ML032690674

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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 2
ML032690674
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: ML032690674 (86)
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Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 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. 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, 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 elevation to define the point of interest (e.g.

The top of the Blind Zone, or bottom of filkt 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.

RefPo in t := 1.544 To place the flaw with repsect to the reference point, the flow tips and center can be located as follows:

1) The Apper "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 := 2.999 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Vedfied by:

B. C. Gray Developed by:

J. S. Brihmadesam

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 20 Page 2 of 1I 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 inr = 1500 T := 604 XOC := 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 R 617 deg. F Thermal activation Energy for Crack Growth {MRP)

Reference Temperature for normalizing Data deg. F R. od id Rid 7=

t:= Ro-Rid t

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

.417*l105 Timopr Cblk

'=-

rimn Pmtblk =

50 L

2 Rm Rt

_Q

-g

.(

I I

1.103-lo 3 T+459.67 T.ef+-459.671 C01 :=

e re v_

c Temperature Correction for Coefficient Alpha CO:= Co]

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 20 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 "O0 = 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 (ks,)

AllData :=

0 1

2 3 X 5

O O

~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 1.98 16.88 12.42 9.56 6.91 4.32 14 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 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 13 3.8

-4.92 4.88 20.34 38.45 57.62 V-I AXLen:= AllData)

IDA11:= A11Data()

ODA11

=A11Data (5)

Stress Distribution 60

.7IDAJI L OD 40 20 0

0.5 1

1.5 2

2.5 3

3.5 4

4.5 AXLen Axial Elevation above Bottom [inch]

Developed by:

J. S. BShmadesam Vendled by:

B. C. Gray

Entergy Operations Inc Central Enginering Programs Appendix "C"; Attachment 20 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 2.079

-0.875 -2.96

-4.82

-6.75 0.811 0.091

-2.37 -4.267 -6.004 -7.552 1.46 5.283 1.686

-0.786 -2.49

-3.469 1.98 16.881 12.419 9.564 6.907 4.319 2.397 24.144 20.894 18.115 16.59 14.513 2.731 26.962 22.672 20.686 24.842 33.523 Data 2.999 23.279 20.902 21.706 37.111 47.395 3.113 17.161 17.101 20.743 41.091 51.762 3.228 11.722 14.424 21.34 43.543 53.688 3.343 6.004 11.108 20.912 43.833 54.154 3.457 1.439 8.085 20.38 43.021 57.025 3.572 -2.175 5.891 19.929 42.405 56.415 3.687 -4.725 4.858 19.994 40.425 58.85 )

I

__ __ I AxI := Data(O)

(3)

MD:

Data ID:= Data(l)

TQ:= Data(4)

QT := Data()

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 RefPo in t -C if Val = 1 Flaw center Location Location above Nozzle Bottom RefPo in t if Val = 2 RefPoint + c0 otherwise UTip := FLCntr + C0 IncStrs avStrsDist U p Developed by:

VBfled by.

J. S. Bnihmadesam B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 5 of 11 Engineering Report M-EP-2003-002-01 TV No User Input is required beyond this Point fSatAug 09 10:21:18AM Developed by:

J. S. Bnhmadesam 2003 Venried by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 1.295 0.6 0

4-.5 u

3 Cd tcS I._

I 0.4 r Flaw Growth in Depth Direction I

I I

I I

I I

I I

III 0.2 t O

0 0.5 1

1.5 2

2.5 3

3.5 Operating Time (years)

Entergy-CEP Model III I

I I

I I

I~~~~~~~~~~~~~~~

1>5

.5 -

0 A

4 0.

v

-0.5 I-I I

i I

I I

I 0 0.5 I

1.5 2

Operating Time 2.5

{years) 3 3.5 4

Entergy-CEP Model Developed by:

1. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 7 of 11 Engineering Report M-EP-2003-002-01 c

01 v) 14 r-vD A

Stress Intensity Factors

0

~I I

I I

I I

I 0

I I

I I

I I

I 2

-2Mu 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 Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 v) 0 E

0 0

r-0.6 0.5 0.4 0.3

....-. d............................................I.....................................................................................................................................I...................I....I..............

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

_..+............

...... 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 Centra I Engineering Programs Appendix "C"; Attachment 20 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)

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017

-0.017 CGRsambi(k,5) 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 Developed by.:

J. S. Brihmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs C

5 0 -

I I

10

-1 0 -

Appendix "C"; Attachment 20 Page 10 of 11 Engineering Report M-EP-2003-002-01 2

3 Distance from Nozzle Bottom

{inches}

0.5 I~0 0

i-0.1

_I

-0 3

-0.

0 1

O p e ra tin g T ime

{y e a rs I 3

4 Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 c0.3

' 0_.

S O) e

-0 3

-0.5 0

I 2

p e ra tin g T im e (y ea rs I 3

4 0.13 -

i5 0. 08 -

il-5 0.03 -

-0.0 2 -

S u rfa ce P o in t {"c"-tip i

Depth Point {"a'- tip}

0 1

2 0 perating Time {years}

3 4

Developed by:

J S. Brihmadesam Verified by.

B. C Gray C -0)O

Entergy Operations Inc.

Cenbal Engineenng Programs Appendix "C"; Attachment 21 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 Re 5 itsd/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, 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 inch/hr.

