Text

Rev. 0 to M-EP-2004-001, Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack Growth in the Un-Inspected Regions of the Control Rod Drive Mechanism Nozzles at ANO, Unit 1, App. C Through P
	ML040540696
Person / Time
Site:	Arkansas Nuclear
Issue date:	02/02/2004
From:	; Entergy Operations
To:	; Document Control Desk, Office of Nuclear Reactor Regulation
References
	CNRO-2004-00008 M-EP-2004-001, Rev 0
	Download: ML040540696 (152)
	v • d • e

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 1 of 10 Engineering Report M-EP-2004-001 -00 Stress Corrosion Crack Growth Analysis Through-wall flaw Developed by Central Engineering Programs, Entergy Operations Inc.

Developed by: J. S. Brihmadesom Verified by: B. C. Gray Note : Only for use when R..,t,.,/t is between 2.0 and 5.0 (Thick-wall Cylinder)

References:

1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"38.5"degree Nozzle, "Uphill" Azimuth Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

Through Wall Axial Flaw BZ := ULStrs.Dist - FSnde.data.sheet Location of Blind Zone above nozzle bottom (inch)

IDeveloped by:

Verified by:

c2'G

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 2 of 10 Engineering Report M-EP-2004-001 -00 InDut Data :

L := 0.25 Initial Crack Length TW axial Based on Stress Distribution. Bottom end to be set @ approximately 1 Oksi.

M I of Crack f

e s

° i

f

° e

05 O

Verified by: l I

r t? \\7 t :

~L.103 10 3 1+459.67 Tref+4 59.67)j Co := e

.aX C Timopr:= Years 365 24 od Ro := -

2 Timopr Cbk:=

'urn Ri:=-id t:= Ro - R; Rm:= Ri +-

2 CFinhr:= 1.417 1 Irim Prntblk:=

50 I

L 2

lDeveloped by:

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 3 of 10 Engineering Report M-EP-2004-001 -00 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

DataAll 0

-20.71

-13.89

-10.09

-6.78

-2.47 1.32 5.79

-0.12

-6.37

-11.55

-16.26 2.38 20.09 19.42 1.11

-21.71

-29.32 3.23 35.24 33.45 21.85

-18.78

-33.48 3.92 46.8 45.16 37.94 8.37

-15.97 4.46 51.85 48.95 42.42 37.19 32.64 4.9 55.05 50.07 49.8 57.89 55.56 5.12 55.22 51.16 55.73 63.87 70.72 5.34 53.1 55.78 60.81 70.8 73.94 5.56 50.45 53.11 62.73 69.7 72.99 AllAxl:= DataAIl AIIID DataAl I)

AIIOD:= DataA l 5 IDeveloped by:

"-) I r-I- R,

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 4 of 10 Engineering Report M-EP-2004-001 -00 100 75

-d 50 25 0

l 1.818 4.$98 2 0

.,I I

I

-25

-50 11 0.5 1

1.5 2

2.5 3

3.5 Axial Distance above Bottom [inch]

4 4.5 5

5.5 6

ID Distribution OD distribution BZ = 1.818 Data:=

0

-20.713 -13.891 -10.091

-6.781

-2.467 )

1.324 5.79

-0.121

-6.365

-11.555 -16.261 2.385 20.088 19.42 1.112

-21.708 -29.318 3.235 35.237 33.451 21.848

-18.777 -33.482 3.916 46.802 45.156 37.936 8.372

-15.972 4.461 51.852 48.945 42.423 37.185 32.638 4.898 55.053 50.07 49.796 57.893 55.558 5.119 55.224 51.157 55.733 63.865 70.724 5.34 53.096 55.783 60.808 70.802 73.937 )

Axl:= Data ID := Data (5)

OD := Data RID:= regress(Axl, ID, 3)

ROD := regress(Axl, OD,3)

IIDeveloped by:V I

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 5 of 10 Engineering Report M-EP-2004-001 -00 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ IflcstrSAvg :=

20 NM__

ffi Sat Aug 09 11:44:49 AM 2003-IDeveloped by.

Verified by. I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 6 of 10 Engineering Report M-EP-2004-001 -00 ProPLength = 3.08 Flaw Length vs. Time 1.5 U

.~TWCJwsccj 0

I 0.5 nA

-0.5 -0 0.2 0.4 0.6 0.8' I

1.2 1.4 1.6 1.8 TWCPSCC(jl)

Operating Time {years)

Entergy Model 2

U Co U

U 1.5 0.5 Increase in Half Length 0 0 0.2 0.4 0.6 0.8 1

1.2 Operating Time (Years) 1.4 1.6 1.8 Devel ped y:

V rifid by IDeveloped by.,

Venfied by. I

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 7 of 10 Engineering Report M-EP-2004-001 -00 IDeveloped by Verili C'2-',7 Q

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 8 of 10 Engineering Report M-EP-2004-001 -00 TWCPscc(j 6)

-14.71

-14.71 TWCp"SCC(j 7) 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.173 6.1731 6.173 6.173 TWCp%%-sCC

.8)

-4.117

-4.117 Developed by:

Verified by:

lIDeveloped by.,

Verifed by.:

I

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 9oflO Engineering Report M-EP-2004-001 -00 Hoop Stress Plot 70 A

30 as

-1 0

-50 0

1 2

3 4

Distance from Nozzle Bottom

{inch) 5 6

0 1

t A -10.

-15 ODSurfaceSIF

-ID Surface SIF

-__ Average SIP I

0.0 0.5 1.0 Operating Time (years) 1.5 2.0 Developed by rf-e11

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 27 Page 10 of 10 Engineering Report M-EP-2004-001 -00 06 -

04a 0A. -

102 -

0.0 -

00 05 1.0 Operating Tkire (pears) 1.5 2.0 IDeveloped by:

Verified by.

Entergy Operations Inc.

Centra I Engineering Programs Appendix C; Attachment 28 Page 1 of 11 Engineering Report M-EP-2004-001 -00 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Programs, Entergy Operations Inc.

Developed by: J. S. Brihmadesam Verified by: B. C. Gray

References:

1) "Stress Intensity factors for Part-through Surface Cracks"; NASA TM-11707; July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"38.5" Degree Nozzle, "Mid-Plane" Azimuth Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmlt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

ID Surface Flaw Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray cwzlz~

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 28 Page 2 of 11 Engineering Report M-EP-2004-001-00

MM M

od R.

2 id Rid := 2 t:= R-Rid Rm :Rid + 2 Timopr := Years*365-24 CFnhr := 1.417-105 Timopr Cblk:= -p htim I

I T+459.67 Trefi+459.6'~

'=im Pmtblk :=

50 L

Co =- 2 Rm Rt e I.I03*I0-

)]°Oc Temperature Correction for Coefficient Alpha Co1 =

C0

-Co0 1 75 th percentile MRP-55 Revision 1 Developed by; J. S. Brihmadesam Verified by:

B. C Gray

Entergy Operations Inc.

Centra I Engineering Programs Appendix C; Attachment 28 Page 3 of 11 Engineering Report M-EP-2004-001-00 AllData :=

0 10.95 4.51 0.52

-3.32

-7.65 0.85 1.32

-0.95

-2.65

-3.1

-3.55 1.52 4.77 4.12 5.01 4.33 1.79 2.07 15.55 13.98 12.9 10.29 7.18 2.5 15.65 12.98 14.76 16.94 17.57 2.85 4.83 8.83 13.89 24.74 33.61 3.13

-7.46 3.51 12.56 30.99 41 3.31

-16.1

-2.81 11.74 31.31 44.81 3.5

-19.77

-4.84 10.36 31.62 44.87 3.69

-18.2

-5.8 11.63 30.03 40.1 AXLen := AlIData(°)

IDAI := ADataP')

ODA

= AllData(5)

RefPoint = 1. 15 Developed by:

J. S Bnihmadesam Verifled by:

B. C. Gray c

, ~:

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 28 Page 4 of 11 Engineering Report M-EP-2004-001 -00 Data :=

0 0.846 1.524 2.067 2.502 2.85 3.13 3.315 3.5 10.954 1.32 4.766 15.552 15.655 4.83

-7.464

-16.1

-19.775 4.51

-0.955 4.123 13.981 12.983 8.828 3.508

-2.811

-4.84 0.522

-2.652 5.007 12.901 14.758 13.891 12.564 11.744 10.363

-3.322

-3.103 4.329 10.287 16.943 24.741 30.987 31.306 31.622

-7.653 )

-3.549 1.791 7.177 17.57 33.61 40.998 44.814 44.873 )

AxI := Data(°)

MD:= Data(

ID:= Data(l)

TQ := Data(4)

QT := Data(2)

OD := Data(5)

RID := regress(Axl,ID,3)

RQT:= regress(AxI,QT,3)

ROD := regress(AxI, OD,3)

RMD := regress(Axi, MD, 3)

RTQ := regress(Axl, TQ, 3)

Developed by.

J. S. BSihmadesam Verified by:

B. C Gray

Enitergy Operationis hic.

Central Engineering Programs Appendix C; Attachment 28 Page 5 of 11 Engineering Report M-EP-2004-001 -00 FLCntr =

-co if Val=I Flaw center Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + cO otherwise UTip := FLCntr+ CO InlcStrs.avg :

ULStrs.Dist-UTip 20 NWRIMIMMMEMOMMAZINIMPIM ffi Sat Aug 09 10:59:39 AM 2(

ProPLength = 1.805 Developed by:

J. S. Brihmadesam in'A Venfled by:

S. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 28 Page 6 of 11 Engineering Report M-EP-2004-001-00 0.6

._c U

0.4 C)

I-P 0.2 0

0 2

Flaw Growth in Depth Direction I

I I

IIII I

I I

IIII I

0.2 0.4 0.6 0.8 1

Operating Time 1.2

{years}

1.4 1.6 1.8 1.5 i 0

c; c

c 31 lI 0.5 [

I I

I III I

I I

I 0

-0.5

-I L(o 0.2 0.4 0.6 0.8 1

Operating Time 1.2

{years}

1.4 1.6 1.8 Developed by:

J. S. Bnhmadesam Verf ied by:

B. C. Gray

Entergy Operations Inc.

Centra I Engineering Programs Appendix C; Attachment 28 Page 7 of 11 Engineering Report M-EP-2004-001-00 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Appendix C; Attachment 28 Engineering Report Central Engineering Programs Page 8 of 11 M-EP-2004-n01 -00 Developed by.

J. S. Brihmadesam Verified by.

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs CGRsambi (k, 8) 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 Appendix C; Attachment 28 Page 9 of 11 Engineering Report M-EP-2004-001 -00 CGRsambi(k 6) 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 2.733 CGRsambi 5) 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 2.195 Developedby:

J. S. Brihmadesam Venffied by:

B. C. Gray

Entergy Operationis Ic.

Central Engineering Programs Appendix C; Attachment 28 Page 10 of 11 Engineering Report M-EP-2004-001 -00 4.

I I

2 3

AxIal D Istance From N ozzle BIto m (Inch) 0.4 5

0.2-nn0 0 0 0.5 1.0 Operatirg Timsle wars) 1.5 2.0 Developed by:

J. S. Bnhmadesam Vetifled by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 28 Page 11 of 11 Engineering Report M-EP-2004-001-00 0.5 2'0.4-c02 SI o 0.1 -

0.0 0.0 0.5 1.0 Operating Time {years) 1.5 2.0 2.7 -

W tF Depthi n 1=

l

SF=SraePointl i 2.5 -

IL 2.3 -

2.1 0.0 0.5 1.0 OperatingTine T

yeer 1.5 2.0 Developed by.

J. S. Blihmadesam Verified by:

B. C. Gray C%;%

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 1 of 11 Engineering Report M-EP-2004-01 -00 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw Developed by Central Engineering Programs, Entergy Operations Inc.

Developed by: J. S. Brihmadesam Verified by: B. C. Gray

References:

1) "Stress Intensity factors for Part-through Surface Cracks"; NASA TM-1 1707; July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"38.5" Degree Nozzle, "Mid-Plane" Azimuth Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

OD Surface Flaw Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray C

2q

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 2 of 11 Engineering Report M-EP-2004-001-00 Input Data :-

M M

od id Rid2 t:= Ro - Rid t

Rm :=Rid+ -

Timopr := Years-365-24 CFih := 1.417-105 Timopr Cblk

'= -

1im Pmtblk 5=

l0 L

Oc

= -2 Rm Rt L

1.103-103T+4567 Tref+4 59.67 C0 = C 1%c0c Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:

J. S. BrIhmadesam Verified by:

B. C. Gray c,'7 7

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 3 of 11 Engineering Report M-EP-2004-001 -00 Stress Input Data AllData :=

0 10.95 4.51 0.52

-3.32

-7.65 0.85 1.32

-0.95

-2.65

-3.1

-3.55 1.52 4.77 4.12 5.01 4.33 1.79 2.07 15.55 13.98 12.9 10.29 7.18 2.5 15.65 12.98 14.76 16.94 17.57 2.85 4.83 8.83 13.89 24.74 33.61 3.13

-7.46 3.51 12.56 30.99 41 3.31

-16.1

-2.81 11.74 31.31 44.81 3.5

-19.77

-4.84 10.36 31.62 44.87 3.69

-18.2

-5.8 11.63 30.03 40.1 AXLen := A1Data(o)

IDAII := AIIDatael) 0DA11 := AllData(5)

RefPoint -=1.15 Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray 0

r,.?-

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 4 of 11 Engineering Report M-EP-2004-001 -00 Data :=

0 0.846 1.524 2.067 2.502 2.85 3.13 3.315 3.5 10.954 1.32 4.766 15.552 15.655 4.83

-7.464

-16.1

-19.775 4.51

-0.955 4.123 13.981 12.983 8.828 3.508

-2.811

-4.84 0.522

-2.652 5.007 12.901 14.758 13.891 12.564 11.744 10.363

-3.322

-3.103 4.329 10.287 16.943 24.741 30.987 31.306 31.622

-7.653)

-3.549 1.791 7.177 17.57 33.61 40.998 44.814 44.873 )

Axl := Data(°)

MD:= Data&

ID:= Data(l)

TQ := Data(4)

QT.= Data(2)

OD := Data(5)

RID := regress(Axl, ID,3)

RQT := regress(Axl,QT,3)

ROD := regress(Axl,OD, 3)

RMD := regress(Axl, MD,3)

RTQ:= regress(Axl,TQ,3)

FLCntr Refpoint - c0 if Val = I Flaw center Location Location above Nozzle Bottom RefPo i nt if Val = 2 RefPoint + c0 otherwise UTip := FLCntr + co InCStrs.avg =

ULStrs.Dist - UTip 20 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Enitergy Operatioins bic Central Engineering Programs Appendix C; Attachment 29 Page 5 of 11 Engineering Report M-EP-2004001-00 fSat Aug 09 10:21:18AM 2003-Developed by:

J. S. Bflhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Centra I Engineering Programs Appendix C; Attachment 29 Page 6 of 11 Engineering Report M-EP-2004-001-00 ProLength = 1.805 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray C7Z 33

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 7 of 11 Engineering Report M-EP-2004-001 -00 Developed by:

