ML032690702

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Engineering Report M-EP-2003-002, Rev. 1, Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrossion Crack Growth in the Uninspected Regions of the Control Element Drive..., Appendix C, Attachments 4
ML032690702
Person / Time
Site: Arkansas Nuclear 
Issue date: 08/26/2003
From:
Entergy Nuclear South, Entergy Operations
To:
Office of Nuclear Reactor Regulation
References
CNRO-2003-00033 M-EP-2003-002, Rev. 1
Download: ML032690702 (95)
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Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 1 of 11 Engineering Report M-EP-20034002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:

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 2 Component: Reactor Vessel CEDM -!'8" Degree Nozzle, Downhill Azimuth, 1.25" above Nozzle Bottom 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 inchor.

OD Surface Flaw 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 necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.

This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the noozk end.

Refp0 int := 1.25 This is the reduced blind zone providing a propagation length of 0.376 inch; freespan of 0.536 To place the flow with repsect to the reference point, the flow 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 Upper limit to be selected for stress distribution (e.g. Weld bottom ).

This is the ekvation from Nozzle Bottom. Enter this value below ULStrs.Dist :=I1.786 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

J. S. Blihmadesam Vedrifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 40 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt := 2.235 Years := 4 hjim := 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 R

2 id Rid:2 t:= Ro-Rid Rm :=Rid +

Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr him

'urn Pmtblk :=50 L

Co0

-~

Rm Rt :=-

-Q g C

[.131 3T re Xa Temperature Correction for Coefficient Alpha C0 1 =

00 Co:= C0 1 Stress InDut Data 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 3 of 11 Engineering Report M-EP-2003.002-01 Input all available Nodal stress data in the table below. The column designations are as follows:

Column "0 = Axial distance from minumum 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 (ksl)

AllData:=

-1 2

3 4

5 O

0

-27.4

-24.36

-22.21

-20.41

-18.98 0.48 0.63

-1.49

-3.6

-4.44

-5.27

]2 0.87 17.66 16.42 14.61 12.41 9.38 3

1.18 29.8 26.05 22.72 18.95 14.2 4~

1.43 33.62 27.79 24.8 24.32 26.99 r5 1.63 32.36 28.47 27.59 34.28 45.1 6

1.79 27.39 28.92 31.39 43.88 63.72 7

1.92 21.5 25.56 33.55 48.09 66.36 2.05 16.94 23.79 34.06 49.47 67.67 2.18 14.83 22.26 34.78 49.05 63.38 AXLen:= AllData(°)

IDA11:= A11Data(')

0DA11:= AlIDatP)

Stress Distribution I-IDA 50 -

-50 0

0.5 1

1.5 2

2.5 AXLen Axial Elevation above Bottom [inch]

3 Developed by:

J. S. Bnhmadesam Verified by:

8. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAle 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

-27.404 -24.356 -22.209 -20.407 - 18.978)

Data :=

0.483 0.633 0.87 17.665 1.18 29.798 1.428 33.623 1.627 32.364 1.786 27.394 1.919 21.498 2.051 16.944 16.422 14.61 12.415 9.376 26.049 22.723 18.95 14.201

-1.486

-3.599

-4.44

-5.268 27.792 24.8 24.321 26.989 28.469 27.591 34.284 45.104 28.918 31.388 43.882 63.718 25.556 33.55 48.089 66.365 23.793 34.064 49.472 67.672 )

Ax. := Data(°)

MD:= Data(3)

ID:= Data(l)

TQ := Data(4)

QT := Data(2)

GD := Data~~

RID := regress(AxI, ID,3)

RQT:= regress(Axl,QT,3)

ROD:= regress(Axl,OD, 3)

RMD := regress(AxI, MD, 3)

RTQ:= regress(Axl, TQ,3)

FLCntr RefPo in t - c0 if Val = i Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 Refpoint + c0 otherwise UTip := FLCntr + co Incstrs.avg ULStrs.Dist - UTip Developed byV

1. S. Brihmadesam Vedried by.-

B. C Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM 2003 Developed by.

J. S. Bdhmadesam Verlffedby B. C. Gray

I Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 0.376 Flaw Growth in Depth Direction 0.6 c

a aS 0.4 0.2 O "0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model 0.8

._a on 0.6 i

.5 0.4 L

0 I-I I

1',5 I,

.376

_~~~~~~~~~~~~

II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I-v._

0 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by:

J. S. Bnhmadesam Vernied by:

B. C. Gray

Entergy Operations Inc Central Engneering Programs Appendix "C"; Attachment 40 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 0

rI.

a, 5-60 I I

I I

I I

II 40 r 20 1 A,

o0 0.5 1

1.5 2

2.5 Operating Time (years}

Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 3

3.5 4

Developed by:

J. S. Bnhmadesam Verifled by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.9 0.8 (L) 0 a.'

a) a)

0

.U a.)-

a..

a..

0.7 0.6 0.5 0.4 0.3

...................................... -,................................................................. I.............................................................................................................

0.2 0.1 0

----------------------- ----------------------- --------------------- I.......................................................

0 0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniform "a" - Tip -- Linear Ia" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear

"c" - Tip -- Quadratic

. "c" - Tip -- Cubic Developed by.

J. S. Brnhmadesam Verified by:

B. C. Gray Ca-7

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi k, 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 0.83 CGRsambi (k, 6) 11.395 12.403 12.405 12.408 12.41 12.412 12.415 12.417 12.419 12.422 12.424 12.426 12.429 12.431 12.433 12.436 CGRsambi (k, 5) 8.469 9.162 9.165 9.168 9.171 9.174 9.177 9.18 9.183 9.186 9.189 9.192 9.195 9.198 9.201 9.204 Developed by:

J. S. Bffhmadesam Veriied by:

B. C. Gray

Entergy Operations Inc Centra I Engineering Programs IODlDi 60 E

ODD 40 20 0 -40 0.0 I

0.10 0.08 -

0.0 hi 0 03 0.04 0.02 0.00 Appendix "C"; Attachment 40 Page 10 of 11 Engineering Report M-EP-2003-002-01

).5 1.0 1.5 2.0 2.5 3.0 Distance from Nozze oftlom (inches) 0 1

2 3

4 Operating Timre (years)

Developed by.

J. S. Brlhmadesam Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Is.

0 08 -

0 06 e

0 04 e 0 02-0.00 Appendix "C"; Attachment 40 Page 11 of 11 Engineering Report M-EP-2003-002-01 2

p era tin g Time (years}I 2 0 -

1 8 -

0 u 148 I=

jff 1 6 -

IL1 4-E 12 -

10 -

8 Su rfa c e Po in t ("c " -tip I-De p th Po in t

("a "- tip 3

4 O perating Tim e (years)

Developed by:

J. S. Brnhmadesam Verified by.

S. C. Gray CO"

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:

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 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, 22.5 dgeree from Downhill Azimuth, 1.30" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "R,/t" - between 1.0 and 300.0 Note: Used the Metric fonn 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 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 necessar to evaluate the stress distribution on the flaw both for the fnitial flaw and for a growing flaw.

