ML032690658

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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..., Appendic C, Attachments 1
ML032690658
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: ML032690658 (96)
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Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 1 of 11 Engineering Report M-EP-2003-00201 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-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 2 Component: Reactor Vessel CEDM -'8" Degree Nozzle, Mid-Plane Azimuth, 1.544" 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 ekvation 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 flow. This is defined as the reference point. Enter a number inch) that represnets the reference point elevation measured upward from the nozzle end.

Refpoint =.1544 To place the flaw 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)

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

3) The lower "-

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 = 2-087 Developed by:

J. S. Bnhmadesam Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 11 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 Ilim := 1500 T :=604 aoC := 2.67 12 Qg := 31.0 Tref = 617 Design Operating Pressure (intemal)

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

Rm : Rid+ +2 Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk:= -

im Pmtblk :=50 L

2 Rm Rt:=t J.1o 3 -o-3T+459.67 Tref+4 5 9.6 7 01 co:= C0

)Ia0C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developedby:

. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

Column "O' = Axial distance from minumum to maximum recorded on data sheet(inches)

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

Column f2f = Quarter Thickness Stress data at each Elevation (ksi)

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

Column Y4W = Three Quarter Thickness Stress data at each Elevation (ksi)

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

AllData :=

01 2

3 4

5 o

o

°

-24.18

-21.84

-20.55

-19.44

-18.5 1

0.56

-1.41

-3.32

-4.98

-6.48

-7.75 2

1.02 22.03 16.77 12.53 8.72 4.43 3

1.38 29.96 26.48 21.85 16.05 9.43

.4 1.67 34.51 28.44 24.2 22.09 22.08 5

1.9 33.22 28.07 26.32 32.42 42.48 6

2.09 28.22 28.59 29.91 41.71 57.59 7

2.22 22.01 25.06 31.61 45.62 63.12 8

2.36 17.22 23.06 32.35 47.57 64.11

'9 2.5 14.68 21.28 33.22 47.8 60.65 AXLen := AData(o)

IDAll:= ADatP~)

0DA11 := AData()

Stress Distribution 100

-IDAII 50 0

-50 _0 0.5 1

1.5 2

2.5 3

3.5 AXLen Axial Elevation above Bottom [inch]

Developed by:

J. S. Brihmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 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).

(

0

-24.18 -21.838 -20.55 -19.438

-18.504)

Data :=

0.564 -1.412 1.016 22.032 1.378 29.956 1.668 34.51 1.9 33.218 2.087 28.217 2.224 22.006

-3.32

-4.982 -6.476 16.773 12.529 8.722 26.483 21.849 16.053 28.439 24.198 22.09 28.069 26.319 32.416 28.594 29.911 41.713 25.059 31.606 45.624 23.064 32.349 47.567

-7.753 4.428 9.428 22.082 42.48 57.592 63.118 64.115 )

K2.361 17.219 AxI : Data(O)

MD:= Data(3)

(1)

ID: Data TQ := Data(4)

QT := Data(2)

(5)

OD:= Data 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 Refpint -c 0 if Val =

Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 Refpoint + c0 otherwise ULStrs.Dist - UTip UTip := FLCntr + O Developed by:

J. S. Bnhmadesam Incstsave :

in Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 5 of 11 Engineering Report M-EP-2003-00201 v

No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM "Firl-A Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 6 of 11 Engineering Report M-EP-2003-00201 PrOPLength 0.3 0.6 c

C 0

0.4 r Flaw Growth in Depth Direction I

I I I

I I

I I

I III 0.2 0 aI 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

Entergy-CEP Model 0.8

  • Bi) 0.6 5

0.4 0

0 0

I I

I I

I I

I I

11 5

.383 I

An v

0.5 I

1.5 2

2.5 3

Operating Time {years}

3.5 4

Entergy-CEP Model Developed by:

J. S. Brihmadesam Verified by:

B. C. Gry

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 7 of 1 Engineering Report M-EP-2003-002-01

.C 0

C 1:r U

C

~T.

C

.cAi c

v]

80 60 40 20 n

Stress Intensity Factors I

I I

I I

I I

1.-*-

~

~

~

~

~

~ ~ ~ ~~~....

I I

I I

I I

I 0

0.5 1

1.5 2

2.

Operating Time {years}

Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 5

3 3.5 4

Developed by:

J. S. Biihmadesam Verified by:

B. C Gray

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

'n 0

v-E

._-o 0

0 c-0 0.7 0.6 0.5 0.4 0.3

~ ~ ~ ~ ~ ~ ~ ~

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

0.2 0.1 0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.........

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

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 9 of 11 Engineering Report M-EP-2003-00201 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) 10.735 11.648 11.65 11.652 11.654 11.656 11.658 11.66 11.662 11.663 11.665 11.667 11.669 11.671 11.673 11.675 CGRsambi 8.046 8.676 8.679 8.681 8.684 8.687 8.689 8.692 8.694 8.697 8.7 8.702 8.705 8.707 8.71 8.713 Developed by:

J. S. Bfihmadesam VedrIed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs 60-

[

40 i

j 20 0

-20

-40 0 08 -

c I

° 06 ian iE 0 0 4-i (0

0, 0.0 2 0 00 Appendix "C"; Attachment 11 Page 10 of 11 Engineering Report M-EP-2003-002-01 1.0 1.5 2.0 D istance from N ozzle ottom

{inches}

0 1

2 3

4 0 p e ra tin 9 T im e

{y e a rs Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs

0. 8 -

c 0 0 6 -

06 04 02 00 0 024 i

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

1 2

3 4

O p e ra tin g T im e

{y e a rs 16 -

V) r5 I

5 1 4 -

~?c e10-8

=Su rfa ce Po in t "c"-tip)

I

- De pth Po in t

("ad-tip} lI l~~~~~~~

0 2

O pera tin g Time

{years) 3 4

Developed by.

J. 5. Brihmadesam Verified by:

B. C. Gray

Entergy Operatons Inc.

Central Engineenng Programs Appendix "C"; Attachment 12 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby:

. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when R 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, Mid-Plane Azimuth, 1.544 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 inchlur.

Through Wall Axial Flaw The fst DIput is to locate the Reference line (eg. top of the Blind Zone).

