ML032790033

From kanterella
Jump to navigation Jump to search
Rev. 1 to Engineering Report M-EP-2003-002, Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack Growth Un-Inspected Regions of the Control Element..., Appendix C, Attachments 38-46
ML032790033
Person / Time
Site: Arkansas Nuclear Entergy icon.png
Issue date: 08/26/2003
From:
Entergy Operations
To:
Document Control Desk, Office of Nuclear Reactor Regulation
References
CNRO-2003-00033 M-EP-2003-002, Rev. 1
Download: ML032790033 (95)
v • d • e


Text

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw beveloped by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmodesom Verified by: B. C. Gray Note : Only for use when Ros/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 -"49"Degree Nozzle, 45 degree from Downhill Azimuth, Augmented Analysis I

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 inchchr.

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

The throughwall flaw uVpper Tip" is located at the Reference Line.

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

BZ:= 1.544 This is the as-built blind zone location The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. Thi is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzk bottom) below.

ULStrs.Dist := 2.1632 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Developed by:

Verified by:

IDeveloped by.

Verffled by. I

Entergy Operations Inc.

Cental Engineering Programs Appendix "C"; Attachment 38 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 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

Tube OD Tube ID Design Operating Pressure (internal)

Number of Operating Years Irim:= 1500 T := 604 v := 0.307 Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F aOc:= 2.67-I0 12 Qg:= 31.0 Turf := 617 1.103 10 Q

T+459.67 Tf+459.67) ao Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)

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

Ri:= id t := RP - Ri Rm:= Ri + 2 2

CFinh,:= 1.417-1 05 Cbk=Tir%pr Cblk 'ur Prntblk:= l-50"m I

L 2

lDeveloped by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 38 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 "I" = ID Stress data at each Elevation (ksi)

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

DataAIl :=

0

° 1

2 3

4 5

O 0

-0.41

-1.36

-1.84

-2.37

-3.16 1

0.58

-1.26

-1.49

-1.71

-1.95

-2.07 2

1.05

-1.02

-0.22 0.35 0.52

-0.5 3

1.43

-1.56 0.62 2.58 4.9 4.26 4

1.73 4.17 4.31 8.86 13.38 15.25

5 1.97 16.26 12.54 16.93 28.26 32.67 6

2.16 21.13 17.13 20.09 34.28 36.98 7 -

2.31 21.59 19.09 21.93 34.05 41.72 8

2.46 17.7 17.82 22.18 34.47 41.21 9

2.6 10.69 14.25 21.11 33.32 39.55 AIIAxli=Data 11II MD=DataAIIW (5)

All0D= DataAII Developed by:

Verified by:~~~

IDeveloped by.,

Verified by. I

Entergy Operatfons Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 4 of 10 Engineering Report M-EP-2003-002-01 50 40 A.

In U

30 20 10

-101 I0 0.5 1

1.5 2

2.5 3

3.5 4

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).

( 0

-0.414 -1.359 -1.842 -2.369 -3.157) 0.585 -1.256 -1.488 -1.714 -1.95

-2.073 1.053 -1.023 -0.223 0.347 0.516

-0.495 1.429 -1.559 0.622 2.583 4.895 4.258 Data:= 1 1.729 4.165 4.315 8.86 13.38 15.252 1.97 16.258 12.541 16.926 28.26 32.667 2.163 21.131 17.131 20.087 34.279 36.98 2.31 21.593 19.093 21.933 34.049 41.718

( 2.457 17.702 17.82 22.18 34.468 41.213)

Axl:= Data (P

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

ROD:= regress(Axi, OD, 3)

IDeveloped by.

Verified by. I De eo e by eife y

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ IflCStrs.avg :=

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

Verified by I Developed by:

Verified by:

Entergy Operadons Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 0.619 Flaw Length vs. Time 1.5

.619 X TwC1~

j,3 0

0 I

0.5 0

-0.5 )0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCpwsc(j I)

Operating Time {years}

Entergy Model Increase in Half Length 2

C.)

tb C.)

1.5 I

0.5 0 0 0.5 I

1.5 2

2.5 Operating Time (Years) 3 3.5 4

l e eo e y V rfe y

IDeveloped by-Verffied by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 t~

Cd C,,

0 ri.

