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The views expressed herein are those of the authors and do not reflect the viewsof the U.S. Nuclear Regulatory Commission.

Outline U.S.NRC

" Introduction and Motivation

* Analysis Methods

" Results

" Conclusion

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Outline -`U.S.NRCPW~tf 'Wp Jtwo &W

" Introduction and Motivation

" Analysis Methods

* Results

" Conclusion'

RG 1.161 and Appendix KOverview

-ý US.NRCt~~m'wrJ• I•,........' ...t~~~t~

Regulatory Guide 1.161 and ASME Section XI, NonmandatoryAppendix K provide procedures for calculating adequate Charpyupper shelf energy to protect against ductile fracture of the vessel.

The applied J-Integral is estimated from stress intensity factorequations.

6 r (7,

r, -, 0,982 + I006(ail): • 'Re-evaluate using a,.giving K,,,' and K,,'

F= i,694. 1_117u/1)'- 7 435(v11 -2 3,512(at)' ,J = 100o (• ' ÷ 'I,'

E,

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RG 1.161 and Appendix KOverview

* Flaw geometry, a/c = 1/3

R I -J... .. .....

.....

--U.S.NRCf4~wong~4./ Ankd d Etnswvmmea

RG 1.161 and Appendix KMotivation

-IU.S.NRC

. These stress intensity factor equations were derived for Rlt = 10,which applies to pressurized water reactor vessels.

* Boiling water reactor vessels typically have Rit = 20.

* The thinner vessels are expected to be less susceptible to steepthermal gradients.

This work further explores the validity of using the derived equationsfor the Rit = 20 case, through the use of independent methods ofcalculating stress intensity factor.

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Outline UUS.NRC

° Introduction and Motivation

• Analysis Methods

" Results

" Conclusion

Temperature ProfilesThe Heat Equation

--;U.SNRC

* Parabolic partial differential equation:

" Boundary conditions:

OTC1 I r ke

= 1( (T.f1 - Tý) for r -R, aind all r

q = for 1, - R, anid till r

T -- TO - ((-'R ) 7

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The Heat EquationSolving Strategies for Temperature Profiles

U.S.NR(S... n~ K-a,

r~II.pk *n4 rn~pwus,.

• Finite element analysis

" Crank-Nicolson method

" Analytical solutions

" Resource: Kreyszig, Advanced Engineering Mathematics

" This work

- Commercial engineering coding software with a built-in PDE solver

- Skeel and Berzins, "A Method for the Spatial Discretization of ParabolicEquations in One Space Variable," SIAM J. Sci. and Stat. Comput.

A

'I

II

Calculation of StressesPressure and Thermal Hoop Stresses

-10,U.S.NRC

* Pressure stresses in a thick-walled cylinder:

• Thermal stresses in a cylinder:

e _ I- _+ RJ Tzdr f"Tr -T(+O tR2 -I).

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Calculation of Stress Intensity Factor ''U.S.NRCThree Independent Methods ,

• American P etroleum Institute Standard 579-1:

GX t " G' """'t ±CJ" ('; -

I t-r 1,64 fO .0 1 0= I ±ý 1,464(. fOr 11/c 1.0L

Calculation of Stress Intensity Factor •'U.S.NRCThree Independent Methods - - ,

Fracture Analysis of Vessels - Oak Ridge (FAVOR) method:

- Similar to the API-579-1 method, except that a 3 rd order polynomial isused for the stress distribution.

Newman and Raju for internal pressure:

K, 7- ' 0

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Calculation of Stress Intensity Factor -It U.S.NRCApplication of the Methods Pift.•Ia.,- p ad,,d a.n,,,

" API-579-1 and FAVOR methods:

- Are based upon the principle of elastic superposition.

- May be applied for multiple loading conditions, if:

* All conditions are mode I and

* The polynomial used to describe the stress fits the actual stress profile well.

" The Newman and Raju equation was derived only for internalpressure and should be used only for that case.

InputsGeometry, Material Properties, etc.

U.S.NRC

Description valm~e

___________________0 16m [0.51 ft)R"( 20,6at__________ 0.1to 0,0

(1_____________C____ 113

K-terial Propertie ______________2,0006 Wla f4.200O' kipeft)

___________________0.30

'4 ~1.30100 mmlmK [7.20x10" MtftR]k 38 W/(m-K) [22 STUI(hr-fl.R)I

7770 k~/m4 [485 lbnft,']1536 J/(IrgK) [ 0.13 BTUI(Ib,.R)]I

Thermal Loading Conditions __________________________________5673 Wt~rm2-K) [ 1000 BTUI(hr-tt.R[

('R 0.02 Kis 1100 R/lir]________________561 K [1010 R)

fhnical Loin Conditici

I 19 -~.- 0 NI6kpt

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Outline -U.S.NRC

" Introduction and Motivation

" Analysis Methods

" Results

" Conclusion

Temperature DistributionContour Plots

350000

3DOOIT [K]

2500 n2250001•

20000 A

ýU.S.NRC

" Small gradients at the beginningand end of the cooldown.

° Highest gradient observedbetween 15 000 s and 20 000 s.

18000

U Fesive . Pamton u nlioO I..lOm " "

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Thermal Stress DistributionHoop Stress Contour

-t U.S.NRCMW~fWs od

tAv a-'m

3o•=

2900C

200CK -I".41444? I?

* Vanishing thermal stresses earlyand late in the transient.

• Highest magnitude stressesobserved between 5 000 and20 000 s.

* Tension at ID, compression at OD.

500C

Stress Intensity Factor: ThermalTime History

~U.SNRC

° API-579-1 method with a/c = 1/3,a/t = 1/4.

* Highest stress intensity factorobserved at 14 000 s.

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Stress Intensity Factor: ThermalComparison of Different Methods

12

"--'IA6M6OoE , -MaxiI- - . A,,.676 I10 FAVORI

• RGIi

API-o~fnra,

,U.S.NRC

mum K in the transient.

ASME Code equations bound579-1 and FAVOR methods/t < 0.55.

for a

Subsequent agreement.

Stress Intensity Factor: ThermalEffect of Vessel Thickness

I S RG/ASconsermethod

U.S.NRC

ME Code equationvatively bounds the API-579-1

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Pressure Stress DistributionHoop Stress

tU.S.NRC

4A'

395 I

300

.............

Approximately linear distribution

ID: -400 MPa, OD: -380 MPaI.

•wv i-

800 -

Stress Intensity Factor: PressureComparison of Different Methods

~U.S.NRC

40U

400

3000

2000

ISO

0 0APME co0o

40;

* Agreement up to a/t = 0.5.

RG/ASME Code equation becomesincreasingly conservative for a/t >0.5.

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Outline ,tU.S.NRC

" Introduction and Motivation

" Analysis Methods

" Results

" Conclusion

Conclusion tU.S.NRC

" The RG/ASME Code equations for estimating stress intensity factorunder thermal and internal pressure loading conditions agree with orconservatively bound independent methods for R/t = 20.

Reference: Conference Proceeding PVP2012-78229.

12