This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.

Refpoint := 1.3 This is the reduced blind zone providing a propagation length of 0.347 inch; freespan of 0.5067 inch To place the flow with repsect 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 := 2 Upper Limit to be selected for stress distribution (e.g. Weld bottom ).

Ths is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.8067 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

Venfi ed by:

J. S. Bdhmadesam B. C. Gray

Entergy Operations Inc Central EngineeringPrograms Input Data :-

Appendix "C"; Attachment 41 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4

'Jim = 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 Rid := id Rid:

2 t:= Ro - Rid Rm:= R

+

Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk ilim IJim Prntblk =

50 L

Co := 2 Rm Rt:=-

g

.r I

CI L 103.1-3 T+459.67 Tref+459.67}

Co:= C00 Stress InDut Data (X

00C Temperature Correction for Coefficient Alpha 75 e, percentile MRP-55 Revision 1 Developed by:

1. S. Blihmadesam Velified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data in the table below. The column designations are as follows:

Column "0" = Axial distance from minumum 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 (kst)

AllData :=

0 1

2 3

4 5

0 0

-27.12

-24.15

-22.09

-20.36

-18.98 1

0.49 0.65

-1.53

-3.7

-4.6

-5.47 2

0.88 17.95 16.43 14.45 12.12 8.99 3

1.19 29.83 26.1 22.67 18.71 13.83 4

1.44 33.68 27.82 24.72 24.1 26.54 5

1.65 32.39 28.39 27.45 34.12 44.82 6

1.81 27.39 28.8 31.16 43.6 61.24 7

1.94 21.48 25.46 33.3 47.74 65.93 8

2.07 16.92 23.7 33.85 49.22 67.24 9

2.21 14.77 22.09 34.56 48.87 62.96 AXLen:= AllData(°)

IDAHO:= AllData('>

0DA11:= AIIData('

Stress Distribution 100

=,7 r

OD

'A 0Dl 50 0

-50 )0 0.5 1

1.5 2

2.5 AXLen Axial Elevation above Bottom [inch]

3 Developed by.:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region In the table above labeled DataAM, 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

-27.118 -24.146 -22.087 -20.358 -18.981 )

Data :=

0.488 0.65 0.88 17.955 1.193 29.829 1.444 33.679 1.646 32.389 1.807 27.386 1.94 21.477 2.074 16.919

-1.526

-3.699

-4.599

-5.468 16.435 14.447 12.118 8.995 26.102 22.672 18.714 13.833 27.823 24.722 24.104 26.541 28.385 27.447 34.121 44.818 28.803 31.156 43.603 61.245 25.458 33.3 47.738 65.934 23.701 33.846 49.217 67.244 )

AxI := Data(O)

MD:= Data(3)

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)

FLCntr = Refpit - co if Val = 1 Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c0 otherwise UTip = FLCntr + C0 fl~st~.ag ULStrs.Dist - UTip U~~ip := FL~~ntr

+CO Inc~~~trs~avg :=

~20 Developed by:

J. S. Bn'hmadesam Verified by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point nSat Aug 09 10:21:18AM 2003 Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix C"C; Attachment 41 Page 6 of 11 Engineering Report M-EP-2003-002-01 Propkengh =- 0.347 Flaw Growth in Depth Direction 0.6 W

r.I

'Ei 00 11 0

W, Lu 0.4 t I

I I

I I

I I

I I

I I

I I

I 0.2 t 0 0 0.5 1

1.5 2

2.5 3

3.5 Operating Time {years)

Entergy-CEP Model 4

I t

-3 3-0.8 0.6 0.4 0.2 I

I I

I I

I I

I I ~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~15

.347-I I

I I

0.CI 0.5 I

1.5 2

2.5 3

Operating Time {years) 3.5 4

Entergy-CEP Model Developed by:V J. S. Bnhmadesam Velirled by.'

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 7 of 11 Engineering Report M-EP-2003-002-01 Ln S.

5-80 60 1 Stress Intensity Factors I

I I

I I

I I

--,****-...-~~~~~~~~ ~~~~~~...-.......-

40 1 20 1 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 Developed by:

J. S. Brlhmadesam Verified by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 8 of 11 Engineering Report M-EP-2003-002-01 0.8 0.7 Influence Coefficients - Flaw

...I......................................I...

......................... I................................................................................................................

0n

'A 0

U-Q Cn U-v 0.6 0.5 0.4 0.3

I................ ------------- ----------------------- ----------------------- ----------------------- --------- ------------- ---------

0.2 0.1 0

............I....... -,............. ------------------------ ----------------- --------------------------------------------------- ----------------------------------

0 0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniform "a" - Tip -- Linear la" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray c-3o

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi (k, 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 CGRsambi (k, 6) 11.9 12.895 12.897 12.9 12.903 12.905 12.908 12.91 12.913 12.916 12.918 12.921 12.923 12.926 12.929 12.931 CGRsambi(k, 5) 8.835 9.52 9.524 9.527 9.53 9.533 9.536 9.539 9.542 9.546 9.549 9.552 9.555 9.558 9.561 9.564 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs 60

-l ODD 40 -

A S20 0

-20 0.0 c

0.12 -

.S I

200 iL 0

0.00 Appendix "C"; Attachment 41 Page 10 of 11 Engineering Report M-EP-2003-002-01 1.0 1.5 2.0 Distance from Nozze Bottom (inches) 0 1

2 3

4 Operating Time {years)

Developed by.

J. S. Blihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs 0.12-I I

_ 0.0 84 C)

, 0 4

0 0

0 0-Appendix "C"; Attachment 41 Page 11 of 11 Engineering Report M-EP-2003-002-01 2

O p e ra tin g T im e

{y e a rs )

20 -

0 9

15 -

U-Ce c

1 0 5 -

Su rfa ce Po in t f% `-tip I -

De p th Po in t f" a "- tip 0

2 O perating Time {years}

3 4

Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 1 of 11 EngineerIng Report M-EP-2003402-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Progrqnms, Entergy Operations Inc Developedby: J. S. Brihmadesom Verified by: B. C. Gray Refrences:

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 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, 45 dgeree from Downhill Azimuth, 1.644" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmdt" - 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 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 necessar 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 represnets the reference point elevation measured upward from the no2zle end.

Refpoint := 1.544 This is the as-built blind zone providing a propagation length of 0.167 inch; freespan of 0.3274 inch To place the flow with repsect 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).

Vat := 2 Ulpper Limit to be selected for stress distribution (e.g. Weld bottom ).

