effect of radiation embrittlement to reactor pressure

46
Effect of radiation embrittlement to reactor pressure vessel steels and its surveillance Luigi Debarberis Luigi Debarberis Institute for Energy (IE) Petten, The Netherlands http://www.jrc.ec.europa.eu Ti t A il 2009 Ti t A il 2009 1 T rieste, April 2009 T rieste, April 2009

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Page 1: Effect of radiation embrittlement to reactor pressure

Effect of radiation embrittlement to reactor pressure vessel steels p

and its surveillance

Luigi DebarberisLuigi DebarberisInstitute for Energy (IE)Petten, The Netherlands,

http://www.jrc.ec.europa.eu

T i t A il 2009T i t A il 2009

1

Trieste, April 2009Trieste, April 2009

Page 2: Effect of radiation embrittlement to reactor pressure

CONTENTCONTENTEC JRC IE- EC-JRC-IE

- AGEING NPPs in the EU- RPV Embrittlement- MATERIAL ISSUES- Modeling / Assessment- Surveillance of RPV- Towards GEN IV - CONCLUSIONS

2

CONCLUSIONS

Page 3: Effect of radiation embrittlement to reactor pressure

JRC - Joint Research Centre7 Institutes in 5 Member States:

JRC Joint Research Centre

IE - Petten The Netherlands- Institute for EnergyIRMM G l B l iIRMM - Geel Belgium- Institute for Reference Materials and Measurements

ITU - Karlsruhe Germany- Institute for Transuranium elements- Institute for Transuranium elements

IPSC - IHCP - IES - Ispra Italy- Institute for the Protection and the Security of the Citizen- Institute for Health and Consumer Protection- Institute for Environment and Sustainability

IPTS - Seville Spain- Institute for Prospective Technological Studies

3

Page 4: Effect of radiation embrittlement to reactor pressure

Institute for Energy

44

Petten site

Page 5: Effect of radiation embrittlement to reactor pressure

AGEING NPPs in the EUNuclear Safety- Cross-national issue Factors/issues:

D l ti

G G s t e U- Public concern- Needs for EU guidelines

- Best-practices

- Deregulation- Probabilistic approaches- Economical/cost savingp

- Deterministic & risk-based - National standards

5

Page 6: Effect of radiation embrittlement to reactor pressure

AGEING NPPs in the EU

PWR, BWR, VVER VVER, RBMK,CANDUCANDU,MAGNOX, AGR AGR, HTR,FR

6

FR

Page 7: Effect of radiation embrittlement to reactor pressure

EvolutionGEN IV

Future reactorsEPRGEN III

Advanced LWRGEN II

Commercial reactorsGEN I

Commercial reactors

Early prototypes

50s-60s (devel. 90s)70s-80s7

50s-60sNote: GEN III expected till 2015-2020

(devel. 90s)70s-80s

Page 8: Effect of radiation embrittlement to reactor pressure

Present generationLWR PWR, BWR, VVER, RBMKHW CANDUHW CANDUGCR MAGNOX, AGRGCR MAGNOX, AGRLM FR

708090

100> 20 years> 30 years

• >100 NPPS• >30% electricity• ageing! 20

30405060

8

• ageing!01020

2000 2005 2010

Page 9: Effect of radiation embrittlement to reactor pressure

Ageing mechanisms of RPV & RVIAgeing mechanisms of RPV & RVI

Irradiation hardeningIrradiation hardeningIrradiation embrittlement Irradiation embrittlement

loss of work hardening capabilityloss of work hardening capability-- loss of work hardening capabilityloss of work hardening capabilityThermal embrittlementThermal embrittlementSwelling Swelling -- incl. void induced embrittlementincl. void induced embrittlementincl. void induced embrittlementincl. void induced embrittlementIrradiation creep Irradiation creep -- incl. creepincl. creep--swelling interactionswelling interactionStress relaxationStress relaxation

h lh l-- thermalthermal-- radiation assistedradiation assistedFatigue Fatigue (vibration or/and environment)(vibration or/and environment)CorrosionCorrosion –– SCCSCC -- IASCCIASCC

WWER-440

Corrosion Corrosion SCC SCC IASCCIASCCPittingPittingWearWear

S iS i

9

WWER 440 SynergismsSynergisms

Page 10: Effect of radiation embrittlement to reactor pressure

embrittlementembrittlement

Use of the Semi-Mechanistic Analytical Model to Analyse Radiation Embrittlement of M.A.: Cu and P Effects - Debarberis, Kryukov, Gillemot, Valo, Morozov, Brumovsky et al. International Journal of Problems of Strengths, ISSN 0556-171X, 2004, No.3

