JAERI Research

7/27/2019 JAERI Research

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JAERI-Research2 0 0 0 - 0 1 2 JP0050355

m mF R A C T U R E M E C H A N I C S A N A L Y S I S A N D E V A L U A T I O N F O R T H E R P V O F

T H E C H I N E S E Q I N S H A N 3 0 0 M W N P P U N D E R P T S

March 2 0 0 0

Yinbiao HE and Toshikuni ISOZAKI

J a pan A tomic E ne rgy R es ea rch Ins t itu te


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^ T319-H95

(=P319-1195

This report is issued irregularly.Inquiries about availabili ty of the reports should be addressed to Research

Information Division, Department of Intellectual Resources, Japan Atomic KnergyResearch I nstitute , Tokai-mura, Naka-gun, Ibaraki-ken T 319-11 95, Japan.

CC) Japan A tomic Knergy R esearch Ins titu te, 2000


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JAERI-Research 2000-012

Fracture M echanics Analysis and Evaluation for the RPV of the C hineseQinshan 300MW NPP under PTS

YinbiaoHE * and Toshikuni ISOZAKIDepartment of Reactor Safety Research

Nuclear Safety Research CenterTokai Research EstablishmentJapan Ato mic E nergy Research InstituteTokai-mura, Naka-gun, Ibaraki-ken(Received January 31 , 2000)

One of the most severe accident conditions of a reactor pressure vessel(RPV) in service is the loss of coolant accident (L OC A) . Cold safety injectionwater is pumped into the downcomer of the RPV through inlet nozzles, whilethe internal pressure may remain at high level. Such an accident is calledpressurized thermal shock (PTS) transient according to 10 CFR 50.61definition. This paper illustrates the fracture mechanics analysis for theexisting RPV of the Chinese Qinshan 300MW nuclear power plant (NPP)under the postulated PTS transients that include SB-LOCA, LB-LOCA ofQinshan NPP and Rancho Seco transients. 3-D models with the flaw depthrange a/w=0.05~0.9 (a: flaw depth; w: wall thickness) were used to probewhat kind of flaw and what kind of transient are most dangerous for the RPVin the end of life (EOF). Both the elastic and elastic-plastic material modelswere used in the stress analysis and fracture mechanics analysis. The differenttypes of flaw and the influence of the stainless steel cladding on the fractureanalysis were investigated for different PTS transients. Comparing with thematerial initiation crack toughness KjC, the fracture evaluation for the RPV inquestion under PTS transients are performed in this paper.

Keywords: RPV, Core Beltline, PTS, Shallow and Deep Flaws, FractureMechanics* on leave from Shanghai Nuclear E ngineering Research and Design Institute

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(2000

3OOMW mLOC A


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Contents1. Introduction 12. Structural Model andAssumptions fortheAnalysis 23. Material Properties andLoading C onditions 34. Method ofFracture M echanics A nalysis 45. Results 5

5.1 Verification fortheModel and the Method (NoThermal Shock) 55.2 TheResults from Qinshan SB-L OC A andRancho Seco 65.3 TheResults from LB-LOCA 75.4 Surface Flaw andSub-surface Flaw 75.5 Influence ofCladding 8

6. Conclusion 9Acknowledgment 9References 10Appendix 22

1. it to i3 I2. m^m(DmB^ri)vtu^ 23. Mftft&iiffim&ft 34. w&ti^mvif-m 4

5 4iH c. TO7K J5.1 ^?)lh^&(Dmi. (MH&L) 55.2 | g i l j/J \ f lgfL0CAi :7>^-3^-bnl i i^ 65.3 *5r LOCA (Dffim 75.4 affi^l^i:S?S^^ 75.5 y F & # 8

6. #> 99

1022


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1. IntroductionThe reactor pressure vessel (RPV) integrity is ensured by a margin betweenits load bearing capacity (material properties) and the applying loads duringoperation. Structural integrity research for RPV is a large-scale researchproject including the thermal hydraulic analysis concerning selectingtransients, the structural analysis concerning fracture mechanics assessmentand the material properties concerning embrittlement, annealing behavior. Forthe RPV integrity it is not adequate to fulfill the fracture evaluation inaccordance with App. G of ASME B&PV code III[1 ] and the additional worksshould be taken into account after the plant got the operating license. Such

works should m eet the requirements of 10 CFR 50.61 [2], R.G 1.154[3] andR.G 1.99[4] to ensure the RPV integrity under the pressurized thermal shock(PTS), which would occur during the postulated loss of coolant accident(LOCA). It is mentioned in 10 CFR 50.61 that for each pressurized waternuclear power reactor, the value of R T ^ for any material in beltline isprojected to exceed the PTS screening criterion using EOF (end of life)fluence. The licensee must submit a safety analysis at least three years beforeRT PTS RTNDT for EOF fluence, exceeds the PTS screening criterion. It meansthe plant cannot continue to operate without justification when RTp^ isbeyond PTS screening criterion.The objective of the research described in this paper was to perform thefracture mechanics analysis for the existing RPV of Qinshan NPP under thepostulated PTS transients. Such an analysis is both a part of PTS analysisreport, which shall be submitted when the RTp^ is anticipated to exceed thePTS screening criterion, and an assessment method for the flaw, which mightbe detected during inservice inspection in accordance with ASME B&PV codeThe different flaw sizes, different types of flaw and different PTS transientswere considered and compared to determine what kind of flaw and what kind

of transient are most dangerous for the RPV. During the analysis two materialmodels were applied to the stress calculations of the RPV. One is the thermal-elastic material model and the other is thermal-elastic-plastic material model.The analysis accounted for the influence of the stainless steel cladding on thefracture analysis. The fracture mechanics analysis was performed by theinternationally used ADIN A code [6]. The virtual crack extension (VC E)method [7] was employed to obtain the fracture mechanics parameter J-integral, and then converted to the stress intensity factor K, for the com parison

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with the material fracture toughness. The analytical calculation [8-9] andASME code method [1] for K, had been taken into account to verify thereliability of the models and the computation method and the applicability ofADINA code. The comparison shows that the result from FEM has a goodagreement with the results from the other two methods.The fracture mechanics analysis and evaluation for the RPV in question areset forth by a flow chart, which is shown in Fig.l.