The throughwall flow pper 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 nput is the UIpper Limit for the evluation, 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.

ULSMDist:= 2.087 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Developed by:

Verified by:

IDeveloped by.

Verified by: I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 12 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :-

L := 0.744 od:= 4.05 id:= 2.728 Pint:= 2.235 Years := 4 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

Tube OD Tube ID Design Operating Pressure (internal)

Number of Operating Years Ilim:= 1500 T := 604 v := 0.307 Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F a0c := 2.67-10 Qg:= 31.0 Tref := 617 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 (

I CO:10311OCI

(~T+459.67 Tref-F459.67)_

Timopr:= Years 365.24 Ro:= od 2

Ri:= id 2

t R0 - Ri Rm:= R + -

2 CFinhr:=.A17-105 Cbk=Tirrlopr Cbik Pmtblk:=

-l I,0 I

L 2

Developed by:

Verified by:

IDeveloped by Verified by. I

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 12 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 A5e = OD Stress data at each Elevation (ksi)

DataAII :=

0 1

2 3

4 5

0 0

-24.18

-21.84

-20.55

-19.44

-18.5 1

0.56

-1.41

-3.32

-4.98

-6.48

-7.75 2

1.02 22.03 16.77 12.53 8.72 4.43 3

1.38 29.96 26.48 21.85 16.05 9.43 4

1.67 34.51 28.44 24.2 22.09 22.08 5

1.9 33.22 28.07 26.32 32.42 42.48 6

2.09 28.22 28.59 29.91 41.71 57.59 7

2.22 22.01 25.06 31.61 45.62 63.12 8

2.36 17.22 23.06 32.35 47.57 64.11 9

2.5 14.68 21.28 33.22 47.8 60.65 AllAxl:= DataAIl I AIIID:= DataAIl l AIIOD := DataAII Developed by:

Venfied by:

lIDeveloped by:

Verifed by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 12 Page4of10 Engineering Report M-EP-2003-002-01 20 10

-20

-40 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).

-24.18 -21.838 -20.55 -19.438 -18.504) 0.564 -1.412

-3.32

-4.982

-6.476 1.016 22.032 16.773 12.529 8.722 1.378 29.956 1.668 34.51 26.483 21.849 16.053 28.439 24.198 22.09 Data:=

-7.753 4.428 9.428 22.082 42.48 57.592 63.118 1.9 33.218 28.069 2.087 28.217 28.594 2.224 22.006 25.059 26.319 32.416 29.911 41.713 31.606 45.624 32.349 47.567 p2.361 17.219 23.064 64.115 )

Axl:= Data ID:= Data (5)

OD:=Data RID := regress(Axl, ID,3)

ROD:= regress(Axl, OD,3) lIDeveloped by:

Verified by: I Developed by:

Verified by:

= - -

Entergy OPerations Inc.

Central Engineering Programs Appendix "C"; Attachment 12 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ Strs.avg :=

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

Verified by:~~~~~~~~~

IDeveloped by Veffled by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 12 Page 6 of 10 Engineering Report M-EP-2003-002-01 PrOPjjength = 0.543 1.5 U

-a~" TWCPWC

.< TWpwsccj. 3 v

l 0.5 0

-0.5 "0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCpWSCC 0 I)

Operating Time {years}

Entergy Model Increase in Half Length 2

-C' 1.5 l

0.5 0 0 0.5 I

1.5 2

Operating Time IYears}

2.5 3

3.5 4

Developed by:

Verified by:~~~~

IDeveloped by:

Verified by.- I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 12 Page 7 of 10 Engineering Report M-EP-2003-002-01 300

= 200 0

100 a

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time (Years}

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

Verified by:

co I.

Entergy Operations Inc.

Cental Engineering Programs Appendix "C"; Attachment 12 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCC j6) 18.194 23.154 23.166 23.178 23.191 23.203 23.215 23.228 23.24 23.252 23.265 23.277 23.289 23.302 23.314 23.327 TWCpwscc(j 7) =

29.656 33.394 33.407 33.419 33.432 33.445 33.458 33.471 33.483 33.496 33.509 33.522 33.535 33.548 33.561 33.573 TWCpwc TwPWSCC (j, )

25.114 29.591 29.605 29.619 29.632 29.646 29.66 29.674 29.687 29.701 29.715 29.729 29.742 29.756 29.77 29.784 Developed by:

Verified by:

lIDeveloped by.,

Verified by.:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 12 Page 9of10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 60 4 0 2 0 e

Co X 0

-2 0

-4 0 I

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 D is ta n c e fro m N o z z le B o tto m

[in c h )

200 -

6 iS

,c 1 5 0 (0

5 0 -

0-O D S urfa c e S IF ID S urfa ce S IF A v e ra gre S IF 0

1 2

3 4

O p e ra tin g T ime

{y e a rs }

IDeveloped by:

Verified by:

Co 5

Entergy Operatfons Inc.

Central Engineenng Programs Appendix "C"; Attachment 12 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.2 -

I I O.8 -

I1 0.4 O.0 0

1 2

3 4

O perating Time ay*ars)

Developed by:

Verified by:

lIDeveloped by:

Venfied by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 13 Page I of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.

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

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 2 Component: Reactor Vessel CEDM -"28" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmit" - 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 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 evalwte 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 To place the flow with repsect to the reference point, the flow tips and center can be located as follows:

1) The tipper "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"o located at the reference point (Enter 3).

Val := 2 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 := 1.704 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by:

J. S. Bnhmadesam Verified by B. C. Gray

Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 13 Page 2 of I 1 Engineering Report M-EP-2003-002-01 Input Data :-

L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Pint := 2.235 Years := 4 im r

= 1500 T := 604 aoc := 2.67-10 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)

Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)

Tube OD Tube ID 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 := 2 id Rid T=

t:= Ro-Rid t

Rm := Rid + -2 Timopr :=Years-365-24 CFinhr l=

.417*105 Timopr Cb~k.

'im

'=im PMtb~k =

5 L

Co := -

Rm Rt= t 1.103-10 3

T+459.67 ref+459.67 Co I :=

.] a0C Temperature Correction for Coefficient Alpha CO:= Co1 75 th percentile MRP-55 Revision 1 Developed by.