This is the elevation from Nole Bottom.

Enter this value below ULStrs.Dist := 1.8714 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

J. S. Brihmadesam Veniried by:

B. C. Gray

Entergy Operations Inc Central Engineerng Programs Input Data :-

Appendix "C"; Attachment 42 Page 2 of 1 1 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.6610.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID P Int := 2.235 Years := 4 him = 1500 T := 604 OCOC := 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 O*

2 id Rid:= 2 t:= Ro-Rid t

RIM:=Rid+ -

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

h1im,

'=im Pmntblk :=50 L

Co := 2 Rm Rt

_L 1.1e03 li 3 (T+459.67 Tref+459.67)

C01 C0

= C 0 1 Stress Input Data Developed by.

.1. S. Bnhmadesam ao 0C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Venred by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data In the table below. The column designations are as follows:

Column "0" = Axial distance from minumum 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 'WI = Three Quarter Thickness Stress data at each Elevation (ksi)

Column "5" = OD Stress data at each Elevation (ksW7 AllData :=

.0 1

2 4

5 o

0

-26.31

-23.54

-21.72

-20.18

-18.94 1

0.51

-0.38

-2.22

-3.97

-5.04

-6.03 2

0.91 20.09 16.85 14.02 11.34 7.92 3

1.24 29.93 26.24 22.49 18.07 12.79 E4 1.5 33.83 27.91 24.53 23.55 25.42 1.7 32.49 28.21 27.05 33.58 44.17 6

1.87 27.43 28.6 30.66 42.95 60.21 7

~

2.01 21 A3 25.17 32.65 46.97 64.95

-'8 2.14 16.79 23.32 33.24 48.59 66.19 2.28 14.56 21.63 33.98 48.34 62.07 AXLen := AllData()

IDAII:= A11DatP) 0DA11:= A11DatP)

Stress Distribution 100 U) n1/)

'A~

IDAII ODAII 50 0

-50 _0 0.5 1

1.5 2

2.5 3

AXLen Axial Elevation above Bottom [inch]

Developed by:

J. S. Bnhmadesam Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 4 of 11 Engineering Report M-EP-2003-002-01 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 tight of the Mathcad Equals sign below (paste symbol).

0

-26.311 -23.544 -21.718 -20.18 -18.943) 0.506 -0.377

-2.222

-3.968

-5.036 -6.028 0.911 20.089 16.851 14.017 11.337 7.917 1.236 29.934 26.239 22.486 18.067 12.788 Data :=

1.496 33.829 27.906 24.526 23.554 25.421 1.704 32.487 28.206 27.053 33.58 44.169 1.871 27.432 28.598 30.659 42.946 60.214 2.006 21.433 25.168 32.645 46.971 64.949 2.141 16.793 23.322 33.237 48.59 66.19 )

AxI := Data(°)

MD:= Data(3)

ID:= Data(l TQ :=Data(4)

QT := Data(2)

OD:

Data(5)

RID := regress(Axl, ID, 3)

RQT:= regress(AxlQT,3)

ROD := regress(Axl,OD,3)

RMD:= regress(Axl, MD, 3)

RTQ:= regress(Axl, TQ,3)

FLCntr Refpoint-c0 if Val = 1 Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c0 otherwise UTjp := FLCntr + Co ULStrs.Dist - UTip InCStrs.avg =

20 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix 'C"; Attachment 42 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point

& SatAug 09 10:21:18AM 2003 Developed by:

J. S. Bdhmadesam Veriied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 6 of 11 Engineering Report M-EP-2003-002-01 PrOPLength = 0.167 Flaw Growth in Depth Direction 0.6 U

c.

0 C7 as 0.4 I I

I I

I I

I I

I I

I I

I I

I 0.2 0 0 0.5 1

1.5 2

2.5 3

3.5 Operating Time {years}

Entergy-CEP Model 4

U a

0.8 U.6 II I

I I

I I

1:5 I

_I6 I

I I

I I

I 0.4 0.2 t U -0 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by:

J. S. Bnhmadesam Verified by.-

B. C. Gray

Entergy Operations Inc Centra I Engineering Programs Appendix "C"; Attachment 42 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.)

0 4)E a.)

C.Q 0

0.

Q.

r-U.

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0 0.5 1

1.5 2

2.5 3

3.5 Operating time {years}

- a" - Tip -- Uniform "a" - Tip-- Linear

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

"c" - Tip -- Quadratic "c" - Tip -- Cubic 4

Developed by.

J. S. Brhmadesam Veribed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors Q

0-5-t 0

U.

r-(A~

80 601 I

I I

I I

I I

40 1 20 U

0 0.5 1

1.5 2

2.5 Operating Time {years}

Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 3

3.5 4

Developed by:

J. S. Brihmadesam Verfied by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.828 0.828 0.828 CGRsambi (k, 6) 15.851 16.873 16.878 16.883 16.888 16.894 16.899 16.904 16.909 16.915 16.92 16.925 16.93 16.936 16.941 16.946 CGRsambi(k 5 11.542 12.24 12.245 12.249 12.254 12.258 12.263 12.267 12.272 12.276 12.281 12.285 12.29 12.294 12.299 12.303 Developed by:

J. S. Bnhmadesam VerIfied by.-

B. C. Gray

Entergy Operations Inc Central Engineering Programs 60 40 I 20 II 0

-20

-40 I

0.0 0.3 -

c I

0.1 2 0O2 -

i 0

0~0 Appendix "C"; Attachment 42 Page 10of I Engineering Report M-EP-2003-002-01 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Botom {iches) 0 1

2 3

4 Operating Time {years)

Developed by.

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs03-021 I

I e 0 2 cs ° 1 tO r2 00 Appendix "C"; Attachment 42 Page 11 of 11 Engineering Report M-EP-2003-002-01 2

0 p e ra tin 9 T int e (y e a rs )

40 -

_ 35

F

'a 30 uX20 IS 20-15 -

10 -

I=

Surface Point ac. tip}

-Depth Point {"a"- tip)I 0

I 2

Operating Time {yearst 3

4 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmodesam Verified by: B. C. Gray Note: Only for use when Rosd/tis between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

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 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, 22.5 degree from Downhill Azimuth, Augmented Analysis 1.3 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 Flaw The first Input is to locate the Reference Line (eq. top of the Blind Zone).

The throughwall 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:= 1.3 This is the reduced blind zone providing a propagation length of 507 inch; freespan is 0.507 inch The Second Inplut 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:= 1-8067 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom) lDeveloped by:

Verified by:.

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :

L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 1Iim:= 1500 T := 604 v := 0.307 aoc:= 2.67.10 12 Qg:= 31.0 Tref := 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

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

-Qg r(

I L 1.103. 10- 3 T+459.67 Trf+459.67)J Tinlopr:= Years 365.24 od 2

id 2

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

2 CFinhr:= 1.417-105 Cbk=Timlopr Cblk'ur Ihrn Prmtblk:=

-50"m I

L 2

Developed by:

Verified by:

IDeveloped by.