2. Structural m odel and assum ptions for the analysisThe R PV of Qinshan 300M W NPP w as designated to bear high temperature,

high pressure and corrosion of the primary system coolant and the neutronirradiation for the core beltline during the license lifetime. The weld issensitive to the irradiation embrittlement caused by the relatively high neutronflux on the vessel wall. The core beltline was manufactured by the SA-508class 3 ring forging to avoid the axial welding seam and connected to nozzlebelt and bottom head with two circumferential welding seams. Comparingwith other parts of the RPV, the core beltline suffers the strongest neutronirradiation leading to a significant nil-ductility transition temperatureincrement and embrittlement in EOF. So the core beltline was taken as amodel for the fracture mechanics analysis. The main design parameters anddimensions are as follows:

Main design parameters:Design pressure 17.2MPaNorm al operating pressure 15.2MPaHydrostatic test pressure 21.5MPaDesign temperature 350CNorm al operating inlet temperature 288.8CNormal operating outlet temp erature 315.2CHydrostatic test temperature 33C (shop test) /60C ( site test)Design life 30 yearsM ain dimensions for core beltline:Inner diameter of core beltline 3374m mWall thickness of core beltline 174mm (including the cladding)Thickness of cladding 4mm

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An axial inner surface flaw or sub-surface flaw is assumed to exist in thebeltline before the PT S transient occurs. Several m odels with different flawsizes (a/w=0.05~0.9) were created using ADINA-IN in order to investigate theinfluence of the flaw size. The parameter design technology was applied to themodel creating procedure to reduce the pre-processing work of several modelsas possible. To eliminate the boundary effects, the model with 90 degree alongcircumferential direction and 1500mm height along axial direction wereadopted for both the thermal analysis and the stress analysis. The discretemodel was obtained with about 6400 3-D elements with middle nodes and32000 nodes. The model and mesh are shown in Fig. 2.The stainless steel cladding is involved in these models. For the worst

condition, it was assumed that there were map cracking in the cladding beforethe LOCA would occur. It means that the cladding would be able to conductheat flux but lose its strength to bear the loads. Omitting the couple effect, theuncoupled thermal and stress analyses were performed respectively. Thediscontinuity of stress at the interface between the base and cladding due tothe difference in Youn g's m odulus is taken into account.3. Material properties and loading conditions

The core beltline was manufactured using SA-508 class.3 forging and itsinner surface was welded using E308L weld metal to form a stainless steelcladding of 4mm in thickness. For the transient thermal and stress analyses, allthermal and mechanical properties of the base and cladding materials arechanged w ith the relevant temperature and listed in the Table 1 and Table 2.Table 1 Thermal and mechanical properties for the base material

TemperatureC5010015020025030 0350

ConductivityW/(mXC)

38.338.838.838.638.137.536.8

Specific heatJ/(m 3XC)3.61 X 10 63.79 X1 0 63.94 X1 0 64.09 X1 0 64.23 X1 0 64.4 X1 0 6

4.56 X1 0 6

Young'smodulusGPa

20 0196193189187184177

Poisson'sratio0.30.30.30.30.30.30.3

Mean coef. of thermalexpansion1/C

11.75 X 1 0 612.07 X1 0 612.39 X 1 0 612.69 X 1 0 612.99 X 1 0613.29 X 1 0 613.57 X1 0 6

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Table 2 Thermal and mechanical properties for the cladding materialTemperature

C50100150200250300350

ConductivityW/(mXC)13.9

14.615.616.317.218.018.6

Specific heatJ/(m 3XC)3.94 X1 06

4.0 X1 064 .17X1064.19 X1 0 64.3 X1 06

4.35 X 1064.38 X 10 6

Young'smodulusGPa193190186183179175172

Poisson'sratio0.30.30.30.30.30.30.3

Mean coef. of thermalexpansion1/C15.45 X10"6

15.86 X 1 0 616 . 26X 10 616.63 X 1 0 616.96X10"617.25 X 1 0 617.52 X1 0'6

On the basis of the material tensile tests, the four stress-strain curves wereused to simulate the base and the cladding elastic-plastic behavior in the roomand high temperatures respectively. The curves are shown in Fig.3.

The initial reference nil ductility transition temperature was measured byCharpy impact and Drop weight tests and RTND T=-20 "C for belt line . The K1Cfracture toughness curve, which is provided in ASME B&PV code XI, wasused in fracture evaluation. It is assumed that the same shape of the curve maybe used for all material state and the curve is only shifted along thetemperature axis corresponding to the RTND T. During service the neutronirradiation can cause damage in microstructure of materials and leads to anincrease in strength and a decrease in toughness. Consequently, the K 1C curvewill be shifted to high temperature. According to 10 CFR 50.61 and R.G 1.99the final adjusted RTND T was estimated in the design stage , ARTND T=70 C[10],but the value must be corrected based on the periodical capsule specimen testsand the actual neutron irradiation fluence. For the PTS safety analysis, theARTNDT is that very RTPTS defined in 10 CFR 50.61.

The full power state was regarded as the so-called initial condition for boththermal analysis and stress analysis. The SB-LOCA, LB-LOCA[11] andidealized Rancho Seco[12] PTS transients are treated as the loads for thefracture analysis and shown in Figs 4-6.4. Method of fracture mechanics analysis

The axial semi-elliptical inner surface flaw was assumed for each modeland the aspect ratio of the depth (a) to the length (2c) is 1/6. The models with

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flaw depth range a/w= 0.05~0.9 were considered.The effects of thermal loads and pressure loads on the faces of the crack canbe included in computed J-integral. The stress intensity factor was derivedfrom the following formula:

KK) = - v 2

The linear and nonlinear fracture mechanics analysis can be performed forthe elastic and the elastic-plastic material models with ADINA.5. Results5.7 Verification for the model and the method (no thermal shock)

The model with the axial inner surface flaw of a/w=0.25 in depth subject tothe normal operating internal pressure ( p=15.2 MPa ) was computed by threemethods: code method, analytical method and FEM.Code method:

According to ASM E B&PV code III App. G:^M m l v l m m

whereo m = pR/t = 151.2 MPaMm = 0.3984 Jen obtained from Fig. G-2214-1 of App . GSo K lm = 60.24 M Pa Vm.Analytical method:According to ref. [8-9]:

K - P * L - F (where

Fj: Boundary correction factorF - U R

R K n K

Gj: Influence coefficients correspond to the j-th stress distributionQ: Square root of the com plete elliptical integral of the second kindc


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and is approximated byQ = l + 1 .4 6 4 ( a/ c) 1 6 5$ : Shown in Fig. 7

The K, can be derived from the above formulas:0 .0

42.6522.5

46.3845.0

55.3867.5

61.6990.0

63.88Finite Element Method:The stress intensity factor K, calculated using ADINA VCE method isshown in Fig. 7 and compared with the results from analytical and code

methods. The comparison is shown that the results from both methods have agood agreement. At the deepest point the K, from code method is smaller thanthe results from other two methods, but the safety factor of two is required forK lm calculation in accordance with App. G.So it was verified that the model in question is reliable and the FEM code,ADINA, is applicable for the fracture mechanics analysis.5.2 The results from Qinshan SB-LO CA andRancho Seco

The elastic and elastic-plastic material modes were assumed for the fracturemechanics analysis and the results are shown in Figs 8 and 9 respectively forQinshan SB-LOCA and Rancho Seco transient. It is observed that the elasticresults always are conservative, regardless of the different flaw depth or thedifferent transients. Due to the irradiation effect in EOF the yield strength ofthe material will enhance. For the condition there is a lack of the irradiatedmaterial data in EOF, the elastic results can be used to estimate the fracturebehavior of RPV conservatively. The largest K, occurs at the specific time thatthe drop rate in temperature is the fastest during the transients and thetemperature distributions through the wall thickness are shown in Figs 10 and11.

