient heat transfer and stress analyses considering linear-elastic ma-

terial behavior the following material properties are required:

- Young’s modulus (E)

- Poisson ratio ()

- Coefficient of thermal expansion ()

- Thermal conductivity ()

- Specific heat (c)

- Density ()

These material properties are required as a function of temperature (from room tem-

perature up to 350 °C) for the ferritic RPV materials (base and weld material) at the

core as well as flange and nozzle region and for the austenitic cladding material.

Based on the characteristic values of physical properties given in KTA Standard

3201.1 [9] and the evaluation of research projects of MPA [10] - [17] as well as data

available from the literature [18] and the MPA material data base, the following prop-

erties are recommended for the analyses to be performed.

- Young’s modulus E

The temperature dependent Young’s modulus can be described by the following eq-

uations:

- Ferritic RPV materials (22NiMoCr3-7, 20MnMoNi5-5 and corresponding weld materials)

E = -0.0601 T + 208.66 T in [°C], E in [GPa] (3.1)

- Heat affected zone (HAZ) below the cladding

E = -0.0797 T + 233.51 T in [°C], E in [GPa] (3.2)

- Cladding

E = -0.1022 T + 172.17 T in [°C], E in [GPa] (3.3)

These equations and the related data values (as measured) are shown in Figure 3–1

in comparison with the characteristic values according to KTA 3201.1. The statistical

evaluation of the values at room temperature is depicted in Table 3-1 for the low alloy

steels 22NiMoCr3-7 and 20MnMoNi5-5 and for the cladding material. The Young’s

modulus of the cladding is significantly lower as the values acc. to KTA 3201.1 for

austenitic material 1.4550 (X6CrNiNb18-8).

- 9.16 -

0

50

100

150

200

250

-200 -100 0 100 200 300 400 500 600

Yo

un

g's

mo

du

lus

E /

GP

a

Temperature / °C

HAZ1)

Base material

Cladding

20MnMoNi5‐5 acc. to KTA

X6CrNiNb18‐8 (1.4550) acc. to KTA

Note: 1) HAZ below 

submerged 2 layer band cladding

Regression lines:

CladdingE = ‐0.1022 T + 172.17

HAZ E = ‐0.0797x + 233.51

Base Material (22NiMoCr3‐7 and 20MnMoNi5‐5)E = ‐0.0553x + 207.75

Note: T in °C, E in GPa

Figure 3–1: Young’s modulus as function of temperature

Table 3-1: Young’s modulus at room temperature

Mean Value Standard deviation 1s Material GPa GPa

Ferritic Material 207 9,9

Cladding 169 10,9

- Poisson ratio :

Within the temperature range below 450 °C a constant value of = 0.3 is normally

used for steel materials. A more detailed description of the temperature dependency

is given by Richter [18] and is used for the computations performed:

- Low alloy steel:

010T10042830 5 ... T in [°C] (3.4)

- Austenitic steel:

0080T10062760 5 ... T in [°C] (3.5)

- Coefficient of thermal expansion :

Within the research project [10] thermal expansion coefficients of the RPV base ma-

terial and the cladding have been determined in detail. These values coincide with

the characteristic values acc. to KTA 3201.1, Figure 3–2.

- 9.17 -

1,00

1,10

1,20

1,30

1,40

1,50

1,60

1,70

1,80

1,90

2,00

0 100 200 300 400 500 600

line

ar

the

rma

l ex

pa

ns

ion

co

eff

icie

nt

/ 1/K

Temperature / °C

Cladding

Base material (22NiMoCr3-7)

1.4550 acc. to KTA

20MnMoNi5-5 acc. to KTA

= ‐3.273768E‐07 T2 + 6.042531E‐04 T + 1.597386

= ‐2.676429E‐07 T2 + 6.309342E‐04 T + 1.159554

Figure 3–2: Coefficient of thermal expansion

To describe the thermal expansion, the linear thermal expansion coefficient acc. to

the following equations is used:

- Cladding:

= 10-5(-3.273768E-07 T2 + 6.042531E-04 T + 1.597386) T in [°C], in [1/K] (3.6)

- Ferritic materials:

= 10-5(-2.676429E-07 T2 + 6.309342E-04 T + 1.159554) T in [°C], in [1/K] (3.7)

- Thermal conductivity :

For the thermal conductivity the values acc. to KTA 3201.1 are used, Figure 3–3.