200 I 100 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 IDeveloped by:

Verified by:

Entergy Operatfons Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 8 of 10 Engineering Report M-EP-2003-002-01 Twc~~~~~~~~~~~~~~~~~~~~~~~~~~~~

TWCPWSC'(j,6) =

7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 7.444 TWCpwscc(j,7) =

3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 3.789 TwcpwscC(

8) 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 5.648 lDeveloped by:

Verified by:.

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P to t 40 3 0 2 0 10 0

-1 0 2

3 D is tl n c e fro m N o z z le B o tto m I in c h }

l o0 D S u rfa c e S IF ID S u rface S IF I

A v e ra g e S IF 7

6 a

St j5 4

3 0

1 2

O.p e ratin g T im e (y anrs l

3 4

IDeveloped by:

Verified by:

I C(oZ-

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 38 Page 10 of 10 Engineering Report M-EP-2003-002-01 I

0.5 0.3 0.1

-0.1 No.3

-0.5 0

I 2

O perating Time*

(years) 3 4

lDeveloped by:

Verified by:.

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programns, Entergy Operations Inc bevelopedby: J. S. Brihrnadesom 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 -'0" Degree Nozzle, All Azimuth, Augmented Analysis 1.26" 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 forn of the equation from EPRI MRP 55-Rev. 1.

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

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 := 1.25 This is the reduced blind zone; providing a propagation length of 0.386 inch; freespan length is 0.546 inch To place the flow with repsect to the reference point, the flaw tips and center can be located as follows:

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

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

3) The lower "T-tipI located at the reference point (Enter 3).

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

This is the levation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.796 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

v J. S. Blihmadesam Veffied by B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 39 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 (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 id Rid T=

t:= Ro - Rid Rm:= Rid +

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

50 L

C0 2 Rt :=-R C0

.103 3

l aOc Temperature Correction for Coefficient Alpha Co:= C01 Stress InDut Data 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Brihmadesam Veiffied by B. C Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data In the table below. The column designations are as follows:

Column "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 l

° 1

l 2

3 4

5 0

0

-25.09

-27.55

-27.79

-25.62

-23.76 1

0.49

-0.56

-0.54

-2.11

-4.85

-6.16 2

0.87 21.52 18.64 17.12 14.84 10.09 3

1.19 32.75 28.49 24.14 19.64 14.45 4

1.44 35.67 29.6 26.17 25.59 28.42 5

1.64 34.24 29.57 28.29 35.41 45.38 6

1.8 29.45 29.81 31.39 43.34 61.71 7

1.93 23.67 26.5 33.26 47.61 64.65 8

2.07 18.93 24.56 33.97 49.07 65.88 9_

2.2 16.54 22.85 34.79 49.52 62.8 AXLen:= A(oData<°)

IDA11:= A11DatP) 0DA11 := AlIData()

Stress Distribution 100 U2._

'A P]

cE IDAII ODAII 50 I I I

II I

1 14$44 1,796 1

I

-I1 I

I I

I I !

0

-50 L-o 0.5 1

1.5 2

2.5 3

AXLen Axial Elevation above Bottom [inch]

Observina the stress distribution select the reaion in the table above labeled Data Al that represents the Seve.oped by.

J. S. Blihmadesam Vedffedtpy..

B. C Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 4 of 11 Engineering Report M-EP-2003-002-01 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

-25.088 -27.546 -27.787 -25.624 -23.763) 0.485

-0.563 0.874 21.515

-0.539

-2.111

-4.851

-6.157 18.635 17.122 14.843 10.089 Data :=

1.186 32.751 28.494 24.136 19.645 14.45 1.436 35.667 29.598 26.166 25.589 28.417 1.635 34.244 29.574 28.286 35.408 45.379 1.796 29.45 29.814 31.385 43.337 61.713 1.932 23.674 26.502 33.261 47.609 64.65 K2.068 18.928 24.564 33.968 49.071 65.876 )

AxI : Data(0)

(3)

MD: Data ID:= Data< )

TQ := Data(4)

QT := Data(2)

(5)

OD:= Data RID := regress(Axl, ID, 3)

RQT:= regress(Axl,QT,3)

ROD:= regress(Axi, OD, 3)

RMD := regress(Axl, MD, 3)

RTQ:= regress(Axl,TQ,3)

FLCntr Refpoint -CO if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c0 otherwise UT.p := FLCntr + co ULStrs.Dist - UTip U~~~ip Cntr

+ CO

~

~

~

~

Il~tis vg20 Developed by:

J... Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 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. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central EVgineerng Programs Appendix "C"; Attachment 39 Page 6 of I 1 Engineering Report M-EP-2003-002-O1 Propkengh =0.386 0.6

_0 0.4 C

0.2 W

Flaw Growth in Depth Direction IIII I

I I

I I I

I I

I I

I I.