J. S. Buhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 13 Page 3 of 1 1 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

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

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

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

Cloumn "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 :=

l 0 1

7 1

1 2

3 4

5 0

0

-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 7

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 AXLen:= AIIData(P)

ID

= AllData(l)

All ODAII:= AllData(5)

Stress Distribution MU 3-1

'A~

50 t I

I I

III 1544 1.704 I

I

~~~~~~I I 1

"".~~~~~~~~~~~~~~~~~

l l 1,

1 1

1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0

-50 0 0.5 I

1.5 2

Axial Elevation above Bottom [inch]

2.5 3

3.5 ID Distribution

OD Distribution Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 13 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. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.

When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.

Data :=

0 0.461 0.83 1.126 1.363 1.552 1.704 1.825 1.946 2.066

-17.414

-8.494 0.089 7.025 8.215 13.266 20.627 29.036 33.945 29.591

-13.552

-6.31 0.179 6.953 10.954 16.41 22.237 28.83 30.929 31.788

-11.113

-4.924 0.11 6.314 10.85 16.061 25.413 31.285 36.407 40.536

-8.884

-3.706 0.186 5.208 9.512 17.131 43.58 53.547 61.6 64.612

-6.628)

-2.541 0.284 4.646 5.646 25.256 53.784 64.082 71.01 76.418 )

AxI := Data(°)

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(Axi, MD,3)

RTO:= regress(Ax1,TQ,3)

Developed by:

J. S. Bnhmadesam Verifled by:

B. C. Gray

J Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 13 Page 5 of 1 1 Engineering Report M-EP-2003-002-01 FLCntr =

Refpoint - cO if Val = I RefPoint if Val = 2 Refpoint + co otherwise UTip := FLCntr + Co Flaw center Location above Nozzle Bottom ULStrs.Dist - UTip Incta

=

ors.avg 20 No User Input is required beyond this Point M Sat Aug 09 10:59:39.'

Developed by:

J. S. Bnihmadesam NM 2003 Verified by:

B. C. Gray

Entergy Operations Inc.

Appendix "C"; Attachment 13 Engineering Report Central Engineering Programs Page 6 of 11 M-EP-2003-002-01 ProPLengh = 0 Flaw Growth in Depth Direction 0.6 04 c,

0.4__

3 0.2 -

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

2 c~ 0 0

0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Developed by:

Verifed by:

J. S. Balimadesam B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 13 Page 7 of 11 Engineering Report M-EP-2003-002-01 100 U

._7

(/

I-cU cd Cw us

'A 80 1 60 1 Stress Intensity Factors I

I I

I I

IIII I

I I

40 t 20 1 0 0 0.5 I

1.5 2

Operating Time 2.5 (years}

3 3.5 4

Depth Point Surface Point Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 13 Page 8 of 1 1 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9

,.n U0 C

0

.InC ajE C

C)

.Q 1=1 U

0U V

U C

CD 1-C 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 ------I-------------------------------------- --------------------------------- ------I....................................................................................

0 0.5 I

1.5 2

2.5 3

3.5 4

Operating time {years}

i"- Tip -- Uniform it"- Tip -- Linear tia - Tip -- Quadratic

?a"~ - Tip -- Cubic ti"- Tip -- Uniform V-Tip -- Linear tc" - Tip -- Quadratic ti"- Tip -- Cubic Developed by.,

J. S. Brihmadesam Verified by:

B. C. Gray

l Entergy Operations Inc.

Central Engineering Programs CGRsambi(k 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 13 Page 9 of 1 1 Engineering Report M-EP-2003-002-01 CGRsambi (k, 6) 8.464 10.317 10.318 10.318 10.318 10.319 10.319 10.32 10.32 10.321 10.321 10.322 10.322 10.323 10.323 10.323 CGRsambi (k, 5) 7.148 8.617 8.617 8.618 8.618 8.618 8.618 8.619 8.619 8.619 8.62 8.62 8.62 8.62 8.621 8.621 Developed by.

J. S. Bnihmadesam Verified by.-

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs 8 0-Appendix "C"; Attachment 13 Page 10 of 11 Engineering Report M-EP-2003-002-01 AIn I

40 2 0 0

-2 0 0.- 0 0.5s 1A.0 I1.5 2.0 2F.5

3. 0 A xialI D ista nce F romr N ozzle Boattom rn inch )

0 053 -

20.0 51 00 04 9 -

C-0.04 7 -

0.045 - _

0 1

2 3

4 0 p e ra tin g T ime

{y e a rs }

Developed by; J. S. BrIhmadesam Verified by' B. C. Gray

Entergy Operations Inc.

Central Engineering Programs 0.03 -

c c

z 0.0 I

Go 0.01 -

To T1 0.00 -

Appendix "C"; Attachment 13 Page 11 of 11 Engineering Report M-EP-2003-002-01 0

1 2

3 4

O perating Tim e (years) 11 C

1 0 I

ub 9

c j 87-7 -

S: F S u ~~rfa c e P 0 in I I 0

I 2

O perating Time {years}

3 4

Developed by:

J. S. Bribmadesam Verified by.

B. C. Gray Co C 1

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page I of 11 Engineering Report M-EP-2003.00241 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 -"28" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RMIt" -- 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 ekvation measured upward from the nozzle end.

RefPoint = 1.544 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 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 ).

This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.704 Developed by:

J. S. Blihmadesam Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Verfled by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 14 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 P Int := 2.235 Years := 4 Iiim := 1500 T := 604 a0C := 2.67 lo-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 R.=--

id Rid T=

t:= Ro - Rid i

Rm :=Rid+ -2 Timopr := Years-365-24 CFnhr := 1.417 105 Timopr Cblk

'=-

'=iml Pmrtblk =

5 L

C0 2

Rm Rt :=

1.103 10- 3T+459.67 Tref+459.67J)

C0 1 := e

.a0c Temperature Correction for Coefficient Alpha CO:= Co 1 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Blnhmadesam Verffied by B. C Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

Column "On = Axial distance from minumum to maximum recorded on data sheet(inches)

Column 'Il = ID Stress data at each Elevation (ksi)

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

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

Column w4 5

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