- Specific heat c:

For the specific heat the mean data values as described in [18] are used

- Ferritic materials:

3623 T10642T10142T9310422c ... T in [°C], c in [J/kgK] (3.8)

- Cladding:

3724 T1011T10223T3880454c ... T in [°C], c in [J/kgK] (3.9)

These values are comparable with the values of KTA 3201.1, Figure 3–4.

- 9.18 -

0

5

10

15

20

25

30

35

40

45

50

0 100 200 300 400 500 600

the

rma

l co

nd

uc

tivi

ty

/ W/m

K

Temperature / °C

20MnMoNi5-5 acc. to KTA

1.4550 acc. to KTA

Figure 3–3: Thermal conductivity acc. to KTA

400

450

500

550

600

650

0 100 200 300 400 500 600

Sp

ec

ific

he

at c

/ J

/kg

K

Temperature / °C

1.4550 acc. to KTA

20MnMoNi5-5 acc. to KTA

Low alloy steel

Austenitic Cr‐Ni steel

Figure 3–4: Specific heat acc. to KTA in comparison with literature data [18].

- Density :

For the density the following equations acc. to [18] are used

- Ferritic materials:

07.84922421T 63-0.0003497 T in [°C], in [10³kg/m³] (3.10) - Cladding (strip weld cladding):

47.91044711T 03-0.0004493 T in [°C], in [10³kg/m³] (3.11) - Cladding (manual cladding):

57.97746420T 10-0.0004531 T in [°C], in [10³kg/m³] (3.12)

Because of the differences in the chemical composition between strip weld cladding

and manual cladding the density is slightly different as shown in Figure 3–5.

- 9.19 -

7,5

7,6

7,7

7,8

7,9

8

8,1

0 100 200 300 400 500 600

De

ns

ity

/ 1

03

kg

/m3

Temperature / °C

1.4550 acc. to KTA at RT

manual cladding

strip weld cladding

= -0,000453110 T + 7,977464205

= -0,000449303 T + 7,910447114

Figure 3–5: Density of the cladding as a function of temperature acc. to [18]

in comparison with KTA 3201.1 [9] at room temperature

3.1.2 Elastic-plastic material characteristics

To perform finite-element analyses considering elastic-plastic material behavior, true

stress – true strain curves are required in addition to the linear-elastic material char-

acteristics as described in chapter 3.1.1.

For the different regions of the RPV under investigation only the tensile properties

yield strength (Rp0,2) and ultimate strength (Rm) are available - both for irradiated

(EOL fluence) and non-irradiated (BOL) material. On the basis of these values tem-

perature dependent mean values as well as upper and lower limits were estimated.

As an example Figure 3–6 shows the results for NECKAR II RPV.

Using these values and the slope of representative stress-strain curves (available

from the MPA data base for RPV materials) stress-strain curves were estimated for

the RPV materials under investigation. As an example Figure 3-7 shows some re-

sults for the irradiated core weld material of NECKAR II RPV.

The J-integral calculation is influenced by the strain hardening behavior of the elastic-

plastic material. Depending on the type of the applied load more or less conservative

results are derived, Figure 3–8. Under dominant thermal transient loading conditions

higher stress-strain curves cause higher J-integral values. Under such loading condi-

tions linear-elastic material behavior causes the most conservative J-integral values.