10

Semi-mechanistic analytical model for radiation embrittlement/re-embrittlement Debarberis et al., International Journal of Pressure Vessels and Piping, Vol. 82, 2005

Page 11: Effect of radiation embrittlement to reactor pressure

RPV materialsRussian design Western design

low Cr: 0.1-0.14 %Cr: 2-3 % - V

Mn Ni MoC M V & C Ni M V

A302BWWER-440C 0 16 %C 0 10 %

Low Ni

Mn-Ni-MoCr-Mo-V & Cr-Ni-Mo-V

Cu: 0.16 %P: 0.011 %

Cu: 0.10 %P: 0.02 %

P: 0.007 %P: 0.009 %

High Ni A533B Ni~0.6%

A508Bcl3 Ni~0.7%VVER-1000 weld seams:up to Ni ~ 1.9%

High Ni

11

16MND512KhMFA, 15A2MFA,15Kh2NMFAA

Page 12: Effect of radiation embrittlement to reactor pressure

Embrittlement

- neutron fluence (matrix damage)

impurities (late 60s: Cu & later P L E- impurities (late 60s: Cu & later P - L.E. Steele and co-workers at ONRL)

- alloying elements

- Ni identified ~10 y later

- Today, indications on Mn, etc.y, ,- thermal ageing, etc.

-Prediction models & formulas

- Surveillance programmes

Radiation Embrittlement Understanding for PLIM Activities at EC-JRC-IEDebarberis Sevini Acosta Pirfo Bieth Weisshaeupl Törrönen Kryukov & Valo

12

Debarberis, Sevini, Acosta, Pirfo, Bieth, Weisshaeupl, Törrönen, Kryukov & ValoInternational Journal Strength of Materials, ISSN 0556-171X, No. 1 (367) 2004

Page 13: Effect of radiation embrittlement to reactor pressure

Radiation-induced micro-structure and micro-chemistryyMicro-chemistry evolution

At grain boundary

dpa Freely Migrating Defects

Re-combination/annihilation

At matrix sink

Micro-structural evolution

13direct MATRIX DAMAGE

Page 14: Effect of radiation embrittlement to reactor pressure

TSH

IFT,

°C TRadiation-induced Cu precipitation

C C

MD

Fluence

DB

TT Cu precipitation

Fluence

T, °C

DB

TTSH

IFT

T

Effect of irradiation temperature in PWR RPV materials and its inclusion in Fluence

D

PRE

14

ff f psemi-mechanistic model - Debarberis et. al, - Scripta Materialia, Vol. 53, 2005

Page 15: Effect of radiation embrittlement to reactor pressure

Reactor Pressure Vessel Materials

15

Page 16: Effect of radiation embrittlement to reactor pressure

C C

Cu

P

16

”Comparison of Nickel Effects on Embrittlement Mechanisms in Prototypic WWER-1000 and A533B Steels"; R.K. Nanstad, M.A. Sokolov, M.K. Miller, and G.R. Odette - ORNL - UCSB

Page 17: Effect of radiation embrittlement to reactor pressure

Atom Maps Reveal Irradiation-Induced Precipitates Enriched in Cu, Mn, Ni, P, and Si in the KS-01 Weld

(M.Miller, ORNL, USA)Neutron irradiation produces an extremelyproduces an extremely high number densityNv = 3 x 1024 m-3

of nanoscale copper-of nanoscale copper , manganese-, nickel-, phosphorus- and silicon-enriched precipitates.

The number density is

Cu Ni Mn Si P Cr NEach dot is an atom.

Box is 19 x 19 x 110 nm

significantly higher than other RPV steels irradiated to similar or hi h fl

17

Box is 19 x 19 x 110 nm and contains 1.5M ions. higher fluences.

Page 18: Effect of radiation embrittlement to reactor pressure

18

”Comparison of Nickel Effects on Embrittlement Mechanisms in Prototypic WWER-1000 and A533B Steels"; R.K. Nanstad, M.A. Sokolov, M.K. Miller, and G.R. Odette - ORNL - UCSB

Page 19: Effect of radiation embrittlement to reactor pressure

Schematic Embrittlement Process

C P Ni tUlt fiUltrafine

precipitatesCu, P, Ni, etc.