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

AllData :=

AXLen IDAII In ODAI 0

1 2

-3

--4 5

O 0

-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 0.28 253 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

,7 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

=AllData(°)

IDA~ := A1lDatP~)

ODA

AllData(5)

Stress Distribution I ft.

11 1VU I i

I CAA 1'7flA S

~

I l

50.

I I

1 I

0 1

I I

I

-50 )

0.5 I

1.5 2

2.5 3

3.5 AXLen Axial Elevation above Bottom [inch]

Developed by:

J S Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 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).

Data :=

0 0.461 0.83 1.126 1.363 1.552 1.704 1.825 1.946 2.066 2.187

-17.414

-8.494 0.089 7.025 8.215 13.266 20.627 29.036 33.945 29.591 23.26

-13.552

-6.31 0.179 6.953 10.954 16.41 22.237 28.83 30.929 31.788 29.738

-11.113

-4.924 0.11 6.314 10.85 16.061 25.413 31.285 36.407 40.536 41.2

-8.884

-3.706 0.186 5.208 9.512 17.131 43.58 53.547 61.6 64.612 64.193

-6.628)

-2.541 0.284 4.646 5.646 25.256 53.784 64.082 71.01 76.418 79.626 )

AxI := Data(0)

MD:= Data)

ID:= Databi)

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 =

Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + c0 otherwise U

=

FL Cntr C0 ICStrsaa =ULStrs.Dist - UTip Developed by:

Verifed by:

J. S. Blihmadesam B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 5 of 11 Engineering Report M-EP-2003-002-01 TV No User Input is required beyond this Point Sat Aug 09 10:21:18AM Developed by:

J. S. Bnhmadesam 2003-Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programns Appendix "C"; Attachment 14 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength= 0 Flaw Growth in Depth Direction 0.6 u

a CL 3

j-0.4 1 I

I I

I I

I I

I I

I I

I I

I 0.2 0 C 0.5 l

1.5 2

2.5 Operating Time {years}

3 3.5 4

Entergy-CEP Model U

0c

-J 0.81 0.6 1 I

I I

I I

I I

I I~~~~~~

15 Hi I

I I

I o

0.4 0.2 0

o 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by:

J. S. Bnbmadesam VeTlfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 7 of 11 Engineering Report M-EP-2003-002-01 0~

t; 5-(j3I..

80 60 I Stress Intensity Factors I

I I

I I

I I

I I

I I

I I

I 40 1 20 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. Blihmadesam Verfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 8 of 11 Engineering Report M-EP-2003-002-01 0.8 0.7 0

C:

V)a V

V 0

VQ CE U

C 0.6 0.5 0.4 0.3 Influence Coefficients - Flaw I...........I......................

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

0.2 0.1 0

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

0 0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

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

"a" - Tip -- Quadratic I"a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear i"c" - Tip -- Quadratic t"c" - Tip -- Cubic Developed by:

J. S. Br~hmadesam Verified by; B. C. Gray C09

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 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 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi k 6) 15.529 19.971 19.978 19.986 19.994 20.002 20.009 20.017 20.025 20.033 20.04 20.048 20.056 20.064 20.072 20.079 CGRsambi 11.322 14.55 14.555 14.56 14.565 14.57 14.575 14.58 14.585 14.59 14.595 14.6 14.605 14.61 14.615 14.62 Developed by.

J S. Bdhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 10 of 11 Engineering Report M-EP-2003-002-01 80 60 40 1

20 0

-2 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istonce from N ozzle B ottom

{incheos 0 3 0.2 -

-0 6

C) 0.0 -

u 0 o0 I

I I

0 1

2 3

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

Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray C1I

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.3 0

S 0.0 I

o o 0

1 2

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

l__

Surface Point (c-tip} I

l.

Depth Point ('a"- tip}

35 -

. 30 -

225 A 2 0 i

1 5 0-0 1

2 3

4 Operating Time (years)

Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 15 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. Brihmadesam Verified by: B. C. Gray Note: Only for use when RSnijd/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"Degree Nozzle, Downhill Azimuth, 1.544 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 (eg. top of the Mind Zone).

The throughwall flow "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 :=1-704 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Developed by:

Verified by:

IDeveloped by Verified by I

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :

L := 0.25 od:= 4.05 id:= 2.728 Plt:= 2.235 Years:= 4 rimn:= 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 L1.103. 10-3

+459.67 Tref+459.67)J Co:= e

.a~~~~~~~~~~cL~

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 Ro:= od2 Ri2= id t:= Ro - Ri Rm:= Ri + -2 CFinhr:= 1.417-105 Cblk:Tiop

'urn Irim PMtbik:=

50 I

L 2

Developed by:

Ventied by:

IDeveloped by Verified by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 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)

DataAIl :=

0 1

2 3

4 0

0

-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 7

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 AllAxl:= DataAII)

AIIID DataAll l AIIOD:= DataAII5 Developed by:

Verified by:

lIDeveloped by.

Venfied by-I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 15 Page 4 of 10 Engineering Report M-EP-2003-002-01 "W

75 I 50 1 a'

E 1.544.704 e

10

........ ~

25 0

-25

-50 )

0.5 I

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 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 fData" statement below and delete It from the edit menu. Type fData and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

I A

1741A

-12R

-11 11

-R QQA S

RN I

I.-.-

-....1 I

Data:=

0.461

-8.494 0.83 0.089 1.126 7.025 1.363 8.215 1.552 13.266 1.704 20.627 1.825 29.036 1.946 33.945 2.066 29.591 2.187 23.26

-6.31 0.179 6.953 10.954 16.41 22.237 28.83 30.929 31.788 29.738

-4.924

-3.706 -2.541 0.11 0.186 0.284 6.314 5.208 4.646 10.85 9.512 5.646 16.061 17.131 25.256 25.413 43.58 53.784 31.285 53.547 64.082 36.407 61.6 71.01 40.536 64.612 76.418 41.2 64.193 79.626