For the shallow cracks (a/w=0.05~0.25), the fracture evaluation are shownin Figs 12 and 13 in comparison with K IC [5]. Based on the ART calculation inEOF in accordance with R.G 1.99 and the screening criterion specified in 10CFR 50.61, the ART were chosen as 70 C and 132 C respectively. It isobserved that for the given SB-LOCA the RPV has enough safety marginagainst the fracture failure even for the most severe postulated Rancho Seco


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PTS transient.The fracture analysis for a series of different flaw depth models

(a/w=0.05~0.9) were performed to investigate the behavior of shallow anddeep flaws subject to SB-LOCA and Rancho Seco PTS transients. The K, vs.a/w at the deepest point of the crack front are described in Fig. 14. The Kjincreases with the flaw depth. In order to investigate what kind of flaw is moredangerous the K1C at ART=208 C and 170 C were used to compare withthe Kj from SB-LOCA and Rancho Seco in Fig. 14. The shallow flaws withthe depth a/w =0.1-0.2 are more dangerous than others. The distributions ofKj along the crack front are shown in Figs 15 and 16. The same trend wereobserved for the both conditions that for the base material that the K, increaseswith angle wh ile a/w less than 0.5 and decreases with 4> while a/w greaterthan 0.5.5.3 T he results from LB-LOC A

Shown in Fig 5, the LB-LOCA occurs in very short times with the largedrop in temperature and pressure. The temperature distribution through thewall thickness is shown in Fig. 17. The two models with a/w=0.05 and 0.25were chosen to perform the fracture analysis under LB-LOCA. The results areshown in Fig. 18 and indicate that the major factor affecting the K, is theinternal pressure for the deep flaws and the drop rate in temperature for theshallow flaws. But the Kj under LB-LOCA is so small that it does not exceedthe threshold value of K1C throughout the LB-LOCA transient. Consequently,LB-LOCA is not a dangerous transient for the PTS safety analysis.5.4 Surface flaw and sub-surface flaw

In this paper sub-surface flaw means the flaw exists behind of the claddingand the depth, a, is the distance from the inner surface to the deepest point ofthe flaw. The two models with sub-surface flaw (a/w=0.05 and 0.25) wereperformed and compared with the models with surface flaw. The comparisonis shown in Figs 19 and 20 at the deepest points of the flaw. It can beestimated how much the results from sub-surface flaw reduce comparing withsurface flaw and shown in Table 3. It can be observed that for the sub-surfaceflaw the KJmax reduction rate comparing with surface flaw is almost identicalfor the different PTS transients and a certain a/w and decreases with the flaw

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deepening.Table 3 Comparison between surface flaw and sub-surface flaw

a/w0.050.25

\C 1'Vlmax 'surface flawS.B.43.6471.73R.S.60.58104.34

MPaVi^sub-surface flawS.B.19.9350.84R.S.27.4274.21

reduction rateS.B.%54.3329.12

R.S.%54.7428.88The elastic-plastic calculation always leads to higher K, of the sub-surface

flaw than the linear elastic calculation for the different PTS transients. Thecom parison is shown in Fig. 21 . This rule is very different from the surfaceflaw.5.5 Influence of cladding

In the above analyses it was assumed that the cladding always bear theloads along with the base material during the PTS transients. But it wasreported that the map cracking existed in cladding before PTS transientoccurred. So the supplement analysis was carried out with the conservativeassumption that the cladding would be able to conduct heat flux but lose itsstrength to bear the loads during PTS transient. In order to observe thecladding influence on K, the two models with a/w=0.05 and 0.25 were carriedout considering the cladding lost the ability to bear loads and the results areshown in Table 4.Table 4 Influence of the cladding m ap cracking (M .C.)

a/w0.050.25

K I m a x / M P a V ^without M.C43.6471.73

with M.C30.6287.12For the shallow flaw (a/w=0.05) the map cracking of cladding means to

release the constraints for the flaw and K, would reduce if M.C. exited. But forthe deep flaw the surface constraints is so small that it can be omitted and M.C.would reduce the thickness to bear loads leading to increase Kj.


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6. Conclusion(1) The RPV core betline of Qinshan NPP has enough safety margin to resistthe fracture failure under SB-LOCA and idealized Rancho Seco PTStransient in EOF.(2) The flaws with depth of a/w=0.1-0.2 are more dangerous than othersduring PTS transients.(3) LB-LOC A is not a dangerous transient for PTS safety analysis.(4) For the surface flaws the elastic calculation always leads to higher K,than elastic-plastic, but for the sub-surface flaw this rule is reverse.(5) For the shallow flaws the map cracking influence can be conservatively

ignored but for deep flaws should be considered.

AcknowledgmentThe research was carried out in JAERI according to the STA scientistexchange program. I am grateful to my counterpart, the director and thecolleagues of my Laboratory for helping me throughout the research. Withouttheir helping I could not complete the research successfully.

Yinbiao HENov., 1999

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References1. American Society of Mechanical Engineers: Boiler and Pressure VesselCode, Section III, "Nuclear Power Plant Components - Division 1,Appendix G - Protection Against Non Ductile Failure", New York,(1998) .2. Code of Federal Regulations: Title 10, Part 50, Section 50.61, "FractureToughness Requirements for Protection Against Pressurized ThermalShock Events", and Appendix G, "Fracture Toughness Requirements",Washington, DC , (1996) .3. U.S. Nuclear Regulatory Commission: "Format and Content of Plant-

Specific Pressurized Thermal Shock Safety Analysis Reports forPressurized Water Reactors", Regulatory Guide 1.154, Washington, DC,(1987).4. U.S. Nuclear Regulatory Commission: "Radiation Embrittlement ofReactor Vessel Materials", Regulatory Guide 1.99 (Rev. 2), Washington,DC, (1988) .5. American Society of Mechanical Engineers: Boiler and Pressure VesselCode, Section XI, "Rules for Inservice Inspection of Nuclear Power Plant

Com ponents", New York, (1998) .6. AD INA R & D, Inc.: "A Finite Element Program for Autom atic Dynam icIncremental Nonlinear Analysis-ADINA/Version 7.2", (1998) .7. D. M. Parks: "A Stiffness Derivative Finite Element Technique forDetermination of Crack Tip Stress Intensity Factors", International Journalof Fracture, 1Q, 487 ( 19 74 ).8. I. S. Raju and J. C. Newman, Jr.: "Stress-Intensity Factor for Internal andExternal Surface Cracks in Cylindrical Vessels", Trans. ASME, Ser. J, J.Pressure Vessel Technology, Vol. 104, 293 (1982).9. J. C. New man , Jr. and I. S. Raju: "Stress-Intensity Factor for InternalSurface Cracks in Cylindrical Pressure Vessels", Trans. ASME, Ser. J, 102,

342, (1980) .10. J. D. Qu: "Temperature-Pressure Limits of Qinshan 300MW NPP",SNERDI Technical Report, VSA SR-8, (1990) .11 . S. L. Xu et al.: "Design Transients for Qinshan 300MW PWR NPP",SNERDI Technical Report, (1989).12. W. E. Penell: "Heavy Section Steel Technology Program Fracture Issues",

NUR EG/CP-0105, (1989) .