- 9.20 -

0

100

200

300

400

500

600

700

800

Re

/ M

Pa

mean values

lower limits

upper limits

23°C

80°C

150

°C

350

°C

GKN II

Ring I, II, non-irradiated

Weld material Core weld, non-irradiated

Flange Ring, non-irradiated

Ring I, II, irradiated

Weld material Core weld, irradiated

0

100

200

300

400

500

600

700

800

Rm

/ M

Pa

mean values

lower limits

upper limits

23°C

80°C

150

°C

350

°C

GKN II

Ring I, II, non-irradiated

Weld material Core weld, non-irradiated

Flange Ring, non-irradiated

Ring I, II, irradiated

Weld material Core weld, irradiated

Figure 3–6: Estimated values for the yield and ultimate strength of NECKAR II

RPV

- 9.21 -

0

100

200

300

400

500

600

700

800

900

0 0,05 0,1 0,15 0,2 0,25

tru

e st

ress

/

MP

a

plastic strain pl / -

GKN2, SG, irrad., 23°C

GKN2, SG, irrad., 80°C

GKN2, SG, irrad., 150°C

GKN2, SG, irrad., 350°C

based on mean data

0

100

200

300

400

500

600

700

800

900

0 0,05 0,1 0,15 0,2 0,25

tru

e st

ress

/

MP

a

plastic strain pl / -

GKN2, SG, irrad., 23°C

GKN2, SG, irrad., 80°C

GKN2, SG, irrad., 150°C

GKN2, SG, irrad., 350°C

based on upper limits

0

100

200

300

400

500

600

700

800

900

0 0,05 0,1 0,15 0,2 0,25

tru

e st

ress

/ M

Pa

plastic strain pl / -

GKN2, SG, irrad., 23°C

GKN2, SG, irrad., 80°C

GKN2, SG, irrad., 150°C

GKN2, SG, irrad., 350°C

based on lower limits

Figure 3–7: Examples of true stress-true plastic strain curves for the irradi-

ated weld material (core weld) of NECKAR II RPV

- 9.22 -

higher stress‐strain curves lead to higher J‐values

U2 > U1  J2 > J1

Deformation

Stress

U1

U2

Displacement controlled

higher stress‐strain curves lead to lower J‐values

U2 < U1  J2 < J1

Deformation

Stress

Load controlled

U1

U2

Figure 3–8: Effect of strain hardening behavior to the J-Integral calculation

3.2 Material characteristics for brittle fracture assessment

The brittle fracture assessment is based on the RTNDT – Concept. Within this frame-

work lower bound KIc - or KIR (KIa) - curves are used to evaluate the safety against

brittle fracture. These curves are adjusted by means of the reference transition tem-

perature RTNDT on the temperature axis. The determination of the RTNDT – tempera-

ture for non-irradiated material is based on criteria temperatures determined by

Charpy-V-impact tests (TKV(68J), TKV(0.9mm)) and Pellini drop weight tests (TNDT).

The RTNDT- temperature is defined as the maximum of the following three criteria

temperatures T1, T2 and T3:

T1 = TNDT °C (3.13)

T2 = TKV (68 J) - 33 K °C (3.14)

T3 = TKV (0,9 mm) - 33 K. °C (3.15)

The reference transition temperature RTNDTj for irradiated (embrittled) material is de-

termined by means of the temperature shift of the Charpy-V-impact energy at the

level of 41J (T41):

RTNDTj = RTNDT + T41 °C (3.16)

3.2.1 Reference temperature RTNDT for the core region

Within the core region the neutron embrittlement of the RPV material has to be con-

sidered. Based on the material tests during fabrication and by the results of the sur-

veillance program the leading RTNDT-temperature for the RPVs under investigation

could be determined. As an example, Table 3-2 and Table 3-3 summarize the avail-

- 9.23 -

able data for the Core region of the NECKAR II RPV. The leading RTNDT-temperature

of RTNDTj = -20 °C has been determined for the base material of Ring 2, Table 3-3.