~2.308 18.689 27.734 41.29 61.777 78.117)

(5:

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

ROD:= regress(Axl, OD,3)

Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom UI-Stm.Dist - BZ IfCStrs.avg =

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

Verified by:

lIDeveloped by:

Verified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLngth = 0.16 Flaw Length vs. Time 1.5 1

6 TWCpwscc
  • j,3 0

To.

I 1-5--

I I

I i

i i

I I

I

.16 t

i 0.5 0

-0.5 I

0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCPWSCC 0 I )

Operating Time (years)

Entergy Model Increase in Half Length 2

s r-c u-V C)

C V)

C*

1.5 0.5 O0 0.5 1

1.5 2

2.5 3

3.5 Operating Time {Years}

4 Developed by:

Verified by:

lIDeveloped by.

Verified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 0

L..

U-200 100 0

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

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

0 0.5 I

1.5 2

Operating Time (Years) 2.5 3

3.5 4

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

Verified by I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCC 6) 19.249 20.707 20.715 20.724 20.732 20.741 20.749 20.758 20.766 20.774 20.783 20.791 20.8 20.808 20.817 20.826 TWCpwscc(j 7) =

12.744 13.424 13.43 13.436 13.442 13.447 13.453 13.459 13.465 13.471 13.476 13.482 13.488 13.494 13.5 13.506 Twcpwscc(j 8) 16.124 17.198 17.205 17.212 17.22 17.227 17.234 17.242 17.249 17.257 17.264 17.271 17.279 17.286 17.293 17.301 IDeveloped by:

Verified by.-

Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 80 60 40 a

2 0 0

-2 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istance from N ozzle B ottom (inch) 80 -

.e8 0 -

60 it 6 0 -

W 2 0 -

0 -

o D S urface S IF ID Su rfa ce S IF Average SIF 0

1 2

3 4

O perating Time (years)

D IDeveloped by:

Verified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 15 Page 10 of 10 Engineering Report M-EP-2003-002-01 0.5 0.4 0.3 1 0.2 0.1 0.0 0

1 2

O perating Tim a lyears)

Developed by:

Verified by:

I Developed by.

Veriffedby. I

Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 16 Page I of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.

Developed by: J. S. Brihmadesam 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 -'28" Degree Nozzle, UPhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" - 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 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.

RefPoint 1.544 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 flow at the reference point (Enter 2)
3) The lower "C-tip" located at the reference point (Enter 3).

Val := 2 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 := 4.268 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 2 of I1 Engineering Report M-EP-2003-002-01 Input Data :-

L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Plnt := 2.235 Years := 4 Iiim := 1500 T := 604 aOc := 2.67-l 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)

Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)

Tube OD Tube ID 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 Rid2 t:= Ro -Rid t

Rm : Rid+ +2 Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk :=

i him

'=im Pmtblk :=

5 L

Co := -

Rm Rt :=-

F Qg

(

I XI J1.103 10-3 T+459.67Tref+49.67 C0 1 *-

Co := COI

)a.0C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

l Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 3 of 1 1 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

Column UO' = Axial distance from minimum to maximum recorded on data sheet (inches)

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

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

Cloumn "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

-9.03

-5.86

-4.25

-2.69

-1.03 1

1.15

-6.76

-6.74

-7.24

-7.66

-7.8 2

2.08 7.97 1.74

-6.23

-11.85

-16.39 3

2.82 23.85 21.76 8.56

-6.39

-17.65 4

3.41 43.99 38.07 29.83 13.47

-1.63 5

3.89 47.95 41.75 35.45 33.32 35.85 6

4.27 43.76 39.21 38.4 53.02 57.54 7

4.38 40.77 36.24 41.27 61.45 62.19 8

4.49 39.28 35.33 44.86 64.2 63.9 9

4.6 36.02 35.39 46.84 64.32 62.93 AXLen:= AllData(0)

ID

= AlIData(l)

All ODAII:= AllDataP Stress Distribution 100 50 0

-50 0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

5.5 6

Axial Elevation above Bottom [inch]

ID Distribution

OD Distribution Developed by.

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 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. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.

When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.

Data :=

0 1.154 2.078 2.819 3.412 3.888 4.268 4.377 4.486

-9.034

-6.761 7.965 23.851 43.99 47.954 43.756 40.773 39.277

-5.855

-6.739 1.742 21.763 38.072 41.753 39.214 36.237 35.327

-4.246

-7.237

-6.23 8.555 29.826 35.453 38.4 41.27 44.863

-2.689

-7.662

-11.848

-6.39 13.47 33.324 53.023 61.453 64.204

-1.031

-7.803

-16.387

-17.647

-1.632 35.846 57.543 62.189 63.895 )

AxI := Data MD:= Data ID:= Data(l)

TQ :=Data(4)

QT:= Data(2)

(5)

OD:= Data RID := regress(Axl,ID,3)

RQT:= regress(Axl,QT,3)

ROD := regress(Axl, OD, 3)

RMD := regress(AxI, MD,3)

RTQ := regress(Ax1,TQ,3)

Developed by:

J. S. Bdhmadesam Verfired by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 5 of 1 1 Engineenng Report M-EP-2003-002-01 FLCntr Refpoint -

if Val =I Flaw center Location above Nozzle Bottom Refpoint if Val = 2 RefPoint + cO otherwise ULStrs.Dist-UTip UTip := FLCntr +Co InCStrs.avg :

20 No User Input is required beyond this Point A. Sat Aug 09 10:59:39 AM 2003-Developed by:

J. 5 Bnthmadesam Verified by:

B C Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 2.564 Flaw Growth in Depth Direction I

I I

I I

I I

0.6 (U

a)

I-0.4 _

0.2 -

I I

1 O L0 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

2 U

c I-SV

-1 I

I I

I I

I I

I I

I I

I I

I I

0

-I 0

0.5 I

1.5 2

Operating Time 2.5

{years}

3 3.5 4

Developed by:

J. S Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors Q

ctCA

-~1 0u Cl) 1" U)

(n 6

4 2

0 I

I I

I I

I I

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

-2 0 0

0.5 I

1.5 2