0*

A0 0.5 1

1.5 2

2.5 3

3.5 Operating Time {years}

Entergy-CEP Model 4

u CJ U

0 0.

I I

IIIII lt5

.8 _

.6 -

.386

.4 -_--_--__-----

r

.2 -

n~~~~~~~~~~

a 0.

V0 0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

Entergy-CEP Model Developed by:

J. S. Btihrnadesam Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 7 of 11 Engineering Report M-EP-2003.002-01 Stress Intensity Factors

-I-U C

co m

80 60 -

40 20 nU0 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. Blhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 CA 0

0

.)

0 c-c'-

0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 I

1.5 2

2.5 Operating time {years}

3 3.5 4

"a" - Tip -- Uniform ia" - Tip -- Linear ia" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.

J. S. Brihmadesam Verfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 CGRsambi(k 6) 11.641 12.616 12.618 12.621 12.623 12.625 12.628 12.63 12.633 12.635 12.637 12.64 12.642 12.645 12.647 12.649 CGRsambi(k, 5) 8.723 9.389 9.392 9.395 9.398 9.401 9.403 9.406 9.409 9.412 9.415 9.418 9.421 9.424 9.427 9.43 Developed by.

1. S. Brihmadesam Vedried by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 10 of II Engineering Report M-EP-2003-002-01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distnce from Nozzle Bottom (Iches) 0.12 1 0.10 i 0.05 1 0.06.

X 0.04 1 0.02 0.00-0 1

2 Cperstm kih

&arsm) 3

~

4 Developed by:

J S. Bnhmadesam Veniled by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs 0.12-201 0 081 oh 0.0 6 0

0 4 0 0 2 0 0.02 20 18 10 18

§14-1}12-

[

10-Appendix "C"; Attachment 39 Page 11 of 11 Engineering Report M-EP-2003-002-01 2

3 4

O p e ra tin g T im e

{y e a rs )

=

Surface Point (c"-tip)

Depth Point ("a'- tip) 0 1

I 2

3 4

opera~ntilinlle~ 6yearn)

Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray (jQ4J`t

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw beveloped by Central Engineering Programs, Entergy Operations Inc bevelopedby: T. S. Brihmadesom 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, Downhill Azimuth, 1.25" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmt"- 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 (7nch) that represnets the reference point elevation measured upward from the nozzle end.

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

This is the elevation from Nozzle Bottom. Enter this value below ULSrs.Dist := 1.786 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developedby.:

J. S. Blfhrndesam VernTed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 40 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him := 1500 T := 604 aOC := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)