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

The thromghw/l flaw '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 Location of Blind Zone above nozzle bottom (inch)

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

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

ULStrs.Dist:= 2.999 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Developed by:

Verified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix wC"; Attachment 21 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :-

L := 0.25 od:= 4.05 id:= 2.728 Pnt := 2.235 Years:= 4 hiim:= 1500 T := 604 v := 0.307 aoc:= 2.67 10- 12 Qg:= 31.0 Tref := 617 Initial Flaw Length 7W 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 Q

Qg

.(

I I

0L 3

10. 10-3 T+459.67 Trf+459.67)

Tinopr:= Years*365*24 Ro:= od 2

id R := id t:= R, - Ri Rm:= Ri + 2 2

CFjinr:= 1.417-105 Tifllopr Cblk :=

im hlim Prntblk:=

50 2 L Developed by:

Verified by:

IDeveloped by:

Verffied by: I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 21 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 "5" = OD Stress data at each Elevation (ksi)

DataAI :=

0 3

O 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 3.34 6

11.11 20.91 43.83 54.15 1

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 AllAxl:= DataAIl 0 MUHD= DataAlI~l AIIOD := DataAII 5)

Developed by:

Verified by:

IDeveloped by.

Venfied by.- I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 21 Page 4 of 10 Engineering Report M-EP-2003.002-01 60 4

46.67 7

~

33.33 20 6.67

-6.67

-20 0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 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 0.811 1.46 1.98 2.397 2.731 2.999 3.113 3.228 3.343 3.457 2.079 0.091 5.283 16.881 24.144 26.962 23.279 17.161 11.722 6.004 1.439

-0.875

-2.37 1.686 12.419 20.894 22.672 20.902 17.101 14.424 11.108 8.085

-2.96

-4.267

-0.786 9.564 18.115 20.686 21.706 20.743 21.34 20.912 20.38

-4.82

-6.004

-2.49 6.907 16.59 24.842 37.111 41.091 43.543 43.833 43.021

-6.75 )

-7.552

-3.469 4.319 14.513 33.523 47.395 51.762 53.688 54.154 57.025)

Axi:= Data (1)

ID:

Data (5)

OD: Data RID := regress(Axl, ID, 3)

ROD:= regress(Axl, OD,3)

Deeoe byIeife y

IDeveloped by.

Verified by I

Entegy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 21 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 M Sat Aug 09 11:44:49 AM 2003 Developed by:

Verified by:

IDeveloped by.

Verified by I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 21 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPfength = 1.455 1.5 U

j, 0

0.5

-0.5 0 Ei 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCPWSCC Operating Time {years}

ntergy Model 2

z c

Co U

CS C

1.5 1

0.5 Increase in Half Length

_ I

__I I

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 21 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 r-r.)

C)

C)

Cj:

200 100

:

-H. ---, ----

-

v 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 IDeveloped by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 21 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC TWCpwsccj6 =

-1.027C'(j,6)

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027

-1.027 TWCpWSCC(j 7) =

5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 TwcpwscCj( 8) =

2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 Developed by:

Verified by:

lIDeveloped by.

Vietified by: I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 21 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 50

.3 0 8-10 1 0

-1 0 0

1 2

3 4

D is ta n c e fro m N o z z le B o tto m (in c h }

6 -

=

OD Surface SIF IDSurfaceSIF Average SF 0.

4-v 4,

e 2 S 5I ~

.2 -,

0 1

2 Operating Time {years}

3 4

IDeveloped by:

Verified by:

Entergy Operadons Inc.

Cenral Engineering Programs Appendix "C"; Attachment 21 Page 10 of 10 Engineering Report M-EP-2003-002-01 I

0.5 -

0.3 -

0.1

.0.1 -

-0.3 -

-0.5 -

a 1

2 O perating Tim e (years) 3 4

Developed by:

Verified by:

IDeveloped by.

Verified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 22 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. 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 -"49" Degree Nozzle, Downhill 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.

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 gowing flaw. This is fined 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 := 1.889 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by:

Vea ried by:

J. S. Brihmadesam B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 22 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 him. := 1500 T := 604 aOC, := 2.67 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)

Initial Flaw Depth (Minimum Detecteble Depth was 5% 1W)

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 id Rid T=

t Ro - Rid t

Rm:=Rid+ 2 Timopr= Years-365-24 C~inr :=1.417I105 Timopr Cblkr:= -

hlim,

im, Pmtblk :

50 L

co:

-~

Rm Rt:=-t

[

g (1

C 1. 103 IC 3 T+459.67 Tref+459.67 j C0 1 e-.

,ao Temperature Correction for Coefficient Alpha Co:= Co1 75 t percentile MRP-55 Revision 1 Developed by:

J. S. Brihmadesam Veriffed by:

B. C. Gray

Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 22 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 "0" = Axial distance from minimum to maximum recorded on data sheet (inches)

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

Cloumn "2" = Quarter Thkkness 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

5 0

0

-28.32

-18.3

-12.16

-6.2

-0.02 1

0.35

-18.79

-12.49

-6.61

-1.37 3.65 2

0.63

-17.84

-10.52

-4.41

-0.48 2.08 3

0.85

-20.52

-12.97

-5.9

-0.87

-1.54 4

1.03

-19.66

-11.83

-5.29 0.23 1.46 5

1.18

-17.2

-10.59

-0.52 16.33 21.02 6

1.29

-8.02

-2.2 10.46 32.66 37.29 7

1.44 4.78 9.56 24.9 38.18 54.09 8

1.59 13.25 18.57 35.28 52.81 66.52 9

1.74 16 22.02 39.19 62.95 75 10 1.891 15.86 23.14 40.23 64.33 74.87 AXLen:= AllData(O)