Operating Time 2.5

{years}

3 3.5 4

Depth Point

-.. -Surface Point Developed by.

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9

'A 0

va E

-0 0

0 c-)

c vo I-c 0.8 0.7 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 {years}

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

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

- "c' - Tip -- Linear l"c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs CGRsambi (k, 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 16 Page 9 of I 1 Engineering Report M-EP-2003-002-01 CGRsambi (k, 6)

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323

-0.323 CGRsambi (k, 5)

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397

-0.397 Developed by.

J. S. Bubmadesam

Entergy Operations Inc.

Centra I Engineering Programs 6 0 Appendix "C"; Attachment 16 Page 10 of 11 Engineering Report M-EP-2003-002-01 9

a A

9X 40 20 0

-2 0 0

1 2

3 4

A xia iD is tan ce From No zz le Bo tto m (in c h )

0.07 -

0 04 -

C, 0.03 -

0.02 0

1 2

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

3 4

Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 16 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 c

0 3

-S 0.1

~S r

-0.1 I(3

) -0.3

-0.5

-0.32 -

-03 I

-0.3 4

-0.4 60 Z; -0.3 8 -

.0.40 -i 0

1 2

p era tin g Time (years) 3 4

0 I

2 O perating Timea (years) 3 4

Developed byV J. S. Brthmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 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. S. Brihmadesam 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 -"28" Degree Nozzle, Uphill Azimuth, 1.544" above Nozzle Boffom 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 flow both for the initial flaw and for a growing flow.

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 To place the flow with repsect to the reference point, the flaw tips and center can be located as follows:

1) The tipper "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 elevation from Nozzle Bottom. Enter this value below ULStrs.Dist :=4.268 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 17 Page 2 of I1 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 him = 1500 T := 604 aoc :=2.67 10- 2 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 R0.

2 id Rid T=

t:= Roi-Rid t

Rm:=Rid+ j2 Timopr := Years-365-24 CFinhr := 1.417*105 Timopr Cblk 11im

'=im Prntblk =

5 L

C0 2

Rm Rt :=-

-Q g

.(

I I

1. 10 3 10-r3(T+459.67 Tref+459.67' CO = C0 1 io0C Temperature Correction for Coefficient Alpha 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 17 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

Column "O" = 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 (ksi)

ANData :=

.i, 10 ~

t

~

l 2

0 0;

l C30 l

0005i;S 740 o

0

-9.03

-5.86

-4.25

-2.69

-1.03 1

1.15

-6.76

-6.74

-7.24

-7.66

-7.8 2

2.08 7.97 1.74

-6.23

-11.85

-16.39 3

2.82 23.85 21.76 8.56

-6.39

-17.65 4

3.41 43.99 38.07 29.83 13.47

-1.63 5

3.89 47.95 41.75 35.45 33.32 35.85

-6 4.27 4376 39.21 38.4 53.02 57.54 7

4.38 40.77 36.24 41.27 61.45 62.19 8

4.49 39.28 35.33 44.86 64.2 63.9 9

4.6 36.02 35.39 46.84 64.32 62.93 AXLen:= AllData(°)

IDAII:= A11Data(')

0DA11:= AlIData()

Stress Distribution I-En en IDAII ODAII

-50' 0 1

2 3

4 5

6 AXLen Axial Elevation above Bottom [inch]

Developed by:

J. S. Brlhmadesam Verif ed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 4 of 1 1 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

-9.034 -5.855 -4.246 -2.689

-1.031 'I 1.154 -6.761 -6.739 -7.237 -7.662 2.078 7.965 2.819 23.851 1.742

-6.23

-11.848 21.763 8.555

-6.39 Data := 1 3.412 43.99 38.072 29.826 13.47

-7.803

-16.387

-17.647

-1.632 35.846 57.543 62.189 63.895 )

3.888 4.268 47.954 41.753 35.453 43.756 39.214 38.4 33.324 53.023 4.377 40.773 36.237 41.27 61.453 35.327 44.863 64.204 k4.486 39.277 Axi := Data(O)

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(Ax1,TQ,3)

FLCntr RefPoint CO if Val= i Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 RefPoint + CO otherwise ULStrs.Dist - UTip UTip := FLCntr +C 0 InCStrsav2 IA Developed by:

J. S. Bnihmadesam Veniried by.

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 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. Brhmadesam Venlfed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 6 of I1 Engineering Report M-EP-2003-002-01 ProPLength = 2.564 0.6 C.

C@

0

-c 1PC 0.4 1 Flaw Growth in Depth Direction I

I I

I I

I I

I I

I I

III 0.2 [

( _0 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

Entergy-CEP Model U

oC tD 3

Co C

-J U-0.

0.

I I

I I

I II 8

6-

.383 4

-I 2

n

~I I

I I

I I

0.

0.

0 0.5 I

1.5 2

Operating Time 2.5

{years}

3 3.5 4

Entergy-CEP Model Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Centra I Engineering Programs Appendix "C"; Attachment 17 Page 7 of 11 Engineering Report M-EP-2003-002-01 I.

or 0

U a) a)

I-* u MC c) us En 50 0

Stress Intensity Factors I

I I

I I....

I I

I I

III jIu 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. Bnlmadesam Verfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix '"C"; Attachment 17 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 En v

0 r-)

0 0.6 0.5 0.4 0.3 0.2.

0.1 0-0

............. 1-- --- ------------------------ --------------------- ----------------------- ----------------------- ----------------------- ----------------------- ---.......

0.5 I

1.5 2

2.5 Operating time fyears}

3 3.5 4

Il"- Tip -- Uniform Ia" - Tip -- Linear Ila - Tip -- Quadratic Ia"* - Tip -- Cubic tic - Tip -- Uniform

'c 1 -Tip -- Linear ti"- Tip -- Quadratic tic" - Tip -- Cubic Developed by:,

J. S. Brihmadesam Verifiedf by:

B. C. Gray C) 7

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 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 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k, 6)

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284

-5.284 CGRsambi (k,-5)

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812

-3.812 Developed by:

J. S. Brihmadesam Venirfed by:

8. C. Gray

Entergy Operations Inc Central Engineering Programs 8 0 -_

60 -

I

-2 o

2 0 -

O -