PP

UltrafinePrecipitates

Cu, etc.

precipitatesCu, etc.

PNi

PP

P

PP

PGrain

boundary PP P

PsegregationP, Mn, etc..

V i i t ti i l

Grain boundary

ti Vacancies, intersticials, transmutacion prod.

segregationP, Mn, etc.

19

Page 20: Effect of radiation embrittlement to reactor pressure

Prediction formulas

∆RT [17 3+1537*(P 0 008)+238*(C 0 08)+191*Ni2*C ]* Φ 0 35FIM (PWR)

∆RTNDT = [17.3+1537*(P-0.008)+238*(Cu-0.08)+191*Ni2*Cu]* ΦFIM0.35

∆RTNDT = 800*(P+0.07*Cu)*ΦPNAE1/3

PNAE (VVER)

P, Cu concentrations in wt% , Ni, %ΦFIM neutron fluence (1019 cm-2 s-1, E>1 MeV)

,

ΦPNAE neutron fluence (1018 cm-2 s-1, E>0.5 MeV)

20

Page 21: Effect of radiation embrittlement to reactor pressure

EMBRITTLEMENT SURVEILLANCE

Neutron embrittlement

21

Page 22: Effect of radiation embrittlement to reactor pressure

MARGIN

KI, KIC

KI

KIC

I

TinitialRTNDT

Material propertiesLoads evolution

transients

22

degradation

Page 23: Effect of radiation embrittlement to reactor pressure

MARGIN

KI, KIC

KI

KIC

I

TinitialRTNDT

Material propertiesLoads evolution

transients

23

degradation

Page 24: Effect of radiation embrittlement to reactor pressure

MARGIN

KI, KIC

KI

KIC

I

TinitialRTNDT RTNDT

Material propertiesLoads evolution

transients

24

degradation

Page 25: Effect of radiation embrittlement to reactor pressure

Different prediction formulas

paccepted by Regulators

Elements considered

Country Fluence power exponent

Remarks

Cu, P USA Reg.Guide 1.99 Rev.1

0.5 No cross factors – Thresholds

Cu, Ni USA Reg.Guide 1.99 Rev.2

0.28-0.10Logφ Cross factor Ni-Cu - No thresholds

Cu, P Germany KTA Not given No cross factors – Thresholds Cu, P Russia PNAE 0.33 No cross factors - No thresholdsCu, P Russia PNAE 0.33 No cross factors No thresholds Cu, P, Ni France FIS, FIM 0.35 Cross factor Ni-Cu – Thresholds Cu, P, Ni France Miannay et al. 0.7 Cross factor Ni-Cu – Thresholds Cu, P, Ni Japan JEPE BASE 0.29-0.04Logφ Cross factor Ni-Cu - No thresholds Cu P Ni Si Japan JEPE WELD 0 25 0 10Logφ Cross factor Ni Cu No thresholdsCu, P, Ni, Si Japan JEPE WELD 0.25-0.10Logφ Cross factor Ni-Cu - No thresholds

25

Page 26: Effect of radiation embrittlement to reactor pressure

Different prediction formulas

paccepted by Regulators

Elements considered

Country Fluence power exponent

Remarks

Cu, P USA Reg.Guide 1.99 Rev.1

0.5 No cross factors – Thresholds

Cu, Ni USA Reg.Guide 1.99 Rev.2

0.28-0.10Logφ Cross factor Ni-Cu - No thresholds

Cu, P Germany KTA Not given No cross factors – Thresholds Cu, P Russia PNAE 0.33 No cross factors - No thresholdsCu, P Russia PNAE 0.33 No cross factors No thresholds Cu, P, Ni France FIS, FIM 0.35 Cross factor Ni-Cu – Thresholds Cu, P, Ni France Miannay et al. 0.7 Cross factor Ni-Cu – Thresholds Cu, P, Ni Japan JEPE BASE 0.29-0.04Logφ Cross factor Ni-Cu - No thresholds Cu P Ni Si Japan JEPE WELD 0 25 0 10Logφ Cross factor Ni Cu No thresholdsCu, P, Ni, Si Japan JEPE WELD 0.25-0.10Logφ Cross factor Ni-Cu - No thresholds

26

Page 27: Effect of radiation embrittlement to reactor pressure

Schematic Embrittlement Process

C P Ni tUlt fiUltrafine

precipitatesCu, P, Ni, etc.