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Crack shape andsize from NDE

Model(beltline)

Code Materialproperties

Choose specifictransient as PTS

TemperaturePressure

Test

Loading

Heat transfercoefficient fromthermal h ydraulic

Thermalanalysis

Stress analysis underthermal +mechanicalloading

and fracture analysis usingVCE methodJ-integral

Annealing and othermeasures

No K,ic

Crack fronttemperature T

K lc=36.46+3.083exp[0.036(T-ARTND T+56)]

PTS reportART,ND T

Surveillancecapsule test

Neutron fluxcalculation

modified by fluxmeasure

Fig.l Flow chart of fracture mechanics analysis forbeltline of RPV under PTS11 -


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CRACK FRONT

Fig.2 Structural model and mesh

700

600

500

. 400U)10> 300

200

100

- - 2 5 C Base- - 3 5 0 C Base- A - 2 5 C Cladding-X -3 50 C Cladding

0 10 15True strain i

20 25 30

Fig.3 Stress-strain curves in tension for base and cladding

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Temperature (C) Temperature (C)eno o 03OO CO0 1o

era

035n>03

2O5

00

i i i i i

/

-Tmaue

-Peue

T Jq o"03rn033

00

3CD

" co"CDooQ.

3T

tooooIo

Pressure (MPa) Pressure (MPa)


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300

250

- 2 0 0

I| 150C D

100

50

-Temperature- Pressure

1000 2000 3000 4000 5000Time (second)

Fig.6 Idealized Rancho Seco (RS) PTS transient

16

12

10

6000

250.

200. -

a.150.

100. -

50. -

CRA CK

Claddim

ADINA

Newman+Raju

10 . 30 . 40 . 50 .* (degree)

ASME

80 . 90

Fig.7 Comparison of stress intensity factor between different methods (no PTS)

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250.

200. -

- 150. -

100. -

SB+ a/w=0.05 & PL. - a/w=0.05 & EL

-K a/w=0 .10&P L A- a/w=0.10&EL.* a /w=0 .15&PL. - I - a /w=0 .15&ELJ^- a/w=0.20 & PL. -x- a/w=0.20 & EL.* a/w=0.25 & PL. -*- a/w=0.25 & EL.

CRACK FRONT

DEEPEST POINT2100. sec.

TIME (SECOND)" 1 0 3

Fig.8 Comparison of K, between elastic and p lastic calculations under SB-LOC A

250.

2 - TIME (SECOND) 4

Fig.9 Comparison of K, between elastic and plastic calculations under RS PTS

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300. -i

200. -

5UJ100. -

o .

inner surface

SB

time=1000. sec.

outer surface

0. 20. 40. 60. 80. 100. 120. 140. 160. 180WALL THICKNESS (mm)

Fig. 10 Temperature distribution through the wall thickness under SB-LOCA

300.

200. -

100. -

time=1200. sec.

inner surface

R Souter surface

- 1 1 1 1 1 1 1 1 I 1 I T 1 1 1 T 1 0. 2 0. 40. 60. 80. 100. 120. 140. 160. 180WALL THICKNESS (mm)

Fig. 11 Temperature distribution through the wall thickness under RS PTS

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250.

150. 200. 250.TEMPERATURE AT CRACK FRONT (C) 300. 350.

Fig.12 Fracture evaluation for shallow cracks under SB-LOCA

250

100. 150. 200. 250.TEMPE RATUR E AT CRAC K FRO NT (C)

300 350.

Fig. 13 Fracture evaluation for shallow crack s under RS PTS

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250.

a.I 200.111.

2We nt -co~"o100. -CO05HI

50 . -

CRACK FRONT

a/w

Fig. 14 Kj and KIC for different flaws (a/w=0.05~0.9) and PTS transients

Fig. 15 D istribution of K, along crack front for a/w=0.1 ~ 0 .9 under SB-LO CA

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250.Cladding

0. 10. 20. 30, 40 . 50. (degree) 60 .

Basecrack front

80 . 90

Fig. 16 Distribution ofK; along crack front fora/w= 0.1~0 .9 under RS PTS

100.

oTURE(

orUJ0 -

300.~riwIt00. - JIir\ time=2\ ^ ^ time=4.

\ ^ time=6.\ / ^ time=8.

^ time=9.

inner surface

secsecsecsecsec.

outer surface

0. 20. 40. 60 . 80. 100. 120.WALL THICKNESS (mm) 140. 160. 180.

Fig. 17 Temperature distribution through the wall thickness under LB-LOCA

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250.

200. -

tr 150.O

5 ioo.C O(/>wocS o

50 . -

LB

t ime=2. sec.

DEEPEST POINTCRACK

t ime=9. sec.

TIME (SECOND) 10

Fig.18 Kj time history under LB-LOCA fora/w=0.05 and 0.25

250.

200. -

150. -

C OS ioo.

50 . -

SB Claddingtime=2100. sec.

interface

a/w=0.25 su rface Haw

a/vM).25 sub-sufface flaw a/w=U05 surface flawin te r face

a/w=0.dS sub-surface flaw0. 10. 20. 30 . 40 . 50. 60. 70 . 80 . 90

* (degree)

Fig. 19 Com parison of K,between surface andsub-surface flaw under SB-LOCA

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250.

a/w=0.25 sub-surface flaw a/w=0.05 surface flawinterface

a/w=0.06 sub-surface flaw0. 10 20. 30. 60 . 70. 80. 90.

(degree)

Fig.20 Com parison of K,between surface andsub-surface flaw under RS PTS

250. -

200.

I^ ^ J ^^^ t ime=2100 . sec .

DC1 1 V ^ / tme-2400. sec

Cladding

Tc1

- BaseSub-surface flaw

a [

w 100. -

50 . -

interface

deepest point

0. 10. 20. 30. 40 . (degree)

50.a/w=0.05 SB PL a/w=0 05 SB EL

60 . 70 . 80. 90

Fig.21 Comparison of K,between elastic andplastic calculations forsub-surface flaw

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Appendix: Data for curve figures

Data for Fig.3 Stress-strain curves in tension for base and claddingmaterial: base 25 Ctrue strain

0.00000E+002.18905E-015.21900E+001.02190E+011.52190E+01

true stress0.00000E+004.40000E+026.00000E+026.50000E+026.63000E+02

material: base 350 Ctrue strain0.00000E+001.92090E-015.21900E+001.02190E+011.52190E+01

true stress0.00000E+003.40000E+025.00000E+025.50000E+025.63000E+02

material: cladding 25 Ctrue strain0.00000E+001.06154E-015.00000E-011.25000E+007.60000E+002.80000E+01

true stress0.00000E+002.07000E+022.59300E+023.12500E+024.38800E+024.92000E+02

material: cladding 350 Ctrue strain0.00000E+007.38372E-025.00000E-011.25000E+007.60000E+002.80000E+01

true stress0.00000E+001.27000E+021.79000E+022.32500E+023.58800E+024.12000E+02

Data for Fig.4 SB-LOCA (SB) transient

t ime pressure

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0.00000E+001.00000E+022.00000E+021.34000E+035.00000E+03