Table 3-2: RTNDT at Begin of Life (BOL) for NECKAR II

NECKAR II Begin of Life (non-irradiated)

Core region = 0 n/cm2

TN

DT

= T

1

TK

V(6

8J)

TK

V(4

1J)

TK

V(0

,9 m

m)

T2=

TK

V(6

8J)-

33K

T3=

TK

V(0

,9m

m)-

33K

RT

ND

T

Ring 1 -37 -14 -37 -28 -47 -61 -37

Ring 2 -47 8 -19 -10 -25 -43 -25 b)

Core Weld -60 -31 -66 -30 -64 -63 -60

HAZ -60 -90 -60

Leading RTNDT -25

Table 3-3: RTNDT at the expected End of Life (EOL) for NECKAR II

NECKAR II Surveillance data set 1 50%

Surveillance data set 2 100%

EOL Fluence

Core region = 2.3 E18 n/cm2 = 8.72 E18 n/cm2 = 8 E18 n/cm2

TK

V(4

1J)

T41

RT

ND

Tj

TK

V(4

1J)

T41

RT

ND

Tj

RT

ND

Tj

Ring 1 -41 -4 -41 -30 7 -30 -30

Ring 2 -28 -9 -34 -14 5 -20 -20

Core weld -54 12 -48 -53 13 -47 -47

HAZ -80 10

Leading RTNDTj -34 -20 -20

For the Core region of the NECKAR I RPV the leading RTNDT-temperature of RTNDTj =

29 °C has been determined for Ring 2.

- 9.24 -

3.2.2 Reference temperature RTNDT for the nozzle region

At the nozzle region the neutron embrittlement of the RPV material has not to be

considered. According to the KTA standard, Pellini drop weight tests are only re-

quired at a temperature of 0 °C for this region. Therefore, Pellini drop weight tests

were performed only for this temperature during the fabrication of the RPVs. Based

on these tests only an upper limit for TNDT (T1) of ≤ 0 °C (that implies an approved

TNDT temperature of -5°C) has approved for the RPV flange material.

Only for different segments of the NECKAR I RPV flange some specimens (Charpy-V

and Pellini) with simulated heat treatment were tested. At these tests, an approved

TNDT-Temperature of -22 °C in tangential direction (relevant direction for the postu-

lated flaw orientation) was determined. But unfortunately for no segment all three re-

quired criteria temperatures were determined.

Table 3-4 and Table 3-5 summarize the available data for the flange region of the

NECKAR I and NECKAR II RPV.

Table 3-4: RTNDT – temperature for the flange region of NECKAR I RPV

NECKAR I Begin of Life (non-irradiated)

Flange region = 0 n/cm2

orientation d) T

1=T

ND

T

TK

V(6

8J)

TK

V(4

1J)

TK

V(0

,9 m

m)

T2=

TK

V(6

8J)-

33K

T3=

TK

V(0

,9 m

m)-

33K

RT

ND

T

tangential -5 +8 - +7 -25 -26 ≤ -5 a)

tangential b) -22 +15 c) - - -18 - -

leading RTNDT ≤ -5

a) based on approved TNDT ≤ 0°C b) simulated heat treatment (no consistent data set available for all three criteria temperatures) c) based on all available Charpy-V-impact energy data d) the tangential orientation is relevant for the postulated flaw orientation

- 9.25 -

Table 3-5: RTNDT – temperature for the flange region of NECKAR II RPV

NECKAR II Begin of Life (non-irradiated)

Flange region = 0 n/cm2

orientation b) T

1=T

ND

T

TK

V(6

8J)

TK

V(4

1J)

TK

V(0

,9 m

m)

T2=

TK

V(6

8J)-

33K

T3=

TK

V(0

,9 m

m)-

33K

RT

ND

T

tangential -5 -4 - -8 -37 -41 ≤ -5 a)

leading RTNDT ≤ -5

a) based on approved TNDT ≤ 0°C b) the tangential orientation is relevant for the postulated flaw orientation

Based on the evaluation of all available Charpy-V-impact energy data as simulated

heat treatment and acceptance tests from various positions of the flange ring, Figure

3–9 and Figure 3–10, the onset of the upper shelf (US) of the impact energy can be

defined at TUS = 30°C for the flange region of both RPVs. This means, that at tem-

peratures higher than TUS = 30°C brittle fracture has not to be taken into account but

ductile fracture assessments have to be performed.

