CRISM “Prometey”, Saint-Petersburg, Russia 1 ПОСТРОЕНИЕ РАСЧЕТНОЙ...

CRISM “Prometey”, Saint-Petersburg, Russia 1

ПОСТРОЕНИЕ РАСЧЕТНОЙ ТЕМПЕРАТУРНОЙ ЗАВИСИМОСТИ ВЯЗКОСТИ РАЗРУШЕНИЯ

КОРПУСНЫХ РЕАКТОРНЫХ МАТЕРИАЛОВ: ОБЩИЕ ПРИНЦИПЫ И РЕЗУЛЬТАТЫ

CONSTRUCTION OF THE DESIGN TEMPERATURE DEPENDENCE OF FRACTURE TOUGHNESS

FOR RPV MATERIALS: BASIC PRINCIPLES AND RESULTS

B. Z. Margolin, V.N. Fomenko, A.G. Gulenko, V.A. Shvetsova,V.A. Nikolaev, A.M. Morozov, L.N. Ryadkov

CRISM “Prometey”, Saint-PetersburgV.A. Piminov

FSUE EDO “Gidropress”, Podol’skV.G. Vasiliev

Concern Rosenergoatom, MoscowN. A. Shulgan

Izhorsky Zavody, Saint-Petersburg

presented by Valentin Fomenko


OUTLINE OF PRESENTATION

1. Introduction: advanced methods of prediction of fracture toughness

2. The Unified Curve concept - main considerations and some results

3. Basic principles of construction of the design temperature dependence of fracture toughness, KJC(T)

4. Determination of the margins when constructing the KJC(T) curve with regard for

- the uncertainty caused by restricted number of tested specimens

- the uncertainty connected with spatial non-homogeneity of RPV material

- type of tested specimens

5. Conclusions


ADVANCED METHODS OF PREDICTION OF FRACTURE TOUGHNESS

Method Advantages Shortcomings

1Master Curve

[ASTM E 1921]Simple use and

calibration

The lateral temperature shift

condition is used non-conservative predictions

for highly irradiated steels2Basic Curve

[РД ЭО 0350-02]

3Probabilistic

Prometey model[РД ЭО 0350-02]

Prediction for any degree of material

embrittlementIntensive calculations

4Unified Curve

[standard underellaboration]

Simple use and calibration.

Any degree of material embrittlement


THE UNIFIED CURVE CONCEPT

1. The temperature dependence of fracture toughness for RPV steel for any degree of material embrittlement is described by

for В=25 mm и Pf=0.5.

When degree of embrittlement increases the parameter decreases.

2. The parameter may be determined by single temperature method and multiple temperature method on the procedure like as To determination in the Master Curve

3. For multiple temperature method, is calculated by equation

mMPа ,105

130Ttanh1KK shelf

JС)med(JC

N

1i KK105

130Ttanh1

15

KK105

130Ttanh1

)2ln(4KK

shelfJCmin

ishelfJCmin

i

min)i(JC

where KJC(i) –the experimental value of KJC obtained at Ttest=Ti.


NEW ENGINEERING METHOD (UNIFIED CURVE) FOR PREDICTION OF KJC(T) FOR DIFFERENT MATERIALS

WITH VARIOUS DEGREES OF EMBRITTLEMENT

1. AS-RECEIVED STATE

MA

ST

ER

CU

RV

EU

NIF

IED

CU

RV

E

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0

t em p er a tu r e , o C

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5T o = -82 .5o C - t est s

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0


0

1 0 0

2 0 0

3 0 0

4 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

T o = -67 .4o C - t est s

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0


0

1 0 0

2 0 0

3 0 0

4 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5T o = -61 .3o C - t est s