1.52000E+011.32000E+017.70000E+008.70000E+008.70000E+00

time0.00000E+001.25000E+032.10000E+035.00000E+03

temperature2.88800E+022.33800E+021.83800E+021.55800E+02

Data for F ig.5 LB -LOCA (LB) transienttime

0.00000E+002.50000E-012.00000E+004.00000E+006.00000E+008.00000E+009.00000E+00

pressure1.52000E+01

8.70000E+006.20000E+003.70000E+007.00000E-010.00000E+000.00000E+00

time0.00000E+002.00000E+004.00000E+006.00000E+008.00000E+009.00000E+00

temperature2.88800E+022.69800E+022.36800E+021.78800E+028.88000E+012.48000E+01

Data for Fig.6 Idealized Rancho Seco (RS) PTS transienttime

0.00000E+006.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+03

pressure1.03000E+011.17500E+011.30000E+011.40000E+011.46200E+011.47000E+011.45000E+011.42000E+01

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4.80000E+035.40000E+036.00000E+03

1.38000E+011.35000E+011.32000E+01

time0.00000E+006.00000E+021.20000E+031.80000E+032.40000E+033.00000E+O33.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

temperature3.12000E+022.55000E+022.12000E+021.75000E+021.50000E+021.42000E+021.38000E+021.40000E+021.41000E+021.50000E+021.62000E+02

Data for Fig.7 Comparison of stress intensity factor between different methods (no PTS)ADINA

degree0.00000E+008.33300E+001.66660E+012.50000E+013.16670E+013.83330E+014.50000E+014.95000E+015.40000E+015.85000E+016.30000E+016.75000E+017.20000E+017.65000E+018.10000E+018.55000E+019.00000E+01

stress intensity factor4.53800E+014.41900E+014.58700E+014.87500E+015.17800E+015.43900E+015.64300E+015.81400E+015.94200E+016.05500E+016.15300E+016.23600E+016.30300E+016.35600E+016.39400E+016.41700E+016.42400E+01

Newman+Rajudegree

0.00000E+002.25000E+01stress intensity factor

4.26500E+014.63800E+01

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4.50000E+016.75000E+019.00000E+01

5.53800E+016.16900E+016.38800E+01

ASME degree9.00000E+01 stress intensity factor6.02400E+01

Data for Fig.8 Comparison of KJ between elastic and plastic calculations under SB-LOCAa/w=0.05 & EL.

TIME0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.13000E+034.42000E+034.71000E+035.00000E+03

KJ2.67800E+011.77900E+012.20800E+012.59100E+012.93200E+013.23400E+013.51000E+013.75600E+013.97900E+014.18100E+014.36400E+014.11400E+013.87700E+013.67400E+013.50400E+013.36300E+013.24600E+013.14900E+013.06900E+013.00400E+012.95100E+01

a /w=0.10&EL.TIME

0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+03

KJ3.80500E+012.41200E+012.92900E+013.39600E+013.80900E+014.17300E+014.49200E+01

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1.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.13000E+034.42000E+034.71000E+035.00000E+03

4.77700E+015.03600E+015.26700E+015.47300E+015.17600E+014.86900E+014.59900E+014.36900E+014.17700E+014.01500E+013.88000E+013.76700E+013.67400E+013.59600E+01

a/w=0.15 & EL.TIME

0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.13000E+034.42000E+034.71000E+035.00000E+03


a/w=0.20 & EL.TIME

0.00000E+002.50000E+025.00000E+02

KJ5.45100E+013.25600E+013.84100E+01

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7.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.13000E+034.42000E+034.71000E+035.00000E+03


a/w=0.25 & EL.TIME



a/w=0.05 & PL.

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TIME0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.130OOE+034.42000E+034.71000E+035.00000E+03


a/w=0.10& PL.TIME

0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.13000E+034.42000E+03

KJ3.80400E+012.40900E+012.92100E+013.36200E+013.73100E+014.05100E+014.32800E+014.57600E+014.80000E+014.99800E+015.17100E+014.87000E+014.55600E+014.28000E+014.04400E+013.84500E+013.67800E+013.53800E+013.42000E+01

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4.71000E+035.00000E+03 3.32200E+013.24000E+01

a/w=0.15 & PL.TIME0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+033.55000E+033.84000E+034.13000E+034.42000E+034.71000E+035.00000E+03


a/w=0.20 & PL.TIME

0.00000E+002.50000E+025.00000E+027.50000E+021.00000E+031.25000E+031.42000E+031.59000E+031.76000E+031.93000E+032.10000E+032.39000E+032.68000E+032.97000E+033.26000E+03

KJ5.45200E+013.25400E+013.83400E+014.36100E+014.81700E+015.21800E+015.54000E+015.83300E+016.10000E+016.33800E+016.54700E+016.26400E+015.91800E+015.60000E+015.32400E+01

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3.55000E+033.84000E+034.13000E+034.42000E+034.71000E+035.00000E+03

5.09000E+014.89200E+014.72600E+014.58600E+014.46900E+014.37000E+01

a/w=0.25 & PL.TIME



Data for Fig.9 Comparison of KJ between elastic and plastic calculations under RS PTSa/w=0.05 & EL.

TIME6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+03

KJ3.90100E+015.19200E+015.92800E+016.05800E+015.57100E+015.02400E+014.42300E+013.97100E+01

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5.40000E+036.00000E+03

3.41700E+012.89200E+01

a/w=0.10 & EL.TIME6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ5.08100E+016.68000E+017.55600E+017.67300E+017.03000E+016.30300E+015.52200E+014.92500E+014.23200E+013.58100E+01

a/w=0.15 & EL.TIME

6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ5.87200E+017.68200E+018.67400E+018.82100E+018.12100E+017.30600E+016.43500E+015.75700E+014.99000E+014.27000E+01

a/w=0.20 & EL.TIME

6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ6.47900E+018.43100E+019.50800E+019.69300E+018.97500E+018.11500E+017.19400E+016.46600E+015.66000E+014.90100E+01

a/w=0.25 & EL.TIME KJ

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6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

6.99800E+019.05300E+011.02030E+021.04330E+029.72800E+018.85100E+017.91000E+017.15100E+016.32800E+015.54800E+01

a/w=0.05 & PL.TIME

6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ3.64000E+014.67000E+015.21100E+015.26500E+014.71600E+014.08700E+013.37100E+012.79700E+012.03200E+011.12300E+01

a/w=0.10 & PL.TIME

6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ4.91600E+016.39000E+017.17800E+017.24500E+016.57100E+015.80100E+014.96600E+014.31200E+013.53500E+012.77500E+01

a/w=0.15 & PL.TIME

6.00000E+02I.20000E+031.80000E+032.40000E+033.00000E+03

KJ5.74000E+017.44000E+018.36900E+018.47000E+017.75800E+01

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3.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

6.91600E+016.01000E+015.29500E+014.48100E+013.70000E+01

a/w=0.20 & PL.TIME

6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ6.37100E+018.22300E+019.25000E+019.39800E+018.67300E+017.79300E+016.85000E+016.09500E+015.26000E+014.46400E+01

a/w=0.25 & PL.TIME6.00000E+021.20000E+031.80000E+032.40000E+033.00000E+033.60000E+034.20000E+034.80000E+035.40000E+036.00000E+03

KJ6.90000E+018.85200E+019.94400E+011.01480E+029.43300E+018.54500E+017.59100E+016.81700E+015.98000E+015.18300E+01

Data for Fig. 10 Tem perature distribution through the wall thickne ss under S B-LO CAtime=1000. sec.