J. S. Bnhimadesam Verified by:

B. C Gray C'7- -W

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 8 of 11 Influence Coefficients - Flaw 0.8 0.7 0.6 0

w.2 9

1)2

.9 t0E 8U 4) 00 8

19 0.5 0.4 0.3

~~~~~~~~~~_

0.2 0.1 Engineering Report M-EP-2004-001-00 Verified by.

B. C. Gray O_0 L 0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniforn

."..Va"

- Tip --Linear

"a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform

.I"c'

- Tip -- Linear c" - Tip -- Quadratic t"c" - Tip -- Cubic Developed by:

J. S. Bnhmadesam

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 9 of 11 Engineering Report M.EP-2004-001-00 CGRsambi(k,8) 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 CGRsambi(k,6)

-0.314

-0.314 CGRsambi 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 0.062 Developedby:

J. S. Blhmadesam Verfied by:

B. C. Gray

Eatergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 10 of 11 Engineering Report M-EP-2004-001-00 40 1

0 Distrbudo A20

~

B'f~

.20

i.n0 1

2 3

-z4 s

Dstanc. fromNozb Botto (inched )

08 I

10 is X.

n0.

0 0.0 05 1.0 Operating Time {years) 1.5 2.0 Developed by:

J. S. Blihmadesam Venfled by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix C; Attachment 29 Page 11 of 11 Engineering Report M-EP-2004-001-00 0.0

Si

,4.1 it 4 -0.2 3

-. 3 04.4, 0.0 0.5 1.0 Operatng Time (years) 1.5 2.0 Developed by.

J. S. Blihmadesam Verified by:

B. C. Gray C

1 3-3

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 1 of 10 Engineering Report M-EP-2004-001-00 Stress Corrosion Crack Growth Analysis Through-wall flaw Developed by Central Engineering Programs, Entergy Operations Inc.

J. S. Brihmadesam Verified by: B. C. Gray Developed by:

Note: Only for use when R.... id/t is between 2.0 and 5.0 (Thick-wall Cylinder)

References:

1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"38.5"degree Nozzle, "Mid-Plane" Azimuth Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

Through Wall Axial Flaw BZ := ULStrs.Dist - FSnde.datasheet Location of Blind Zone above nozzle bottom (inch)

IDeveloped by:

c'237

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 2 of 10 Engineering Report M-EP-2004-001 -00 InDut Data :

L := 0.25 Initial Crack Length TW axial Based on Stress Distribution. Bottom end of Cr to be set @ approximately 1 Oksi.

I M

M rack 0

i f

0 i

ed by: l I

C23%-

Co: e g

l 0

Timopr:= Years 365.24 R(

od 2

Tifllopr Cblk :=T r

1lim id 2

t:= Ro-Rj Rm:= Ri + -

2 CFinhr:= 1.417-105 Prntblk:=

50 I

L 2

De eoeIy eii lIDeveloped by:

Verifl(

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 3 of 10 Engineering Report M-EP-2004-001 -00 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

DataAII k

10.95 451t 0.52

-3.32

-7.65 0.85 1.32

-0.95

-2.65

-3.1

-3.55 1.52 4.77 4.12 5.01 4.33 1.79 2.07 15.55 13.98 12.9 10.29 7.18 2.5 15.65 12.98 14.76 16.94 17.57 2.85 4.83 8.83 13.89 24.74 33.61 3.13

-7.46 3.51 12.56 30.99 41 3.31

-16.1

-2.81 11.74 31.31 44.81 3.5

-19.77

-4.84 10.36 31.62 44.87 3.69

-18.2

-5.8 11.63 30.03 40.1 AllAxl:= DataAII °)

AIIID:= DataAll AIIOD:= DataAII 5 Developed by:

Venfied by:

I I

3R

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 4 of 10 Engineering Report M-EP-2004-001-00 60 46.67 33.33 m

20 (A~

6.67

-6.67

-20 I-0 0.5 1

1.5 2

2.5 3

3.5 Axial Distance above Bottom [inch]

ID Distribution

.GOD distribution 4

BZ = 1.15 Data:=

0 0.846 1.524 2.067 2.502 2.85 3.13 3.315 3.5 10.954 4.51 0.522

-3.322 1.32

-0.955 -2.652 -3.103 4.766 4.123 5.007 4.329 15.552 13.981 12.901 10.287 15.655 12.983 14.758 16.943 4.83 8.828 13.891 24.741

-7.464 3.508 12.564 30.987

-16.1

-2.811 11.744 31.306

-19.775

-4.84 10.363 31.622

-7.653)

-3.549 1.791 7.177 17.57 33.61 40.998 44.814 44.873)

Axl := Data ° ID:= Data (5)

OD := Data RID:= regress(Axl, ID,3)

ROD:= regress(Axl, OD,3)

IDeveloped by:

Vrified by: l

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 5 of 10 Engineering Report M-EP-2004-001 -00 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ lncStrs.avg :=

20 713-WERIMUIR11

6) Sat Aug 09 11:44:49 AM 2003 IDeveloped by.,

Verified by. I Deeoe by eife y

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 6 of 10 Engineering Report M-EP-2004-001 -00 ProPLength = 1-98 1.5 S

i TWCpwsccj 3 0

l 0.5 0

-0.5 '-0 0.2 0.4 0.6 0.8 1

1.2 1.4 1.6 1.8 TWCpWSC(j. I)

Operating Time (years)

Entergy Model Increase in Half Length 2

0 U

CJ c

4 1.5 0.5

-a ---- -

0 C I

0.2 0.4 0.6 0.8 1

1.2 1.4 1.6 1.8 Operating Time (Years) lIDeveloped by.,

Venfied by. I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 7 of 10 Engineering Report M-EP-2004-001-00 Developed by:

Venfied by:

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 8 of 10 Engineering Report M-EP-2004-001-00 TWCPI%,Scc (j 6)

-1.24

-1.24 TWCpVSCC(j,7) =

2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 2.824 TWCPWSCC (j.8) =

0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842 Developed by:

Verified by:

lIDeveloped by.,

Veriffedby: I

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 9 of 10 Engineering Report M-EP-2004-001-00 Hoop Stress Plot 40 Go 2 0 I

0

-20 0

1 2

3 4

Distance from Nozzle Bottom (inch)

Ut At, 3

OD Surlace SIF 2

ID SurfaceSF Average SIF 0

-1 O-0.0 0.5 1.0 Operathrg Time (years) 1.5 2.0 Developed by:

Verified by:

IA2 C'?-tk2a

Entergy Operations Inc.

Central Engineering Programs Appendix C: Attachment 30 Page 10 of 10 Engineering Report M-EP-2004-001-00 Os -

I

.10 0.0 -

1 0.2 -

O.0 -

0.0 0.5 10 Operaong rime (years) 1.5 2.0 lIDeveloped by.,

Ventled by. I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 1 of 11 Engineering Report M-EP-2004-001 -00 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Programs, Entergy Operations Inc.

Developed by: J. S. Brihmadesam Verified by: B. C. Gray

References:

1) "Stress Intensity factors for Part-through Surface Cracks"; NASA TM-1 1707; July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"38.5" Degree Nozzle, "Mid-Plane" Degree Azimuth, Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

ID Surface Flaw Refpoint := 0.4 Note the Ref Point is set such that flaw is in the tension zone Developed by.

J. S. Bnihmadesam Verifed by:

B. C. Gray 0

C 2-

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 2 of 11 Engineering Report M-EP-2004-001-00 M

M od R := 2 id Rid:= 2 t:= Ro - Rid Rm := Rid+

Timopr := Years-365*24 CFinhr := 1.417-105 Timopr Cblk:

11im rnim Prntblk =

50 L

Co0 :

-~

Rm Rt

-=

=

103 10-3 (+459.67 Tref+4 59.67)

C0

= Col

°Cc Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray C.2V4-

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 3 of 11 Engineering Report M-EP-2004-001-00 AllData :=

° 10.95 4.51 0.52

-3.32

-7.65 0.85 1.32

-0.95

-2.65

-3.1

-3.55 1.52 4.77 4.12 5.01 4.33 1.79 2.07 15.55 13.98 12.9 10.29 7.18 2.5 15.65 12.98 14.76 16.94 17.57 2.85 4.83 8.83 13.89 24.74 33.61 3.13

-7.46 3.51 12.56 30.99 41 3.31

-16.1

-2.81 11.74 31.31 44.81 3.5

-19.77

-4.84 10.36 31.62 44.87 3.69

-18.2

-5.8 11.63 30.03 40.1 N

3.87

-16.36

-3.95 11.96 27.26 40.74 AXLen:= AliData(°)

A l:=

AllData(0)

OD Al := AllData 5)

RefPoint = 0.4 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray C

Aft-

Entergy Operations Inc.

Centra I Engineering Programs Appendix C; Attachment 31 Page 4 of 11 Engineering Report M-EP-2004-001-00 Data :=

0 0.846 1.524 2.067 2.502 2.85 3.13 3.315 3.5 10.954 4.51 0.522

-3.322 -7.653 )

1.32

-0.955

-2.652 -3.103 -3.549 4.766 4.123 5.007 4.329 1.791 15.552 13.981 12.901 10.287 7.177 15.655 12.983 14.758 16.943 17.57 4.83 8.828 13.891 24.741 33.61

-7.464 3.508 12.564 30.987 40.998

-16.1

-2.811 11.744 31.306 44.814

-19.775

-4.84 10.363 31.622 44.873 )

Axi := Data(°)

MD:= Data(3)

ID:= Data(')

TQ := Data(4)

QT := Data(2)

OD := Data(5)

RID := regress(AxI, ID, 3)

RQT:= regress(Axl,QT,3)

ROD := regress(Axl,OD, 3)

RMD := regress(Axl, MD, 3)

RTQ:= regress(Axl,TQ,3)

Developed by.

J. S. Brfhmadesam Verified by:

B. C. Gray C-2 9&;

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 5 of 11 Engineering Report M-EP-2004-001 -00 FLCntr =

Refpoint - CO if Val = I RefPoint if Val = 2 RefPoint + CO othervise Flaw center Location above Nozzle Bottom UTip := FLCntr+ CO IflcStrs.avg :

ULStrs.Dist - UTip 20 ffi Sat Aug 09 10:59:39 AM 2003 ProPLength = 2.555 Developed by:

J. S. Blihmadesam Venried by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 6 of 11 Engineering Report M-EP-2004-001-00 Flaw Growth in Depth Direction 0.6 c

0 2

I-u 0.4 _

I I_

l l

ll l

l1!

l 0.2 I-O L0L 0.2 0.4 0.6 0.8 1

1.2 1.4 Operating Time {years}

1.6 1.8 2

I I

I I I

I 1.5 _

c C) c 34 it_

0.5 _

0

-0.5 I

i n

I I

I I8I I

I I

I IA l

A l n

A1 f2 I

I1)

I.1 I

I R

-l u

I Operating Time {years}

_ a.v

^.v Developed by:

J. S. Bahmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 7 of 11 Engineering Report M-EP-2004-001 -00 Developed by' J. S. Bnifmadesam Verified by:

B. C. Gray c

,I tp..

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 8 of 11 Engineering Report M-EP-2004-001-00 Developed by:

J. S. Bnrmadesam Verified by.,

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs CGRsambi(

8) 1.0 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 Appendix C; Attachment 31 Page 9 of 11 Engineering Report M-EP-2004-001 -00 CGRsambi(

6) 2.3516 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 2.351 CGRsambi(

5) 13698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 1.698 Developed by:

J. S. Btibmadesam Verified by:

B. C. Gray

Entergy Operationis Inc.

Central Engitneering Progrants Appendix C; Attachment 31 Page 10 of I1 Engineering Report M-EP-2004-401-00 I..-!

10 Hoop Si 4 0 -

~. I0 2 0 I

a 1.

I i.I Ho o p S l I

=

,O O H

a o p S

,....... 4Z@

l W

Ca enP's..

I.

'.~z.n.

I D 1***.I.02 k.1 O-.

~......

......t.

W olId Bto tt o m

......'i,

" ' 'k I

.'~

0 I

I 22 3

i 4'

AxlalI D stanca From Nozzl Bottom (InchI)

I.

u.lu Jdepth Growth 0.08 1008.

50 0.04

1-0.0 0.5 1.0 Operaotig Trie (years) 1.5 20 Developed by:

J. S. finhmadesam Velirled by.-

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 31 Page 11 of 11 Engineering Report M-EP-2004-001 -00 0.5 c 0.3 -

0S c -0.1 -

i0 Llength Growth 0.0 0.5 1.0 Operating Time {years}

1.5 2.0 2.3 -

i. 2.1

.j1.9 -

~19 1.75 1.5 l~-

SIFDetPon]

F 0.0 0.5 1.0 Operating Time {years) 1.5 2.0 Developed by.

J. S. Brlihmadesam Verified by:

B. C. Gray C 24-f9

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 1 of 12 Engineering Report M-EP-2004-001 -00 Through-wall Cracks: The Edge Flaw Analysis Developed by Central Engineering Programs, Entergy Operations Inc Developed by: J. S. Brihmadesom Verified by: B. C. Gray

References:

1) "Stress Intensity Factors Handbook - Volume 1"; Y Murakami, Editor-in-Chief; Pergamon Press; Section 1.3;

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CEDM -"38.5"degree Nozzle, "90" Degree Azimuth; 0.5 inch above Nozzle Bottom Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

Through-Wall Axial Edge Crack The first Input is to locate the Reference Line (eg. top of the Blind Zone).

The through-wall flaw "Upper Tip" is located at the Reference Line.

Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.

BZ := 0.5 Location of Blind Zone above nozzle bottom (inch)

The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.

This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.

ULStrs.Dist := 3.13 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Entergy Operations Znc.

Central Engineering Programs Appendix C; Attachment 32 Page 2 of 12 Engineering Report M-EP-2004-001 -00 Input Data :

L := 0.5 OD:= 4.00 ID:= 2.765 Pint:= 2.235 Years:= 2 Ijim:= 16000 T:= 600 v := 0.307 aoc:= 2.67.10- 12 Qg:= 31.0 Tref:= 617

[

Qg

(

I

= l3*l10 tT+459.67 Tref+459.67)J Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)

Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)

Reference Temperature for normalizing Data deg. F Timopr:= Years-365.24 OD 2

ID2-t := Ro - R Rm:= Ri +-

CFinhr:= 1.417-10 Timopr Cblk =Ii Pmtblk:=

50 50" 2

Li:= BZ

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 3 of 12 Engineering Report M-EP-2004-001 -00 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:

Column "0" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "5" = OD Stress data at each Elevation (ksi)

DataAll :=

0 1

2 3

4 5.

0 0

10.95 4.51 0.52

-3.32

-7.65 0.85 1.32

-0.95

-2.65

-3.1

-3.55 2

1.52 4.77 4.12 5.01 4.33 1.79 3

2.07 15.55 13.98 12.9 10.29 7.18 4

2.5 15.65 12.98 14.76 16.94 17.57 5

2.85 4.83 8.83 13.89 24.74 33.61 6

3.13

-7.46 3.51 12.56 30.99 41 7

3.31

-16.1

-2.81 11.74 31.31 44.81 8

3.5

-19.77

-4.84 10.36 31.62 44.87 9

3.69

-18.2

-5.8 11.63 30.03 40.1 AllAxl:= DataA ll AlID:= DataAll AIIOD:= DataAll(5) 60 46.67 33.33 20 6.67

-6.67

-20 0 ID Di!

OD di 0.5 1

1.5 2

2.5 3

3.5 Axial Distance above Bottom [inch]

tribution stribution 4

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 4 of 12 Engineering Report M-EP-2004-01 -00 Observing the stress distribution select the region in the table above labeled DataAl that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

(

0 10.954 4.51 0.522 -3.322 -7.653' Data:=

0.846 1.32

-0.955 1.524 4.766 4.123 2.067 15.552 13.981 2.502 15.655 12.983 2.85 4.83 8.828 3.13

-7.464 3.508 3.315

-16.1

-2.811 3.5