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80

Ch

arp

y-V

-im

pac

t en

erg

y /

J

Temperature / °C

simulated heat treatment

acceptance tests

lower bound curve

mean data curve

68 J

GKN I, RPV flange, tangential specimens

upper shelf

TKV (68 J)  15 °C

Figure 3–9: Charpy-V-impact energy data for NECKAR I RPV flange

- 9.26 -

0

50

100

150

200

250

-40 -20 0 20 40 60 80

Ch

arp

y-im

pac

t-en

erg

y /

J

Temperature / °C

mean data curve

lower bond curve

TKV (68 J)  ‐4 °C

68 J

GKN II, RPV flange, tangential specimens

upper shelf

Figure 3–10: Charpy-V-impact energy data for NECKAR II RPV flange

3.3 Material characteristics for ductile fracture assessment

To perform ductile fracture assessments, crack initiation values (Ji) and crack resis-

tance curves (JR-curves) are required. Actual data for the RPV regions under consid-

eration (flange regions) are not available. Therefore based on KV-Ji correlations and

lower bound assessments conservative Ji-values and JR-curves were determined.

The NECKAR I RPV is made of the low alloy steel 22NiMoCr3-7. For this type of ma-

terial the KS 01 material from the MPA research data base can be considered as a

lower bound material, Figure 3–11.

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80 100

Ch

arp

y-V

-im

pac

t en

erg

y /

J

Temperature / °C

simulated heat treatment

acceptance tests

mean data curve

KS01 mean data curve

KS 01: TUS = 65 °C

GKN I: TUS = 30 °C

GKN I, RPV flange, tangential specimens

GKN I upper shelf

Figure 3–11: Impact energy values of material KS01 compared with the

NECKAR I RPV flange data

- 9.27 -

The NECKAR II RPV is made of the low alloy steel 20MnMoNi5-5. For this type of

material the KS17 material from the MPA research data base can be considered as a

lower bound material, Figure 3–12.

0

50

100

150

200

250

-40 -20 0 20 40 60 80

Ch

arp

y-im

pac

t-en

erg

y /

J

Temperature / °C

mean data curve

Mittelwertskurve KS17 T-L

GKN II, RPV flange, tangential specimens

GKN II: TUS = 30 °C

KS 01: TUS = 65 °C

KS 17: TUS = 45 °C

GKN II upper shelf

Figure 3–12: Impact energy values of material KS17 and KS01 compared with

the NECKAR II RPV flange data

Using the KV-Ji correlation of the MPA (valid at the upper shelf) the crack initiation

values as summarized in Table 3-6 are determined. For the evaluation of crack initia-

tion the use of the Ji (-2s) values (-2s = - twice of standard deviation) are recom-

mended.

Table 3-6: Ji-values based on the MPA KV-Ji correlation

RPV (flange region) NECKAR I NECKAR II Upper shelf impact energy KVUS 160 J 215 J Ji (mean value) 148 N/mm 220 N/mm Ji (-2s value) 67 N/mm 137 N/mm

To quantify stable crack growth after ductile crack initiation the JR-curve of the KS01

material, Figure 3–13, can be used as a lower bound curve for the NECKAR I RPV

flange material and the JR-curve of the KS17 material, Figure 3–14, for the NECKAR

II RPV flange material respectively.

- 9.28 -

0

50

100

150

200

250

0 0,5 1 1,5 2 2,5

J-I

nte

gra

l / N

/mm

a / mm

KS 01 (C(T)100)T ≥TUS

Ji (GKN I,Ji‐KV‐corrleation,  ‐2s) = 67 N/mm

Figure 3–13: Lower bound JR-curve (KS01) for NECKAR I RPV flange region

0

200

400

600

800

1000

1200

1400

0 0,5 1 1,5 2 2,5

J-I

nte

gra

l / N

/mm

a / mm

KS 17 (C(T)25)T ≥TUS

Ji (GKN II),Ji‐KV‐corrleation,  ‐2s) = 135 N/mm

Figure 3–14: Lower bound JR-curve (KS17) for NECKAR II RPV flange region

- 9.29 -

4 Fracture mechanics

4.1 Procedure

Previously determined thermo-hydraulic results are used as parameter values for

fracture mechanics analyses. Internal pressure, fluid temperature and heat transfer

coefficient are applied to the inner face of the model dependent on location and time.