PP

UltrafinePrecipitates

Cu, etc.

precipitatesCu, etc.

PNi

PP

P

PP

PGrain

boundary PP P

PsegregationP, Mn, etc..

V i i t ti i l

Grain boundary

ti Vacancies, intersticials, transmutacion prod.

segregationP, Mn, etc.

27

Page 28: Effect of radiation embrittlement to reactor pressure

Damage = (MD PRE SEG )∑MD(Φ,T,Ni) PRE(Φ,Cu,T,Ni, Φrate,Mn)SEG(Φ,T,P,Ni, Φrate)Damage = (MD, PRE, SEG, …)∑ SEG(Φ,T,P,Ni, Φrate)

180200

FT, °

C

120140160

TOTAL

- linear summation- quadratic option- synergisms

TT S

HIF

6080

100

Precipitation (Cu))

DB

T

02040 segregation (P)

Direct matrix damage

Fluence, n cm-21.00E+18 5.10E+19 1.01E+20 1.51E+20 2.01E+20

Semi mechanistic analytical model for radiation embrittlement and

28

Semi-mechanistic analytical model for radiation embrittlement andre-embrittlement data analysis- Debarberis, Kryukov, Gillemot, Acosta and Sevini International Journal of Pressure Vessels and Piping, Volume 82, Issue 3, March 2005, 195-200

Page 29: Effect of radiation embrittlement to reactor pressure

400

low Ni model alloys – HFR-LYRA + KOLAVVER 440VVER 440

300

400

TT S

hift

, °C

180

210

240

, Co

63 points – Welds; 10KhMFT

VVER 440VVER 440

100

200

Kola – MA low Nieasu

red

DB

T

90

120

150

180

∆T k

,as

ured

0

0 100 200 300 400

Kola MA low NiLYRA-HFR; low NiM

e

30

60

90

Mea

Calculated DBTT Shift , °C

E l ti f WWER440 di ti b ittl t d t i th i h i ti d l

0 30 60 90 120 150 180 210 2400

∆Tk, CoCalculated

Evaluation of WWER440 radiation embrittlement data using the semi-mechanistic modelZhurko, Krasikov, Kryukov, DebarberisIAEA Specialist Meeting on Radiation Embrittlement, Gus, Russia, May 2004

Advanced method for WWER RPV embrittlement assessment

29

Advanced method for WWER RPV embrittlement assessment, L. Debarberis et al., International Journal of Pressure Vessels and Piping, Vol. 81, 2004

Page 30: Effect of radiation embrittlement to reactor pressure

HFR KOLA

Extended analysis of VVER-1000 surveillance data, Kryukov, Debarberis et al., International Journal of Pressure Vessels and Piping, Vol. 79, 2002

model alloys400

Ni=1.2 wt %

HFR KOLA

Ni200

300hi

ft, °

C

Cu= 0.4 wt%, P=0.009 wt%

Ni100

200

DB

TT S

h

Ni 0 004 t %

00 20 40 60

Ni=0.004 wt %Cu= 0.41 wt%, P=0.012 wt%

0 20 40 60

fluence value, 1018 n cm-2 (E>0.5 MeV)

Ni inclusion in semi-mechanistic analytical model for Radiation embrittlement of d l ll d bi d ff t ith C d P

30

model alloys and combined effects with Cu and PDebarberis, Kryukov, Gillemot, Valo, Nikolaev, Brumovsky, Acosta & Sevini, Specialist Meeting, Gus, Russia, May 2004

Page 31: Effect of radiation embrittlement to reactor pressure

Nickel inclusion

Cu Ni Mn Si P

[ ] ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Φ−Φ

+⋅+−⋅+Φ⋅= ΦΦ−

dcebaDBTT start

shiftsat tanh5.05.01 /5.0

Cu Ni Mn Si P

b = b1*Cu c = c1*Pf(Ni)

[ ] ⎥⎦

⎢⎣ ⎠⎝ df

31

Role of nickel in a semi-mechanistic analytical model for radiation embrittlement of model alloysJournal of Nuclear Materials, Volume 336, Issues 2-3, February 2005, Pages 210-216 Debarberis, Acosta, Sevini, Kryukov, Gillemot, Valo, Nikolaev, Brumovsky