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0


0

2 0 0

4 0 0

6 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

= 2196 M P a m - t est s

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0


0

1 0 0

2 0 0

3 0 0

4 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

= 1695 M P a m - t est s

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0


0

1 0 0

2 0 0

3 0 0

4 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5= 1472 M P a m - t est s


NEW ENGINEERING METHOD (UNIFIED CURVE) FOR PREDICTION OF KJC(T) FOR DIFFERENT MATERIALS

WITH VARIOUS DEGREES OF EMBRITTLEMENT

2. HIGH DEGREE OF EMBRITTLEMENT

MA

ST

ER

CU

RV

EU

NIF

IED

CU

RV

E

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0


0

1 0 0

2 0 0

3 0 0

4 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5T o = 57.1o C - t est s

-2 0 0 -1 0 0 0 1 0 0 2 0 0


0

1 0 0

2 0 0

3 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

T o = 86.9o C - t est s

-2 0 0 -1 0 0 0 1 0 0 2 0 0


0

4 0

8 0

1 2 0

1 6 0

2 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5T o = 137o C - t est s

-2 0 0 -1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0


0

1 0 0

2 0 0

3 0 0

4 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

= 199 M P a m - t est s

-2 0 0 -1 0 0 0 1 0 0 2 0 0


0

1 0 0

2 0 0

3 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

= 142 M P a m - t est s

-2 0 0 -1 0 0 0 1 0 0 2 0 0


0

4 0

8 0

1 2 0

1 6 0

2 0 0

KIC

, KJC

, MP

am

P f = 0 .05

P f = 0 .95

P f = 0 .5

= 73.4 M P a m - t est s


SCHEME FOR CONSTRUCTION OF THE DESIGN KJC(T) CURVE

4 – the curve constructed with the margin on the tested specimen type. Curve 4 takes into account that constraint for a zone of RPV may be larger than for sub-sized

specimen of Charpy type. 5 – the design curve – the curve constructed with all the considered margins and recalculated for crack

front length B=150 mm and the brittle fracture probability Pf=0.05. Curve 5 shows that only 5% of specimens from RPV zone with the worst properties have KJC

corresponding to curve 5.

Temperature

KJC

2 3 4 51

P f=0.5, B=25 mm

P f=0.05, B=150 mm

1 – the curve determined from test results of (612) surveillance specimens The restricted number of specimens may provide KJC larger than actual properties of a material.2 – the curve constructed with the margin on the restricted number of surveillance specimens. KJC for material of surveillance specimens with the confidential probability 95% is larger than KJC for

curve 2. 3 – the curve constructed with the margin on spatial non-homogeneity of RPV material. KJC for any zone of RPV with the confidential probability 95% is larger than for curve 3.


The function may be found with statistical theory when taking

into account the Weibull distribution function for brittle fracture probability

and the normal distribution function for average values of experimentally

determined parameters.

Nsp

The margin sp is introduced to take into account this uncertainty.

THE UNCERTAINTY IN THE DETERMINATION OF CAUSED BY RESTRICTED NUMBER

OF TESTED SPECIMENS

The relative margin is a function of the number N of tested specimens

has to be determined. sp


Main considerations and steps:

1. Value is described by normal distribution function.

2. When using 95% confidential probability for the low boundary of the parameter min= - sp,

Ωsp=1.6[Ω], σ[Ω] - standard deviation

DETERMINATION OF THE MARGIN δΩsp CAUSED BY RESTRICTED NUMBER OF TESTED SPECIMENS

3. From the Unified Curve

105130T

th1

KK shelfJCJC(med)

105130T

th1

]K[K][

shelfJCJC(med)

sp

Task: to find the dependence of Ωsp on the number N of tested specimens.


4. When replacing on (as these values are very close ) the relative margin as a function of the number N of

tested specimens is written as

3. For the normal distribution function for KJC(med) and three-parameters Weibull distribution for brittle fracture probability

b

min0

minICf KK

KKexp1P

N

0.45][ 1.6 spsp

shelfJCK

N

0,28KK

N

]KD[K]KK[ minJC(med)minJC

minJC(med)

N

KK]KK[ minJC(med)

minJC(med)

For example, for N=10 the value of δΩsp corresponds to (T0)sp=11°C

m26MPaK shelfJC Kmin

m20MPaKmin

if the coefficient b is unknown

if the coefficient b=4


INFLUENCE OF SPECIMEN TYPE ON FRACTURE TOUGHNESS

where and - values of the temperature Т0 in Master Curve for СТ specimens and SE(B)-10 specimens.

СТ0

T SEB0

T

The margin Ttype is introduced to take into account the difference in the value of determined on the basis of test results of specimens of different types.

Pre-cracked Charpy s SE(B)-10 pecimens are usually used as surveillance specimens.

Available fracture toughness data allow the determination of Ttype as

SEBСТtype TTТ

00


TEST RESULTS OF FRACTURE TOUGHNESS SPECIMENS OF VARIOUS TYPES

-120

-100

-80

-60

-40

-20

0

20

40

60

80

22NiMoCr3.7* A533B* 2CrNiMoV(in) 2CrNiMoV(embr)

C(T)

SE(B) -10

SE(B) -10SG50

* - Transferability of Fracture Tougness Data for Integrity Assessment of Ferritic Steel Component