-19.775 -4.84

-2.652 -3.103 -3.549 5.007 4.329 1.791 12.901 10.287 7.177 14.758 16.943 17.57 13.891 24.741 33.61 12.564 30.987 40.998 11.744 31.306 44.814 10.363 31.622 44.873)

(5)

OD:

Data Axl:= Data (I)

ID:

Data RID:= regress(Axl,lD,3)

ROD:= regress(Axl,OD,3)

FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist -

BZ Incstrs.ag =

20 ULStrs.Dist - BZ IncrEdg:=

20 RID,N1l:= regress(AIIAxI,AIIID,3)

RODAII := regress(AIIAxl, AIIOD,3)

No User Input required beyond this Point I

I

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 5 of 12 Engineering Report M-EP-2004-01 -00 Calculation to develop Stress Profiles for Analysis Hoop Stress Profile in the axial direction of the tube for ID and OD locations N := 20 Number of locations for stress profiles Loc0 := FLCntr - L i:= I..N + 3 Incr. :=

I if i <4 I lncstrs.avg otherwise Loc. := Loc I + Incr; SID. = RID3 + RID 4Loc. + RID -(Loc.i

+ RID6- (LoCi)

Incredg if i <4 I

2 IncrEdg otherwise Locl i:= 10 if i = I Loc; i-I + Incredg otherwise SOD := ROD + ROD.LoC + ROD' ( LoCi) + ROD 6 (Loci) 3 4

I 5

n 6

SIDAII = RIDAJI + RIDAII LLoc I + RIDA,5.(Loc I) 2 + RIDAII. (Loci )3 2

34 3

15 6

SODAII.:

RODAII + RODAII -Locl.i + RODAII.(Loci. 2+ RODAI.( LocI.3 1

3 4

115 1j6~I I

I

fntergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 6 of 12 Engineering Report M-EP-2004-001 -00 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j:= I..N Sidj :=

SID. + SID j+ + SIDj+2 if j = I 3

Sod. =

SOD. + SOD.

+ SOD.J+2 if j = I Sodj * (j + 1) + SODj+2 2otherwise j+2 Sidj X (j + I) + SIDj+2 j +2 otherwise SIDAII. + SIDAxj+j

+ SIDAIIj Sid.all:=

3 i+ f j = I Sid.ailj.

(j + I) + SIDAII J-j otherwise j+2 SODAII + SODAII

+ SODAII Sod.all.:=

3 if j = I Sod.all (j + I) + SODAIIj+2 jj othervise j + 2 Sod. + Sid.

a

= J

' j 15M. i i+

Pint 2

Sod. - Sid.

b 2

Sod.all. + Sid.all.

Om.all- =

2 J + Pint j

2 i

i

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 7 of 12 Engineering Report M-EP-2004-001 -00 Stress Distributions for use in Fracture Mechanics Analysis Membrane Stress Bending Stress OD Stress ID Stress Membrane stress (Edge Crack) -I 2

T 6

T5 9

11 12 13-iT

0 0

1.41 0.857 0.588 0.519 0.608 0.829 1.161 1.587 2.092 2.661 3.282 3.941 4.625 5.322 6.02 0

1 2

3 4

5 6

7 8

1T 11 12 13 14 15 0

0

-6.497

-5.906

-5.489

-5.18

-4.945

-4.763

-4.614

-4.487

-4.366

-4.241

-4.099

-3.929

-3.72

-3.461

-3.142 Sod =

, 0o :

0

-7.322

-7.284

-7.136

-6.896

-6.572

-6.168

-5.688

-5.134

-4.509

-3.814

-3.051

-2.223

-1.33

-0.374 0.643 Sid =

0 5.672 4.528 3.841 3.464 3.319 3.357 3.541 3.839 4.223 4.667 5.146 5.635 6.11 6.548 6.926 am.all =

151 5

7 IT

. 0t 0

1.841 1.527 1.408 1.43 1.566 1.796 2.108 2.489 2.929 3.418 3.948 4.508 5.089 5.684 6.284 PropLength := ULStrs.Dist - (FLCntr + I)

Pr°PLength =2-63

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 8 of 12 Engineering Report M-EP-2004-001-00 Recursive Loop For Edge Crack Model TWCEDGpVscc:=

i-0 Li 1LII NCB 0 (- Cbik while i S rlim l Um.appld (

Gmall if LI *<LI Gm.all, if LI 0<LIj S Ll 0 + InCrEdg Gm.all3 if LI 0 + Incrl dg < Llj <LI + 2-IncrEdg Gm.all4 if L10 + 2*incrEdlg < LL S 1

L

+ 3-lncrEdg Gm.ail5 if L I + 3I1ncrEdg < LI S 0

L

+ 4-lncrEdg Gm.ali6 if LI + 4-ncrE(dg < LI S L

+ 5-lncrEdg Gm.all7 if LI 0 + 5-incrEug < LI. S L

+ 6-IncrEdg Gm.all8 if Li 0 + 6. nCrEdlg < LI S L I + 7 -IncrEdg Gm all 9if Li 0+ 7-ncrE,lg < LIj S<LI + 8-IncrEdg Gm.ali 1 if Li0 + 8-IncrEdg < LI 0

S<LI + 9-lncrEdg Gm.allll if Li 0 + 9-IncrEdg < LI 0

S<LI + 10-IncrEdg Gm.ali12 if LI c

+ 10-incrEdg <Lj 0

LI0+ II-IncrEdg Gm.all13 if Li0 + I-IncrEdg < L 1

i <LI0+ 12-IncrEdg Gm.all 4 if Li0 + 12iOncrEdg < Lj < LI + 13 IncrEdg Gm.all 1 if LfL + 13 IncrEdg < Llj S LI 0 + 14 IncrEdg Gm.all,5 if LI0 + 14 3 1ncrEdg < Ll; S LI0 + 15lncrEdg Gm.ali1 7 if LI0 + 15. IncrEdg < LI SL

+ I16IncrEdg G9m.a 1 8 if Li 0 + 16 IncrEdg < LI SL

+ I 7I ncrEdg am.all19 if L1 + 17*IncrEdg < L1i S Li + 18*IncrEdg m all0 othenrvise b *- ULStrs.Dist I

I

Entergy Operations Inc.

Appendix C; Attachment 32 Engineering Report Central Engineering Programs Page 9 of 12 M-EP-2004-001-00 Z.

1 0.99 if 2 1.0 L

b otherwise Fabi & 1.12 - 0.231.(Z) + 10.55. (Z;)

- 21.72 (Zi)3 + 30.39. (Z) 4 Kedg.Crk-G lm.appld' 4f if (am.app1dj-I) S 0 lm.appld (7t LIJ)0 5 Faab. otherwise KA. i Kedg.Crk; 1.099 Ka+

9.0 if KA S 9.0 KA; otherwise Dien C0 (Ka - 9.0)1.16 Dlengrth. +-

Dien,-CFinhrCblk if Ka. S 80.0 4--1

CFinhr Cblk otherwise P (i,0)

NCB.

oUtput(i. 1) + 365.24 output(i 2 ) -- L -Ll output(i 3 )

- Dlengrth; output(i 4 )

K kedg.Crk output(i 5) & Fab1 i4-i+ I LIj*

LI 1 + Djengrth NCB; NCB i-I + Cbk output j:= I -Jim

Entergy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 10 of 12 Engineering Report M-EP-2004-001-00 ProPLength = 2-63 Flawv Length vs. Time 3

2.5 1 2

u

'a X

2 cu

._C*

1.5 __-_

l 0.51 i

I I.I I

0 0.2 0.4 0.6 0.8 1

Operating Time 1.2

{years) 1.4 1.6 1.8 K

Entetyy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 11 of 12 Engineering Report M-EP-2004-001 -00 5

4.5 4

3.5 zr-t C

?-

V:

V V,

3 2.5 2

1.5 0.5 0-0 0.2 0.4 0.6 0.8 1

1.2 Operating Time (Years) 1.4 1.6 1.8 I

I

Entregy Operations Inc.

Central Engineering Programs Appendix C; Attachment 32 Page 12 of 12 Engineering Report M-EP-2004-001 -00 0.5 0.3 -

90.1 -

0 2 4.

(3.

0

-0.3

-0.5 0.3 0.8 1.3 Operating Time (years) 1.8 9

7 0

V5 Th lltS SIF P4WSCC raw* Gsh pw~cc cl rassa Pt.SIkv SIF ip A.kV 0.3 0.8 1.3 Operating Time (years) 1.8

_o A

Cage

Engineering Report M-EP-2004-001 -00 Appendix D Appendix D Contains Mathcad worksheets for;

1) Evaluation of Curve Fitting method.

2) Demonstration of the validity of the Moving Average method.

3) Comparison of SICF for the Edge Crack Formulation and Current model.

4) Comparison of Conventional and Current model for OD Surface Crack.

5) Comparison of Current model with Conventional model and Edge Crack model for Through-wall Crack.

6) Curve Fitting for 38.50 nozzle at the mid-plane location at nozzle bottom.

This Appendix has six (6) Attachments.

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment I Page 1 of 7 Enginering Report M-EP-2004-001 -00 Evaluation of Curve fit for Stress Profile Generation along the Tube Axis In this worksheet the effect of data set selection for curve fitting, using a third order polynomial is evaluated. The data table below is form a data set used in the CEDM analyses. This data set is imported directly from the Excel spreadsheet provided by Dominion Engineering for the CEDM. The evaluation considers the full data set and a limited data set spanning the region of interest.

The purpose of this evaluation is to demonstrate the need for the proper selection of a subset of nodal stress data (in the region of interest) to ensure the accuracy of the analysis.

Data set imported from Excel spreadsheet.

AllData:=

0

-1 2

3 4

5 0

0

-9.81

-9.21

-9.15

-9.11

-9.01 7

0.69

-5.96

-6.67

-7.6

-8.5

-9.17 2

1.24 5.97 1.89

-1.41

-3.64

-4.89 3

1.68 27.3 20.8 14.76 9.07 2.76 4

2.04 38.32 34.26 28.39 21.56 14.2 5

2.32 46.03 38.24 33.08 32.77 40.16 6

2.55 44.34 40.22 38.94 48.67 60.18 7

2.73 35.38 36.51 40.84 54.4 68.18 8

2.92 26.51 32.53 41.33 56.35 69.72 9

3.1 21.36 29.6 40.6 53.91 66.27 10 3.29 22.66 28.09 39.31 52.05 65.07 11 3.47 29.36 30.5 38.36 47.56 57.08 12 3.65 37.59 36.02 38.91 45.89 49.47 13 3.84 43.93 40.89 43.16 46.29 45.27 14 4.02 48.9 44.81 47.03 52.1 45.31 15 16 17

_18 Ax]Len:= AllData(

(1)

(3)

IDAII:=AMl=t MidWall:=All=t ODAII:= AllData S

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment I Page 2 of 7 Enginering Report M-EP-2004-001 -00 Data:=

1.24 1.681 2.035 2.319 2.546 2.731 2.916 5.968 27.297 38.318 46.033 44.342 35.382 26.506 1.891 20.8 34.255 38.236 40.223 36.514 32.532

-1.405 14.757 28.387 33.079 38.935 40.837 41.33

-3.639 9.074 21.562 32.77 48.672 54.397 56.353

-4.887) 2.762 14.198 40.164 60.179 68.177 69.718)

Selected subset from the data table above ALen:= Data (I)

IDlim= Data (3)

N'IVIlim= Data ODlim:= Data Regression for the full data set RIDAII := regress(AxlLenjDA11,3)

RMWAII := regress(AxlLen,vMidWall,3)

RODAII:= regress(AxlLen,ODA11,3)

Regression for selected data set RIDdata:= regress(ALen,lDljm,3)

RMtWdata:= regress(ALen, MWlim, 3)

RODdata:= regress(ALenODljm,3)

WBB 2.91 Bottom:= 0 Top:= 4.02 Dist:= Top - Bottom Dist Incr:=

20 D := WB -

Bottom Incri :=-

20

Entergy Operations Inc.

Central Enginening Programs Appendix D; Attachment 1 Page 3 of 7 Enginering Report M-EP-2004-401 -00 L0 := 0 - Incr i:= I.. 20 L; := L I + Incr LenO := 0 - Incrl Len. := Len i-I + Incrl Determination of Stresses at three locations across wall thickness, using the full data set IDall := RIDA13 + RIDA14 *L.+ RIDAl5.(Lj) + RIDA'6 (Li)3 MINall := RMWAII + RMW'All L; + RMWAII * (Li) 2 + RMWAII.(Li)

MDall = RODAII + RODAIl 4 L; + RODAII (Li) + RODAI.(L.)3 Determination of Stresses at three locations across wall thickness, using the selected data set IDdata:= RIDdata + RIDdata Len. + RIDdata.(Len\\) + RIDdata *(Leni)3 dat 4 dt 5 ~;

dt 6

MWdatai:= RMVdata + RMNVdata -Leni + RM Wdata.(Leni) + (RMVdata6) (Lcni)3 ODdata = RODdata 3 + RODdata.Len. + RODdata -(Len;)2+ RODdata *(Leni)3 i3 415

Entergy Operations Inc.

Central Enginefing Programs Appendix D; Attachment 1 Page 4 of 7 Enginering Report M-EP-2004-001 -00 Graphical Display of Results Distribution Full Nodal Stress Data 80 60 0

0A To 40 20

-20 _

0 1

2 3

Axial Length (inch)

ID Distribution

..-- OD distribution 4

5 Nodal stress data plotted for the ID and the OD distribution. This plot is based on the full data set.

ID Stress Distribution:-

Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.

60 40 j

'A 2

C-00 20 0

-20 l_

0 1

2 3

Axial Eleveation from Bottom {inch)

ID Regression using All Data

-.. -ID All Nodal Data 4

5

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 1 Page 5 of 7 Enginering Report M-EP-2004-001 -00 v)

C-00 OD Stress Distribution:-

Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.

-50 0 1

2 3

Axial Elevation from Bottom {inch)

OD Regression Using All data

~OD All Nodal Data I

5 60 40 ir, C-0 Mid-Wall Stress Distribution:-

Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.

20 0

-20 v

0 1

2 3

4 Axial elevation from Bottom {ksi)

Mid-Wall Regression using All data Mid-Wall All Nodal Data 5

Entergy Operations Inc.

Central Enginedng Programs Appendix D; Attachment I Page 6 of 7 Enginering Report M-EP-2004-001 -00 ID - Selected Data Set 60 40 ID Stress Distribution (Selected Data Set):-

Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.

A

'A 20 o r

-2a -

v 0

0.5 1

1.5 2

2 Axial Elevation from Bottom (inch)

ID Regression using Selected Data ID Selected Nodal Data 2.5 3

Mid-Wall - Selected Data Set 60 40 Mid-Wall Stress Distribution (Selected Data Set):-

Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.

A 0.

20 0

-20

-40

-60 I_

0 0.5 1

1.5 2

2 Elevation from Bottom (inch)

Mid-Wall Regression Selected Data Set Mid-Wall Selected Data Set

.5 3

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 1 Page 7 of 7 Enginering Report M-EP-2004-001 -00 OD - Selected Data Set 400 300 200 0

E!

0 100 0

-100 OD Stress Distribution (Selected Data Set):-

Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.

0 1

2 Elevation from Bottom (inch)

OD Regression using selected data Set OD Selected Data Set 3

Conclusion :- By selecting the data judiciously, in the region of interest, facilitates an accurate regression fit of the data.

Entergy Operations Inc.

Central Engineering Programs Apendix D; Attachment 2 Page 1 of 8 Engineering Report M-EP-2004-001-00 Example Worksheet Developed by Central Engineering Programs, Entergy Operations Inc.

Developed by: J. S. Brihmadesam Verified by: B. C. Gray Example to Evaluate Moving Stress Averaging Technique Basis :- In this worksheet the moving average method is exercised to demonstrate that no numerical errors exist. In this example a linear through-wall stress distribution that remains constant over the length of the nozzle is used. Thus the moving average method, if working properly should provide the same linear through-wall distribution at all segments considered.

This worksheet is developed using the stress distribution analysis portion from the working worksheets used in the analyses. The data table in the worksheet was modified with the entry of a linear throughwall stress distribution at all axial height locations. The result of the moving average technique was output as a table.

The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.

The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessary to evaluate the stress distribution on the flow both for the initial flaw and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represents the reference point elevation measured upward from the nozzle end.

RefPoint = 1.544 To place the flaw with respect to the reference point, the flaw tips and center can be located as follows:

1) The Upper "c-tip" located at the reference point (Enter 1)

2) The Center of the flow at the reference point (Enter 2)

3) The lower "C-tip" located at the reference point (Enter 3).

Val := l The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.

ULStrs.Dist = 2.75 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by:

J. S. Bflhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Apendix D; Attachment 2 Page 2 of 8 Engineering Report M-EP-2004-001 -00 Only input data pertinent to this worksheet are provided. The internal pressure and the information for the PWSCC crack growth, which are not essential to the example problem, have been removed.

Input Data :-

L :=.35 ao := 0.035 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID od Ro

=

0:

2 L

C0 2 id Rid :

t := Ro -Rid t

Rm:= Rid+ +2 Timopr := Years-365-24 Rm Rt Developed by:

J. S. Blihmadesam Verifed by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Apendix D; Attachment 2 Page 3 of 8 Engineering Report M-EP-2004-001 -00 The stress input table that is used to import the nodal stress data was modified. The stress input was manually entered as a linear through-wall distribution at all axial height locations. The table entries below shows the entries used.

Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

Column "0o = Axial distance from minimum to maximum recorded on data sheet (inches)

Column "1n = ID Stress data at each Elevation (ksi)

Column "2" = Quarter Thickness Stress data at each Elevation (ksi)

Column "3" = Mid Thickness Stress data at each Elevation (ksi)

Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)

Column "5" = OD Stress data at each Elevation (ksi)

AllData :=

0 1

2 3

4

.- 5 0

0 8

10 12 14 16 1

0.35 8

10 12 14 16 2

0.63 8

10 12 14 16 3

0.85 8

10 12 14 16 4

1.03 8

10 12 14 16 5

1.18 8

10 12 14 16 6

1.29 8

10 12 14 16 7

1.44 8

10 12 14 16 8

1.59 8

10 12 14 16 9

1.74 8

10 12 14 16 10 1.89 8

10 12 14 16 11 2.04 8

10 12 14 16 AXLen := AllData(°)

IDAII := AllData(l) 0DA11 := A1lData(5)

Developed by:

J. S. Bflhmadesam Verifed by:

B. C. Gray

Entergy Operations Inc.

Apendix D; Attachment 2 Engineering Report Central Engineering Programs Page 4 of 8 M-EP-2004-0011-00 The graph below is a plot of the table data in the previous page. Note the horizontal lines for the ID and OD stress distribution along the nozzle length. Therefore, the input data shows that there is a constant distribution along the nozzle length Stress Distribution 20 15__

Ce 10 _

5 l

0 0.5 1

1.5 2

2.5 3

3.5 Axial Elevation above Bottom [inch]

ID Distribution OD Distribution 0

8 10 12 14 16) 0.35 8 10 12 14 16 0.63 8 10 12 14 16 0.854 8 10 12 14 16 1.034 8 10 12 14 16 1.178 8 10 12 14 16 The data matrix to the left is the selection of data from the data table used to input the data. All entries have 1.293 8 10 12 14 16 been selected. The matrix is exactly the same as the 1.442 8 10 12 14 16 input data table Data 1.591 8 10 12 14 16 1.74 8 10 12 14 16 1.889 8 10 12 14 16 2.038 8

10 12 14 16 2.187 8 10 12 14 16 2.336 8 10 12 14 16 2.485 8

10 12 14 16 2.634 8 10 12 14 16 2.783 8 10 12 14 16)

Developed by:

J. S. Blihmadesam Veifled by:

B. C. Gray

Enitergy Operations Iic.

Central Engineering Programs Apendix D; Attachment 2 Page 5 of 8 Engineering Report M-EP-2004-001-00 The statements below are the assignment statements defining the column arrays for the axial height followed by the five locations across the tube wall thickness.

AxI := Data(°)

MD:= Data(')

ID = Data(')

TQ := Data(4)

QT := Data(2)

OD:

Data(5)

RID := regress(Axl,ID,3)

RQT:= regress(Axl,QT,3)

ROD := regress(Axl,OD,3)

RMD := regress(Axl,MD,3)

RTQ:= regress(Axl,TQ,3)

The statement below defines the flaw location to be used in the analysis, based on the entry for the variable 'Val" entered on the first page.

FLCntr =

RefPoint - c0 if Val = I RefPo in t if Val = 2 RefPoint + c0 otherwise Flaw center Location above Nozzle Bottom The two statements below are as follows:

1) The statement on the left defines the upper crack tip based on the flaw location determined above.

2) The statement on the right computes the segment height for the segments above the upper crack tip based on twenty equal segments.

UTip := FLCntr+ CO IflcStrs.avg :

ULStrs.Dist - UTip 20 Developed by:

J. S. Brihmadesam Velirled by B. C Gray

Entery Operations Inc.

Central Engineering Programs Apendix 0; Attachment 2 Page 6 of 8 Engineering Report M-EP-2004-0i -00 The statements below develops the through-wall stress profiles at the twenty-three segments (three segments for the initial flaw length and twenty segments above the upper tip of the flaw.

Calculation to develop Stress Profiles for Analysis N := 20 Number of locations for stress profiles Loco := FLCntr - L i:= I.. N +3 Incr; :=

c0 if i < 4 IncStrs.avg othenvise Loci Loci-, + Incri SIDi RID3 + RID4 Loci + RID 5 (Loci) 2 + RID (Loci)3 SQTi RQT3 + RQT4 LOCi + RQT.(Loci) 2 + RQT. (Loci) 3 SMlDi RMD + RMD *LoCi + RMD (Loci) 22+ RMD *(Loc;)3 STQ.

RTQ + RTQ.Loci + RTQ.(Loci) 2 + RTQ (LoCe) 3 SODi ROD3 + ROD4 Loci + ROD.(Loc,) 2 + ROD *(Loci)3 Developed by:

J. S. Snihmadesam Verfied by:

f. C. Gray

Entergy Operations Inc.

Central Engineering Prograins Apendix D; Attachment 2 Page 7 of 8 Engineering Report M-EP-2004-001 -00 The statements below perform the moving average stress profile calculations. The first profile, at location 1, is the average profile for the initial crack. The remaining profiles are the average profiles for the twenty segments above the upper tip of the crack.

j I..N Sidi SID + SIDj+,-l-SIDj+2 3

Sid

-,(j

+i) +SIDj+ 2 jJ-I if j = I Sqt. =

SQTj + SQTj+l + SQTj+2 3

Sqt (. 1 (i + I) + SQTj+2 j+2 if j = I otherwise othenvise SMDj + SMDj+1 + SMDj+2 Smd-J if j= I 3

Smd

(j + i) + SMDj+2 j+2 5tqj.:

STQj + STQj+j + STQj+2 if j = X 3

Stq

(j + I) + STQj+2 othervise j+2 othervise Sod :=

J SODj + SODj+, + SODj+2 3

Sod

(j + i) + SODj+2 if j = I

)therwvise I

j+2 Developed by:

J. S. Brhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Apendix D; Attachment 2 Page 8 of 8 Engineering Report M-EP-2004-001 -00 Presented below is the output at each location defined for the moving average stress profile. The first element in each array is for the average stress profile for the initial crack. The subsequent elements in each column array are for the equal segments above the upper tip of the flaw. Each column array represents one of the five locations across the wall thickness (marked).

ID sidj 8

8 8

81 Quarter Thickness Sqt =

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Mid-Wall Thickness Smd. =

12 12 12 12 12 12 12 12_

12 12 12 12 12 121 Three -Quarter Wall Thickness OD Stqj 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 Sod 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 The output of the moving average evaluation is the same as the input data. This ensures that the moving average technique is functioning properly.

Developed by:

J. S. Bdhmadesam Venfled by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 3 Page 1 of 6 Engineering Report M-EP-2004-001 -00 Comparison of Edge Crack Model With Through-wall Model {SICF)

Developed by Central Engineering Programs, Entergy Operations Inc Developed by: J. S. Brihmadesam Verified by: B. C. Gray

References:

1) Murakami; "Stress Intensity factors handbook"; 1.3 Single Edge Cracked Plate; page 771.

Generic Stress Distribution Component: Reactor Vessel Head Penetration In this worksheet a comparison between the SICF for an Edge Crack and the axial through-wall crack of the current model are compared. For the edge crack the SICF is dependent on the ratio of crack length to plate height. For the application to the CRDM nozzle the plate height can be assumed at three locations, these are:

1) The nozzle length upto the bottom to the J-weld (the bottom point of fixity for the nozzle)

2) The nozzle length upto the top of the J-weld (the upper point of fixity for the nozzle)

3) The nozzle length assuming no fixity.

For the current model only the SICF for the membrane loading is used for comparison because the SICF for these two conditions are separate and are applied to the SIF for equivalent plate geometry. Hence three is no single SIF that represents a composite SICF. However a comparison using the membrane SICF should facilitate a rational assessment.

The first Input is to locate the Reference Line (eg. top of the Blind Zone).

The through-wall flaw "Upper Tip" is located at the Reference Line.

Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.

BZ := 1.544 Location of Blind Zone above nozzle bottom (inch)

The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.

This is shown on the Excel spread sheet as weld bottom.

Enter this dimension (measured from nozzle bottom) below.

ULStrs.Dist:= 1.796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Atth Edge Crack-Entergy-Comparison-OOO.mcd

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 3 Page 2 of 6 Engineering Report M-EP-2004-001-oo The input data below are only for those variables essential to this assessment.

InDut Data :

L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 v := 0.307 Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)

Poissons ratio at 600 deg. F od Ro :=-o Ri:= id t:= Ro - Ri Rm:= Ri +-

2 N:= 500 The plate height are set to three elevations as follows:

1) Bottom of the J-weld.

2) Top of the J-weld.

3) Full length of Nozzle.

b:= ULStrs.Dist bl := 2.886 b2:= 20 Bottom of J-weld Top of J-Weld Top of Nozzle Inc := b N

It is important to note that the SICF for the Edge Crack model are limited to the a/b ratio (Crack length/height) of 0.6.

Therefore, for the crack length when the a/b ratio is violated are as shown below.

Case 1: Plate height equal to nozzle length to bottom of weld:-

b 0.6 = 1.078 Case 2: Plate height equal to top of J-weld:-

bi-0.6 = 1.732 Case 3: Plate height equal to Nozzle Length :-

b2 0.6 = 12 Atth Edge Crack-Entergy-Comparison-OQO.mcd

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 3 Page 3 of 6 Engineering Report M-EP-2004-001 -00 Calculations:

a0 = 0 j :=I.. N - I ai = aj_1 + Inc a.j

x.

J b

a.

XI :=

J i

bl a.

x2 :=

J j

b2 Brown and Srawley Model For edge Crack in a Plate Fbs i:= 1.12-0.231-x. + 10.55. (xj) - 21.72.(xj)3 + 30.39.(x.)4 FbsI I=

1.12 - 0.231.xli + 10.55. (xIj) 2 21.72. (x' )+ 30.39. (xI )4 Plate height as length below Fillet weld to tube bottom Plate height as length below Top of J-weld to tube bottom Fbs2 I:=

1.12 - 0.231.x2 + 10.55. (X2)

- 21.72 (X2j) 3 + 30.39 (x2j)4 Plate height as F Through-wall Axial crack in a Thick Cylinder (Entergy Model)

((

( 0.25 2

]

Full length of Nozzle AeM := 1.009 + 0. 3 621 -j + 0.0565.(Xj) 2 - 0.0082. (j) 3 + 0.0004. (Xj)4 - 8.326. 10 6. (Xj)

AeB. := 0.0029 + 0.0707. (Xj) - 0.0197. (j) 2 + 0.0034. (Xj)3 - 0.0003.(j)4 + 8.8052. 10 6.(Xj)5 AbM. := -0.0063 + 0.919.kj - 0.168 (Xj)2 - 0.0052.(Xj) 3 + 0.0008.(Xj) 4 - 2.9701. 1o 5-(A)

AbB. := 0.9961 - 0.3806 Aj + 0.1239 (A;)2 - 0.021.(Xj) 3 + 0.0017. (Xj)4 - 4.9939. 10 5-(A) 5 AM := AeM.+ AbM.

AB := AeB.+ AbB.

Atth Edge Crack-Entergy-Comparison-OOO.mcd

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 3 Page 4 of 6 Engineering Report M-EP-2004-001-00 20 19 18 17 16 15 14 va 0

C.)

0 U

E ao em A:

to ct 13 12 11 10 9

8 7

6 5

4 3

2 0.803592 0.12 0.24 0.36 0.48 0.6 0.72 0.84 0.96 1.08 1.2 1.32 1.43 1.55 1.67 1.79 Flaw length {inch}

Edge Crack Panel Height upto Bottom of fillet weld Edge Crack Panel Height upto Top of J-weld Edge Crack Panel Height equal Full Nozzle Length {20 inches}

Entergy Model Membrane I

Atth Edge Crack-Entergy-Comparison-OOO.mcd clZ5)-

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 3 Page 6 of 6 Engineering Report M-EP-2004-001 -00 Axum Plot showing SICF Comparison between Edge Crack SICF and Current Model SICF 20 15

_10-

6 0

0.05 0,30 0.55 0.80 1.05 1.30 1.55 1.80 Length of Crack {inch}

I Atth Edge Crack-Entergy-Comparison-OOO.mcd C 2 5z-:

Entergy Opertions Inc.

Central Engineering Programs Appendix D; Attachment 3 Page 5 of 6 Engineering Report M-EP-2004-001-00 Axum Plot showing SICF for Edge Crack for different Panel Heights I

Atth Edge Crack-Entergy-Comparison-OOO.mcd

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 1 of 32 Engineering Report M-EP-2004-0o01-0 Comparison of Surface Crack Models: Conventional Model with the Current Model Developed by Central Engineering Programs, Entergy Operations Inc Developed by: J. S. Brihmadesam Verified by: B. C. Gray

References:

1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Purpose :- This worksheet is used to compare the crack growth and SIF results between the conventional model (using a fixed R/t ratio and a fixed flaw aspect ratio-a/c) and the current model. The current model uses the R/t ratio appropriate to the CEDM nozzle tube geometry and the flaw aspect ratio is not fixed. The flaw aspect ratio is determined at each crack growth interval based on the seperate growth for both the depth direction (a-tip) and the length direction (c-tip). Therefore, the current model permits the evaluation of crack growth through the wall thickness and along the nozzle surface simultaneously.

The evaluation, using the same residual stresses distribution, compares the results form both models. The worksheet is essentially the same as that used in the analyses. The only difference is that a separate loop. The graphical presentations towards the end of the worksheet present the comparative results.

Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"18.2" Degree Nozzle, "Downhill" Azimuth, Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inch/hr.

Developed by:

J. S. Bflhmadesam OD-Surface Flaw Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Progranms Appendix D; Attachment 4 Page 2 of 32 Engineering Report M-EP-2004-001-00 The first Required input is the Freespan length from the NtDE data sheet (Excel spread sheet)

FSnde data.sheet = 0.430 To place the flaw with respect to the reference point, the flaw tips and center can be located as follows:

1) The Upper "c-tip" located at the reference point (Enter 1)

2) The Center of the flaw at the reference point (Enter 2)

3) The lower "C-tip" located at the reference point (Enter 3).

Val := 2 Enter the upper extent of the Stress distribution used for analysis ULStrs.Dist = 1-712 RefPoint = ULStrs.Dist - FSnde.data.sheet Developed by:

J. S. Bnhmadesam Venirled by:

B. C. Gray

Enterly Operations Inc Central Engineering Programns Input Data :-

Appendix D; Attachment 4 Page 3 of 32 Engineering Report M-EP-2004-01 -00 L := 0.35 ao := 0.09872 od := 4.00 id := 2.765 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt := 2.235 Years := 2 him = 1500 T := 604 aOc := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)

Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)

Reference Temperature for normalizing Data deg. F od Ro := 2d id Rid :

t = Ro - Rid t

Rm2 Timopr := Years-365-24 CFjnhr := 1.417-105 Timopr Cblk :=-

IJim Pmtblk =

50 L

Co 0

=

Rm Rt :=

Lll3l-3 t+459.67 T 59.ss67)0 C0 1

= e aoc Temperature Correction for Coefficient Alpha Co := CoI 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Slihmadesam Verified by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 4 of 32 Engineering Report M-EP-2004-001-00 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

Column "0" = Axial distance from minimum to maximum recorded on data sheet(inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = Quarter Thickness Stress data at each Elevation (ksi)

Column "3" = Mid Thickness Stress data at each Elevation (ksi)

Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)

Column "5" = OD Stress data at each Elevation (ksi)

AllData :=

0

° 2

3 4

0 0

-32.98

-29.55

-27.62

-25.63

-23.66

1 0.46 4.42 1.43

-2.62

-5.98

-7.49 2

0.83 23.6 20.13 17.47 13.58 8.56 3

1.13 39.38 33.76 28.59 23.55 16.9 4

1.37 41.08 35.6 32.56 29.09 28.07 5

1.56 35.47 35.03 34.72 41.39 51.48 6

1.71 25.31 30.93 36.76 48.63 57.32

.7 1.85 18.48 26.76 37.58 49.67 67.27 8

2 15.18 24.43 37.51 53.17 72.59 9

2.14 16.04 22.8 36.7 51.39 59.83 AXLen := AliData(°)

IDAI := AllData~l)

ODAI := AllData(5)

Stress Distribution 100 IDAHI

.id

(/2 50 0

-50 _0 0.5 1

1.5 2

2.5 AXLen Axial Elevation above Bottom [inch]

3 RefPoint = 1.282 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergiy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 5 of 32 Engineering Report M-EP-2004-001-00 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

(

0

-32.98 -29.552 -27.619 -25.631

-23.659)

Data :=

0.463 4.418 0.834 23.603 1.131 39.381 1.369 41.077 1.56 35.472 1.712 25.309 1.854 18.476 1.996 15.182 20.133 17.472 33.757' 28.588 13.58 8.558 23.549 16.901 1.431

-2.622

-5.982

-7.485 35.596 35.035 30.935 26.759 24.435 32.564 29.095 28.069 34.721 41.389 51.476 36.756 48.633 57.324 37.578 49.667 67.274 37.506 53.17 72.592 )

AxI :- Data(0)

MD := Data(3)

ID := Data(l)

TQ := Data(4)

QT := Data(2)

OD:= Data(5)

Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Enttergy Operations Inc Central Engineering Programs RID := regress(Axl,ID,3)

Appendix D; Attachment 4 Page 6 of 32 Engineering Report M-EP-2004-001-00 RQT:= regress(AxI,QT,3)

ROD := regress(Axl,OD,3)

RMD := regress(Axl,MD,3)

ULStrs.Dist = 1.786 UpperA) nozzle bN RTQ := regress(AxI,TQ,3) cial Extent for Stress Distribution to be used in the Analysis (Axial distance above Attom)

FLCntr :=

Refftint -

if Val X

RefPoint if Val = 2 RefPoint + CO othenvise Flaw center Location Location above Nozzle Bottom UTip := FLCntr + C0 InCStrs.avg =

ULStrs.Dist - UTip 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles in the Axial Direction for Fracture Mechanics Analysis N :=20 Number of locations for stress profiles Loco := FLCntr L

i:= i.. N +3 Incri :=

c0 if i < 4 InCStrs.avg otherwise Loci := Loci-j + Incri SID; RID3 + RID4-Loci + RID.(Loc,) 2 + RID 6 (Loci)'

Developed by:

J. S. Blhmadesam Verifed by.

B. C. Gray

Enttergy Operations Itic Central Engineering Programs Appendix D; Attachment 4 Page 7 of 32 Engineering Report M-EP-2004-001-00 SQT RQT3 + RQT 4-Loci + RQT.(Loci) 2 + RQT6.(Loc;)3 SMD:

RMD3 + RMD 4Loci + RMD *(Loci)2 +[RMD * (Loc;)3]

STQi = RTQ + RTQ -Loci + RTQ.(Loci) 2 + RTQ (Loc;)3 SOD; ROD3 + ROD 4Loci + ROD.(Loc;)2 + ROD *(Loc;)3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j

I..N Sidj =

SIDj + SlDj+, + SIDj+2 f j =

3 Sid

(j + 1) + SIDj+2 iI otherwise j +2 Sqtj =

SQTj + SQTj+I + SQTj+2 3

sqt

)(j + 1) + SQTj+2 j+2 if j = I otherwise SmdJ =

SMDj + SMDj+l + SMDj+2 if j = 1 3

Stq =

Smd

(j + I) + SMDj+2 j+2 STQj + STQj+l + STQj+2 if j =

3 Stq. *(j + I) + STQj+2 otherwise j+2 otherwise Developed by:V J. S. Bnihmadesam Venfred by:

B. C. Gray

Entergy Operations Inc Central Engineering Progranms Appendix D; Attachment 4 Page 8 of 32 Engineering Report M-EP-2004-001-00 Sod. =

J SODj + SODj+l + SODj+2 if j =

3 Sod

(j + I) + SODj+2 j+2 othernvise Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution)

U0 := 0.000 U I := 0.25 U2 := 0.50 U3 := 0.75 U4 = 1.00 Y := stack(u 0 lu 1,u 2,u3,u4 )

SIGI :=stack ( Sod,9 Stq', Smd1 ' Sqti ' Sid1)

SIG 3 := stack(Sod3 Stq3 Smd3'Sqt 3' Sid 3)

SIG5 := stack(Sod 5 Stq5' Smd5' 5qt5' Sid 5)

SIG7 := stack(Sod7 9 Stq7' Smd 71 S5qt7' Sid7)

SIG9 := stack(Sod9 Stq9' Smd 99Sqt9 Sid 9)

SIG II := stack( Sod i' Stq ',Smd 1, Sqt 1 S'id 11)

SIG2 := stack(Sod2Stq2Smd2 Sqt2, Sid2)

SIG4 := stack(Sod 4 Stq4 Smd4 Sqt Sid4)

SIG6 := stack(Sod 66 Stq6 ' Smd(

qt6 Sid 6 )

SIG 8 := stack(Sod 8 9Stq 8 ' Smd '

4qt 8 ' Sid 8 )

SIGI 0 := stack(Sod0' Stq,( 'Sind 1 qt 10 id o)

SIG 1 2

= stack(Sod12,Stq12Sind qt 12 id 12)

Developed by:

J. S. Bnihmadesam Veirifed by B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 9 of 32 Engineering Report M-EP-2004-001 -00 SIG 13 = stack (Sod 13 ' Stq13 ' Smd13' Sqt13 'Sid13)

SIG 15 = stack(Sod 5, Stq' 5,Smd 15 ' Sqty5 'Sid 15)

SIG 1 7 = stack( Sod 7Stq17'Smd17'Sqt17 Sid17)

SIG 1 9 := stack ( Sod19 'Stqg,9 smd 9 'Sqt 19 ' Sid19)

SIG 14 = stack(Sod14 ' Stql 1 Smd14 Sqt14 'Sid 14)

SIG 16 = sackSo 16 stq 6 ' Smd16 ' Sqt16 ' Sid16)

SIG1 8 = stack (Sod 8'Stq'8Smd8 Sqt18 Sid8)

SIG 2 0 := stack (Sod 20 ' Stq20 ' Smd 20 ' qt2 'Sid20)

Regression of Through-wall Stress distribution to obtain Stress Coefficients through-wall using a Third Order polynomial ODRGI := regress(Y,SIG1,3)

ODRG2 := regress(Y,SIG2,3)

ODRG3 regress(Y,SIG 3,3)

ODRG5 regress(Y,SIG5,3)

ODRG7 regress(Y,SIG 7,3)

ODRG9 regress(Y,SIG 9,3)

ODRG 1 regress(YSIG, 1,3)

ODRG 13 regress(YSIG 13,3)

ODRG15 regress(YSIG 1 5,3)

ODRG1 7 regress(Y,SIG 1 7,3) 0DRG 9 : regress(Y,SIG 1 9,3)

Developed by:

J. S. Bnihmadesam ODRG4 := regress(Y,SIG4,3)

ODRG6 := regress(Y,SIG6,3)

ODRG8 := regress(Y,SIG 8,3)

ODRG 10 := regress(Y,SIG 1 0,3)

ODRG 12 := regress(Y,SIG 1 2,3)

ODRG1 4 := regress(YSIG14'3)

ODRG 16 := regress(Y,SIG 1 6,3)

ODRG 1 8 := regress(Y,SIG 1 8,3)

ODRG2 0 := regress(YSIG2 0,3)

Venified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 10 of 32 Engineering Report M-EP-2004-001-00 Stress Distribution in the tube. Stress influence coefficients obtained from third order polynomial curve fit to the throughway stress distribution ProPLength = ULStrs.Dist - FLCntr-Co ProPLength = 0.329 Data Files for Flaw Shape Factors from NASA (NASA-TM-111707-SC04 Model)

{NO INPUT Required}

Mettu Raju Newman Sivakumar Forman Solution of ID Part through-wall Flaw in Cylinder Jsb :=

0: !

1 A.

2 0

1.000 0.200 0.000 I

1.000 0.200 0.200 2

1.000 0.200 0.500 3

1.000 0.200 0.800 4

1.000 0.200 1.000 5

1.000 0.400 0.000 6

1.000 0.400 0.200 7

1.000 0.400 0.500 8

1.000 0.400 0.800 9

1.000 0.400 1.000 10 1.000 1.000 0.000 11 1.000 1.000 0.200 12 1.000 1.000 0.500 13 1.000 1.000 0.800 14 1.000 1.000 1.000 15 2.000 0.200 0.000 16 2.000 0.200 0.200 17 2.000 0.200 0.500 18 2.000 0.200 0.800 19 2.000 0.200 1.000 20 2.000 0.400 0.000 21 2.000 0.400 0.200 22 2.000 0.400 0.500 23 2.000 0.400 0.800 Developed by:

J. S. Bnhmadesam Verfired by:

8. C. Gray

Entergy Operatioms hic Central Engineering Programs Appendix D; Attachment 4 Page 1I of 32 Engineering Report M-EP-2004-001-00 24 2.000 0.400 1.000 25 2.000 1.000 0.000 26 2.000 1.000 0.200 27 2.000 1.000 0.500 28 2.000 1.000 0.800 29 2.000 1.000 1.000 TO 4.000 0.200 0.000 31 4.000 0.200 0.200 32 4.000 0.200 0.500 33 4.000 0.200 0.800 34 4.000 0.200 1.000 35 4.000 0.400 0.000 36 4.000 0.400 0.200 37 4.000 0.400 0.500 38 4.000 0.400 0.800 39 4.000 0.400 1.000 40 4.000 1.000 0.000 41 4.000 1.000 0.200 42 4.000 1.000 0.500 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 51 10.000 0.400 0.200 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 0.400 0.200 Developed by:

J. S. Brihmadesam Verified by:

8. C. Gray

Entergy Operations Inc Certral Engineering Programs Appendix D; Attachment 4 Page 12 of 32 Engineering Report M-EP-2004-001-00 67 300.000 0.400 0.500 68 300.000 0.400 0.800 69 300.000 0.400 1.000 70 300.000 1.000 0.000 71 300.000 1.000 0.200 72 300.000 1.000 0.500 73 300.000 1.000 0.800 74 300.000 1.000 1.000 Sambi :=

j'i.

1 2

3.

4'

-5. -

6 7

0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1

1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2

1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3

2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4

4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5

1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032

6.

1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7

1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033

,8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9

2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 Developed by:

J. S. Bnhmadesam Veniried by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 13 of 32 Engineering Report M-EP-2004-001-00 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.0681 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 0.596 1.16 0.242 0.097 0.051 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 35 1

0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Developed by:e J. S. Bnhmadesam Venired by:-

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 14 of 32 Engineering Report M-EP-2004-001-00 Wv JbMP X :=Jsb(1)

Y s(2) a =Sambi(O)

Sambi~ ')

aL =

aQ := Sambi(2)

Sambi(6) ac :=Sambi (3) cc : Sambi(7)

CU := Sambi(4)

Sambi (5)

CL =

CQ :=

n :=

3 if Rt < 4.0 2 otherwise "a-Tip" Uniform Term MaU= augment(W,X,Y)

VaU :=a u Rau : regress(Mau, VaU,n) faU (W, X, Y) faU(4,.4,.8) = 1.741

= interP[Rau, MaU, VaU, X Ij Check Calculation Linear Term MaL := augment(W, X, Y)

VaL := aL RaL :=regress( MaL, VaL, n) faL(W, X, Y) :=interp RaL, MaL, VaL{ XIj Developed by:

J. S. Slihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 15 of 32 Engineering Report M-EP-2004001-00 faL(4,.4,.8) = 0.919 Check Calculation Quadratic Term MaQ := augment(W, X, Y)

VaQ := aQ RaQ := regress( MaQ, VaQ~ n) faQ(W,X,Y) := inte faQ(4,.4,.8) = 0.656

!MaQ, VaQ, X I Check Calculation Cubic Term MaC := augment(W,X,Y)

VaC := aC RaC := regress(MaC, VaC, n) faC(W,X,Y) = inte faC(4,-4,-8) = 0.524 (W)-

MaC, VaC, X I Check Calculation Developed by.

J. S. Bnlhmadesam Verified by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 16 of 32 Engineering Report M-EP-2004-001-00 "C" Tip Coefficients Uniform Term McU := augment(WX,Y)

RCu := regress(MCuVcun)

'W)-

fcU(WXY) := interp{Rcu McU VcU{ X I f-u~KYx)Y fCU(4,.4,.8) = 1.371 Check Calculation Linear Term M'cL augment(W,X,Y)

VcL := cL RcL := regress(McLVcLn) fcL(W X, Y) = interP[RcL MCL VCL{ X I fcL(2,.4,.8) = 0.319 Check Calculation Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Prograins Appendix D; Attachment 4 Page 17 of 32 Engineering Report M-EP-2004-001-00 Quadratic Term McQ := augment(W,X,Y)

VCQ := CQ RcQ := regress(MCQ, VcQ, n) feQ (WXV,XY) :=interp RCQ 9MCQ IVCQ{X I1 fcQ(4 4 8) = 0.126 Check Calculation Cubic Term MCC= augment(W,X,Y)

VCC := Cc R~cC= regress( MCC, VcC,n) fCC(4,.4,.)

= 0.068 ewA

,MCC,V cc, X I Check Calculation Developed by:

J. S. BnShmadesam Verifiedby:

B. C. Gray

Entergy Operationts Inc Central Engineering Programns Appendix D; Attachment 4 Page 18 of 32 Engineering Report M-EP-2004-001-00 Calculations: Recursive calculations to estimate flaw growth.

Recursive Loop for Calculation of PWSCC Crack Growth Entergy Model CGRsambi =

aO C

aO co WE C0 NCBo - Cblk wvhile j < Ilim 0o-ODRG3 if cj < co ODRG2 if co < cj < co+ lnCStrs.avg ODRG3 if co + Incstrs.avg < cj < Co + 2Ifncstrs.avg ODRG4 if co + 2flncstrs.avg < cj < co + 3IncStrs.avg 3

ODRG5 if co + 3flncstrs.avg < cj < co + 4.lncStrs.avg ODRG6 if Co + 4-lncstrs.avg < cj < co+ +5 IncStrs.avg ODRG7 if Co + 5-lncStrs.avg < Cj < co + 6.flCStrs.avg 73 ODRG8 if co + 61fncstrs.avg < cj < co + 7.flCStrs.avg ODRG9 if Co + 7-Ilncstrs.avg < cj < C0 + 8llncStrs.avg ODRG1O if co + 81fnCStrs.avg < Cj < co + 9dfnCStrs.avg ODRGI 13 if co + 91fnCStrs.avg < cj < co + i olnCStrs.avg ODRG1 2 3 if co+

0o.IncStrs.avg < cj < co + IIlnCStrs.avg ODRG1 3 if co+ I-IncStrsavg i