IDAII:= AIIData(l)

ODAII = AllData(5)

Stress Distribution (J

(j

-50 o 0.5 ID Distribution OD Distribution I

1.5 2

2.5 3

3.5 Axial Elevation above Bottom [inch]

Developed by:

J. S. Bdhmadesam Verifed by.

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 22 Page 4 of 11 Engineering Report M-EP-2003.002-01 Observing the stress distribution select the region in the table above labeled DataAlU 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 WMatrix" 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 0.35 0.63 0.854 1.034 1.178 1.293 1.442 1.591 1.74 1.889

-28.324

-18.794

-17.838

-20.517

-19.663

-17.203

-8.023 4.778 13.252 16.001 15.857

-18.299

-12.495

-10.518

-12.968

-11.831

-10.587

-2.205 9.557 18.569 22.017 23.14

-12.16

-6.607

-4.407

-5.902

-5.288

-0.515 10.461 24.903 35.278 39.194 40.235

-6.201

-1.366

-0.477

-0.874 0.227 16.326 32.658 38.177 52.808 62.945 64.335

-0.021) 3.655 2.08

-1.536 1.46 21.019 37.289 54.089 66.517 75.001 74.874 )

AxI := Data(0)

MD:= Data(3)

ID:= Data(l)

TQ :=Data~~

QT := Data OD := Data~~

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)

Developedby:

J. S. Bdhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 22 Page 5 of 11 Engineering Report M-EP-2003-002-01 FL Cntr :=

Refpoint - co if Val = I Flaw center Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + cO otherwise ULStrs.Dist - UTip UTip FLCntr + C0 IfCStrs.avg -

20 No User Input is required beyond this Point nSat Aug 09 10:59:39AM 2003 Developed by:V J. S. Bnhmadesam Venfied by B. C Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 22 Page 6 of 11 Engineering Report M-EP-2003-002-01 Propkength = 0.185 Flaw Growth in Depth Direction 0.6 ur-

.X!:

ZL (U

in I

8 9

Li.

0.4 0.2 0 _

0.5 1

1.5 2

2.5 3

3.5 Operating Time {years}

4 2

C C

i-0 0

I I

I I

I I

I I

I I

I I

I I

-1 SI 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

I Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 22 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 8

I I

I I

I I

I 0

C

.=7

'~S 0

>a Cn_

Cd 7

6 5

4 _

3 I

I I

I I

I I

2 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 Veri fed by.

B. C. Gray

Entergy Operations Inc.

Centra I Engineering Programs Appendix "C"; Attachment 22 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.I 0.9 C.

0 C.)

C 0.8 1 0.7 0.6 0.5 0.4

.....I.........................................................0........................................................................................................ I....................................................................................

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

0.3 0.2 0.1 0

0 0.5 I

I.5 2

2 Operating time {years}

2.5 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 C

Entergy Operations Inc.

Central Engineering Programs CGRsambi(k 8)

H1.03 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 22 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi (k, 6) 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 CGRsambi(k,5) 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 Developed by:

J. S. Brihmadesam Verfiedby:

S. C. Gray

Entergy Operations Inc.

Centra I Engineering Programs 6 0 Appendix "C"; Attachment 22 Page 10 of 11 Engineering Report M-EP-2003-002-01 I

I i

8X 40 20 0

-2 0

-4 0 Axial Distance From Nozzle Bottom (inch}

0.07 -

0.06 -

0 0.5 T0.04 -

0.03 0 02 0

I 2

0 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 22 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 Z

0.3 -

6 0.1 -

E I

(.3 2.-

IXI

, 2.7 2.8 -

!o 2.5 -

it 2.46 0

I 2

O perating Time (years) 3 4

2.3 -

0 I

2 O perating Time (years) 3 4

Developed by:

J. S. Brihmadesam Verified by.

B. C Gray C.

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 23 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. 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 -"49" Degree Nozzle, Uphill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 tih Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmft" - 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 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 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 flaw 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 filet weld leg.

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

ULStrs.Dist := 6.628 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by:

J. S. 81fhmadesam Verifed by.

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 23 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 aOC := 2.67 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 Rid := id Rid :

t:= Ro-Rid Rm := Rid+

Timopr:= Years-365-24 CFihr := 1.417 105 Timopr hjim hu= l Prntblk :=

50 L

Rm Rt :=-

_Q

-g I(

l l

L 03 T+459.67 Tref+459.67)

Co:= C0 1

)a00C Temperature Correction for Coefficient Alpha 75 t percentile MRP-55 Revision 1 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Ina Central Engineering Programs Appendix "C"; Attachment 23 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 minimum to maximum recorded on data sheet (inches)

Column "I" = ID Stress data at each Elevation (kso-Cloumn "2n = Quarter Thickness Stress data at each Elevation (ksi)

Cloumn "3" = Mid Thickness Stress data at each Elevation (ksl)