WALL THICKNESS0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+00

TEMPERATURE2.46100E+022.47157E+022.48201E+022.49232E+022.50252E+022.50252E+022.52019E+02

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J AE RI- Resea rch 20 0 0 - 0 12

1.18810E+011.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02

2.53715E+022.56154E+022.58439E+022.61625E+022.64494E+022.68287E+022.71473E+022.75284E+022.78040E+022.80546E+022.81336E+02

time=2100. sec.WALL THICKNESS0.00000E+00

1.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02

TEMPERATURE1.86061E+021.88016E+021.89953E+021.91870E+021.93768E+021.93768E+021.96843E+021.99822E+022.04159E+022.08286E+022.14149E+022.19555E+022.26909E+022.33298E+022.41251E+022.47258E+022.52948E+022.54798E+02

time=3550. sec.WALL THICKNESS

0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+01

TEMPERATURE1.70883E+021.71835E+021.72782E+021.73726E+021.74665E+021.74665E+021.76176E+021.77664E+021.79874E+02

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2.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02

1.82029E+021.85180E+021.88186E+021.92442E+021.96312E+022.01377E+022.05409E+022.09407E+022.10751 E+02

time=5000. sec.WALL THICKNESS0.00000E+00

1.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02


Data for Fig. 11 Temperature distribution through the wall thickness under RS PTStime=1200 . sec.

WALL THICKNESS0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+01

TEMPERATURE2.25465E+022.27463E+022.29440E+022.31393E+022.33325E+022.33325E+022.36613E+022.39790E+02

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1.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02

2.44397E+022.48761E+022.54923E+022.60563E+022.68161E+022.74684E+022.82684E+022.88623E+022.94152E+022.95926E+02

time=2400. sec.WALL THICKNESS0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02

TEMPERATURE1.63735E+021.65902E+021.68052E+021.70185E+021.72301E+021.72301E+021.75678E+021.78980E+021.83839E+021.88521E+021.95282E+022.01631 E+022.10473E+022.18364E+022.28486E+022.36374E+022.44055E+022.46603E+02

time=4200. sec.WALL THICKNESS0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+012.38250E+01

TEMPERATURE1.45215E+021.46055E+021.46894E+021.47730E+021.48564E+021.48564E+021.49878E+021.51182E+021.53138E+021.55065E+02

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43/65


2.06560E+021.97270E+021.91600E+021.87320E+021.83480E+021.79860E+021.76390E+021.73030E+021.69750E+021.66560E+021.63420E+021.60340E+02

4.18100E+014.36400E+014.11400E+013.87700E+013.67400E+013.50400E+013.36300E+013.24600E+013.14900E+013.06900E+013.00400E+012.95100E+01

a/w=0.10 TEMPERATURE2.88800E+022.82210E+022.73970E+022.65080E+022.55820E+022.46280E+022.38440E+022.30020E+022.21350E+022.12520E+022.03550E+021.96750E+021.91760E+021.87400E+021.83370E+021.79560E+021.75920E+021.72410E+021.69010E+021.65710E+021.62490E+02


a/w=0.15TEMPERATURE

2.88800E+022.83320E+022.75950E+022.67750E+022.59050E+02

KJ4.67800E+012.87000E+013.43400E+013.94900E+014.40800E+01

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2.49990E+022.42720E+022.34790E+022.26530E+022.18060E+022.09400E+022.01690E+021.96050E+021.91190E+021.86760E+021.82620E+021.78700E+021.74960E+021.71370E+021.67900E+021.64540E+02


a/w=0.20TEMPERATURE2.88800E+02

2.84240E+022.77690E+022.70150E+022.62000E+022.53400E+022.46640E+022.39170E+022.31320E+022.23190E+022.14840E+022.06420E+022.00160E+021.94840E+021.90020E+021.85560E+021.81370E+021.77400E+021.73620E+021.69990E+021.66500E+02


a/w=0.25TEMPERATURE2.88800E+02 KJ6.18000E+01

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KIC: ART=70 CTEMPERATURE0.00000E+003.20000E+01

5.20000E+017.20000E+019.20000E+011.12000E+021.23448E+023.50000E+02

KIC3.83200E+014.23500E+014.85700E+016.13400E+018.75700E+011.41450E+021.95000E+021.95000E+02

KIC:ART=132CTEMPERATURE1.12000E+021.32000E+021.52000E+021.72000E+021.85448E+023.50000E+02

KIC4.77300E+015.96100E+018.40200E+011.34160E+021.95000E+021.95000E+02

Data for F ig. 13 Fracture evaluation for shallow cracks under RS PTS

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a/w=0.05 TEMPERATURE2.74480E+022.37070E+022.02890E+021.76150E+021.62070E+021.53240E+021.50060E+021.47990E+021.52170E+021.60180E+02

KJ3.90100E+015.19200E+015.92800E+016.05800E+015.57100E+015.02400E+014.42300E+013.97100E+013.41700E+012.89200E+01

a/w=0.10 TEMPERATURE2.79500E+022.43760E+022.10320E+021.83160E+021.67530E+021.57400E+021.52860E+021.49930E+021.52870E+021.59810E+02

KJ5.08100E+016.68000E+017.55600E+017.67300E+017.03000E+016.30300E+015.52200E+014.92500E+014.23200E+013.58100E+01

a/w=0.15TEMPERATURE

2.83940E+022.49940E+022.17300E+021.89800E+021.72800E+021.61430E+021.55600E+021.51830E+021.53600E+021.59530E+02

KJ5.87200E+017.68200E+018.67400E+018.82100E+018.12100E+017.30600E+016.43500E+015.75700E+014.99000E+014.27000E+01

a/w=0.20TEMPERATURE

2.87860E+022.55650E+022.23830E+02

KJ6.47900E+018.43100E+019.50800E+01

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1.96090E+021.77840E+021.65310E+021.58260E+021.53680E+021.54370E+021.59330E+02

9.69300E+018.97500E+018.11500E+017.19400E+016.46600E+015.66000E+014.90100E+01

a/w=0.25TEMPERATURE

2.91290E+022.60900E+022.29920E+022.02010E+021.82660E+021.69030E+021.60840E+021.55460E+021.55160E+021.59210E+02

KJ6.99800E+019.05300E+011.02030E+021.04340E+029.72800E+018.85100E+017.91000E+017.15100E+016.32800E+015.54800E+01

KIC: ART=70 CTEMPERATURE0.00000E+00

3.20000E+015.20000E+017.20000E+019.20000E+011.12000E+021.23448E+023.50000E+02

KIC3.83200E+014.23500E+014.85700E+016.13400E+018.75700E+011.41450E+021.95000E+021.95000E+02

KIC:ART=132CTEMPERATURE1.12000E+021.32000E+021.52000E+021.72000E+021.85448E+023.50000E+02

KIC4.77300E+015.96100E+018.40200E+011.34160E+021.95000E+021.95000E+02

Data for Fig. 14 KJ and KIC for different flaws (a/w=0.05-0.9) and PTS transients

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SB time=2100. sec.a/w

5.00000E-021.00000E-011.50000E-012.00000E-012.50000E-013.00000E-014.00000E-015.00000E-016.00000E-017.00000E-018.00000E-019.00000E-01