T0,°С


DETERMINATION OF THE MARGIN FOR FRACTURE TOUGHNESS SPECIMENS OF VARIOUS TYPES

Pre-cracked Charpy specimens

CT-specimens SE(B) specimens with deep (50%) side grooves

KJC

, М

Pа√

m

Temperature, °С

Ttype

Ttype = 15 oC Ttype = 0 oC Ttype = 0 oC


THE UNCERTAINTY IN THE VALUE OF CAUSED BY RPV MATERIAL NON-HOMOGENEITY

1. The design dependence has to be constructed for RPV zone with the minimum resistance to brittle fracture.

2. Tests of surveillance specimens provide average values of

characteristics of resistance to brittle fracture. 3. As quantitative measure of material non-homogeneity, the relative

margin that does not depend on material condition is introduced : pr is determined from test results of surveillance specimens, δΩNH is value of for RPV zone with the minimum resistance to

brittle fracture, δΩNH= Ωpr- ΩNH 4. The margin is found when using the distribution function of the critical

brittle fracture temperature TK for RPV in the as-received (unirradiated) condition.

5. The Unified Curve concept is used to calculate NH corresponding to the maximum TK value (TK value for RPV zone with the minimum resistance to brittle fracture) and pr corresponding to average value of TK.

TKdesignJC

pr

NH


DETERMINATION OF THE MARGIN ON SPATIAL NON-HOMOGENEITY OF RPV MATERIAL

σ(TK)

(TK)1

2Zк2Rк

2кNHк TTTT

(TK)2

(TK)NH=1.6(σ[TK])NH

σ(TK)R

σ(TK)Z

(TK)R1 (TK)R2 (TK)R3

(TK)Z2

(TK)Z1

(TK)Z3

Z

RΘ

Z

RΘ

ΩNH



for weld metal

On the basis of analysis of the distribution of the critical brittle fracture temperature TK for circumferential welds of RPVs for WWER-440 and WWER-1000, the margin on spatial non-homogeneity NH was found.

Non-homogeneity of RPV weld metal was analyzed for two different directions of RPV: - along weld length ( circumferential direction) - on weld height (R radial direction)

δ(TK)NH 0.95))1((Ppr

NHpr

34.0pr

NH

(δTK)R=21°C, (TK)=9°CZ

RΘ

δ(TK)NH≈23°C


On the basis of analysis of the distribution of the critical brittle fracture temperature TK for archive blocks of RPVs for WWER-1000, the margin on spatial non-homogeneity NH was found.

Non-homogeneity of RPV base metal was analyzed for three different directions of RPV: - on RPV height (Z direction) - on RPV wall thickness (R direction) - on circumferential direction ( direction)

0.95))1((Ppr

NHpr

39.0pr

NH

(δTK)R=18°C, (TK)Z=18°C, (TK)=10°C

δ(TK)NH≈27°C


for base metal

δ(TK)NH


If the calculated flaw is located on the distance from surface no larger than ¼ of wall thickness

31.0pr

NH

δ(TK)R = 0


δ(TK)NH ≈ 21 °C

S/4S/4

TK forsurveilancespecimens

TK

δ(TK)RZΘ

wall thickness (S)

Z1 Θ1

Z2 Θ2

δ(TK)ZΘ


,mintype

designminshelfJC

desingJC K

105

130TTth1KKkK

mМPа26KshelfJC

mМPа20Kmin

2

pr

NH

2

pr

spprdesign 1

1/4S than largernot surface RPV wall from distance

the onflaw calculated the of location for21°C)δT( 0,31

flaw calculated the of location any for27°C)δT( 0,39

:metal base for

23°C)δT( 0,34 :metal weldfor

ΩδΩ

K

K

K

pr

NH

where k=0.33 when recalculating from B=25 mm to B=150 mm and from Pf=0.5 to Pf=0.05

EQUATION OF THE DESIGN KJC(T) CURVE CONSTRUCTED WITH ALL THE CONSIDERED MARGINS

The margin on spatial non-homogeneity of RPV material

N

45,0

pr

sp

grooves side deep withspecimens Charpy

cracked for also and sizes larger withspecimens or

specimens 0.5-CT for determined is if 0°С,

specimens Charpy cracked for determined is if 15°С

T pr

pr

type

The margin on the tested specimen number

The margin on the tested specimen type


CONCLUSIONS

2. The numerical values of all the considered margins are determined.

3. Equation of the design temperature dependence of fracture toughness KJC(T) is proposed.

1. Scheme for construction of the design temperature dependence of fracture toughness KJC(T) is proposed.

This curve is constructed on the basis of the Unified Curve concept and the margins that take into account

the uncertainty caused by restricted number of tested surveillance specimens;

the uncertainty connected with spatial non-homogeneity of RPV material;

type of tested specimens.

CRISM “Prometey”, Saint-Petersburg, Russia 1 ПОСТРОЕНИЕ РАСЧЕТНОЙ...

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