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

Reference Temperature for normalizing Data deg. F R

_ od Rid := id Rid T=

t:= Ro - Rid t

Rm=Rid +

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

-' I him Pmbimk

~~~~~~~Prntblk:=

50l L

0.

2 Rm Rt:=-t J[

(g T

I 6

X Tf Coi := eAL 3 IC rea~

Temperature Correction for Coefficient Alpha Co:= C0 1 Stress InDut Data 75 th percentile MRP-55 Revision 1 Developed by:

J. S. Bnlimadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data In the table below. The column designations are as follows:

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

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

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

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

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

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

AllData :=

0 1

2 3

4 5

0 0

-27.4

-24.36

-22.21

-20.41

-18.98 1_

0.48 0.63

-1.49

-3.6

-4.44

-5.27 2

0.87 17.66 16.42 14.61 12.41 9.38 3

1.18 29.8 26.05 22.72 18.95 14.2 4

1.43 33.62 27.79 24.8 24.32 26.99 5

1.63 32.36 28.47 27.59 34.28 45.1 6

1.79 27.39 28.92 31.39 43.88 63.72 7

1.92 21.5 25.56 33.55 48.09 66.36 8

2.05 16.94 23.79 34.06 49.47 67.67 9

2.18 14.83 22.26 34.78 49.05 63.38 AXLen= AIlData(0)

IDA11:= A11Data.(')

0DA11 := AlIData()

Stress Distribution 100 U)d U)

V)

IDAll ODAll 50 0

-50 _

0.5 1

1.5 2

2.5 AXLen Axial Elevation above Bottom [inch]

3 Developed by:

J. S. Bdhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAH that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection In the above table, click on the 'Data' statement below and delete it from the edit menu. Type 'Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

( 0

-27.404 -24.356 -22.209 -20.407 -18.978)

Data :=

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

-1.486

-3.599

-4.44

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

AAi := Data(O)

MD:= Data(3)

ID:= Data)

TQ :=Data~4)

QT := Data(2)

OD := Data(5)

RID := regress(Axl,ID,3)

RQT:= regress(Axl,QT,3)

ROD:= regress(Axi, OD, 3)

RMD:= regress(Axl, MD, 3)

RTQ:= regress(Axl,TQ,3)

FLcntr:

-C 0 if Val = I Flaw center Location Location above Nozzle Bottom if Val = 2

+ c0 otherwise UTip := FLCntr + Co ULStrsDist - UTip Inlc~st.avg -20 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point

&f Sat Aug 09 10:21:18 AM 2003-Developed by:

J. S. Bnihmnadesam Verified by:

B. C. Gray

Entergy Operations Inc Appendix "C"; Attachment 40 Engineering Report Central Engineering Programs Page 6 of 11 M-EP-2003-002-01 ProPLength = 0.376 Flaw Growth in Depth Direction 0.6 0.4 0.2 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model 1,5 0.8 Th 0.6

.376 0.4 Uz.

0.2 0 0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model Developed by.

Verffied by.

J. S. Bnhmadesam B. C. Gray

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

0 4-V)

U)

S..

80 60 1 I

I I

I I

I I

..-..-. ~ ~ ~

~ ~.-....

r--~~~~~.-.-..-.-..-.

~~~~~~~~

I...-

40 1 20 1 00 0.5 1

1.5 2

2.5 Operating Time 1years}

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

3.5 4

Developedby:

J. S. Bnhmadesam Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw I

0.9 0.8 C.,

0 U

0 "a

0 U

0.7 0.6 0.5 0.4 0.3 0.2 0.I

.._1 0 0 0.5 I

I.5 2

2 Operating time {years}

2.5 3

3.5 4

"a" - Tip -- Uniform "aa" - 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 40 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsabi 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 0.83 CGRsambi(k, 6) 11.395 12.403 12.405 12.408 12.41 12A12 12.415 12.417 12.419 12.422 12.424 12.426 12.429 12.431 12.433 12.436 CGRsambi 8.469 9.162 9.165 9.168 9.171 9.174 9.177 9.18 9.183 9.186 9.189 9.192 9.195 9.198 9.201 9.204 Developed by:

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

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page to of 11 Engineering Report M-EP-2003-002-01 A

i20 I

0.0 0.5 1.0 1.6 2.0 2.5 3.0 Dance *um Nozzle Botny {lnea) 0.10 -

O.O -

X.OB -

I.

004 0.02 0.00-0 1

2 3

4 Operuting Thne bears)

Developed by.,

J. S. Brihmadesam Vedried by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 40 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.10 0 0I8 0.06 c 0.0 2

I!

o 0.04 E 0 02 0.0 0

1 2

3 4

O perating Tim e {years}

20 -

v 18 -

1D I6 c1 6 tC 14 -

1 2 -

I 10 '

8-:

u rfa ce Po in t (" C

!ip)

I SD e p th Po in t {"a..,-t

}

Q 11 o p e ra tng Tme

{y ears )

4 Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray CC)o

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

1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-I 1707; July 1992.
2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, 22.5 dgeree from Downhill Azimuth, 1.30" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t"- between 1.0 and 300.0 Note: Used the Metric fonn of the equation from EPRI MRP 55-Rev. 1.

The correction is applied in the determination of the crack extension to obtain the value in inchlbr.

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 meosured upward from the nozzle end.

Refp0 int := 1.3 This is the reduced blind zone providing a propagation length of 0.347 inch; freespan of 0.5067 inch To place the flaw with repsect to the reference point, the flow tips and center can he 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 := 1-8067 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

J. S. Bnhmadesam Voiffied by.

B. C. Gray

Entergy Operations Inc Central Engineering Programs Input Data :-

Appendix "C"; Attachment 41 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 a( := 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 XOc := 2.67.10- 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)

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

Reference Temperature for normalizing Data deg. F

__od R := 2 id Rid:

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

ilim

him Pmtblk

5 L

co:= 2 Rm t

[Qg

(

l 1

C0 1 :=e1.103 lo 3 TT+45967

+4.67 Co:= Co1 Stress Inout Data Developed by:

J. S. Bnhmadesam

) aOc Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision I Verified by:

B. C. Gray

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

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

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

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

Column "31 = Mid Thickness Stress data at each Elevation (ksl)

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

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

AllData :=

0 ff 2

3 4

5 O

0

-27.12

-24.15

-22.09

-20.36

-18.98 1

0.49 0.65

-1.53

-3.7

-4.6

-5.47 2

0.88 17.95 16.43 14.45 12.12 8.99

'3 1.19 29.83 26.1 22.67 18.71 13.83 4

1.44 33.68 27.82 24.72 24.1 26.54 5

1.65 32.39 28.39 27.45 34.12 44.82 6

1.81 27.39 28.8 31.16 43.6 61.24 7

1.94 21.48 25.46 33.3 47.74 65.93 8

2.07 16.92 23.7 33.85 49.22 67.24 9

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

IDA11:= A11DatP) 0DA11 := A11Data.()

Stress Distribution 100 IDAII ODAll 50 0 _ 0 0.5 1

1.5 2

2.5 AXLen Axial Elevation above Bottom [inch]

3 Developed by:e J. S. Blhmadesam Velffied by.-

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 4 of 11 Engineering Report M-EP-2003.002-01 Observing the stress distribution select the region in the table above labeled DataAI that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

( 0

-27.118 -24.146 -22.087

-20.358 -18.981 )

0.488 0.65

-1.526

-3.699

-4.599

-5.468 0.88 17.955 16.435 14.447 12.118 8.995 1.193 29.829 26.102 22.672 18.714 13.833 1.444 33.679 27.823 24.722 24.104 26.541 Data :=

1.646 32.389 28.385 27.447 34.121 44.818 1.807 27.386 28.803 31.156 43.603 61.245 1.94 21.477 25.458 33.3 47.738 65.934 k2.074 16.919 23.701 33.846 49.217 67.244 )

Ax. := Data(0)

(3)

MD: Data (l)

ID :=Data TQ := Data(4)

QT := Data(2)

OD := Data(5)

RID := regress(Axi, ID, 3)

RQT:= regress(Axl,QT,3)

ROD:= regress(Axl, OD, 3)

RMD:= regress(Axl, MD, 3)

RTQ := regress(Axl,TQ,3)

FLCntr := I Refpoint - c0 if Val = I Flaw center Location Location above Nozzle Bottom if Val = 2

+ c0 otherwise UTip := FLCntr + c0 InCstrs.avg :-ULSrs.Dist - Ui Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

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

J. S. Blhmadesam Venrlfedby:

B. C. Gray

Entergy Operations Inc Appendix "C"; Attachment 41 Engineering Report Central Engineering Programs Page 6 of 11 M-EP-2003.002-01 ProPLength 0.347 Flaw Growth in Depth Direction 0.6 0s.

0.4 I.

0.2 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

Entergy-CEP Model i

~

~I I I 0.8 S

0.6 5

0.4

.347-V-

- -i--

v 0.2 0

0 0.5 1

1.5 2

2.5 3

3.5 4

Operating Time {years}

-Entergy-CEP Model Developed by:V

1. S. Bnhmadesam velrledbv.

S. C Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 7'of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 0

4) a)

80 60 I

I ~~~I I

I III I.....

401I 20 1 0 

0I 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 Velrifed by:

B6. C. Gray

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

v/)

E 0

r-V U

VU 0.6 0.5 0.4 0.3 0.2 0.1

I ------------------------------------------------

t..

0 0 0.5 1

1.5 2

2.5 3

3.5 Operating time {years}

"a" - Tip -- Uniform

---. --- "a" - Tip -- Linear "a" - Tip -- Quadratic I"a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic 4

Developed by.