KJ4.36400E+015.47300E+016.21500E+016.74600E+017.17300E+017.41500E+017.97000E+018.42600E+018.79100E+019.09200E+019.18900E+019.04200E+01

RS time=2400. sec.a/w

5.00000E-021.00000E-011.50000E-012.00000E-012.50000E-013.00000E-014.00000E-015.00000E-016.00000E-017.00000E-018.00000E-019.00000E-01

KJ6.05800E+017.67300E+018.82100E+019.69300E+011.04340E+021.09040E+021.19890E+021.29420E+021.37700E+021.45370E+021.50470E+021.53630E+02

KIC: ART=170 Ca/w

5.00000E-021.00000E-011.50000E-012.00000E-012.50000E-013.00000E-014.00000E-015.00000E-016.00000E-017.00000E-018.00000E-019.00000E-01

KIC6.53400E+017.36400E+018.36700E+019.56700E+011.09740E+021.26010E+021.64950E+021.95000E+021.95000E+021.95000E+021.95000E+021.95000E+02

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KIC: ART=208 Ca/w

5.00000E-021.00000E-011.50000E-012.00000E-012.50000E-013.00000E-014.00000E-015.00000E-016.00000E-017.00000E-018.00000E-019.00000E-01

KIC5.21900E+015.61800E+016.08000E+016.60700E+017.19600E+017.84300E+019.27800E+011.08300E+021.23810E+021.38070E+021.49700E+021.57630E+02

Data for Fig.15 Distribution of KJ along crack front for a/w=0.1-0.9under SB-LOCAa/w=0.1

degree0.00000E+006.76000E+001.36100E+011.36100E+012.06700E+012.93400E+013.80200E+014.66900E+015.53200E+016.40000E+017.26900E+018.14300E+019.00000E+01

KJ4.76200E+014.60800E+014.91100E+013.83700E+014.42600E+014.56100E+014.78800E+014.99800E+015.17300E+015.30600E+015.39800E+015.45300E+015.47300E+01

a/w=0.2degree

0.00000E+003.37000E+006.76000E+006.76000E+001.71000E+012.62200E+013.53300E+01

KJ6.49900E+016.22700E+016.82900E+015.35500E+015.62500E+015.82100E+016.07800E+01

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4.44500E+015.35500E+016.26500E+017.17500E+018.08800E+019.00000E+01

6.30100E+016.47700E+016.60300E+016.68400E+016.73000E+016.74600E+01

a/w=0.3degree

0.00000E+002.25000E+004.50000E+004.50000E+001.47700E+012.41700E+013.35800E+014.29800E+015.23900E+016.17800E+017.12000E+018.05600E+019.00000E+01


a/w=0.4degree

O.OOOOOE+001.69000E+003.37000E+003.37000E+001.36100E+012.31600E+013.27000E+014.22600E+015.18000E+016.13600E+017.09100E+018.04600E+019.00000E+01


a/w=0.5degree

0.00000E+001.35000E+002.70000E+00

KJ1.03710E+029.93600E+011.16540E+02

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a/w=0.8

2.70000E+001.36100E+012.31600E+013.27100E+014.22600E+015.18000E+016.13600E+017.09000E+018.04400E+019.00000E+01

8.89500E+018.73600E+018.63700E+018.67800E+018.67300E+018.62900E+018.56200E+018.49300E+018.44400E+018.42600E+01

a/w=0.6degree

0.00000E+001.12000E+002.25000E+002.25000E+001.30300E+012.26500E+013.22700E+014.18900E+015.15100E+016.11400E+017.07500E+018.03900E+019.00000E+01


a/w=0.7degree

0.00000E+009.60000E-011.93000E+001.93000E+002.01500E+012.88800E+013.76100E+014.63500E+015.50800E+016.38100E+017.25400E+018.12700E+019.00000E+01


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degree0.00000E+008.40000E-011.69000E+001.69000E+002.43200E+013.25300E+014.07400E+014.89500E+015.71600E+016.53600E+017.35800E+018.18000E+019.00000E+01


a/w=0.9degree

0.00000E+007.50000E-011.50000E+001.50000E+002.80700E+013.58100E+014.35500E+015.13000E+015.90400E+016.67700E+017.45200E+018.22700E+019.00000E+01


Data for Fig. 16 Distribution of KJ along crack front for a/w=0.1-0.9 under RS PTSa/w=0.1

degree0.00000E+006.76000E+001.36100E+011.36100E+012.06700E+012.93400E+013.80200E+014.66900E+01

KJ6.58000E+016.38300E+016.81100E+015.31200E+016.12400E+016.32000E+016.65200E+016.96200E+01

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5.53200E+016.40000E+017.26900E+018.14300E+019.00000E+01

7.22100E+017.42100E+017.56000E+017.64300E+017.67300E+01

a/w=0.2degree

0.00000E+003.37000E+006.76000E+006.76000E+001.71000E+012.62200E+013.53300E+014.44500E+015.35500E+016.26500E+017.17500E+018.08800E+019.00000E+01


a/w=0.3 degree0.00000E+002.25000E+004.50000E+004.50000E+001.47700E+012.41700E+013.35800E+014.29800E+015.23900E+016.17800E+017.12000E+018.05600E+019.00000E+01


a/w=0.4degree

0.00000E+001.69000E+003.37000E+003.37000E+00

KJ1.27480E+021.22050E+021.40530E+021.07750E+02

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1.36100E+012.31600E+013.27000E+014.22600E+015.18000E+016.13600E+017.09100E+018.04600E+019.00000E+01

1.08580E+021.10060E+021.13440E+021.16120E+021.17960E+021.19030E+021.19570E+021.19810E+021.19890E+02

a/w=0.5degree

0.00000E+001.35000E+002.70000E+002.70000E+001.36100E+012.31600E+013.27100E+014.22600E+015.18000E+016.13600E+017.09000E+018.04400E+019.00000E+01


a/w=0.6degree

0.00000E+001.12000E+002.25000E+002.25000E+001.30300E+012.26500E+013.22700E+014.18900E+015.15100E+016.11400E+017.07500E+018.03900E+019.00000E+01


a/w=0.7degree KJ

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JA ER I- Research 2000-012

0.00000E+009.60000E-011.93000E+001.93000E+002.01500E+012.88800E+013.76100E+014.63500E+015.50800E+016.38100E+017.25400E+018.12700E+019.00000E+01

1.91420E+021.85840E+022.09620E+021.71970E+021.57350E+021.57460E+021.56760E+021.55130E+021.52720E+021.50040E+021.47630E+021.45970E+021.45370E+02

a/w=0.8degree

0.00000E+008.40000E-011.69000E+001.69000E+002.43200E+013.25300E+014.07400E+014.89500E+015.71600E+016.53600E+017.35800E+018.18000E+019.00000E+01

KJ2.15800E+02

2.11930E+022.27460E+021.96910E+021.72800E+021.73830E+021.71400E+021.67490E+021.62900E+021.58270E+021.54240E+021.51460E+021.50470E+02

a/w=0.9degree

0.00000E+007.50000E-011.50000E+001.50000E+002.80700E+013.58100E+014.35500E+015.13000E+015.90400E+016.67700E+017.45200E+018.22700E+01

KJ2.43650E+022.42770E+022.44980E+022.2471 OE+021.89200E+021.90030E+021.85250E+021.79050E+021.72190E+021.65300E+021.59270E+021.55120E+02

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9.00000E+01 1.53630E+02

Data for Fig . 17 Temperature distribution through the wall thickness under LB -LO CAtime=2. sec.