Verified by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 3 of 10 Engineering Report M-EP-2003-002-01 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:

Cloumn "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)

DataAII:=

-T I

I I

7 0

1 2

3 4

C.!i 0

0

-27.12

-24.15

-22.09

-20.36

-18.98 1

0.49 0.65

-1.53

-3.7

-4.6

-5.47 2

0.88 17.95 16.43 14.45 12.12 8.99 3

1.19 29.83 26.1 22.67 18.71 13.83 4

1.44 33.68 27.82 24.72 24.1 26.54 5

1.65 32.39 28.39 27.45 34.12 44.82 6

1.81 27.39 28.8 31.16 43.6 61.24 7

1.94 21.48 25.46 33.3 47.74 65.93 8

2.07 16.92 23.7 33.85 49.22 67.24 9

2.21 14.77 22.09 34.56 48.87 62.96 AI[Axi =DataAIIW AIIID DataAIl l AIMOD DataAII(5 IDeveloped by:

Verified by:

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 4 of 10 Engineering Report M-EP-2003-002-01 100 75 2

un 50 25 0

-25r

-50 0 0.5 1

1.D 2

2.5 3

Axial Disance above Bottom [inch]

ID Distribuion OD distribution Observing the stress distribution select the region In the table above labeled DataAU 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

-27.118 -24.146 -22.087 -20.358 -18.981' Data:=

0.488 0.65 0.88 17.955 1.193 29.829 1.444 33.679 1.646 32.389 1.807 27.386 1.94 21.477

-1.526

-3.699

-4.599

-5.468 16.435 14.447 12.118 8.995 26.102 22.672 18.714 13.833 27.823 24.722 24.104 26.541 28.385 27.447 34.121 44.818 28.803 31.156 43.603 61.245 25.458 33.3 47.738 65.934

~2.074 16.919 23.701 33.846 49.217 67.244 )

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

ROD:= regress(Axl, OD,3)

Developed by:

Verified by:~~~~~

IDeveloped by Verified by. I

t Entergy Operatons Inc.

Central Engineenng Programs Appendix "C"; Attachment 43 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULSrs.Dist - BZ IflcStrs.avg :

)

mu No User Input required beyond this Point Sat Aug 09 11:44:49 AM IDeveloped by.

Venfied by I Developed by:

Verified by:

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.507 Flaw Length vs. Time 1.5

.' TWCP P~~j,3 0

0.5

-0.500 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCpwscc(j 1)

Operating Time {years}

Entergy Model Increase in Half Length 2

C.)

1.5 I

u.j 0 0 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time (Years)

D IDeveloped by:

Verified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 r-Cr:

200 100 0

0 0.5 1

1.5 2

2.5 3

3.5 Operating Time (Years)

OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 4

De el pe by.eife y

IDeveloped by.-

Verified by: I

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC TWC~~~~~~~~~~~~~~~~~~~~~~~~~~~~

TWCpwscc T CWC(j,6) 17.829 24.076 24.087 24.098 24.108 24.119 24.13 24.14 24.151 24.162 24.173 24.183 24.194 24.205 24.216 24.226 Twcpwsc(j,7) 24.642 29.762 29.772 29.783 29.793 29.804 29.814 29.824 29.835 29.845 29.856 29.866 29.877 29.887 29.897 29.908 Twcpwscc(jg) -

22.253 28.126 28.137 28.149 28.16 28.172 28.183 28.194 28.206 28.217 28.229 28.24 28.252 28.263 28.275 28.286 Developed by:

Verified by:

IDeveloped by.,

Vetified by.- I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot 60 -

40 -

i 20-0 - -40 1.0 1.5 2.0 Distance forn Nozzle Bottom finch) 200 -

OD Surface SIF ID Surface SIF Average SIF

~r

. 150 100 a

50 (0

0 1

2 3

4 Operating Time {years)

De eo e

y V rfe y

IDeveloped by:

Verified by.- I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.2 I

0 0.8 3 0.4 O.0 O pera ling TlnIm (yo a rs)

Developed by:

Verified by:~~~~~

IDeveloped by Verified by I

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmodesam Verified by: B. C. &ray Note : Only for use when Ret 5 ;d/t is between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

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 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, 45 degree from Downhill Azimuth, Augmented Analysis 1.544 inch above Nozzle Bottom Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric fonn 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 The first ZIput is to locate the Reference Line (eg. top of the Blind Zone). The throughwaol flow 'tipper Tip" is located at the Reference Line.

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

BZ := 1.45 This is the as-built blind zone providing a propagation length of.421 inch; freespan is 0.421 inch The Second Input Is the Upper Limit for the evaluation, which is the bottom of the fillet weld logj This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from noxzle bottom) below.

ULStrs.Dist:= 1.8714 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

IDeveloped by.

Venfied by. I Developed by:

Verified by:

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data:

L :=.794 od:= 4.05 id:= 2.728 Pitt 2.235 Years:= 4 11im:= 1500 T := 604 v := 0.307 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

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

[

-Qg

.(

I I

1. 03. 103 tT+459.67 Trf+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 Tinfopr:= Years-365-24 od Ro := -

R; = id 2

t:= Ro - Ri Rm:= Ri + -2 CFinhr:= 1.417-10 5 Tifllpr Cblk :=Tilp Chim Prntblk:= l-l 50"m I

L 2

Developed by:

Verified by:

I Developed by.-

Vefified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 3 of 10 Engineering Report M-EP-2003-002-01 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:

Cloumn "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)

DataAll := _--

5-J 0

12 34 0

0

-26.31

-23.54

-21.72

-20.18

-18.94 1

0.51

-0.38

-2.22

-3.97

-5.04

-6.03 2

0.91 20.09 16.85 14.02 11.34 7.92 3

1.24 29.93 26.24 22.49 18.07 12.79

-4 1.5 33.83 27.91 24.53 23.55 25.42 5

1.7 32.49 28.21 27.05 33.58 44.17 6

1.87 27.43 28.6 30.66 42.95 60.21 7

2.01 21.43 25.17 32.65 46.97 64.95 8

2.14 16.79 23.32 33.24 48.59 66.19 9

2.28 14.56 21.63 33.98 48.34 62.07 AllAxl:= DataAII (I)

MIID= DataAIIW AIIOD:= DataAII 5)

Deeoe y

Vrfe y

IDeveloped by Verified by I

Entergy Operations Inc.

Central Engineedng Programs Appendix "C"; Attachment "

Page 4 of 10 Engineering Report M-EP-2003-002-01 100 0_

0.5

__________14 1.525 7 5 50-25

-25 o5 0.5 1

152 2.5 3

Axial Distance above Bottom [inch]

ID Distribution OD distribution 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).