-2 0-Appendix "C"; Attachment 17 Page 10 of 11 Engineering Report M-EP-2003-002-01 2

3 4

D is tan ce from No z z le Bo tto m

[inch es I 6

0.5 c0°3 0o 1

.T0 rS

-03

-0.5 0

I 2

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

3 4

Developed by.

J. S. Bnhmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 11 of 11 Engineering Report M-EP-2003-002-01 0

O.3 -

5 S

I

-0 1 -

fii i.1 I

i -0.1 -

ej 5 -

0 1

2 O pe ra tin g T im e (y ea rs}I 3

4 l____

Su rfa ce Po in t {"c"-tip }

I Depth Point {"a"- tip}

-4.0-U-

t -4.5

  • ii.9 1- -5.0 I

-5 5 0

1 2

O pe rtin g Time ye a r)I 3

4 Developed by.

J. S. Brfhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Contra/ Engineering Programs Appendix "C"; Attachment 18 Page 1 of 10 Engineering Report M-EP-2003-00201 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 Rofj/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"Degree Nozzle, Uphill Azimuth, 1.544 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 inch4,r.

Through Wall Axial Flaw The first Input is to locate the Reference Line (g. top of the Blind Zone). The hroughwall 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:= 1.544 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:= 4.268 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Developed by:

Verified by: I

Entergy Operatons Inc.

Central Engineenng Programs Appendix "C"; Attachment 18 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :-

L := 0.25 od:= 4.05 id := 2.728 Pint:= 2.235 Years:= 4 Tlim:= 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 0 -Qg

(

I I

Lo

=103 lo{T+45967 TrefF459.67)

Co:= e Timopr:= Years-365-24 od 2

Ri:= id t := Ro - Ri Rm:= Ri + -2 CFinhr:= 1.417105 Tiflnopr Cblk :=

r 1lim Pmntblk:=

Ii I

L 2

Developed by:

Verified by:

lIDeveloped by.

Vefrted by:-

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 18 Page 3 f 10 Engineering Report M-EP-2003-00201 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 "" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)

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

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

DataAll:=

0 0

-9.03

-5.86

-4.25

-2.69

-1.03 1

1.15

-6.76

-6.74

-7.24

-7.66

-7.8 2

2.08 7.97 1.74

-6.23

-11.85

-16.39 3

2.82 23.85 21.76 8.56

-6.39

-17.65 4

3.41 43.99 38.07 29.83 13.47

-1.63 5

3.89 47.95 41.75 35.45 33.32 35.85 6

4.27 43.76 39.21 38.4 53.02 57.54 7

4.38 40.77 36.24 41.27 61.45 62.19 8

4.49 39.28 35.33 44.86 64.2 63.9 9

4.6 36.02 35.39 46.84 64.32 62.93 1

4.7 33.54 36.17 48.06 64.48 66.03 11 4.81 32.63 36.62 47.78 67.61 70.36 AllAxl:= DataAII AIIID DataAIlI AIIOD DataAll lIDeveloped by.

Venfied by. I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 18 Page 4 of 10 Engineering Report M-EP-2003-002-01 Cn 100 75 50 25 0.......................

-25

-50 0 0.5 1

ID Distribution OD distribution 1.5 2

2.5 3

3.5 4

4.5 5

5.5 6

Axial Distance above Bottom [inch]

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

-9.034 1.154 -6.761 2.078 7.965 2.819 23.851 3.412 43.99 3.888 47.954 Data:=

4.268 43.756 4.377 40.773 4.486 39.277 4.595 36.022 4.704 33.54 4.813 32.631

( I)

ID:=Data

-5.855

-6.739 1.742 21.763 38.072 41.753 39.214 36.237 35.327 35.389 36.173 36.616

-4.246

-7.237

-6.23 8.555 29.826 35.453 38.4 41.27 44.863 46.842 48.06 47.779

-2.689

-1.031 1

-7.662

-7.803

-11.848 -16.387

-6.39

-17.647 13.47

-1.632 33.324 35.846 53.023 57.543 61.453 62.189 64.204 63.895 64.323 62.934 64.483 66.03 67.612 70.356 )

(5)

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

ROD:= regress(Axl,OD,3)

Developed by:

Verified by:

IDeveloped by:-

Verified by I I

A G 2?- 'D

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 18 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr := BZ - I Flaw Center above Nozzle Bottom ULStr.Dist - BZ 1ncStrs.avg :=

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

Verified by:

lIDeveloped by.

Verified by. I

Entergy Operations Inc.

Centra/ Engineering Programs Appendix "C"; Attachment 18 Page 6 of 10 Engineering Report M-EP-2003-00201 ProPLength = 2.724 TWCpscc 0

0 2

Flaw Length vs. Time 1.5

==

.543 0.5 0

0.5 1

1.5 2

2.5 3

3.5 4

4.5 TWCPw(ss j)

Operating Time (years)

Entergy Model Increase in Half Length___

5 C

e)

W e

r-1.5 0.5 0 0 0.5 I

1.5 2

2.5 Operating Time (Years) 3 3.5 4

Developed by:

Verified by:

lIDeveloped by:

Verified by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 18 Page 7 of 10 Engineering Report M-EP-2003-002-01 300

.)

0 CZ 3

V:

200 100 0 :::::::::::::

-:::::::::::I....................................................:-::::::::.........::::.....:::::::::::::...........:-:::::.....

0 0.5 l

1.5 2

2.5 3

3.5 4

Operating Time (Years}

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

Verified by:

C7 2)

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 18 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCpwscCj,6) =

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322

-10.322 TWCPWSCC(j,7) =

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923

-2.923 Twcpwsc'j 8)

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63

-6.63 Developed by:

Verified by:

lIDeveloped by Verified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 18 Page 9 of 10 Engineering Report M-EP-2003-002-01 Ho o p S tress P lot 80 60 I

40 o

2 0 0

-20

-3 4

2 3

4 Distance from Nozzle Bottom (inch) 0 D S u rfa c e S IF ID S u rfa c e S IF A v era g e S IF iS 1

E i

-5

- 9 -

-1 1 I

0 1

2 pratin g T imea (yea rI 3

4 Developed by:

Verified by:

e2 C 7-17

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 18 Page 10 of 10 Engineering Report M-EP-2003-002-01 0.5 -

I I -

.1 3 -

.5 I

0 1

2 0 peatin g T me (yeaa r) 3 4

Developed by:

Verified by:

IDeveloped by:

Verifed by. I

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 19 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.

Developed by: J. S. Brhmadesam 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 -'28" Degree Nozzle, Mid-Plane Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius 4o-Thickness Ratio:- "RmIt' - 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 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 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:

1) The Upper "-

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 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 = 2999 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 19 Page 2 of 11 Engineering Report M-EP-2003-002-01 Input Data :-

L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Pint := 2.235 Years := 4 im = 1500 T := 604 X0c := 2.67 10- 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)

Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)

Tube OD Tube ID 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

t Rm :Rid+ -2 Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk:=

imn Pmtblk 50 l L

co:=-2 Rm Rt:=-

C.103 lo T+459.67 Tref+45.67 C 0 1 e

C 0

= Ci

)]-0C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:e J. S. Bn'hmadesam Venffed by B. C Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 19 Page 3 of 11 Engineering Report M-EP-2003-0021 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:

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

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

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

Cloumn "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 2.08

-0.87

-2.96

-4.82

-6.75 1

0.81 0.09

-2.37

-4.27

-6

-7.55 2

1.46 5.28 1.69

-0.79

-2.49

-3.47 3>

1.98 16.88 12.42 9.56 6.91 4.32 4:

2.4 24.14 20.89 18.11 16.59 14.51 5

2.73 26.96 22.67 20.69 24.84 33.52 6

3 23.28 20.9 21.71 37.11 47.4 7

3.11 17.16 17.1 20.74 41.09 51.76 8

3.23 11.72 14.42 21.34 43.54 53.69

9.

3.34 6

11.11 20.91 43.83 54.15 10 3.46 1.44 8.09 20.38 43.02 57.02 11 3.57

-2.17 5.89 19.93 42.41 56.41 12 3.69

-4.72 4.86 19.99 40.42 58.85 AXLen :=AllDatP(O IDAll:= AllDatP)

ODA11 := AllData(5) 100 Ai 50 0

Stress Distribution I I I I I

I I

I I

.i44 2."9 I

I I'

I I

i I

I

-on

-Du o 0.5 1

ID Distribution

OD Distribution 1.5 2

2.5 3

Axial Elevation above Bottom [inch]

3.5 4

4.5 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineeng Programs Appendix "C"; Attachment 19 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAbl 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. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.

When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.

Data :=

0 0.811 1.46 1.98 2.397 2.731 2.999 3.113 3.228 3.343 3.457 3.572 3.687 2.079 0.091 5.283 16.881 24.144 26.962 23.279 17.161 11.722 6.004 1.439

-2.175

-4.725

-0.875

-2.37 1.686 12.419 20.894 22.672 20.902 17.101 14.424 11.108 8.085 5.891 4.858

-2.96

-4.267

-0.786 9.564 18.115 20.686 21.706 20.743 21.34 20.912 20.38 19.929 19.994

-4.82

-6.004

-2.49 6.907 16.59 24.842 37.111 41.091 43.543 43.833 43.021 42.405 40.425

-6.75

-7.552

-3.469 4.319 14.513 33.523 47.395 51.762 53.688 54.154 57.025 56.415 58.85 )

AxI := Data(°)

(3)

MD: Data ID:= Data(l)

TQ := Data(4)

QT := Data(2)

T =Data OD := Data(5)

RID := regress(Axl,ID,3)

RQT:= regress(Axl,QT,3)

ROD:= regress(AxI, OD, 3)

RMD := regress(Axl, MD, 3)

RTO:= regress(Axl,TQ,3)

Developed by:

J. S. Bnhmadesam Verifjed by

. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 19 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLCntr =

Refpoint - co if Val = I Refpoint if Val = 2 Refpoint + co otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr + Co InCstrs.avg ULStrs.Dist - UTip 20 No User Input is required beyond this Point 2 Sat Aug 09 10:59:39 AM 20031-Developed by:

J. S. Bdhmadesam Verfiled by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 19 Page 6 of 11 Engineering Report M-EP-2003-00201 ProPLength = 1.295 Flaw Growth in Depth Direction I

I I

I I

i I

0.6 I-C I-c C-:

%a)

-C 1-C5 0.4 -

0.2 -

l l

I l

l l

o )0)I 0.5 l

1.5 2

2.5 Operating Time {years}

3 3.5 4

It

~2 3.

C LT.

4 1 l l

l I

l I

1.295 0

I I

I I

I I

I

  • 1 0 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

Developed by:

1 S. Brihmadesam Venired by BR. C Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 19 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors Inn.

'UU I

I I

I I

I I

U 1~

U U'.

W V]

80 _

60 _

40 -

20 _

1 1

1 1

I I

I I

I I

I 1

{I 0

0.5 I

1.5 2

Operating Time 2.5 (years) 3 3.5 4

Depth Point Surface Point Deve loped by:

J. S. Brlhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

CentralI Engineering Programs Appendix "C"; Attachment 19 Page 8 of 1 1 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9 0

C 0

.V) 0-0 E) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

....................-...................................... 4-......-.................... I......................................................................................................................................................

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

0 0.5 I

1.5 2

2.5 Operating time years}

3 3.5 4

Ia

- Tip -- Uniform Ia" -Tip -- Linear Ia

- Tip -- Quadratic Ila - Tip -- Cubic tc" - Tip -- Uniform V-Tip -- Linear Ic"- Tip -- Quadratic V'- Tip -- Cubic De velopedf by J. S Brlimadesam Verified by B. C. Gray

Entergy Operations Inca Central Engineering Programs CGRsambi (k, 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 19 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi (k, 6) 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 CGRsambi 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs 5 0 Appendix "C"; Attachment 19 Page 10 of 11 Engineering Report M-EP-2003-002-01 co I

30 10

-1 0 0

1 2

3 A x a I D is ta n c e F ro m N o z z le B o tto m (in c h 0.00 0

05 0

E! 0 0 4 0.0 0.03 0.02 0

I 2

O pe rtin g T ite

{y e ars}

3 4

Developed by.

J. S. Brihmadesam Verified by.

. C. Gray C7) I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 19 Page 11 of 11 Engineering Report M-EP-2003-002-01 05 t'

0 3 501

5.

-0 Th

( -0.3

-0.5 5

2 FE PE 5 0 0

I 2

0 p era ting Time (years) 3 4

l___

S I F D e p th P o in t 1

S IF Sa rfa ce P o int 4.4 0

I 2

O pera tin g Timea (years) 3 4

Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray C(2

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