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

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

AllData :=

0 3

4 5

0 o

-20.18

-11.45

-5.94

-1.16 3.7 1

1.79

-3.02

-4.38

-5.44

-5.51

-5.34 2

3.23 9.4 12.13

-0.26

-12.62

-20.23 3

4.38 25.65 24.71 14.58

-15.3

-25.69 04 5.3 36.18 33.79 26.29

-5.92

-24.31 5

6.04 38.11 35.03 31.43 21.21 8.83 6.63 42.19 38.1 36.25 40.68 36.41 7

6.76 45.07 42.22 42.74 47.55 44.23 8

6.9 44.97 43.61 46.01 49.99 48.8 f 9 7.03 44.7 44.12 47.02 51.04 54.11 AXLen:= AlIData(0)

IDAHI:= AllData(1)

ODAII:= AllData)

Stress Distribution inM

,4 (A

B V) 100 I

I 1.544 50_

-50 1

2 0

1 2

ID Distribution OD Distribution 3

4 5

6 7

8 Axial Elevation above Bottom [inch]

9 Developed by.

J. S. Biffhmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 23 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. 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 1.792 3.228 4.378 5.299 6.037 6.628 6.764 6.899

-20.175

-3.024 9.398 25.65 36.179 38.106 42.186 45.067 44.968

-11.45

-4.378 12.134 24.71 33.787 35.028 38.102 42.217 43.606

-5.94

-5.443

-0.258 14.577 26.287 31.43 36.248 42.736 46.007

-1.163

-5.511

-12.622

-15.299

-5.925 21.215 40.684 47.553 49.995 3.704 '

-5.341

-20.232

-25.689

-24.306 8.834 36.405 44.235 48.803 )

AA := Data(°)

MD:= Data ID:= Data(')

TQ := Data(4)

QT := Data(2)

OD:

Data(5)

RID := regress(Axl,ID,3)

RQT:= regress(Axl,QT,3)

ROD:= regress(Axl, OD, 3)

RMD := regress(Axl,MD, 3)

RTO:= regress(Ax1,TQ,3)

Developed by:

J. S. Buihmadesam Verified by:

B. C. Gray

Entergy Operations Ina Central Engineering Programs Appendix "C"; Attachment 23 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLcntr = I Refpoint - co if Val = 1 Flaw center Location above Nozzle Bottom if Val = 2

+ co otherwise UTip := FLCntr + Co Incstrs.avg :ULStrs.Dist - UTip 20 No User Input is required beyond this Point g Sat Aug 09 10:59:39 AM Developed by:

J. S. Bdhmnadesam ZuLrj Verifed by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 23 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 4.924 Flaw Growth in Depth Direction I

I I

I I

I I

0.6

.5 Q.

CD In 0.4 _

0.2 -

I I

I I

I o -o 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

'.)_

-oo 2

A I

I I

I I

I

-L 0

0.5 l

1.5 2

2.5 3

3.5 4

Operating Time {years}

Developed by.:

J. S. Bnhmadesam Velfifed by:

B. C. Graw

Entergy Operations Inc.

Central Engmeering Programs Appendix "C"; Attachment 23 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors I

I I

I I

I i

8 0~

I-._

0

.0 Cx

.E an 4

0 l

l l

l l

1 1

-2 &I 0.5 I

1.5 2

Operating Time 2.5

{years}

3 3.5 4

Depth Point Surface Point Developed by.

J. S. Blhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc.

CentralI Engineering Programs Appendix "C"; Attachment 23 Page 8 of 1 1 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9

.2 C

0 C

(L 0.8 0.7 0.6 0.5 0.4

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

-.-............... i- ----------- 1-1--........................................................... ----------------------............................................

0.3 0.2 0.1 0t0 I-----------------------------------------------------------------------------------------------------------------------------

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

0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

Il"- Tip -- Uniform Via - Tip -- Linear Ia"t - Tip -- Quadratic Ia"1 - Tip -- Cubic ti"- Tip -- Uniform t"cv-Tip -- Linear ti"- Tip -- Quadratic Vi"- Tip -- Cubic Developed by:,

J. S. *5lihmadesam 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 23 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi (k, 6)

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99

-1.99 CGRsambi(k 5)

(1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612

-1.612 Developed by:

J. S. Brihmadesam Verfied by:

S. C. Gray

Entergy Operations Inc.

Central Engineering Programs 6 0 -I 4 0 -

Appendix "C"; Attachment 23 Page 10of 11 Engineering Report M-EP-2003-002-01 I

PE 20 0

-2 0

-4 0 3

5 Axial Distance From Nozzle Bottom (inch}

0.0 7

0. 005 00 04.0 C-)

0 03 0.02 2

3 0 p e ratin g T imea

( yeaa rs Developed by.

J. 5. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 23 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 2

0.3 2

c 0.1 6

E

_ -0.1 2

T O) -0.3

-0.5

-1.6 c

1.7

.S 8

n19

§-I.8 tI I.

-1.9 0

1 2

O peara tin g T im e (yea ars )

4 3

I S IF D ephPon l

S IF S ura ce' P o in I

-2.0 -

I 0

I 2

O perating Time (years) 3 4

Developed by:

J. S. Brihmadesam Verified by:

S. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 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. Brihmnadesom 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 -"49" Degree Nozzle, Uphill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rrlt" -- 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 flow and for a growing flaw. This is defined as the reference point. Enter a number (1nch) 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 con 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.9. Weld bottom )

This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 6.628 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 24 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 him = 1500 T := 604 aOc := 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

~*2 Rid := id Rid:

2 t = Ro - Rid t

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

1lim, Pmtbik 5=

l0 L

2 Rm Rt:=-t C

.03 lo-3

+459.67 Tref+459.67 Co:= C0 1

  • ca0c Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Blihmadesam Venified by B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 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 "0" = Axial distance from minumum to maximum recorded on data sheet(inches)