Cj< co + 12Incstrs.avg Developed by:

J. S. Blihmadesam Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 19 of 32 ODRG14 if co+ 12.lncstrs.avg < cji co++ 3d-Incstrs.avg ODRG15 if co+ 13-ncStrs~avg <ci <co+ 14

-IncStrs.avg 3

ODRG1 6 if CO+ 14-lncstrs.avg < cj < co+ I5flncstrs.avg 3

ODRG 17 if CO+ I4lncstrs.avg < cj < co0+

l16lncstrs.avg 3

ODRG 18 iffco+ 156lncstrs.avg < cj < co+ l17lncstrs.avg 3

ODRG 19 if co+ I7-Incstrs.avg < cj < Co+ I8-fnCStrs avg 3av ODRG2 0 othervise 3

ODRG4 if Cj < CO ODRG2 if co < cj < co

+ lncstrs.avg ODRG3 if c+ Ilncstrs.avg < cj < co + 2f1nCstrs.avg ODRG 4 if co+ 2-lncstrs.avg < cji co + 3-lncstrs.avg ODRG5 if Cco+ 3-InCstrs.avg < cj < co+ 4 lfncstrs.avg ODRG6 ifco + 4d1fncstrs.avg < cj < Co + 5dlncstrs.avg ODRG7 4 ifco+ 5-lncstrs.avg < cj < Co+ 6*IncStrs.avg ODRG 8 ifco + 6.lncstrs.avg < cij CO + 7flncstrs.avg ODRG9 i fco+ 7dflncstrs.avg < Cj < C0 + 8dflncstrs.avg ODRGO4 if co + 8.lncstrs.avg < Cj <C 0 + 9lnCStrs.avg ODRG 1 4 if co+ 9.lncstrs.avg < cj < co+I

+

.Incstrs.avg ODRG 12 ifco+ IOIlncstrs.avg < cj < c 0 +i -I ncstrs.avg ODRG 13 ifco + IIfIncStrs.avg < Cj < Co+ 12f nCStrs.avg ODRG144 ifco+ 12flncstrs.avg < cj co0+ 13lncstrs avg ODRG 15 ifco+ 13-lncstrs.avg < cj < C0 + 14.lncstrs.avg Engineering Report M-EP-2004-001-00 Developed by:

J. S. Blhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 20 of 32 M-EP-2004-001-00 ODRG1 6 if Co+ 14-lncStrsavg < cj < Co+ 15 IncStrs.avg ODRG1 74 if co+ 15 IncStrs.avg < cj < Co+ 16Incstrs.avg ODRG 18 4 if Co+ 16 InCStrs.avg < Cj < Co+ 17IflCStrs.avg ODRG 19 if co+ 17-ncStrsavg< <j<

co + I8 Incstrs.avg ODRG2 0 othenvise 4

02 <- ODRG I if cj < cO ODRG 2 if co < cj < co + InCStrs.avg ODRG3 if c0 + InCstrs.avg < Cj < Co + 2 IncStrs.avg ODRG4 if Co + 2-1nCstrs.avg < cj < Co + 3-InCStrs.avg ODRG 5 if co + 3-InCstrs.avg < cj < C0 + 4-dnCStrs.avg 5

ODRG 6 if co + 4-flCstrs avg < Cj < c0 + 5-flCstrs avg ODRG7 if Co + 5-1nCstrs.avg < cj < C0 + 6-nCStrs.avg 5

ODRG 8 if Co + 6-1nCstrs.avg < Cj < C0 + 7-InCStrs.avg 5

ODRG9 if Co + 7-1ncstrs.avg < Cj < C0 + 8-InCStrs.avg 5

ODRGIO if c0 + s.lncstrs.avg < cj < Co + 9d nCStrs.avg 5

ODRG I I i f co + 9. 1 ncs1rs. avg < cj < co + io Incsrag ODRG12 5 if co + I9dlncstrs.avg < Cj < co+ IIl nCStrs.avg ODRG 1 3 if c0+ I-l nCStrsavg < Cj < Co+ 12Incstrs.avg ODRG145 if Co+ 12iIncStrs.avg < Cj < co+ 13 1ncstrs.avg ODRG15 if co+ 13-IncStrsavg < cj < Co+ 13 lnCStrs.avg ODRG1 6 if Co+

14 Incstrs avg < Cj < Co + 15f nCStrs.avg 5

Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Progranms Appendix D; Attachment 4 Page 21 of 32 UIJKU1 7 It c 0+ 15 IncStrs.avg < Cj S c 0 + 16flnCStrs.avg ODRG1 8 if co+ 16dfnCStrs.avg < Cj S co+ 17flncStrs.avg ODRG19 if co+ 17 fncstrs.avg < cj S c0 + i8sfnCStrs.avg ODRG2 0 otherwise 5

ODRGI if Cj S C0 ODRG2 if co < Cj S co + InCStrs.avg ODRG36 if cO + Ifncstrs.avg < cj S c0 + 2 1nCStrs.avg ODRG46 if co + 2 lnCstrs.avg < cj S c0 + 3-Incstrs.avg ODRG56 if c0 + 3 IncStrs.avg < Cj S co + 4 lncStrs.avg ODRG66 if co + 4flncStrs.avg < Cj o

co + S lncStrs.avg ODRG7 if co + 5l ncstrs.avg < cj S co + 6 InCstrs.avg ODRG86 if co + 6. ncStrs.avg < cj S c0 + 7 lncStrs.avg ODRG96 if co + 7 1ncstrs.avg < CJ S co + 8. 1ncstrs.avg ODRGI 0 if C0 + 8. lCStrs.avg < Cj S Co + 9. lCStrs.avg ODRGI 16 if cO + 9fInCstrs.avg < cj S co + iodfnCStrs.avg ODRG126 if co+ 10 InCstrs.avg < cj S c 0+ I IInCStrs.avg ODRG136 if co+ lII lCStrs.avg < cj S co+ 12 InCStrs.avg ODRG146 i fco + 12 lncStrs avg < cj< Sco+ 13 -IncStrs avg ODRG156 if co+ 13 1ncStrs.avg < Cj S C0+ 14.lnfStrs.avg ODRG1 66 if co+

14 IncStrs.avg < cj c0 + 15 1ncStrs.avg ODRG 176 if co+ 15 InCStrs.avg < cj S C0+ 16.Incstrs.avg ODRG 186 if c0+ 161fncsttrs.avg < Cj S C0+ 171fncstrs.avg Engineering Report M-EP-2004-001-00 Developed by:

J. S. Bnhmadesam Venified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 22 of 32 Engineering Report M-EP-2004-401-00 ODRG19 6 if co + 17-IncStrs.avg < Cj < c0 + 18. nCStrs.avg ODRG20 othervise 0 <- G0 a0 +O0.25 aA +

oa2

+

0.25-aj)3 t I <f

+ (y I t

)+ 02-

+ (YY t

)

42 CO + C I t0.5 aj)

Kt )

(05. aj 2 (0. 5aj)3 a0+o.75-I

+

0.75-aj2 43v0+(1-

)+at J)

+ G.(0.75-aj)3 44E

+

( I

)

(

-.O.

(I.O.aj-3

+ a3-

.t

)

't

)

X0 0.0 x

- 0.25 X2 0.5 X3 0.75 X4 1

l-0 X

stack(xO,xI,x2,x 3,x4)

ST-stack(4Os 1,42444)

RG

- regress(X, ST, 3) 000 -

RG3 + Plnt a 10 RG4 CY20 RG5 (T30 -

RG6 A Rj aj Cj aj

4.

j Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 23 of 32 M-EP-2004-00100 I

Gau.< faU(RtARiATi)

Galiv faL(RtARjATj) j Gaqj <faQ(RtARjATj)

Gacj < faC (Rt, ARj, ATJ)

GC Uj fCU(Rt'ARj'ATJ)

GC1 i fcL(RtARjATj) j Gcq <- fCQ(Rt, ARj, ATJ)

GCC; - fcC(Rt, ARj, ATj) 1.65 Qj;

+ 1.464.(-

if cj > aj l + 1.464-otherwise Ka v

(

i-j (OO Gaujlj G lO GaG qj

+ 3 Gacj)

KC. <- (j.

G i

(O Gcuj + ( ao*Gcl I + (720Gcqj + G3 0 -Gccj)

K a K

Kaj 1.099 Kyj < K

1.099 Ka

9.0 if Ka 9.0 Ka otherwise K

9.0 if K, < 9.0 K KZ otherwise Da <Co(Ka 9.0)1.16 Developed by:

Verified by:

J. S. Brihmadesam B. C. Gray

Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 24 of 32 M-EP2004-001OO Dag E-Da&-CFinhr-CbIk if Ka < 80.0 4-10o -CFinhr-Cblk otherwise Dc < Co-(K

- 9.0)I-16 DCgj &

DC. CFinhr-Cblk if K,, < 80.0 4 -10 '1CFinhr-Cblk otherwise output(j,O) <- j output(j, I) <- aj output(j, 2) <- Cj - CO output(j, 3) <- Dag.

output(j, 4) <- Dcgj output(j,5) <- Ka.

output(j, 6) <- KC NCj OUtPUt(j, 7) <- NCBjI 365.24 output(j, 8) - Gau output(j,9) &- Galj j

output(j, 10) <- Gaqj output(j, II) & Gac OUtpUt(j, 12) < G cuj 0UtPUt(j, 13)

GCl OUtPUt(j, 14)

Gcq OUtPUt(j, 15)

GCC ji<- j +

Developed by.'

Verified by:

J. S. Brihmadesam B C. Gray

Entergy Operations Inc Cen tra I Etgineering Programs Appendix D; Attachment 4 Page 25 of 32 Engineering Report M-EP-2004-001-00 aj <- aj- + Dagj_

cj < Cj~i + Dcg. 1 aj -

t if aj 2 t aj otherwise NCBj <- NCBj-j + CbIk output Developed by:

J. S. Buihmadesam Verified by:

B. C. Gray

Eirtergy Operationis Inc Central Engineering Progranms Appendix D; Attachment 4 Page 26 of 32 Engineering Report M-EP-2004-001-00 Recursive Loop for Industry Model

{R/t = 4.0 and alc=0.33 The R/t lower Limit for Original Raju-Newman model and aspect ratio was fixed at 1:6)

CGRBam.Bamr aO -- aO CO *- CO NCBo - CbIk w~hile i < Ilim (0 - ODRG1

(*-

ODRG 1 02& ODRG1 o3 - ODRG 1

%<- G0 1

<-0.2-aj I1,

0+

-t J +

0.25-aj{)

0.25 aj)3 t

)

fo<a0-a7 W +O2<

aj2 0o.5+aj33 42 (-GO + OI t y+ (2-

+ frY t )

3(I 0.75-a 43~y0+7l t

)

0.75.aj) 2 (0.75.aj 3

t )

~4(-

G+

F -

+t) 2

+03Y.O.a X

(-- 0.0 xi <- 0.25 x2<- 05 x3 -

0.75 x4 (-

10 Developed by:

J. S. Brlhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programns Appendix D; Attachment 4 Page 27 of 32 Engineering Report M-EP-2004-001-00 X - stack (xO,xIx 2,x 3,x 4)

ST - stack(40,41,42,43,44)

RG÷- regress(X, ST, 3) o0 - RG3 IO <- RG4 020<

RG5 30 <- RG6 A Rj v-aj C.

aj ATJ t

Gau< faU(4,*3,ATj)

Gal

faL(4,3,ATj)

Gaq.< faQ (4,*3, ATj)

Gac < faC(4,*3, ATj)

I.6-aj) 1.65 cj)

+ 1.464 -C 1

a'j) if cj 2 aj othenvise La 0.5 Ka. <

i Q

() O 0Gaui + a IO Gali+ 020 Gaqj + O30 Gac7)

KCC E Kaj 1.099 j

KJ <

9.0 if Kaj < 9.0 Ka othervise j

Da v CO (Ka - 9.0)1.16 Developed by:

J. S. Blihmadesam Verifed by:

B. C. Gray

Ebtergy Operatiois Inc Central Engineering Programs Appendix D; Attachment 4 Page 28 of 32 D ag. &-

Daj C(inhrl(rblk if Ka < 80.0 4 0,CF inhr-Cblk otherwise Dcg E Dag-3 output(j,O) <- j output(j, I) <- aj Output(j,2) <- Cj - CO OutPut(j, 3) < Dagj OUtPUt(j 4) <- DCgj output(j, 5) <- Kaj NCB; OutPUt(j, 7) <

365-24 Output(j, 8 ) & Gau output(j,9 ) E Galj output(j, 10) -

Gaq; output(j, II) <- Gacj aj -

aj.i + Dagj_

Cj E-CjH + Dcg. 1 aj <-t if ajŽt aj otherwise NCBj <- NCBj-l + Cbik output Engineering Report M-EP-2004-001-00 k := o.. 1rim Developed by:

I J. S. Bnhmadesam Venfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 29 of 32 Engineering Report M-EP-2004-oO1-00 Flaw Growth in Depth Direction 0.6 -

I I

U s

0.4 0.

0

(

0.2 3

001 o

0.5 1

Operating Time {years}

Entergy-CEP Model Conventional Model 1.5 2

TMrack growth due to PWSCC is not predicted by either models.

Both models do not indicate crack growth due to PWSCC.

I

.0 0

.10 I-J 0

0.5 I Flaw Growth in Length Direction I

I I

I 0

-0.5 0 0.5 1

1.5 Operating Time {years}

Entergy-CEP Model Conventional Model 2

Developedby:

J. S. Bnhmadesam Venifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 30 of 32 Engineering Report M-EP-2004-001 -00 S.-

C.)

7 20 [

Stress Intensity Factors I

i I

I I

10 0.0 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Conventional Model Depth Point The SIF comparison shows that the current model has a similar SIF than that predicted by the conventional model. The current model predicts that the crack would grow preferentially on the surface than in the depth direction. This has been observed in the field for OD initiated cracks for the B&W design CRDM.

Developed by:

J. S. Brihmadesam Verified by:

B. C Gray Z6Fz G

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 31 of 32 Engineering Report M-EP-2004-001 -00 Axum plot showing the ID and the OD stress distribution for the CEDM 70 30

-10

-50 1.0 1.5 2.0 Distance from Nozzle Bottom (inches)

Axum plot showing the comparison for Crack growth between Conventional and Current Model 0.1 c 0.16 IEe C 0.1 4 -

X 0.12 -

L.

0.1 0 0 08 E n te rg y M 0 d e I In d ustry M od e I 0.0 0.5 1.0 1.5 2 0 0 p e ra tin g T im e (y e a rs )

Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray C') 'S

Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 32 of 32 Engineering Report M-EP-2004-001-00 Axum plot showing the SIF comparison between the Conventional and Current Models 22 Conventional Model (ndustry) 20 -

T 18 16 14 -

12 0.0 0.5 1.0 1.5 2.0 Operating Tne (years)

Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray C. 22--s,

Entegy Operations Inc.

Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 1 of 17 M-EP-2004-001-00 Comparison for Through-wall Cracks Developed by Central Engineering Programs, Entergy Operations Inc Developed by: J. S. Brihmadesam Verified by: B. C. Gray

References:

1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}

2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Purpose :- This worksheet is used to compare the results from the conventional model, edge crack model and the current model. The SIF comparison is made between the conventional model and the current model. The crack growth and SIF comparisons are made between the edge crack and current model. The SIF equations for the conventional model are included in the current model's recursive loop structure. The edge crack is modeled separately in a recursive loop immediately following the loop for the current model. Graphical results show the comparisons at the end.

The salient differences between the three models considered are:

1) Current model is based on X, which is limited to 20. The closed form solutions are based on a thick wall cylinder.

The applied stresses are based on a moving average. Therefore an increase in the stress field as the crack advances is considered in the analyses

2) The conventional model is based on a Center Cracked Panel with a SICF of 1.0. The applied stresses are at the initial flaw location and remain constant over the entire crack growth regime.

3) The edge crack model uses the plate height (b) equal to the nozzle length from the bottom of the nozzle to below the weld. The initial flaw length (a) is equal to the blind zone (1.544 inches). When this is done the ratioa/b (crack-length/plate-height) is larger than the validity limit of 0.6. Therefore, the estimated SIF is considered non-representative.

Arkansas Nuckear One Unit 1 Component: ReactorVessel CRDM -"18.2"degree Nozzle, "Downhill" Azimuth Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRIMRP 55-Rev. 1.

Through Wall The correction is applied in the determination of the crack extension to Axial Flaw obtain the value in inch/hr.

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 2 of 17 Engineering Report M-EP-2004-001 -00 The First Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.

This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.

ULStrs.Dist:= 1.712 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

The Second Input is needed to locate the Reference Line (eg. top of the Blind Zone).

The through-wall flaw "Upper Tip" is located at the Reference Line.

Enter the Length of the Freespan from NtDE Data Sheet FSnde.data.sheet := 0.430 Location of Blind Zone above nozzle bottom (inch)

BZ := ULStrs.Dist - FSnde.data.sheet

.I

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 3 of 17 Engineering Report M-EP-2004-001-00 Input Data :-

L := 0.25 OD:= 4.00 ID:= 2.765 Pint:= 2.235 Years:= 2 Ilim:= 1500 T := 600 v := 0.307 Initial Flaw Length TWaxial Tube OD Tube ID Design Operating Pressure (internal)

Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F aOc:= 2.67. 10 12 Qg := 31.0 Tref:= 617 E

_Qg

(

I I

coeL 1.103 103 tT+459.67 Tref+459.67)J Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)

Reference Temperature for normalizing Data deg. F Tinlopr:= Years.365-24 OD 2

Ri:= ID 2

t := Ro - Ri Rm:= Ri + -2 CFinhr:= I417. 10 Tilopr Ck im Prntblk:=

50 50 I I

L 2

LI:= BZ

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 4 of 17 Engineering Report M-EP-2004-001-00 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:

Column "O" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "5" = OD Stress data at each Elevation (ksi)

DataAII :=

.0 1

2 3

I 4

5

-. O I : : I --

2..',

.3

!.-4 1 i I!

5 "

0 0

-32.98

-29.55

-27.62

-25.63

-23.66 0.46 4.42 1.43

-2.62

-5.98

-7.49 2

0.83 23.6 20.13 17.47 13.58 8.56 3

1.13 39.38 33.76 28.59 23.55 16.9 4

1.37 41.08 35.6 32.56 29.09 28.07 5

1.56 35.47 35.03 34.72 41.39 51.48 6

1.71 25.31 30.93 36.76 48.63 57.32 7

1.85 18.48 26.76 37.58 49.67 67.27 8

2 15.18 24.43 37.51 53.17 72.59 9

2.14 16.04 22.8 36.7 51.39 59.83 AllAxl:= DataXll AIIID := DataAllI (5)

AIMOD Data,*ll 100 75 7

50 25 25 V2 0

-25

-50 I-1.282 C

,'...-s_

1.7112I.......

I 10 10 I

0.5 1

1.5 2

Axial Distance above Bottom [inch]

2.5 3

ID Distribution OD distribution BZ = 1.282

Enteriy Operations inc.

Central Engineering Programs Appendix D; Attachment 5 Page 5 of 17 Engineering Report M-EP-2004-001 -00 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

(

0

-32.98 Data:=

0.463 4.418 0.834 23.603 1.131 39.381 1.369 41.077 1.56 35.472 1.712 25.309 1.854 18.476

-29.552 1.431 20.133 33.757 35.596 35.035 30.935 26.759

-27.619 -25.631 -23.659)

-2.622

-5.982

-7.485 17.472 13.58 8.558 28.588 23.549 16.901 32.564 29.095 28.069 34.721 41.389 51.476 36.756 48.633 57.324 37.578 49.667 67.274 37.506 53.17 72.592 )

k1.996 15.182 24.435 Axl:= Data ID:= Data (5)

OD:

Data RID:= regress(Axl,ID,3)

ROD:= regress(Axl, OD,3)

FLCntr:= BZ-I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ IncStrs.avg :=

20 ULStrs.Dist - BZ IncrEdg:=

20 RIDAII := regress(AIIAxl,AIIID,3)

RODAII := regress(AIIAxl,AIIOD,3)

No User Input required beyond this Point

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 6 of 17 Engineering Report M-EP-2004-001-00 Calculation to develop Stress Profiles for Analysis Hoop Stress Profile in the axial direction of the tube for ID and OD locations Number of locations for stress profiles N:= 20 Loco:= FLCntr - L i:= I.. N +3 Incr.:=

I if i <4 I lncstrs.avg otherwise Loc. := Loc iI + Incr.

SID. = RID + RID Loc. + RID.(LocA2 + RID6 (LOC;)

i 3

4' I

5 I)

~

I Incredg Li if i <4 I

2 IncrEdg othervise Loc I:=

0 if i= I Locl I. + lncrcdg otherwise SOD := ROD + ROD Loc. + ROD (LoC.2 + ROD (LoC Y 3

4' I

A5\\lj SIDAlli := RIDAII + RIDAII 4Loc Ii + RIDAII 5(LocIV + RIDAII.(Loc IA)3 SODAII := RODAI1 + RODill 4LocI; + RODA.15 (Loc I) 2 + RODAI16 (LoCI.) 3 I

Entefyy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 7 of 17 Engineering Report M-EP-2004-001 -00 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j:= 1..N Sid.:=

j SIDj + SIDj+l +

Dj+2 ifj=

3 i

SOD. + SOD.j+ + SODj+2 Sodi:

3 +

+

if jl=

Sodj -(j + I) + SODj+2 jotherwise j+2 SidH,-(j + 1) + S1Dj+2 j+2 otherwise Sid.all :=

j SIDAll + SlDAII,

+ SIDAIIj,2 3

Sid.allj (j + 1) + SIDAIIj+2 oti j+2 if j = I Sod.all. :=

i SODAIIj + SODAII j+ + SODAIIj+2 3

Sod.all j (j + 1) + SODAIIj+2 j+2 oth j +2 if j = I

,ierwise lenvise Sod. + Sid.

m.

J + Pint j

2 Sod. - Sid.

b :=

J a J 2

Sod.all. + Sid.all.

Gm.all.:=

2 J + Pint i

2

Entefyr Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 8 of 17 Engineering Report M-EP-2004-001 -00 Stress Distributions for use in Fracture Mechanics Analysis Membrane Stress Bending Stress OD Stress ID Stress Membrane stress (Edge Crack) am =

0 31.422 32.651 33.514 34.19 34.757 35.253 35.7 36.11 36.493 36.852 37.192 37.515 37.824 38.119 38.403

', 0 0

-6.992

-6.232

-5.656

-5.165

-4.719

-4.297

-3.888

-3.485

-3.083

-2.679

-2.272

-1.859

-1.44

-1.014

-0.58 Sod =

of -.

0 22.195 24.184 25.623 26.79 27.803 28.721 29.577 30.391 31.175 31.938 32.685 33.421 34.149 34.871 35.588 Sid =

2 T

T 5.

.4 T

10 0

36.179 36.649 36.935 37.12 37.241 37.315 37.353 37.36 37.34 37.296 37.228 37.139 37.029 36.898 36.747 am.all =

T 2

T 4.

5.5 7.

iT

0 1..

0.

6.374 13.679 18.17 21.253 23.527 25.295 26.724 27.913 28.927 29.808 30.585 31.28 31.908 32.481 33.007 PropLength := ULStrs.Dist - (FLCntr + I)

Pr°PLength = 0-43

Enteryy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 9 of 17 Engineering Report M-EP-2004-001 -00 Calculations: Recursive calculations to estimate flaw growth Recursive loop for Entergy Model and Industry Model TWCpwscc:= FF

-0 0+1 NCB +-Cblk Fvhile i S Ilim lI Om.appid +

am if l;< I0 am3 if 10 < I fS 10 + IncStrs.avg CYM3 if 10+

InCStrs.avg < Ii S 10 + 21IncStrs.avg am4 if 10 + 2-IncStrs.avg < Ii S 10 + 3-fnCStrs.avg aTm 6 if IO + 3-lncstrs.avg < 1i 5 10 + 4-IncStrs.avg aM6 if I + 4 InCStrs.avg < I; S 10 + 5fInCStrs.avg am7 if 10 + 5 InCStrs.avg < Ii S I0 + 6 ncStrs.avg aYm8 if 10 + 6 lncStrs.avg < Ii S 10 + 7SInCStrs.avg Om9 if Io + 7fIncStrs.avg < Ii S 10 + 8-IncStrs.avg Gm 1 if 10+ 8 InCStrs.avg < I;

10+ 9-IncStrs.avg Gm12 if 10 + 9l IncStrs.avg < Ii S 1 + 10 InCStrs.avg (m

if 10 + 1 IlnCstrm.avg < 1i S 10 + I 2IfCStrs.avg am13 if I0 + I I*lncStrs.avg < Ii S 10 + 12InCStrs.avg am14 if 10 + 12I3 ncstrs.avg < I; S 10 + 13 InCStrs.avg GM 15 if I0 + 13 IncStrssavg < I; S 10 +14-IncStrs.avg cm16 if I + 14fIncStrs.avg < I S 10 + 15 ]fnCStrs.avg am if 1I + 15fIncStrs.avg < Ii S Io + 16fInCStrs.avg am 8 if 10 + 16-IncStrs.avg < I 5 10 + 17 ]fnCStrs.avg am19 if I + I7-fncStrs.avg < I; S10 +

I 8 fInCStrs.avg m2 otherwise

Enter.y Operations rnc.

Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 10of 17 M-EP-2004-001-00 Ob.appld <-

Gb if li

10 Gb, if 10 <1 I*10 + InCStrs.avg 0b3 if I + IncStrs.avg < I; f I0+ 2-IncStrs.avg ab4 if 10 + 2-IncStrs.avg < I1 S I0+ 3IncStrs.avg 0b4 if 10 + 32 lncstrs.avg < I;i 10 + 4 lncStrs.avg 0b6 if I + 4 IncStrs.avg < I; f

I0+ 5l1ncstrs.avg

b7 if I0+ 5-InCStrs.avg < 1 *1 + 64lncStrs.avg b8 i f I +

0 InCStrs.avg<I < 1I+ 7IncStrs.avg ab9 if 10 + 74ncStrs.avg < I o'

I0+ 8 InCStrs.avg Oblo if Io+ 8 InCStrs.avg < 1I

10 + 9-Incstrs.avg Obtl if lo + 9IncStrs.avg < I; ' Io+ 10 7

InCStrs.avg 0b12 if lI + 6 IncStrs.avg < 1;

.10+

I lncStrs.avg Obj3 if I0 + I l lncStrs.avg < I; 10+

12lncStrs.avg

(;b14 if I + I2-IncStrs.avg < 1; I

l

+ 13incstrs.avg b105 if I0 + 13 Incstrs.avg < 1;<s1 +94.

ncStrs.avg yb16 if I0 + 14 IncStrs.avg < I i 1 I+

15-inCstrs.avg 1b,7 if I + 15.InCStrs.avg < I

10 + 16[InCStrs.avg Gb 8 if I + 16Incstrs.avg < I;

10 + 17-Incstrs.avg Gb 1 if I + 17-inCStrs.avg < 1;

I0 + 18flncStrs.avg

+

fbl s

other0wise Ai <- 12(-6 v 2)] 0.5 i

(R60 -t)

Aemj i-1.0090 + 0.3621 Ai + 0.0565l (A;)

_ 0.0082 (A;)

+

O.OOO(A;) - 8.326 10 6 (A;)

Abm b-

-0.0063 + 0.0919 A; - 0.0168 (A;)a _ 0.0052 (+i) + 0.0008 (A;) - 2.9701-10 5 (A)

Aebi <-- 0.0029 + 0.0707-if - 0.0197 (A;) + 0.0034 (10 ) 3- 0.0003-(A)

+ 8.8052-10 6 (A)

Abb +- 0.9961 - 0.3806 Ai + 0.1239. (i)

- 0.021.(X) 3+ 0.0017. (X) 4-4.9939 10 5.(XA) 5

Entecyy Operations Inc.

Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 11 of 17 M-EP-2004-001 -00 Kpm O rmnappld.(nE.1;) 0.5 Kpb.

O ab.appid'(n.1i) 0.5 KmembmrODj (Acm, + Abm,) Kpm KmembrnlDi 4(Aemi - Abmi) Kpm KbendOD <- (Aebi

+ Abbj)Kpbj KbendID 4- (Aebi - Abb).Kpbj KAppOD4 - KmembrnOD. + KbendOD.

KApplD. (- KmembmlD. + KbendlD.

Kxj i a ml I(n1 li).

KAppOD. + KAppID.

KAppi 2

KU'l1.lcnr.Strs

- COm.appld.(Qt

)

Ka, +- KApp-1.099 Ka.

9.0 if Ka S9.0 Ka otherwise Dien, < Co (Ka 9.0)1.16 Dlengrth. 4.-

Dlen; CFinhrCblk if Ka S 80.0

-10 4 10 CFinhrCblk otherwise output(isl)

+-

NCB.

output

2) 36-2 oupt(i,l2) 365.2 output(i3) 4 -

I0 output(i 4)

-i output(1 5) -KApp output(i,6)

KAppODi output (,7)

KApplD, i tn,I K. --

- n

Entergy Operations Inc.

Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 12 of 17 M-EP-2004-001-00 output ; 9) 4 KmembmlD; output(j 10) + KbendOD.

output( 1l)

- KbendlD output(i 12)v KWII output(i 13)+

KWIlI.cnr.Strs ii+

I I;- IiI + Dlengrth. 1 NCB.

NCB.

+ CbIk output

Enteryy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 13 of 17 Engineering Report M-EP-2004-001 00 Recursive Loop For Edge Crack Model TWCEDGpWscc:=

NCB 0 4-CM while i :5 IJim Om.appld *-

a' a

a a

a a,

a, al b *- ULStrs.Dist m.allI ym.alL, small3

.13 m.all4 rn.a115 rn.a4l6 m.all7 ym.all g ym.al l9 m.all m.all m.all m.all m.all14 m.alll5 m.all m.all m.all m.a11 if LI *<LI i

0 if LI <LIjS LI + IncrEdg if Li + IncrEdg < LI c

LIj+ 2-1ncrEdg if Li + 2IncrEdg < LIjS Li0 + 3-1ncrEdg if L 0 + 3-IncrEdg < LijS LI0 + 4-1ncrEdg if Ll0 + 4-ncrEdg < Ll LI0 + 5-lncrEdg if L 0 + 5-IncrEdg < Ll I

Ll+ 6LncrEdg if Li 0+ 6-ncrEdg < LI iLI0 + 7-5 ncrEdg if LI +7-incrEdg< LI *j LI + 8.IncrEdg if Ll0 + 8incrEdg < LIjS LI0 + 9-IncrEdg if Ll0 + 97ncrEdg < LI 1 0 + 0-8 IncrEdg if LI + 10-IncrEdg <LI

LI0 + 11-IncrEdg if Li + IIflncrEdg< LIjS LIo+ 12-IncrEdg if Li + 12-incrEdg < Llj LI0+ 13-lncrEdg if Lo + 13-9ncrEdg < LljS LI0+14-IncrEdg if LI + 14-IncrEdg < L jS Li0+ 15-lincrEdg if L l I+

15-ncrEdg < LIj LI0+ 16-lncrEdg if Li + 16-1ncrEdg < L 1

j LIo+ 17-IncrEdg if LI + 17-ncrEdg < LljS LI0+ 18-lIncrEdg otherwvise I

Enitrgy Operations Inc.

Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 14 of 17 M-EP-2004-001-00 LI.

zi

.9 i_

Ž 1.0

- otherwise Fab 4 1.12 - 0.231-(z;) + 10.55.(Z;) - 21.72-(Zi)3 + 30.39.(Zi) 4 Kedg.Crk; v l m.appIdjFi; if (am.appId' >fi)

S 0 am.appld (nt L i.)05. Fab. otherwise KA. v Kedg.Crk. 1-099 Ka 9.0 if KA S9.0 KA. otherwise Dien,

CO0(Ka 9.0)1.16 Dlengrth. -l Dlen; CFinhrCblk if Ka S 80.0 4 10 lCFinhrCbk otherwise outputo

-)

P(i,O)

NCB.

.Output( 1) 365.24 output( 2)

L Ll - Ll output(i 3) v Diengrth.

output(i 4) ~ Kedg.Crk output(i,5)

Fa.b.

i-i+1 LI + LI i-I + Dlengrih. 1 NCB; vNCB iI + CbIk output j:=

I *- Ilim

Entergy Operations Inc.

Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 15of 17 M-EP-2004-001-00 PropL[ngth = 0.43 Flaw Length vs. Time 0.25 Comparison for crack growth 0.2 _

between Edge Crack and Current Model. The edge crack model a/b ratio of 0.6 is reached in 0.5 years, 0.15 therefore the SIF would be invalid for 0.5

/the analysis.

TX 'Cpwscc~j3 x_

~'TCP (Cj 3 )

0.1

' TWCEDGpwscc E -2) 2; --------

0

-0.05 0

0.5 1

1.5 2

TWCPwSCC(

I )

Operating Time (years)

Entergy Model Edge Crack Model I

I

Entergy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 16 of 17 Engineering Report M-EP-2004-001-00 300 250 Q 200 aUv u

150

._1 c

2 V) 100 AGES.

The SIF for the current model is Higher than the SIF for the conventional model. The SIF for the edge crack is very high because the "a/b" ratio is violated.

50 0

0.5 1

1.5 Operating Time {Years}

OD SIF - Entergy Model IID SIF - Entergy Model SIF Conventional approach {Constant Stress Model}

- SIF Conventional approach ( Increasing Stress Model)

Entergy Model - Average used for Flaw Growth Edge Crack I

C. amp

Enteryy Operations Inc.

Central Engineering Programs Appendix D; Attachment 5 Page 17 of 17 Engineering Report M-EP-2004-001 -00 Axum Plot for the ID and OD Stress distribution along nozzle length used in the comparison Hoop Stress Plot 7 0 Xt 3 0 I

-1 0

-50 1.0 1.5 2.0 Distance from Nozzle Bottom {inch)

Axum plot showing the comparison for the SIF between the Current and Conventional Models.

45 -

40 -

vi 35-t 30 -

25 -

20 -

15 Curent Model (Entergy)

Conventional Model (Industry) 0.0 0.5 1.0 Operating Time {years) 1.5 2.0 I

I1.

C-, CW

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 1 of 9 Enginering Report M-EP-2004-001-00 Evaluation of Curve fit for Stress Profile Generation along the Tube Axis In this worksheet the effect of data set selection for curve fitting, using a third order polynomial is evaluated. The data table below is form a data set used in the CRDM analyses. This data set is imported directly from the Excel spreadsheet provided by Dominion Engineering for the CRDM. The evaluation considers the full data set and a limited data set spanning the region of interest.

The purpose of this evaluation is to demonstrate the need for the proper selection of a subset of nodal stress data (in the region of interest) to ensure the accuracy of the analysis.

Data set imported from Excel spreadsheet.

AllData :=

0 12 3

4 5

0 0

10.95 4.51 0.52

-3.32

-7.65 1

0.85 1.32

-0.95

-2.65

-3.1

-3.55 2

1.52 4.77 4.12 5.01 4.33 1.79 3

2.07 15.55 13.98 12.9 10.29 7.18 4

2.5 15.65 12.98 14.76 16.94 17.57 5

2.85 4.83 8.83 13.89 24.74 33.61 6

3.13

-7.46 3.51 12.56 30.99 41 7

3.31

-16.1

-2.81 11.74 31.31 44.81 8

3.5

-19.77

-4.84 10.36 31.62 44.87 9

3.69

-18.2

-5.8 11.63 30.03 40.1 10 3.87

-16.36

-3.95 11.96 27.26 40.74 11 4.06

-6.52

-1.62 14.39 27 37.17 12 4.24 1.58 4.36 14.56 27.38 32.59 13 4.43 11.3 8.91 18.32 23.09 24.52 14 4.61 18.14 15.96 18.93 29.26 19.58 Ax]Len:= AllData (1)

(3)

IDAII= AllData MidWall= AllData ODAII := AIlData(5

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 2 of 9 Enginering Report M-EP-2004-001-00 Data:=

0 10.954 4.51 0.522 -3.322 -7.653) 0.846 1.32

-0.955 -2.652 -3.103 -3.549 1.524 4.766 4.123 5.007 4.329 1.791 2.067 15.552 13.981 12.901 10.287 7.177 2.502 15.655 12.983 14.758 16.943 17.57 2.85 4.83 8.828 13.891 24.741 33.61 3.13

-7.464 3.508 12.564 30.987 40.998 3.315

-16.1

-2.811 11.744 31.306 44.814 3.5

-19.775

-4.84 10.363 31.622 44.873)

Selected subset from the data table above (0)

ALen= Data (I)

IDlim= Data (3)

MPVim= Data ODlim := Data Regression for the full data set RIDAII:= regress(AxILen,IDAII,3)

RMIWAII:= regress(AxlLen,.MidWall,3)

RODAII:= regress(AxlLen,ODA11,3)