WALL THICKNESS0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02




TEMPERATURE2.51743E+022.62331E+022.70306E+022.76330E+022.80955E+022.80955E+022.85894E+022.87761E+022.88606E+022.88750E+022.88797E+022.88798E+022.88800E+022.88800E+022.88800E+022.88800E+02

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1.42480E+021.74000E+02

2.88800E+022.88800E+02

time=6. sec.WALL THICKNESS0.00000E+001.00000E+002.00000E+003.00000E+004.00000E+004.00100E+007.94102E+001.18810E+011.78530E+012.38250E+013.28768E+014.19286E+015.56485E+016.93685E+019.01640E+011.10960E+021.42480E+021.74000E+02





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JA ER I- Research 2000 -012

time=9. sec.WALL THICKNE SS TEMPERATURE0.00000E+00 8.77869E+011.00000E+00 1.40575E+022.00000E+00 1.80214E+023.00000E+00 2.11027E+024.00000E+00 2.35542E+024.00100E+00 2.35542E+027.94102E+00 2.63575E+021.18810E+01 2.77352E+021.78530E+01 2.85629E+022.38250E+01 2.87924E+023.28768E+01 2.88711E+024.19286E+01 2.88767E+025.56485E+01 2.88800E+026.93685E+01 2.88798E+029.01640E+01 2.88800E+021.10960E+02 2.88800E+021.42480E+02 2.88800E+021.74000E+02 2.88800E+02

Data for F ig. 18 KJ time h istory under LB-L OC A for a/w=0.05 and 0.25a/w=0.05 TIME KJ

2.00000E+00 1.27200E+014.00000E+00 1.24400E+016.00000E+00 1.36400E+018.00000E+00 2.07700E+019.00000E+00 2.60300E+01

a/w=0.25 TIME KJ2.00000E+00 2.58000E+014.00000E+00 1.70100E+016.00000E+00 6.82000E+008.00000E+00 6.54000E+009.00000E+00 8.25000E+00

Data for Fig. 19 Com parison of KJ between surface and sub-surface flaw under SB -LOC A

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4.89500E+015.58000E+016.26500E+016.94700E+017.63500E+018.31900E+019.00000E+01

1.54700E+011.68800E+011.79400E+011.87800E+011.93800E+011.97700E+011.99400E+01

Data for Fig.20 Comparison of KJ between surface and sub-surface flaw under RS PTSa/w=0.25 surface flaw

degree5.40000E+001.50000E+012.43700E+013.37500E+014.31200E+015.25100E+016.18700E+017.12300E+018.06100E+019.00000E+01

KJ8.33800E+018.69400E+018.95900E+019.37500E+019.73500E+011.00150E+021.02120E+021.03390E+021.04100E+021.04340E+02

a/w=0.05 surface flawdegree

2.80700E+013.52000E+014.20200E+014.89500E+015.58000E+016.26500E+016.94700E+017.63500E+018.31900E+019.00000E+01

KJ4.56800E+015.26500E+015.37300E+015.53500E+015.68800E+015.82100E+015.92500E+015.99600E+016.03800E+016.05800E+01

a/w=0.25 sub-surface flawdegree

5.40000E+001.50000E+012.43700E+013.37500E+014.31200E+01

KJ4.59800E+014.75100E+015.77500E+016.37600E+016.77500E+01

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5.25100E+01 7.04300E+016.18700E+01 7.22300E+017.12300E+01 7.33700E+018.06100E+01 7.40000E+019.00000E+01 7.42100E+01

a/w=0.05 sub-surface flawdegree KJ

2.80700E+01 1.18600E+013.52000E+01 1.29200E+014.20200E+01 1.81400E+014.89500E+01 2.11600E+015.58000E+01 2.31300E+016.26500E+01 2.46100E+016.94700E+01 2.57900E+017.63500E+01 2.66300E+018.31900E+01 2.71800E+019.00000E+01 2.74200E+01

Data for Fig.21 Comparison of KJ between elastic and plastic calculations for sub-surfaceflaw

a/w=0.05 SB ELdegree KJ

2.80700E+01 8.27000E+003.52000E+01 9.49000E+004.20200E+01 1.33000E+014.89500E+01 1.54700E+015.58000E+01 1.68800E+016.26500E+01 1.79400E+016.94700E+01 1.87800E+017.63500E+01 1.93800E+018.31900E+01 1.97700E+019.00000E+01 1.99400E+01

a/w=0.05 RS ELdegree KJ

2.80700E+01 1.18600E+013.52000E+01 1.29200E+014.20200E+01 1.81400E+014.89500E+01 2.11600E+015.58000E+01 2.31300E+016.26500E+01 2.46100E+01

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6.94700E+017.63500E+018.31900E+019.00000E+01

2.57900E+012.66300E+012.71800E+012.74200E+01

a/w=0.25 SB ELdegree

5.40000E+001.50000E+012.43700E+013.37500E+014.31200E+015.25100E+016.18700E+017.12300E+018.06100E+019.00000E+01

KJ3.29300E+013.42000E+014.11800E+014.50400E+014.74500E+014.89600E+014.99000E+015.04500E+015.07400E+015.08400E+01

a/w=0.25 RS ELdegree

5.40000E+001.50000E+012.43700E+013.37500E+014.31200E+015.25100E+016.18700E+017.12300E+018.06100E+019.00000E+01

KJ4.59800E+014.75100E+015.77500E+016.37600E+016.77500E+017.04300E+017.22300E+017.33700E+017.40000E+017.42100E+01

a/w=0.05 SB PLdegree2.80700E+01

3.52000E+014.20200E+014.89500E+015.58000E+016.26500E+016.94700E+017.63500E+018.31900E+019.00000E+01

KJ9.87000E+001.23600E+011.66600E+011.90600E+012.06700E+012.19000E+012.28500E+012.35000E+012.39100E+012.40800E+01

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a/w=0.05 RS PLdegree

2.80700E+013.52000E+014.20200E+014.89500E+015.58000E+016.26500E+016.94700E+017.63500E+018.31900E+019.00000E+01

KJ1.56200E+011.89100E+012.44300E+012.76400E+012.98900E+013.16100E+013.29500E+013.38900E+013.44500E+013.46900E+01

a/w=0.25 SB PLdegree5.40000E+001.50000E+012.43700E+013.37500E+014.31200E+015.25100E+016.18700E+017.12300E+018.06100E+019.00000E+01

KJ4.33600E+014.53500E+015.05400E+015.38500E+015.61600E+015.77500E+015.88100E+015.94700E+015.98300E+015.99500E+01

a/w=0.25 RS PLdegree

5.40000E+001.50000E+012.43700E+013.37500E+014.31200E+015.25100E+016.18700E+017.12300E+018.06100E+019.00000E+01

KJ6.41500E+016.73400E+017.36200E+017.81400E+018.16700E+018.42800E+018.61300E+018.73400E+018.80200E+018.82500E+01

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JAERI Research

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