J. S. Bnhmadesarm Verified by:

B. C. Gray co-i

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 9ofl1 Engineering Report M-EP-2003-002-01 CGRsambi k 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 CGRsambi (k, 6) 11.9 12.895 12.897 12.9 12.903 12.905 12.908 12.91 12.913 12.916 12.918 12.921 12.923 12.926 12.929 12.931 CGRsambi (k,

5) 8.835 9.52 9.524 9.527 9.53 9.533 9.536 9.539 9.542 9.546 9.549 9.552 9.555 9.558 9.561 9.564 Developed by:

J. S. Bnhmadesam Verlfied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 41 Page 10 of 11 Engineering Report M-EP-2003-002-01 I

a I

0.0 0.5 1.0 1.5 2.0 2.5 3.0 DIstance *on Nozzle Botbnm fmces) 0.12 i 0.08 X 0.04 0.00 0

1 2

3 4

Operating Tire (yaws)

Developed by:

J. S. Blihmadesam Venirfed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs 0.12-I e6 o.o a a5 E, 0.0 4 0

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

p e ra tin g T ime

{y e ars}

I 2 0 -

20 85 uI 15 if3 It-F 10 a2 5.

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

I-De p th Po in t ("a "- tip)

I Ii I

0

  • J 4

'1, 0p e*ra tifg T im-e 0{a rs)

Developed by.

J. S. Brihmadesam Verified by.'

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 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-1 1707; July 1992.
2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, 45 dgeree from Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rlt" -- 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 inchAhr.

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

The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the no:zrle end Refp0 int := 1.544 This is the as-built blind zone providing a propagation length of 0.167 inch; freespan of 0.3274 inch To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:

1) The Upper "C-tip" located at the reference point (Enter 1)
2) The Center of the flaw at the reference point (Enter 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 valve below ULStrs.Dist := 1.8714 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)

Developed by:

J. S. Bnihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engneering Programs Input Data :-

Appendix "C"; Attachment 42 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 (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:= Ro - Rid t

Rm : Rid + -

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

him

'=im Pmtblk :=

50 L

C0 2 Rm Rt *-t

[Qg(1

_g I

eL1.103-1-3 T+45967ref+4.6 Co:= C0 1 Stress Inout Data

  • a10C Temperature Correction for CoefficientAlpha 75 th percentile MRP-55 Revision 1 Developedby:

J. S. Bdhmadesam Verified by:

B. C. Gray

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

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

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

Column W2" = Quarter Thickness Stress data at each Elevation (ksi)

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

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

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

AllData:=

_ 0 1

^

2 3

4 5

0 0

-26.31

-23.54

-21.72

-20.18

-18.94 1

0.51

-0.38

-2.22

-3.97

-5.04

-6.03 2

0.91 20.09 16.85 14.02 11.34 7.92 3

1.24 29.93 26.24 22.49 18.07 12.79 4

1.5 33.83 27.91 24.53 23.55 25.42 5

1.7 32.49 28.21 27.05 33.58 44.17 6

1.87 27.43 28.6 30.66 42.95 60.21 7

2.01 21.43 25.17 32.65 46.97 64.95 8

2.14 16.79 23.32 33.24 48.59 66.19 9

2.28 14.56 21.63 33.98 48.34 62.07 AXLen:= AllData(°)

IDAJI:

AllData(1)

ODAII := AlIData()

Stress Distribution 100 L.

IDAII ODAll

-50 0 0.5 1

1.5 2

2.5 3

AXLen Axial Elevation above Bottom [inch]

Developed by:

J. S. Bnhmadesam Venaied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled 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

-26.311 -23.544 -21.718 -20.18 -18.943")

0.506

-0.377

-2.222

-3.968

-5.036

-6.028 0.911 20.089 16.851 14.017 11.337 7.917 1.236 29.934 26.239 22.486 18.067 12.788 1.496 33.829 27.906 24.526 23.554 25.421 1.704 32.487 28.206 27.053 33.58 44.169 1.871 27.432 28.598 30.659 42.946 60.214 2.006 21.433 25.168 32.645 46.971 64.949 Data :=

~2.141 16.793 23.322 33.237 48.59 66.19 )

AxI := Data(O)

MD:= Data(

ID:= Data(i)

TQ :=DatP)~ 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)

RTQ:= regress(Axl,TQ,3)

FLCntr Refp0 t -co if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c0 otherwise UTip := FLCntr +Co Incstrs avg StrsDst UTip Developed by:

J. S. B/ihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM 2003-Developedby:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength

-0.167 Flaw Growth in Depth Direction 0.6 1-1 0

0.4 t I

I I

I I

I I

I I

I I

I I

I 0.2 t 0 -

0.5 I

1.5 2

2.5 Operating Time {years}

3 3.5 4

Entergy-CEP Model 0

a-0

,c c

i 0.8 0.6 -

II I

I I

I I

1:,5

.167.