Regression for selected data set RIDdata:= regress(ALen, IDlim, 3)

RNIWdata:= regress(ALen, MWlim, 3)

RODdata:= regress(ALen, ODlim, 3)

Bottom:= 0 Top:= 7.0 WB:= 4 Dist:= Top - Bottom Dist Incr :=-

20 D := WB - Bottom Incrl :=-

20

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 3 of 9 Enginering Report M-EP-2004-001 -00 L := 0 - Incr i:= I.. 20 L. := L.

+ Incr Len 0 := 0 - Incrl Len. := Len I + Incrl Determination of Stresses at three locations across wall thickness, using the full data set IDall := RIDA11 + RIDA14 *L;+ RIDAII *(LJi

+ RIDA16 (Li)

MVall:

RM\\VAIl + RMN'All *L + RMN'All.(L) 2 + RM1VAI *(Li)'

ODall.

RODAII 3 + RODA11 L. + RODAII -(L;) + RODAII (Li)3 Determination of Stresses at three locations across wall thickness, using the selected data set MDdatai RIDdata3 + RIDdata4 Leni + RIDdata '(Lena + RIDdata (Len1)3 daa dt 5

da 6

M\\Vdatai:= RM\\Vdata + RMNVdata -Leni + RMWdata. (Leni)2 + (MNVdata

.(Len 3 3

+4 5

ODdata.:

RO~data + RODdata -Leni + RODdata '(Lenl i)+ RODdata -(Leni)3 I3 4

5\\/6

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 4 of 9 Enginering Report M-EP-2004-001-00 Graphical Display of Results Distribution Full Nodal Stress Data 60 j

c 0.

0 40 20 0

Nodal stress data plotted for the ID and the OD distribution. This plot is based on the full data set.

-20 0 1

2 3

4 Axial Length (inch) 5 ID Distribution OD distribution 250 200 ID Stress Distribution:-

Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.

0.

0 0

150 100 50 0

TV0 1

2 3

4 5

Axial Eleveation from Bottom (inch)

ID Regression using All Data ID All Nodal Data 6

7

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 5 of 9 Enginering Report M-EP-2004-01 -00 OD - Regression vs Nodal Data 100 _

0 _

-l Wo g -100 -

C4 0

-200

-300 0 30 -

20 -

OD Stress Distribution:-

Comparison of regression fit versus the full data set. The third-order polynomial does provide an accurate fit. The trend in the data is captured.

2 4

6 Axial Elevation from Bottom (inch)

OD Regression Using All data OD All Nodal Data 8

'A V..

r-CC Mid-Wall Stress Distribution:-

Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.

10 0

-10 I-0 2

4 6

Axial elevation from Bottom (ksi)

Mid-Wall Regression using All data Mid-Wall All Nodal Data 8

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 6 of 9 Enginering Report M-EP-2004-001 -00 ID - Selected Data Set 20 0

cj 9

-20 V)

C-

-40

-60 ID Stress Distribution (Selected Data Set):-

Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.

0 1

2 3

4 Axial Elevation from Bottom (inch)

ID Regression using Selected Data ID Selected Nodal Data Mid-Wall - Selected Data Set 5

20 15 10 Mid-Wall Stress Distribution (Selected Data Set):-

Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.

2 C.

-5 0 1

2 3

Elevation from Bottom (inch)

Mid-Wall Regression Selected Data Set Mid-Wall Selected Data Set 4

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 7 of 9 Enginering Report M-EP-2004-001 -00 OD - Selected Data Set OD Stress Distribution (Selected Data Set):-

Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.

0

-20 '0 1

2 3

Elevation from Bottom (inch)

OD Regression using selected data Set OD Selected Data Set 4

Conclusion :- By selecting the data judiciously, in the region of interest, facilitates an accurate regression fit of the data.

Entergy Operations Inc.

Central Enginering Programs Appendix D; Attachment 6 Page 8 of 9 Enginering Report M-EP-2004-001 -00 I

Co 1:

1 2

Axial Distance from Nozzle Bottom {inch}

I co I

1 2

Axial Distance from Nozzle Bottom (inch)

Entergy Operations Inc.

Central Enginering Programs 50-30 I

Appendix D; Attachment 6 Page 9 of 9 Enginering Report M-EP-2004-001 -00 2

Distance from Nozzle Bottom (inch) r-, U,3 n

ENCLOSURE 4 CNRO-2004-00008 AFFIDAVIT FOR WITHHOLDING INFORMATION FROM PUBLIC DISCLOSURE

DOMINION ENGINEERING, INC.

Aff-4142-00-1, Rev. 0 page 1 of 3 AFFIDAVIT PURSUANT TO 1OClFR2.790 I, E. Stephen Hunt, being duly sworn, affirm, and state as follows:

(1)

This Affidavit supports an application to the Commission for withholding from public disclosure Dominion Engineering, Inc., (DEI) Letter L-4142-00-1, Revision 0, " Material Properties and Modeling Methods Used in ANO Unit 1 Welding Residual Stress Analyses,"

dated January 12, 2004. As stated in this letter, because the non-proprietary version of this letter would remove information to the point of not transmitting any useful information, only a proprietary version will be transmitted.

(2)

I am a Principal Officer of Dominion Engineering, Inc. (DEI), and as such, I have been specifically delegated the function of reviewing the proprietary information sought to be withheld from public disclosure in connection with nuclear power plant licensing and rulemaking proceedings, and am authorized to apply for its withholding on behalf of DEI. I have personal knowledge of the criteria and procedures utilized by DEI in designating information as a trade secret, privileged, or as confidential or financial information.

(3)

I am making the Affidavit in conformance with the provisions of 10CFR §2.790 of the Commission's regulations and in conjunction with the application by Entergy Nuclear Operations for withholding accompanying this Affidavit.

(4)

Public disclosure of the information sought to be withheld is likely to cause substantial harm to DEI's competitive position and foreclose or reduce the availability of substantial profit-making opportunities.

(5)

The specific information in Letter L4142-00-1, Revision 0, sought to be withheld in accordance with 10CFR §2.790 is as follows:

(i)

The specific material property input data used by DEI in performing welding residual stress analyses.

(6)

Pursuant to the provisions of IOCFR §2.790(b)(4) of the Commission's regulations, the following is furnished in consideration by the Commission in determining whether the information sought to be withheld from public disclosure should be withheld.

(i)

DEI has held the subject information in confidence. DEI has controlled the subject information and not disclosed it at any public forum. Any disclosure to third parties has been made pursuant to regulatory provisions or proprietary agreements that provide for maintenance of the information in confidence.

(ii) The information is of a sort customarily held in confidence by DEI. As described in paragraph (v) below, the information is held in confidence by DEI because disclosure would substantially affect DEI's competitive business position. This information principally is related to the methodology, assumptions, and detailed results of welding residual stress analysis finite element models.

DOMINION ENGINEERING, INC.

Aff-4142-00-1, Rev. 0 page 2 of 3 (iii) The information sought to be withheld is being submitted to the NRC in confidence by Entergy Nuclear Operations in conjunction with an application by Entergy Nuclear Operations for withholding.

(iv) To the best of my and DEI's knowledge, no public disclosure of this information has been made, and it is not available in public sources.

(v)

Public disclosure of the information sought to be withheld is likely to cause substantial harm to DEI's competitive position because:

(A) The subject information has substantial commercial value to DEI as significant portions of DEI's future business of providing engineering consulting to nuclear utilities in this area is substantially based upon the information sought to be withheld.

(B) The expertise represented by the subject information is a substantial part of DEl's current position as a competitor in the market of assisting nuclear utilities in the management of stress corrosion cracking material degradation.

Development of this expertise by DEI required the recruitment, training, and employment of skilled engineers working in the nuclear power industry for over 10 years. The information was developed at considerable expense, including attendance at dozens of industry conferences and meetings, over more than a 10 year period of actively working in the technical engineering fields addressed by the report.

(C) Similar products and services are provided by DEI's major competitors.

Acquiring of the information sought to be withheld would allow the competitors to take some share of the market for providing engineering consulting services in this area.

(D) A large effort over a sustained time period would be required by DEI's competitors and others to properly acquire or duplicate the information sought to be withheld by developing the basic methodologies, selecting and justifying the many detailed assumptions, integrating the many technical issues and concerns into a defensible technical presentation, and presenting the results in an easily comprehended manner. In some cases the subject information could only be acquired through a licensing or business agreement.

(E) There is expected to remain a marketplace for services in the areas related to the subject information and currently provided by DEI for many years into the future.

I have read the foregoing and the matters stated therein are true and correct to the best of my knowledge, information and belief. I make this Affidavit under penalty of perjury under the laws of the United States of America and under the laws of the Commonwealth of Virginia.

DOMINION ENGINEERING, INC.

Aff-4142-00-1, Rev. 0 page 3 of 3 Executed at 11730 Plaza America Drive, Suite 310, Reston, Virginia being the premises and place of business of DEL.

January 12, 2004 n to and subscribed before me thisAL-day of____________

Stephen Hunt Wits s h

and official seal.

Principal Officer

(-oJ Notary Public State of Virginia County of Fairfax Anne Doane Notary Public My Comm. Exp. Aug 31, 2005 N

ENCLOSURE 5 CNRO-2004-00008 LICENSEE-IDENTIFIED COMMITMENTS

LICENSEE-IDENTIFIED COMMITMENTS TYPE (Check one)

SCHEDULED ONE-TIME CONTINUING COMPLETION COMMITMENT ACTION COMPLIANCE DATE

1. The final results of the inspections will be X

60 days after included in the 60-day report submitted to startup from the the NRC in accordance with Section IV.E next refueling of the Order.

outage

2. If the NRC staff finds that the crack-growth X

Within 30 days after formula in MRP-55 is unacceptable, the NRC informs Entergy shall revise its analysis that Entergy of an NRC-justifies relaxation of the Order within 30 approved crack-days after the NRC informs Entergy of an growth formula.

NRC-approved crack-growth formula.

3. If Entergy's revised analysis (#2, above)

X Within 72 hours8.333333e-4 days 0.02 hours 1.190476e-4 weeks 2.7396e-5 months shows that the crack growth acceptance from completing the criteria are exceeded prior to the end of revised analysis in Operating Cycle 19 (following the

2, above.

upcoming refueling outage), Entergy will, within 72 hours8.333333e-4 days 0.02 hours 1.190476e-4 weeks 2.7396e-5 months , submit to the NRC written justification for continued operation.

4. If the revised analysis (#2, above) shows X

Within 30 days from that the crack growth acceptance criteria completing the are exceeded during the subsequent revised analysis in operating cycle, Entergy shall, within 30

2, above.

days, submit the revised analysis for NRC review.

5. If the revised analysis (#2, above) shows X

Within 30 days from that the crack growth acceptance criteria completing the are not exceeded during either Operating revised analysis in Cycle 19 or the subsequent operating

2, above.

cycle, Entergy shall, within 30 days, submit a letter to the NRC confirming that its analysis has been revised.

6. Any future crack-growth analyses X

N/A performed for Operating Cycle 19 and future cycles for RPV head penetrations will be based on an acceptable crack growth rate formula.

Page 1 of 2

TYPE (Check one)

SCHEDULED ONE-TIME CONTINUING COMPLETION COMMITMENT ACTION COMPLIANCE DATE

7. The storage data files containing the UT X

During Refueling measurements for CRDM Nozzle 26 were Outage 1R18, if found to be corrupted; therefore, its actual required.

free-span lengths could not be determined. Because of this situation, Entergy will perform a UT examination on Nozzle 26 to determine its actual free-span lengths. If the free-span lengths meet the acceptance criteria for the 26.20 nozzle group (see table above), as documented in Table 1 of Engineering Report M-EP-2004-001 (Enclosure 2), no further actions will be required. If the free-span lengths fail to meet the criteria, Entergy will perform an augmented examination of the blind zone portion of Nozzle 26 not examined by UT. This examination will consist of either ECT or PT, or a combination of both techniques.

8. If performed, this augmented inspection X

60 days after will be included in the 60-day report startup from the required by Section IV.E of the Order.

next refueling outage, if required.

Page 2 of 2

CNRO-2004-00008, Rev. 0 to M-EP-2004-001, Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack Growth in the Un-Inspected Regions of the Control Rod Drive Mechanism Nozzles at ANO, Unit 1, App. C Th

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CNRO-2004-00008, Rev. 0 to M-EP-2004-001, Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack Growth in the Un-Inspected Regions of the Control Rod Drive Mechanism Nozzles at ANO, Unit 1, App. C Th

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