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

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

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

Column w4" = Three Quarter Thickness Stress data at each Elevatfon (ksi)

Column A5" = OD Stress data at each Elevation (ksi)

AllData :=

0 1

2 3

4 5

0 0

-20.18

-11.45

-5.94

-1.16 3.7 1

1.79

-3.02

-4.38

-5.44

-5.51

-5.34 2

3.23 9.4 12.13

-0.26

-12.62

-20.23 3

4.38 25.65 24.71 14.58

-15.3

-25.69 4

5.3 36.18 33.79 26.29

-5.92

-24.31 5

6.04 38.11 35.03 31.43 21.21 8.83 6

6.63 42.19 38.1 36.25 40.68 36.41 7

6.76 45.07 42.22 42.74 47.55 44.23 8

6.9 44.97 43.61 46.01 49.99 48.8 9

7.03 44.7 44.12 47.02 51.04 54.11 10 7.17 43.72 43.97 47.64 50.17 54.17 AXLen := AllData(°)

IDAII:= A11DatP) 0DA11 := A1lData,()

Stress Distribution 100 Un IDAUI ODAIl 50 0

-50 "0 1

2 3

4 5

6 7

8 9

AXLen Axial Elevation above Bottom [inch]

Developed by:

J. S. Bnihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 4 of 11 Engineering Report M-EP-2003.002-01 Observing the stress distribution select the region in the table above labeled DafaAH that represents the region of Interest This needs to be done especially for distributions that have a large compressnWe 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 sym'bol).

0

-20.175 -11.45 -5.94

-1.163 3.704 1.792

-3.024

-4.378 -5.443

-5.511

-5.341 3.228 9.398 12.134 -0.258 -12.622 -20.232 4.378 25.65 24.71 14.577 -15.299 -25.689 5.299 36.179 33.787 26.287

-5.925

-24.306 Data 6.037 38.106 35.028 31.43 21.215 8.834 6.628 42.186 38.102 36.248 40.684 36.405 6.764 45.067 42.217 42.736 47.553 44.235 6.899 44.968 43.606 46.007 49.995 48.803 7.035 44.695 44.12 47.021 51.043 54.113 7.17 43.723 43.973 47.639 50.172 54.17 )

AxI :- Data(0)

(3)

MD: Data ID := Data(')

TQ := DataP4)

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 = Refp;t -co if Val = i Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise UTi. := FL

+

IncStrsUav

=

StrS.Dist - UTip Tn,

~Cntr IflCOrsaA Developed by:

J. S. B6Jhmadesam Verifed by:

B. C. Gray

d Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point tb Sat Aug 09 10:21:18 AM 2003 Developed by:

J. S. Baihmadesam Verifled by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 6 of 11 Engineering Report M-EP-2003-002-01 PrOPLength 4.924 Flaw Growth in Depth Direction I

l l

l l

0.6 0r-9I-.-

1:5 a0

'520 LT

0.4 _

0.2 0

Q tb 0

0.8 0.6 0.4 0.2 0

0.5 1

1.5 2

2.5 3

3.5 Operating Time {years}

Entergy-CEP Model I

I I

I 1'5 I

I i

I I

I I

0 4

0 0 0.5 I

1.5 2

Operating Time 2.5

{years}

3 3.5 4

Entergy-CEP Model Developed by:

J. S. Bnhmadesam Veffifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 7 of 11 Engineering Report M-EP-2003-002-01 2_

._~

Car

'A_

U:

V)

Lo V:

Stress Intensity Factors 80 1

l 60-40-20-0-

- -LU 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 Verified by:

B. C. Gray C, t~ 1) e

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 v) 0-0cV) 0 0

C U

0.6 0.5 0.4 0.3 0.2 0.1 0

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

0 0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniform Ia" - Tip -- Linear va" - Tip -- Quadratic "a" - Tip -- Cubic i"c" - Tip -- Uniform

.,....."c'

- Tip -- Linear

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

J. S. Blihmadesam Verified by:

B. C. Gray C7 4-t

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 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)

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776

-0.776 CGRsambi(k,5)

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013

-1.013 Developedby:

J. S. Bnthmadesam Venfled by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs 60-

[

4 0 -

40

~' 2 0-A>

sc, X 0

-2 0- Appendix "C'; Attachment 24 Page 10of 11 Engineering Report M-EP-2003-002M1 3

5 7

9 Distance from Nozzle Bottom (inches) 0.5 0.3 1

0.1 0

i-0 1 2

(.3

-0 3 0

1 2

o p e ra tin g T im eye a rs }

3 4

Developed by:

J. S. Brilimadesam Verified by:

B. C. Gray C1W

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5

0. 3 I

-0 1 -

tri

!-O

.5 2

-0.

-0.53 0

I 2

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

3 4

i i

S_ u rfa ce Po in t ("c"-tip )

Depth Point {"a"- tip} I

-0.80 -

F 1 -0.85 -

I-0.90 -

05

-0.95 -

a2

-1.00 -

0 1

2 Opareratin g Tim e (yea rs) 3 4

Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray C.L

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 25 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Progrants, Entergy Operations Inc bevelopedby: J. S. Brihmadesom Verified by: B. C. Gray Note: Only for use when RP,W,/t Is between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Modell
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 -"49"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 inch/hr.