I 0

-26.311 -23.544 -21.718 -20.18 -18.943')

0.506 -0.377 0.911 20.089 1.236 29.934 Data :=

1.496 33.829

-2.222 16.851 26.239 27.906 28.206 28.598 25.168 23.322

-3.968 -5.036 -6.028 14.017 11.337 7.917 22.486 18.067 12.788 24.526 23.554 25.421 27.053 33.58 44.169 30.659 42.946 60.214 32.645 46.971 64.949 1.704 32.487 1.871 27.432 2.006 21.433 12.141 16.793 33.237 48.59 66.19 )

Axl:= Data (II ID: Data (5)

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

ROD:= regress(Axl, OD, 3)

IDeveloped by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist -BZ 1ncStrs.avg:=

20 No User Input required beyond this Point g Sat Aug 09 11:44:49 AM 7nn3 Developed by:

Venfied by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment" Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.421 Flaw Length vs. Time 1.5 Q.~~~~.

TWCPWSCC.

0.5 0~~~~

05

_0._

0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCWCC I)

Operating Time (years)

-Entergy Model Increase in Half Length 2

z C.N C

1.5 0.5 0 0 0.5 1

1.5 2

2.5 3

3.5 Operating Time (Years) 4 Developed by:

VerifIed by:

IDeveloped by:

Verified by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 c

v, 200 0

E 100 c

0 0

0.5 1

1.5 2

2.5 3

3.5 Operating Time (Years}

OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 4

De eoeiy Vrfe y

IDeveloped by:

Verified by: I C?;

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC

=~~~~~~~~~

Twcpwsc'(j,6) =

23.343 29.492 29.509 29.526 29.543 29.561 29.578 29.595 29.612 29.629 29.647 29.664 29.681 29.699 29.716 29.733 TWCPWSCC(j,7) =

30.471 34.797 34.813 34.83 34.846 34.863 34.879 34.895 34.912 34.928 34.945 34.961 34.978 34.994 35.01 35.027 TWCPWSCC( 1 8) =

28.154 33.544 33.562 33.58 33.598 33.616 33.634 33.653 33.671 33.689 33.707 33.726 33.744 33.762 33.78 33.799 Developed by:

Verified by:

IDeveloped by:

Veriffied by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 60 4 0 20 A

2 0

-2 0

-4 0 0.0 0.5 1.0 1.5 2.0 2.5 D istance from N ozzle Bottom (inch) 3.0 250 -

i 2 00 -

150 2

-t 100 -

50 0-O D S u rfa e sIF ID S urfa ce S IF A v e rag e S IF 0

1 2

3 4

O p e ra tin g T im e (y e a rs )

Developed by:

Verified by:~

IDeveloped by:

Verified by I

Entergy Operaftons Inc.

Centra/ Engineering Programs Appendix "C"; Attachment 44 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.5 I

v 1.0 X 0. 5

.0 0 0 0

1 2

3 O perating Time (years)

Developed by:

Verified by:~~~~

IDeveloped by Vedfied by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesom Verified by: B. C. Gray Note: Only for use when R.,,Sjd/t is between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

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 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, 67.5 degree from Downhill Azimuth, Augmented Analysis 1.544 inch above Nozzle Bottom Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric forn 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 The first Irnput is to locate the Reference Line (eg. top of the Blind Zone).

The throughwall flow 'Vpper 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 This is the as-built blind zone providing a propagation length of.421 inch; freespan is 0.421 inch The Second Input is the UIpper Limit for the evaluation, which is the bottom of the filet weld leg.

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

ULStrs.Dist:= 1.9699 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

IDeveloped by:

Verified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :

L :=.794 od:= 4.05 id := 2.728 lnt := 2.235 Years:= 4 rimn:= 1500 T:= 604 v := 0.307 aOc := 2.67. 10 12 Qg := 31.0 Tref := 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

Tube OD Tube ID Design Operating Pressure (intemal)

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 C0:

103

.o*IC3 V\\+459.67 Trf-+459.67)_

Timopr= Years-365-24 od 2

Ri:= i2 t:= Ro - Ri Rm:= Ri + 22 CFinhr:= 1.417-105 Cbk=Timopr Cbk lam Prntblk:= l-50"i I I

L 2

Developed by:

Verified by:~~~

IDeveloped by.

Verified by. I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 45 Page 3 of 10 Engineering Report M-EP-2003-002-01 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:

Cloumn "o0 = 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)

DataAlI :=

0 1

2 3

4 0

0

-25.24

-22.71

-21.18

-19.87

-18.8 1

0.53

-1.27

-2.96

-4.4

-5.69

-6.83 2

0.96 21.94 17.09 13.36 10.18 6.33 3

1.3 30.02 26.37 22.21 17.12 11.24 4

1.57 34.09 28.09 24.31 22.83 23.83 5

1.79 32.72 28.04 26.61 32.92 43.29 6

1.97 27.6 28.45 30.15 42.18 58.89 7i 2.11 21.46 24.92 31.94 46.1 63.87 8;

2.24 16.73 22.99 32.59 47.9 65.05 9

2.38 14.34 21.26 33.41 47.85 61.2 AllAxl:= DataAIl I AID:= DataAlI AIIOD:= DataAlI(

IDeveloped by.

Venfied by.- I Developed by:

Venfied by:

Entergy Operatfons Inc.

Central Engineenng Programs Appendix "C"; Attachment 45 Page 4 of 10 Engineering Report M-EP-2003-002-01

-50 0 0.5 1

1.5 2

2.5 3

Axial Distance above Bottom [inch]

3.5 ID Distribution OD distribution 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).

Data:=

0

-25.236 -22.713 -21.175 -19.868 -18.802) 0.533 -1.267

-2.963

-4.403

-5.689

-6.833 0.959 21.942 17.089 13.361 10.182 6.327 1.301 30.023 26.373 22.21 17.121 11.241 1.575 34.094 28.085 24.306 22.834 23.834 1.794 32.716 28.035 26.605 32.916 43.289 1.97 27.602 28.447 30.151 42.181 58.888 2.106 21.457 24.92 31.944 46.103 63.871 12.242 16.731 22.988 32.591 47.9 65.049 )

Axi:= Data (1I ID: Data (5)

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

ROD:= regress(Axi, OD, 3)

Developed by:

Verified by:~~~~

IDeveloped by Venfied by. I

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ incstrs.avg :=

20 No User Input required beyond this Point M Sat Aug 09 11:44:49 AM 2003 Developed by:

Verified by:

IDeveloped by:

Verified by I

Entergy Operations Inc.

Central Engineerng Programs Appendix "C"; Attachment 45 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLengt = 0.426 1.5 C)

I

" TWCpwc.