Page 32: Effect of radiation embrittlement to reactor pressure

Temperature effect

, °C

, °C

DB

TTSH

IFT, T

DB

TTSH

IFT,

T

Fluence

D MD

Fluence

D

PRE

Lower density of small precipitates –4 Lower density of small precipitates –less effective for damage (recovery properties)

2.5

3

3.5

Fact

or T

F

ABCDE ⎤⎡

⎥⎤

⎢⎡

F0.5

1

1.5

2

Tem

pera

ture

EFGHIK

( )⎥⎥⎥

⎢⎢⎢

⎡⋅=

⎟⎠⎞

⎜⎝⎛ −

T

TkEshiftshift

e

FDBTTDBTT

Effect of irradiation temperature in PWR RPV materials and its inclusion in semi mechanistic

⎥⎥⎥

⎦⎢⎢⎢

=⎟⎠⎞

⎜⎝⎛ −

TkE

e

FTF00 100 200 300 400 500 600

Temperature, oC

32

Effect of irradiation temperature in PWR RPV materials and its inclusion in semi-mechanistic model Debarberis, Acosta, Zeman, Sevini, Ballesteros, Kryukov, Gillemot, BrumovskyScripta Materialia, Volume 53, Issue 6, September 2005, Pages 769-773

Page 33: Effect of radiation embrittlement to reactor pressure

Irradiation Temperature monitoring

melting alloys

33

Page 34: Effect of radiation embrittlement to reactor pressure

Fluence rate effect°C

Diffusion & precipitation are time dependent ⇒ less time to complete the processes

FFDBTTDBTT HFshift

LFshift +=

BTT

SHIF

T,

Φrate50

60Cu content:

0,2 w t%

shiftshift

Fluence

D

20

30

40

50

FF, o C

0,15 w t%

0,1 w t%

0,05 w t%

0

10

20

0 2 4 6 8 10[ ]LFsat

HFsat eebFF ΦΦ−ΦΦ− −⋅⋅= //

1 Cu

When ΦstartLF ≈ Φstart

HF

Fluence rate effect semi-mechanistic modelling on WWER-type RPV welds

Fluence, 1019 n cm-2

[ ]1

34

Journal of Nuclear Materials, Volume 350, Issue 1, March 2006, Pages89-95Debarberis, Acosta, Sevini, Chernovaeva, Kryukov

Page 35: Effect of radiation embrittlement to reactor pressure

FOLLOWFOLLOW--UPUPFOLLOWFOLLOW--UPUP• Refinements/verifications

- Data on realistic materials- Recent available results- Realistic welds

M d l t l (Ni M Si C )

• Refinements/verifications• Temperature effect -Different proportion contributions to DBTTshift - Model steels (Ni-Mn-Si-Cr)

- Surveillance data- Re-evaluation, etc.• Elements influence

contributions to DBTTshift• Fluence rate - Mn effect

- Mechanistic interpretation• Elements influence• High Cu & and High P• Verify Cr, Si….

Apply the semi-mechanistic model ?

High Ni

ncre

ase

inld

Str

engt

h

Apply the semi mechanistic model to New Gen. materials!- Higher doses, SS (SFT), Swelling-Voids,

Gas Irradiation creep etc ?

?

Neutron DoseIn

Yiel

35

- Gas, Irradiation creep, etc.?

Page 36: Effect of radiation embrittlement to reactor pressure

Analysis of WWER-440 and PWR RPV welds surveillance data to compare irradiation damage evolution, L. Debarberis et al., Journal of Nuclear Materials, Volume 350, 2006

150

175

200

250

75

100

125

DB

TTsh

ift, o C

200

250

K

0

25

50

D

PWR data

WWER-440 data 100

150

ured

DB

TT s

hift,

0 25 50 75 100 125 150 175 200

Fluence, 10 18 n cm -2 E>1 MeV

0

50

0 50 100 150 200 250m

easu higher Cr welds

Evidence for Chromium stabilisation of irradiation damage in RPV weld metals

0 50 100 150 200 250

predicted DBTT shift, K

36

gL. Debarberis, H. Hein, in press, International Journal of Pressure vessel and Piping, 2006

Page 37: Effect of radiation embrittlement to reactor pressure

PERFECTRadiation Damage of MaterialsRadiation Damage of MaterialsRadiation Damage of MaterialsRadiation Damage of Materials

Multi-scale Mechanical ModellingMesoscopic scale: DD Crystalline aggregateMesoscopic scale: DD Crystalline aggregate

Mechanics ModelingRVE mechanics

Physics modeling

Irrad. microstructure

5 m 100 m10 nm 5 µm• Disloc. interaction • plastic flow• grain boundary ?