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

The t/,ro'hwall flaw 't4per 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:= 6.628 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

I IDeveloped by:

Verified by:

Entergy Operatons Inc.

Central Engineenng Programs Appendix "C"; Attachment 25 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :

L := 0.25 od := 4.05 id:= 2.728 Plnt:= 2.235 Years:= 4 Ilim:= 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 Trf:= 617

-Qg

.(

I I I

.103 10-3 T+459.67 Tref+459.67)J Co := e

.aoc 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 Tirnopr:= Years-365-24 Ro:= od 2

id 2

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

2 CFinhr:= 1.417-105 Cbk=Timlopr Cb lk'ur Prntblk:= l-I L

2 Developed by:

Verified by:

IDeveloped by Verified by. I

Entergy Operations Inc.

Central Engineenng Programs Appendix "Cm; Attachment 25 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 "0o = 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.=

U r

r r

I 5

I



I I

2 4

5

°0 1

  • 2 3
4=

5 0

0

-20.18

-11.45

-5.94

-1.16 3.7 1

1.79

-3.02

-4.38

-5.44

-5.51

-5.34 2

3.23 9.4 12.13

-0.26

-12.62

-20.23 3

4.38 25.65 24.71 14.58

-15.3

-25.69

! 4 5.3 36.18 33.79 26.29

-5.92

-24.31

-5

~

6.04 38.11 35.03 31.43 21.21 8.83

,6 6.63 42.19 38.1 36.25 40.68 36.41

.7 6.76 45.07 42.22 42.74 47.55 44.23

=8 6.9 44.97 43.61 46.01 49.99 48.8 9

7.03 44.7 44.12 47.02 51.04 54.11 10 7.17 43.72 43.97 47.64 50.17 54.17 11 7.31 42.93 43.82 47.52 52.33 56.55 AIiAxl:= DataAll i AIMUD DataAlII AlIOD:= DataAIt a Developed by:

Verified by:

lIDeveloped by.

Veeled by.:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 25 Page4of10 Engineering Report M-EP-2003-002-01 100 1.291044 25 50 2

5 0

1 2

3 4

5 6

7 8

9 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

-20.175 1.792 -3.024 3.228 9.398 4.378 25.65 5.299 36.179 6.037 38.106 6.628 42.186 6.764 45.067 6.899 44.968 7.035 44.695 7.17 43.723 7.305 42.926

-11.45

-4.378 12.134 24.71 33.787 35.028 38.102 42.217 43.606 44.12 43.973 43.816

-5.443 -5.511

-5.341

-0.258 -12.622 -20.232 14.577 -15.299 -25.689 26.287 -5.925 31.43 21.215 36.248 40.684 42.736 47.553 46.007 49.995 47.021 51.043 47.639 50.172

-24.306 8.834 36.405 44.235 48.803 54.113 54.17

-5.94

-1.163 3.704 )

47.515 52.325 56.546 )

Axl:= Data° ID:= Data (5)

OD:=Data RID := regress(Axl, ID,3)

ROD:= regress(Axl, OD,3)

De eoeiy Vrfe y

IDeveloped by:

Verified by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 25 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:

BZ - I Flaw Center above Nozzle Bottom Inctr~ag = ULStrs.Dist - BZ ICStrs.avg :=

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

Verified by:

IDeveloped by Verified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 25 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 5.084 Flaw Length vs. Time 1.5 z

by TWCpWscc 3

j,3 c:

l

-LS

.16 0.5 l

I

-0.5 0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCPWSCC(

I )

Operating Time (years)

Entergy Model z

U 1.

Increase in Half Length 2

i 5

I 5

0.

U0 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 25 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 ar.

a 200 cn co e;

100 v)

Cn 0 0

0.5 I

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:

lIDeveloped by Verified by: I

,~~~~

c LL73

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 25 Page 8 of 10 Engineering Report M-EP-2003-002-01

,6)

TWCPWSCC(j 7) =

4.119 4.119

-4.119

-4.119

-4.119

-4.119

-4.119

-4.119 4.119 4.119 4.119

-4.119

-4.119

-4.119 4.1 19

-4.119 Twcpwscc(j 8) =

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952

-2.952 Developed by:

Verified by:

lIDeveloped by:

Vefifed by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 25 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot 60 40 65 e

0

-2 0

-4 0

-1.7 -

3 5

7 Distance from Nozzle Bottom (inch)

O D S u rfa ce S IF ID S u rfa c e S IF A v e ra g e S IF 60-

-2.2

- -2.7

.e i

-3.2 A -3.7

-4.2 2 -

0 1

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

3 4

Developed by:

Verified by:

C-'I -

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 25 Page 10 of 10 Engineering Report M-EP-2003-002-01 I

0.5 -

0.3 0.1 -

.0.1 -

.3

-0.5 - _

0 I

2 0 perating Time (years) 3 4

Developed by:

Verified by:

IDeveloped by.

Venfied by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 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. 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 -"49" 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:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

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

ID Surface Flaw 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 evalute 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 elevtion measured upward from the no2zle 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 flaw 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 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 nozzk bottom) below.

ULStrs.Dist := 4.034 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).

Developed by:

J. S. Elhmadesam Veniried by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 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 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 R.