.s 0.5 0

c:.

O0.51 I

I I

I 0

0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

Entergy Model TWCpwsoc(jll)

Operating Time (years}

Increase in Half Length 2

C)

C t

4)

CS C) u 1.5 0.5 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {Years}

Developed by:

Verified by:

IDeveloped by Verified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 r.

UC C~

7~)

P Q

200 100 0

0 0.5 1

1.5 2

2.5 3

3.5 Operating Time A Years)

OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 4

Developed by:

Verified by:

C4L

Entergy Operations Inc.

Centra! Engineering Programs Appendix "C"; Attachment 45 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC Twcpwscc

=

pwsc(j.6) 23.707 29.582 29.6 29.618 29.636 29.654 29.672 29.691 29.709 29.727 29.745 29.764 29.782 29.8 29.818 29.837 TWCpwscc(j7) =

32.37 36.353 36.37 36.388 36.406 36.423 36.441 36.458 36.476 36.494 36.511 36.529 36.547 36.564 36.582 36.6 cpwsc(j 8) 29.373 34.44 34.459 34.479 34.498 34.517 34.537 34.556 34.576 34.595 34.615 34.634 34.654 34.673 34.693 34.712 IDeveloped by Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 60 40 3

20 40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom

[inch) 250 -

2 00 -

150-I la 1 00 -

50 -

0-0 D S u rfa ce S IF ID S u rfa c e S IF A v era g e S IF 0

1 2

3 4

O p e ra tin g T im e (y e a rs)

De eo e by eife y

IDeveloped by Verified by: I C~pf

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 10 of 10 Engineering Report M-EP-2003-002-01 1 5 I.0 I 0.

00 0 0 0

1 2

3 4

0 pa rating T Im a (years)

Developed by:

Verified by:~~~~~

IDeveloped by Venfied by.- I

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. 5. Brihmcidesarm Verified by: B. C. Gray Refrences:

1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-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 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, 67.5 dgeree from Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rd/t" -- between 1.0 and 300.0 Note: Used the Metric fonn 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 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 necessar to evaluate the stress distribution on the flaw both for the initial flow and for a growing flaw.

This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.

RefPoint :=--1.544 This is the as-built blind zone providing a propagation length of 0.167 inch; freespan of 0.3274 inch To place the flaw with repsect 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 Z)
3) The lower "C-tip" located at the reference point (Enter 3).

Val := 2 Upper Limit to be selected for stress distribution (e.g. Weld bottom ).

This is the elevation from Nozzle Bottom.

Enter this value below ULStrs.Dist := 1.9669 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

Venified by:

J. S. Bnhmadesam B. C Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 46 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 11im := 1500 T := 604 a0C := 2.67 12 QT

= 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 R := 2 id Rid := 2 t:= Ro - Rid t

Rm,= Rid+ +2 Timopr:= Years-365-24 CFinhr := 1.417- ]05 Timopr Cblk :=-

Ilim,

'urn Prntblk :=50 L

C0 2 Rrn Rt :=

t C0 J.2-3 (T+l 9.67 Coi _= Al 03 lo-3 tT49.7Tref+459.67)

Co:= Co1 Stress InDut Data

) *0c Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Elhmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 3 of 1 1 Engineering Report M-EP-2003.002-01 Input all available Nodal stress data in the table below. The column designations are as follows:

Column "0" = Axial distance from minumum 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 (kstl AllData :=

0 1

2 345 4

0 0

-25.24

-22.71

-21.18

-19.87

-18.8 1

0.53

-1.27

-2.96

-4.4

-5.69

-6.83 2

0.96 21.94 17.09 13.36 10.18 6.33 3

1.3 30.02 26.37 22.21 17.12 11.24 4

1.57 34.09 28.09 24.31 22.83 23.83 5i 1.79 32.72 28.04 26.61 32.92 43.29 6!

1.97 27.6 28.45 30.15 42.18 58.89 7

2.11 21.46 24.92 31.94 46.1 63.87 8

2.24 16.73 22.99 32.59 47.9 65.05 2.38 14.34 21.26 33.41 47.85 61.2 AXLen:= AllData(0)

IDAII:= A11Data(')

0DA11:= Afflata()

Stress Distribution 100 cn Un W.

C-IDAH ODAII

- 0 0.5 1

1.5 2

2.5 3

AXLen Axial Elevation above Bottom [inch]

3.5 Developed by:

J. S. Bdhmadesam Vernied by.:

B. C Gray

Entergy Operations Inc Central Engineerng Programs Appendix "C"; Attachment 46 Page 4 of 11 Engineering Report M-EP-2003.002-01 Observing the stress distribution select the region In the table above labeled DataAI, 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).

-25.236 -22.713 -21.175 -19.868 -18.802')

0.533 -1.267 0.959 21.942

-2.963

-4.403

-5.689

-6.833 17.089 13.361 10.182 6.327 1.301 30.023 26.373 22.21 17.121 11.241 Data := 1 1.575 34.094 1.794 32.716 1.97 27.602 2.106 21.A57 28.085 24.306 22.834 23.834 28.035 26.605 32.916 43.289 28.447 30.151 42.181 58.888 24.92 31.944 46.103 63.871 t2.242 16.731 22.988 32.591 47.9 65.049 )

Axl := Data(0)

MD:= Data)

ID:= Data TQ := Data 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 - c 0 if Val = 1 Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise ULStrs.Dist - UTip UTip := FLCntrC+

0 IClCStrs.avg=

20 Developed by:

J. S. Blhmadesam Verifled by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 5 of 1 1 Engineering Report M-EP-2003.002-01 No User Input is required beyond this Point nSatAugO9 10:21:18AM Developed by:

J. S. Brlhmadesam

-A ](1-4 Venified by.

B. C. Gray

Entergy Operations Inc Appendix "C"; Attachment 46 Engineering Report Central Engineering Programs Page 6 of 11 M-EP-2003-002-01 ProLength 0.263 Flaw Growth in Depth Direction 0.6 0

0.4

-(U 0.2 0

0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model 1C5 p

0.8 0.4

.263 v

0.2 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by:

J. S. BSihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 7 of 11 Engineering Report M-EP-2003-002-O1 Stress Intensity Factors 10C