Due to the multitude of transients to be analyzed, in a first step resistance to brittle

fracture of the RPV was evaluated based on stress intensity factors which had been

determined using analytical calculation methods.

The software BESIT [3], which has been developed for fracture mechanics evaluation

of components with surface cracks exposed to PTS, was applied for the determina-

tion of stress intensity factors.

Finite-Element analyses (FEA) were performed on a flawless vessel to determine the

stress and temperature transients which were needed for calculation of stress inten-

sity factors. Due to symmetry, only a section of the RPV was modeled (Figure 4–1).

The analyses were based on a linear elastic material model.

Figure 4–1: FE-model of the RPV (global model)

For selected load cases (transients), detailed Finite Element Analyses were per-

formed. This was done using the submodel technique of ABAQUS software [19]. Us-

- 9.30 -

ing the submodel technique, the cracked region can be meshed much finer which is

necessary for the accurate calculation of the J-integral. Boundary conditions from the

global model can be transferred to the submodel to account for the global behaviour

of the RPV. For these analyses an elasto-plastic material model was considered. The

Figure 4–2 and Figure 4–3 show the submodels which were used.

Figure 4–2: Submodel core region

Figure 4–3: Submodel cold leg nozzle edge

- 9.31 -

4.2 Results

4.2.1 Finite Element Analyses

Figure 4–4 and Figure 4–5 show examples of stress and temperature distribution in

the RPV.

Figure 4–4: Stress distribution

(global model)

Figure 4–5: Temperature distribution

(submodel cold leg nozzle)

4.2.2 Evaluation according to KTA 3201.2

- Core region and flange weld

Figure 4–6 and Figure 4–7 show results of the analytical calculation for core region

and flange weld.

For all investigated transients, the determined allowable reference temperature ex-

ceeds the reference temperature of the material. This is valid, even if the warm pre-

stress effect is not taken into account (Figure 4–8).

- 9.32 -

Figure 4–6: Evaluation according KTA 3201.2, core region

Figure 4–7: Evaluation according KTA 3201.2, flange weld

- 9.33 -

Figure 4–8: Finite surface crack at core region

Additional analyses for an infinite surface crack in the core region show, that in this

case brittle crack initiation can be precluded too, for all the evaluated load cases

(Figure 4–9).

Figure 4–9: Infinite surface crack at core region

- 9.34 -

- Cold leg nozzle edge

Figure 4–10 shows that analytical calculations do not suffice for verifying the RPV’s

resistance to brittle fracture.

Figure 4–10: Analytical calculations for the cold leg nozzle flaw

Therefore, finite element analyses were performed using an elastic-plastic material

model.

The performed analyses result in a minimum allowable reference temperature of

-2.8°C, Figure 4-11. The leading transient is the hot leg 100 cm² leak at cold leg in-

jection with 1 high pressure injection pump and 1 low pressure injection pump.

Figure 4–11: Elastic-plastic finite-element analysis for the cold leg nozzle flaw

- 9.35 -

Because of the crack tip temperature of 39°C at the maximum value of the J-integral,

we can conclude that the material is in the upper-shelf of the fracture toughness. For

the nozzle edge region, the stress intensity factors lie above the crack initiation value

Ji of the base material. Therefore, we do not only have to check for brittle fracture as

requested in KTA 3201.2, but also account for crack initiation with subsequent stable

crack growth when verifying the integrity of the RPV.

This was performed for the hot leg 200 cm² leak at cold leg injection with 4 high pres-

sure injection pumps. The result for a surface crack with a depth of a=16 mm is

shown in Figure 4-12.

Figure 4–12: Evaluation of crack initiation and subsequent stable crack growth

The evaluated load case resulted in a crack growth of approx. 0,15 mm after crack

initiation.

At the current state of the investigations, failure due to brittle fracture can be pre-

cluded for all evaluated load cases.

Acknowledgments

The authors gratefully acknowledge the support for this work provided by the Ministry

for Environment, Baden-Württemberg.

- 9.36 -

References

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- 9.37 -

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