2 id Rid T=

t = Ro -Rid t

Rm : Rid+2 Tirnopr= Years-365-24 CFinhr:= 1.417-105 Timopr fimrn Prntblk 0=

li L

Co0

-~

Rm Rt:

1.103 l T+459.67 Tref+459.67)

Co:

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

J. S. Bnhmadesam Verffled by.-

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 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 "0o = 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 (kst)

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

Column '4" = Three quarter Thickness Stress data at each Elevation (kso Column "5" = OD Stress data at each Elevation (ksi)

AllData :=

0 1

2 3

4 5

0 0

17.35 8.19 2.28

-3.06

-8.64 1

1.09 6.89 1.47

-2.22

-5.44

-7.2 2-1.96 5.78 2.36 0.75

-0.95

-3.23 3

2.66 10.29 7.15 5.32 3.43 0.49 4

3.23 12.24 7.03 6.83 7.24 5.95 5

3.67 6.58 4.66 5.87 12.45 16.38 6

4.03

-5.62

-1.3 4.18 17.86 24.28 7

4.18

-12.25

-6.01 2.74 20.52 31.88 8

4.32

-15.64

-9.13 2.2 21.5 30.45 9

4.46

-18.61

-11.79 1.32 20.22 30.79 AXLen := AllData(0)

IDA11:= A11Data(')

ODAl1:= AllData(5)