.cJ cj~

80 60 1 I

I I

I I

I I

~~~~~~~~-.1....

.... ~ ~ ~ ~ ~ ~~~~~...1-........

40 t 20 A L 0

0.5 l

1.5 2

2.5 3

3.5 4

Operating Time {years}

Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:

I. S. SWImadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 0

V 0.6 0.5 0.4 0.3 0.2 0.1 0

0 0.5 I

1.5 2

2.5 3

3.5 4

Operating time fyearsl "a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic itc" - Tip -- Cubic 4

t., - ---

Developed by.

S. Sihmaodesam Verified by; B. C. Gray C a-Z

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 9 of 1 1 Engineering Report M-EP-2003-002-01 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 CGRsambi (k, 6) 13.362 14.331 14.334 14.338 14.341 14.345 14.348 14.351 14.355 14.358 14.362 14.365 14.369 14.372 14.376 14.379 CGRsambi (k, 5) 9.842 10.506 10.51 10.513 10.517 10.52 10.524 10.528 10.531 10.535 10.539 10.542 10.546 10.55 10.553 10.557 Developedby:

J. S. Blhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs lIDijist 60 l

OD Di 40 a

20 RA Appendix "C"; Attachment 46 Page 10 of 11 Engineering Report

=

M-EP-2003-002-01 0,0 0.5 1.0 1.5 2.0 2.5 3.0 EAstance from Nozzle Bottom {inches) 0.20 CI

- 0.105 -

w 0 0 0.00 0

1 2

3 4

Operabng Time (year}

Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray C L$3

Entergy Operations Inc Central Engineering Programs 0.20 -

0.1 0 -

!.Z E 0.0 5 T

0 0 0 0 Appendix "C"; Attachment 46 Page 11 of 11 Engineering Report M-EP-2003-002-01 0

1 2

O p e ra tin g T inne

{y e a rs }

Surfac int ("c' -tip)

I ::--

Depth popinot I'a"-tip) 6

.£

. 15

~2O 10 -

5-0 1

2 3

4 Operating Tine (years)

Developed by.

J. S. Bnhmadesam Verified by:

B. C. Gray C LtI-r

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Prograons, Entergy Operations Inc Developedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:

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 2 Component: Reactor Vessel CEDM -"28.8" Degree Nozzle, Downhill azimuth, 1.384" above Nozzle Bottom 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 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 necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.

This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.

Refp0 int := 1.384 Reduced Blind Zone; Free span is 0.16 inch To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:

1) The Upper TD-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 Upper Limit to be selected for stress distribution (e.g_.

Weld bottom ).

This is the ekvation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.704 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developedby:

J. S. Bghmadesam Velil/ed by:

B. C. Gray

Entergy Operations Inc Central Engineering Progrants Input Data :-

Appendix "C"; Attachment 47 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 lim := 1500 T :=604 aOc := 2.67 10- 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 R.

od Rid := id Rid:2 t:= Ro - Rid t

Rm : Rid+ -

Timopr:= Years-365-24 CFinhr :=1.417-I05 Timopr Cblk *=-

1im lbhim 5

Pmntblk := l50l L

co0

-~

Rm Rt =

t F1. 1-13 T+459.67 Tref+459.67)1 COI aOc Temperature Correction for Coefficient Alpha CO= Co0 Stress InDut Data 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Brihmadesam Verfiled by:

B. C Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data in the table below. The column designations are as follows:

Column "Om = Axial distance from minumum 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 (ksW)

AllData :=

9l 0

l 1.0 fl

-2 3-I4 l

5:

l o0o

-17.41

-13.55

-11.11

-8.88

-6.63 1

0.46

-8.49

-6.31

-4.92

-3.71

-2.54 2

0.83 0.09 0.18 0.11 0.19 0.28

-3 1.13 7.03 6.95 6.31 5.21 4.65 4

1.36 8.22 10.95 10.85 9.51 5.65 5

1.55 13.27 16.41 16.06 17.13 25.26 6 -

1.7 20.63 22.24 25.41 43.58 53.78

r7^

1.83 29.04 28.83 31.29 53.55 64.08 8

1.95 33.95 30.93 36.41 61.6 71.01 9

2.07 29.59 31.79 40.54 64.61 76.42 10 2.19 23.26 29.74 41.2 64.19 79.63 11 2.31 18.69 27.73 41.29 61.78 78.12 12 2.43 15.39 26.1 40.67 58.6 72.78 AXLen := Al1Data(o)

IDA11:= A11DatP) 0DA11:= AlIData()

Stress Distribution 100 C,)

IDAII ODAll 50 0

-50 _0 0.5 1

1.5 2

2.5 3

AXLen Axial Elevation above Bottom [inch]

3.5 Developed by:

J. S. Bnhmadesam Venirfed by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 4 of 11 Engineering Report M-EP-2003-002-01 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).

n A

17 AlA I1 CC'

_1 1 I 1`1 QQA Z zno\\

-J

-0.0014

-0.010 I

0.461

-8.494

-6.31

-4.924

-3.706 -2.541 0.83 0.089 0.179 0.11 0.186 0.284 1.126 7.025 6.953 6.314 5.208 4.646 1.363 8.215 10.954 10.85 9.512 5.646 16.41 16.061 17.131 25.256 Data := l 1.552 13.266 1.704 20.627 22.237 25.413 43.58 53.784 1.825 1.946 2.066 2.187 29.036 33.945 29.591 23.26 28.83 31.285 53.547 64.082 30.929 36.407 61.6 71.01 31.788 40.536 64.612 76.418 29.738 41.2 64.193 79.626)

AxI :=Data(0)

MD:= Data(3)

ID:= Data()

TQ := Data(4)

QT := Data(2)

OD:= DatP)

RID := regress(Axl,ID,3)

RQT:= regress(Axl,QT,3)

ROD:= regress(Axl, OD, 3)

RMD:= regress(Axl,MD,3)

RTQ:= regress(Axi,TQ,3)

FLCntr RefPoint -c 0

if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 RefPoint + c0 otherwise U~i :=

FL Cntr + c0 InC~trs a

= ULStrs.Dist - UTip UTip =F nt+C IflCstrs.avg :=20 Developed by:

J. S. Btimadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ff Sat Aug 09 10:21:18 AM 2003 Developed by:

J. S. Bihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Appendix "C"; Attachment 47 Engineering Report Central Engineering Programs Page 6 of 11 M-EP-2003-002-01 ProPLength 0.16 Flaw Growth in Depth Direction 0.6 804 0.2 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model 1',5 0.8 0.4 f

0.2 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by.

J..

S Bui'madesam Verified by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 0~

0 a,

.V U,

coj ou 60.

I I

I I

I II e*......

40.

20.

11,

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 Developed by:

J. S. Bfihmadesam Vendled by:

B. C. Gray

Entergy Operations Inc Centra I Engineering Programs Appendix "C"; Attachment 47 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.9 0.8

.In 0

(1)

E 0

.U r-0.7 0.6 0.5 0.4 0.3

............................................ I.....................................................................................................................................................................................................................

1........

I----------- ----------------------- ----------------- ----- ---------------------------------------------- ----------------------- ------- -..

0.2 0.1

' 0 0.5 l

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniform "a" - Tip -- Linear

"a" - Tip -- Quadratic

. "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear t"c" - Tip -- Quadratic l"c" - Tip -- Cubic Developed by.

J. S. Bribmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsmbi(k 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 0.83 0.83 CGRsambi(k 6) 10.823 12.011 12.014 12.016 12.018 12.02 12.022 12.024 12.027 12.029 12.031 12.033 12.035 12.038 12.04 12.042 CGRsmbi(k 5) 7.907 8.77 8.773 8.776 8.778 8.781 8.784 8.787 8.79 8.793 8.796 8.799 8.802 8.805 8.807 8.81 Developed by:

J. S. Bdhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs 80 I

L--OD D 60 40 020 0

-20 0.0 0.12

.~0.08 0

e 0.04 e 0 Appendix "C"; Attachment 47 Page 10 of 11 Engineering Report M-EP-2003-002-01 1.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (inches}

0 1

2 3

4 Operating Time (years)

Developed by J. S. Brihmadesam Verified by.

S. C. Gray C L!-C

Entergy Operations Inc Central Engineering Programs 012 I

e 0.0 8 Th ID

, 0.04 -

I T~~

0.00 G; 20 -

0 15-A10 Appendix "C"; Attachment 47 Page 11 of 11 Engineering Report M-EP-2003-002-01 0

1 2

O p e ra tin g T im e

{y e a rs I Surface Point ("c-tipI Depth Point {"a"- tip) tiC 0

1 2

3 4

Operating Time (years)

Developed by:

J. S. BrIhmadesam Verified by:

B. C Gray

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when Ro,,tj,/t is between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

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 2 Component: Reactor Vessel CEDM -"28.8"Degree Nozzle, 22.5 degree from Downhill Azimuth, Augmented Analysis 1.544 inch above Nozzle Bottom Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metic 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 The first Input is to locate the Reference Line (eg. top of the Blind Zone).

The throughwoll flaw 'Vpper Tip" is located at the Reference Line.

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

BZ:= 1.544 This is the normal blind zone The Second Input is the Uipper 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:= 1.8317 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom) lDeveloped by:

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Central Engineenng Programs Appendix "C"; Attachment 48 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :

L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 Ilim:= 1500 T := 604 v := 0.307 arc:= 2.6710- 12 Qg:= 31.0 Trf := 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

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 E -Qg

(

1 C 110310 t\\T+459.67 T3ef+459.67)J Tinilopr= Years-365-24 Ro:= od 2

Ri:= i2 t :R

- Ri Rm:= Ri + -

2 CFinhr:= 1.417-105 Cbk=Tifllopr Cblk imr Prntblk:=

20 2

IDeveloped by.

Verffled by. I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 3 of 10 Engineering Report M-EP-2003-002-01 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:

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

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

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

DataAlI :=

0 1 2