100 µm• Complex loading • rotation-equilibrium• grain boundary ?

37

• grain boundary ?

Homogenization micro-meso Homogenization micro-macro Homogenization

• grain boundary ?

Page 38: Effect of radiation embrittlement to reactor pressure

Radiation Damage of Materials: MultiRadiation Damage of Materials: Multi--scale (spacescale (space--time)time)

Displacement cascade Defect Migration,Clusters, Nucleation, Growth

Primary Damage

Stage

MacroscopicProperty Change

Collisions Recombination

Neutron /PKA /Primary Collisions

Diffusion &Cascade

Acc m lationMicrostructural

ChangesFailure:MaterialAccumulation g

RelaxationDislocation/

Defect InteractionEnhanced Creep

MaterialLifetime

10-15 10-13 10-12 10-8 100 101 10310-11 10-9

Enhanced Creep

104 107 108 109

Time-scale in seconds

Molecular Dynamics

(QuantumMechanics)

Kinetic Monte Carlo

DislocationsDynamics

ElasticityPlasticity

38

Theories & models

Page 39: Effect of radiation embrittlement to reactor pressure

Manuel Perlado, University of Madrid

39

Page 40: Effect of radiation embrittlement to reactor pressure

CONCLUSIONSCONCLUSIONSEC JRC IE- EC-JRC-IE

- AGEING NPPs in the EU- RPV Embrittlement- MATERIAL ISSUES- Modeling / Assessment- Surveillance of RPV- Towards GEN IV - CONCLUSIONS

40

CONCLUSIONS

Page 41: Effect of radiation embrittlement to reactor pressure

RESERVES

41

Page 42: Effect of radiation embrittlement to reactor pressure

Segregation term saturation

80.00

P = 0.03 wt. %

50 00

60.00

70.00

ion,

°C

P 0.03 wt. %

30.00

40.00

50.00

shift

P-c

ontr

ibut

i

P = 0 01 wt %

10.00

20.00DB

TTs P 0.01 wt. %

0.000 20 40 60 80 100 120 140 160

Dose, mdpa

42

Page 43: Effect of radiation embrittlement to reactor pressure

At high irradiation doses…M t i d h ld ’t i till i fi it ⇒ t ti f th dMatrix damage shouldn’t increase till infinite ⇒ saturation of the damage

800

900

1000

[ ]

21_ Φ⋅= aDBTT matrixshift7.0

DBTTYS

∆=∆σ

500

600

700

YS, M

Pa

[ ] 21_ 1 oeaDBTT matrixshift

ΦΦ−−⋅=

200

300

400∆σ

Y

PWR clean440 clean

0

100

1 10 100 1000 10000 100000Dose mdpa

MA cleanEUROFER

43

Dose, mdpa

Page 44: Effect of radiation embrittlement to reactor pressure

1 4

1.6

1.8

R2 > 93%STEAM vs TRANSITION TEMPERATURE

0 8

1

1.2

1.4

EAM

, µV/

o C

0 2

0.4

0.6

0.8

∆ST

E

GRETE0

0.2

0 50 100 150 200 250 300∆TT 09, o C

GRETE

0.3

0.2

0.25

µ V/ o C

irradiated 3.7E+19

4,5E+19 - annealed 3,5E+19 - annealed - 4E+19

STEAM vs TRANSITION TEMPERATURE

0.05

0.1

0.15

Shift

STE

AM

Annealed

5,5E+19 - annealed - 7,5E+19 - annealed

44

00 5 10 15 20 25 30 35 40 45 50

Transition Temperature Shift oC

Fresh

Page 45: Effect of radiation embrittlement to reactor pressure

And at low temperatures?A “s-type” function for TF is required to fit the dataA s-type function for TF is required to fit the data

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

+⋅=90

240tanh185.2)( TTTF

3.5

4AB

⎦⎣ ⎠⎝

2.5

3

Fact

or T

F

CDEF

1

1.5

2

Tem

pera

ture

GHIK

0

0.5

1

0 100 200 300 400 500 600

LMN

45

0 100 200 300 400 500 600

Temperature, oC

Page 46: Effect of radiation embrittlement to reactor pressure

Fabrication configuration of BWR beltline shells

46