Stress Distribution 40 20 0

I I

~~~I I'

LJ44 4.,~

I I

I.

I I

I I

I!.

-20

-40 DI 0.5 1

1.5 2

2.5 3

3.5 4

Axial Elevation above Bottom [inch]

4.5 5

5.5 6

ID Distribution

~----

OD Distribution Developed by:

J. S Brihmadesam Verifed by:

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 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. 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 1.091 1.964 2.664 3.225 3.674 4.034 4.176 4.317 17.354 6.892 5.781 10.289 12.243 6.579

-5.621

-12.251

-15.641 8.186 1.47 2.359 7.148 7.028 4.659

-1.296

-6.006

-9.131 2.284

-2.224 0.754 5.324 6.829 5.865 4.184 2.741 2.2

-3.064

-5.444

-0.955 3.428 7.244 12.453 17.859 20.517 21.496

-8.637)

-7.199

-3.232 0.494 5.952 16.377 24.278 31.88 30.446 )

Axi := Data(0)

(3)

MD:

Data/

ID:= Dataei)

TQ := Data(4)

QT := Data(2)

(5)

OD:= Data RID := regress(Axl,ID,3)

RQT:= regress(Ax1,QT,3)

ROD:= regress(Axl, OD, 3)

RMD := regress(Axl, MD, 3)

RTO:= regress(Axl,TQ,3)

Developed by:

J. S. Bnhmadesam Vedried by B. C Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 Page 5 of 11 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 Incstrsav ULStrs.Dist - UTip IflC~tj.~*a~g20 No User Input is required beyond this Point n Sat Aug 09 10:59:39 AM 2003-Developed by J. S. Bnhmadesam Verified by:

S. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProLength = 2.33 Flaw Growth in Depth Direction I

I I

I 0.6 u

0.

0 I-a 2

B.d 0.4 _

0.2 _

u Z-03 13 lo 1

I 1

1 I

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

2 0

11 I

1 I

I 0

0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Developed by-J. S. Bahmadesam Venired by:-

B. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 Page 7 of 11 Engineering Report M-EP-2003-002-01 8

U 4-.

(12 7

6 5

4 3

Stress Intensity Factors I

I I

I III I

I I

I III 2 0 0.5 I

1.5 2

Operating Time 2.5 (years) 3 3.5 4

Depth Point Surface Point De veloped by-,

J. S. Blihmadesam Venrifed by:-

S. C. Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9 r-cj 0

.°)

r-c E

U

._i 0

U U

fr-U c) c-0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 I*

(I -

0 0.5 l

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniform fa" - Tip -- Linear "a" - Tip -- Quadratic f"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 II-I

Entergy Operations Inc.

Central Engineering Programs CGP-sambi(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 26 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGP-sambi(k, 6) 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 CGRsambi(k,,)

2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 Developedby J. S. Bnhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc.

Centra I Engineering Programs Appendix "C"; Attachment 26 Page 10 of 11 Engineering Report M-EP-2003-002-01 O D Hoop Strss ID H oo p S tres 30 -

Top of Bi

.11.

i 10 -

-1 0

-411111, W Wd Bottom

-3 0 -

0 I

2 3

4 Axial Distance From Nozzle Bottom 5

6 finch) 0.0 7 0.6 o O.0 5 t

0 0 4 0

0 03 -

0.02 - _

0 1

2 0 p e ra tin g T ime

{ye a rs )

l 3

4 Developed by.

J. S. Brihmadesam Verified by:

B. C Gray

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 26 Page 11 of 11 Engineering Report M-EP-2003-002-01 o.s5 -

c0o3 Z*

0 3-i3 j

0 o 1 -

0-o.3 -

I 2.

3.4 -

ci

g 3.2 -

b

-f 3.~O -

Ag 2.8 -

2.6 -

0 I

2 O pera tin g Time (years I 3

4 l

s D epth P oint l

l S IF S f

P o in J 0

1 2

O perating Time a yearsl 3

4 Developed by:

J. 5. Brlhmadesam Verified by:

B. C. Gray C 47~

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 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-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 -"49" 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:- "Rr/t"

- between 1.0 and 300.0 Note: Used the Metric fom, 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 elevfion 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 nifial 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 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 ).

This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 4.034 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 27 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 him := 1500 T := 604 aOC := 2.67 12 Qe := 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 T=

t:= Ro - Rid Rm:= Rd Timopr := Years-365-24 CFihr~u :=.417-105 CbkTirnopr

'tim Pmtblk 0=

sl L

co:

0 Rm t

1J103-10-3 (T+459.67 Tref+459.67)l C0 1 : e-*oc Temperature Correction for Coefficient Alpha Co Coi 75 th percentile MRP-55 Revision 1 Deve/opec/by:

J. S. Bdhmadesam Venirled by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 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)

AllData :=

_.,.0 1

S. 2

-j fl.

3 4

5 O

0 17.35 8.19 2.28

-3.06

-8.64 1

1.09 6.89 1.47

-2.22

-5.44

-7.2 2

1.96 5.78 2.36 0.75

-0.95

-3.23 3

2.66 10.29 7.15 5.32 3.43 0.49 4

3.23 12.24 7.03 6.83 7.24 5.95 5

3.67 6.58 4.66 5.87 12.45 16.38 6

4.03

-5.62

-1.3 4.18 17.86 24.28 7

4.18

-12.25

-6.01 2.74 20.52 31.88 8

4.32

-15.64

-9.13 2.2 21.5 30.45 9

4.46

-18.61

-11.79 1.32 20.22 30.79 10 4.6

-21.26

-13.55 0.57 19.39 32.09 AXLen:= AllData(°)

IDA11:= AlMataK')

0DA11:= A11Data()

Stress Distribution 40 I-co IDAHO ODAII 20 0 -40 -0 1

2 3

4 5

AXLen Axial Elevation above Bottom [inch]

6 Developed by:

J. S. BrShmadesam Veried by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 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 "equaln sign (Shift-Colon) then Insert the same to the right of the Mathcad Equals sign below (paste symbol).

/

A 17 tot I De n

r A _Q o1-\\

U 1 1-50q 0.100 Z.OI

-a.3U0o 1.091 6.892 1.47

-2.224 -5.444 1.964 5.781 2.359 0.754

-0.955 2.664 10.289 7.148 5.324 3.428 3.225 12.243 7.028 6.829 7.244 3.674 6.579 4.659 5.865 12.453

-O.W

) 1

-7.199

-3.232 0.494 5.952 16.377 24.278 31.88 30.446 30.786 Data :=

4.034

-5.621 4.176 -12.251 4.317 -15.641

-1.296 4.184 17.859

-6.006 2.741 20.517

-9.131 2.2 21.496 4.459 -18.614 -11.785 4.601 -21.257 -13.548 1.319 20.216 0.574 19.393 32.088 )

AxI := Data(O)

(3)

MD: Data ID := Data()

TQ :=Data(4)

QT := Data(2)

OD:= Data(5)

RID := regress(Axl, ID, 3)

RQT := regress(Axl, QT, 3)

ROD:= regress(Axl,OD,3)

RMD := regress(Axl, MD, 3)

RTQ := regress(Axl, TQ, 3)

FLCntr Refpoint - c0 if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c0 otherwise UTiP := FLCntr + c0 Developed by:

J. S. Brihmadesam InlcStrs~avR

_ ULStrs.Dist - UTip

.-~~1 Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 5 of 11 Engineering Report M-EP-2003-002-01 v

No User Input is required beyond this Point n Sat Aug 09 10:21:18 AM ?nn, Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 2.33 0.6 I-,

a r-0.4 _

Flaw Growth in Depth Direction I

I I

I I

I I

I I

III 0.2 [

o 0 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

Entergy-CEP Model u

V..

0b 0.8 t-0.6 1-I I

I I

I I

I1 011IIIIII II I

I 0

1 i

I I

I I

0.41-0.2 I-0oL 0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by:

J. S. Bnhmadesam Verfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 7 of 11 Engineering Report M-EP-2003-002-01 Q

0 0

a,)

(7 W-41 r-cn 80 60 40 20 0

-20 Stress Intensity Factors I

I I

I I

I~ -

-- -l l-l-

l

- -I 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. Brihmadesam Verified by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw

'A 0

C 0

vL) 0c

._A a

V C

C-0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

..........1................................

...I.........b...................................................

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

-"a"

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

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

J. S. BrIhmadesam Verified by:

B. C. Gray C,

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 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)

-1 939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939

-1.939 CGRsambi (k,5)

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233

-1.233 Developed by:

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 10 of 11 Engineering Report M-EP-2003-002-01 30 10 I1

-1 0

-30 0 5 I

I

=

ID D istrib u tio n 0 D Dis trib u tio11 5OtOfl

nI W eld Top of B lin d Z ne I

I r

I I

I T

7 0

1 2

3 4

5 6

Distance from Nozzle Bottom (inches) 0,

I

-0.

-r I

i

-0.1 2

(>0

-O 0

I 2

O peara tin g T im e (yea ars )

3 4

Developed by.

J. S. BrIhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 -

0.3 -

-S i

-0 1 -

C) -0.3 -

-0.5 l

0 1

2 o

p e ra tin g T im e fy a a rs j 3

4

-1.2 -

c -1.4 rn 2;

tU. -1.6 -

C

-a1

-2.0 -

Surface Point {c"-tip} I I -

Depth Point {'a"- tip} [

0 I

2 Opaeratin g Timea (years I 3

4 Developed by:V J. S. BSnhmadesam.CG Verified by.

B. C. Gray

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