~~~~~~~~~3 4

5 0

0

-14.21

-11.51

-9.79

-8.24

-6.72 1

0.5

-6.49

-5.19

-4.42

-3.8

-3.18 2

0.89 1.55 1.02 0.56 0.26

-0.08 3

1.21 8.43 7.98 7.2 6.19 5.29 4

1.46 10.25 12.71 12.22 11.35 8.36 5

1.67 15.66 18.34 18.7 20.84 29.7 6

1.83 24.32 24.53 26.71 44.52 57.73 7

1.95 31.5 28.7 31.23 53.02 63.55 8

2.07 31.98 30.11 35.63 59.45 69.03 9

2.19 26.83 29.95 38.37 61.12 72.69 1

2.31 20.84 27.29 38.5 59.95 75.04 11 2.43 15.99 24.67 38.16 58.17 73.85 AIIAxi =DataAill A1113D=DataA~ll AIIOD DataAII5 IDeveloped by Verified by. I Developed by:

Verified by:

Entergy Operatons Inc.

Central Engineenng Programs Appendix "C"; Attachment 48 Page 4 of 10 Engineering Report M-EP-2003-002-01 80 63.33

[

.5,4 O

l-0 46.67 30

_13

___e33 A

=

< a

- - - -us -

-3.33 _,__

-20 0

0.5 1

1.5 2

2.5 3

3.5 Axial Distance above Bottom [inch]

ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataAle 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).

Data:=

0 0.495 0.892 1.21 1.464 1.668 1.832 1.951 2.071 2.19 2.31

-14.205

-6.493 1.555 8.43 10.247 15.665 24.321 31.496 31.975 26.833 20.84

-11.506

-5.188 1.021 7.98 12.709 18.335 24.532 28.696 30.109 29.946 27.287

-9.79

-4.425 0.565 7.199 12.22 18.703 26.71 31.228 35.633 38.369 38.5

-8.243

-3.796 0.257 6.186 11.35 20.835 44.525 53.015 59.449 61.124 59.952

-6.722)

-3.176

-0.076 5.292 8.364 29.697 57.729 63.555 69.026 72.691 75.043)

Ax:= Data 6 (I D ID: Data OD:= Data RID: regress(Axl, ID, 3)

ROD:= regress(Axl, OD, 3)

Deeoe by eife y

IDeveloped by.,

Verffied by I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 48 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ InCStrs.avg :=

20 No User Input required beyond this Point Sat Aug 09 11:44:49 AM Developed by:

Verified by:

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Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 6 of 10 Engineering Report M-EP-2003-002-01 Propiength~ = 0.288 1.5 z

TWCPWC j,3 0

l 0.5 0- 0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCPsc' 1)

Operating Time (years) fttergy Model Increase in Half Length z

0 C

U C

1.5 0.5 0 0 0.5 1

1.5 2

2.5 3

3.5 Operating Time {Years}

4 De eo e by eife y

IDeveloped by.-

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Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 c

a 200 4C 100 va Cva 0

0.5 l

1.5 2

2.5 3

3.5 4

Operating Time IYears}

OD SIF - Entergy Model ID SIF - Entergy Model SIF Average Developed by:

Verified by:

C LF

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCCj,6) 16.053 22.574 22.579 22.585 22.59 22.595 22.6 22.605 22.611 22.616 22.621 22.626 22.631 22.637 22.642 22.647 TWCpwscC

,7) 13.281 17.602 17.606 17.61 17.615 17.619 17.623 17.627 17.631 17.636 17.64 17.644 17.648 17.652 17.657 17.661 TWCpwsccjs)

Tcwc(j.8) 15.158 20.728 20.733 20.738 20.743 20.748 20.753 20.758 20.763 20.768 20.773 20.778 20.783 20.788 20.793 20.798 Developed by:

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Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot i

is I

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Distance from Nozzle Bottom {inch) 2 3

Operating Time {years)

Developed by:

Verified by:

n

=

IDeveloped by:

Verified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 48 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.2 1.0 f0.8 X 0.4 0.2 0.0 0

1 2

3 4

O perafing Time ayearsI Developed by:

Verified by:

IDeveloped by Verified by. I

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