I I

I I

I 0.4 -

0.2k o )

)

0.5 I

1.5 2

2.5 3

Operating Time {years}

3.5 4

Entergy-CEP Model Developedby:

J. S. Bdhmadesam Vedlied by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 7 of 11 Engineering Report M-EP-2003-002-01 0~

VI 14 3n V-.

80 60 I Stress Intensity Factors I

I I

I I

I I

L.

I..

~.

. ~

I I

I I

I II 40 1 20 A

v 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. Brlhmadesam Verifed by B. C. Gray

Entergy Operations Inc CentralI Engineering Programs Appendix "C"; Attachment 42 Page 8 of 1 1 Engineering Report M-EP-2003-002-01 0.8 0.7 Influence Coefficients - Flaw C

0 U

0.6 0.5 0.4

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

0.3 0.2

-1.1

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

..... 1.1-1

.................... -.1......-................................I............................. I.......................-..........-

0.1 00 0.5 1

1.5 2

2.5 3

3.5 4

operating time {years)

"la" - Tip -- Uniform

".......Ia"

- Tip -- Linear

"----Ia"

- Tip -- Quadratic

".....Ia"

- Tip -- Cubic

" tc" - Tip -- Uniform "CI......

V-Tip -- Linear

"----tc"

- Tip -- Quadratic

".....tc"

- Tip -- Cubic Developed by.,

J. S. Bnhmadesam Verified by:,

B. C. Gray co

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

J. S. Bnhmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 42 Page 10 of 11 Engineering Report M-EP-2003-002-01 E

a I

I 1.0 1.5 2.0 lstanoe hPm Nozzl BSotom (kiches) 0.3-I 021 X0.10 0.O1 0

1 2

Operating Time yarsl 3

4 Developed by:

J S. Bnihmadesam Verified by B. C. Gray

Entergy Operations Inc Central Engineering Programs 0.3 -

I 0.2 2

a ID 0.0 0.0 Appendix "C"; Attachment 42 Page 11 of 11 Engineering Report M-EP-2003-002-01 O p e ra tin g T im e

{y e a rs }

40' 3S

.5 If 30 i2 25 t

15 -

10 -

1=

S.,Ia.- Fin'intM 0 ~

I 2

operbngtee frir.

30~ I a t

4 Developed by.

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc.

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

Refrences:

1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, 22.5 degree from Downhill Azimuth, Augmented Analysis 1.3 inch above Nozzle Bottom Calculation

Reference:

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

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

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

The throughwall flow Upper 7r7p is located at the Reference Line.

Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle b0ftom in inches.

BZ:= 1.3 This is the reduced blind zone providing a propagation length of 507 inch; freespan is 0.507 inch The Second Input is the Uipper Limit for the evaluation, which is the bottom of the fillet weld eg.

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

Enter this dimension (measured from nozzle bottom) below.

ULStrs.Dist:= 1.8067 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)

Developed by:

Verified by:~~~~~~

IDeveloped by.-

Verified by-I

Entergy Operations Inc.

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

L:=.794 od:= 4.05 id:= 2.728 Pint := 2.235 Years:= 4 1Iim:= 1500 T := 604 v := 0.307 aoc:= 2.67-10 12 Qg := 31.0 Tref := 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)

Tube OD Tube ID Design Operating Pressure (internal)

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

Reference Temperature for normalizing Data deg. F

-Qg I

I1

[ I

.103-103 yT+459.67 Trir-459.67JI Co: e_-

c Tifllopr= Years-365-24 od 2

id 2

t:= Ro - Ri Rm:= Ri + -2 CFihr:= 1.417-105 Cblk:

Timopr

'urn Pmntblk:=I fi1 I

L 2

IDeveloped by.,

Verified by. I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 3 of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

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

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

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

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

DataAll 0

CataAII0

=

lI 2

i 3

l 4

l 5

l o

o

-27.12

-24.15

-22.09

-20.36

-18.98 1

0.49 0.65

-1.53

-3.7

-4.6

-5.47 2

0.88 17.95 16.43 14.45 12.12 8.99 3-1.19 29.83 26.1 22.67 18.71 13.83 4

1.44 33.68 27.82 24.72 24.1 26.54 5

1.65 32.39 28.39 27.45 34.12 44.82 6

1.81 27.39 28.8 31.16 43.6 61.24 7

1.94 21.48 25.46 33.3 47.74 65.93 8

2.07 16.92 23.7 33.85 49.22 67.24 9

2.21 14.77 22.09 34.56 48.87 62.96 AlIAxlI DataAll (p)

A111D= DataA~l AMOD= DataAlII5 IDeveloped by.,

Verified by. I Deeoe by eife y

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 43 Page4of 10 Engineering Report M-EP-2003-002-01

-50 0

0.5 1

1.5 2

2.5 3

Axial Distance above Bottom [inch]

ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection In the above table, click on the "Datae statement below and delete It from the edit menu. Type wData and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

0

-27.118 -24.146 -22.087 -20.358 -18.981) 0.488 0.65

-1.526

-3.699

-4.599

-5.468 l 0.88 17.955 1.193 29.829 Data:= 1 1.444 33.679 16.435 14.447 12.118 8.995 26.102 22.672 18.714 13.833 27.823 24.722 24.104 26.541 28.385 27.447 34.121 44.818 28.803 31.156 43.603 61.245 25.458 33.3 47.738 65.934 1.646 32.389 1.807 27.386 1.94 21.477 k2.074 16.919 23.701 33.846 49.217 67.244 )

(: )

Axi: Data ID:= Data I (5)

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

ROD:= regress(Axi, OD, 3)

Developed by:

Verified by:

lIDeveloped by.

Verfied by. I

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 43 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:

BZ -I Flaw Center above Nozzle Bottom In~ts~vg:~ULStrs.Dist -BZ ICStrs.avg :=

20 No User Input required beyond this Point

& Sat Aug 09 11:44:49 AM 2003 IDeveloped by Verified by. I Developed by:

Verified by:

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 0.507 1.5 61 TWCpwscc

  • j,3 0

U-I 0.5 0

-0.5 0 0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

TWCPWSCC(i l)

Operating Time (years)

-Entergy Model 2

z f.

.9 1.5 0

0.5 Increase in Half Length

/:

.I

._ I

t.

1 -

0 0

0.5 I

1.5 2

2.5 Operating Time (Years) 3 3.5 4

I Developed by:

Verified by:

Entergy Operations Inc.

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

r-r-

.9 uS 0

0.5 1

1.5 2

2.5 3

3.5 Operating Time {Years}

D-----

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

IDeveloped by.

Verified by I Developed by:

Verified by:

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC TWC TWC Twcpwsc(,6) 17.829 24.076 24.087 24.098 24.108 24.119 24.13 24.14 24.151 24.162 24.173 24.183 24.194 24.205 24.216 24.226 TWCpwsc(j,7) 24.642 29.762 29.772 29.783 29.793 29.804 29.814 29.824 29.835 29.845 29.856 29.866 29.877 29.887 29.897 29.908 PWScC(0 8) =

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

Verified by:~~~~

IDeveloped by Verified by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot g 20 1.0 1.5 2.0 Distance from Nozzle Bottom finch) 200 -

6 1 150-Itoo OD Surface SIF

-ID)

Surf ace SIF

-__ Average SIP 0

t 2

OperdGfTlme Iyears),

3 4

IDeveloped by:

Venfied by:

ClI

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 43 Page 10 of 10 Engineering Report M-EP-2003-002-01 1 2 XO 8 S

04 O.0 2

O perating Time ( years)

Developed by:

Venfied by:.

Entergy Operations Inc.

Central Engineering Programs Appendix WC"; Attachment 44 Page I 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 R,,t/t is between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, 45 degree from Downhill Azimuth, Augmented Analysis 1.544 inch above Nozzle Bottom Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric 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 Oput is to locate the Reference Line (e. top of the B/knd Zone).

The throihwull 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:= 1.45 This is the as-built blind zone providing a propagation length of.421 inch; freespan is 0.421 inch The Second rZput is the Upper Lmit 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:= 1.8714 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom) lDeveloped by:

Verified by:.

Entergy Operations Inc.

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

L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 Ilim:= 1500 T:= 604 v := 0.307 a0c:= 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 E

. 103* IC I~T+459.67 Tf-+459.67)_

Co: e

.ao c

Tifllopr= Years-365-24 od 2

R := id t:= Ro-Ri Rm:= Ri + -

2 CFinhr:= 1.417-105 Cblk:= Timopr him Pmtblk:=

-linl 150 I

L 2

Developed by:

Verified by:

IDeveloped by.,

Verffied by. I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 3 of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

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

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

Column f1" = ID Stress data at each Elevation (ksi)

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

DataAIl :=

I 4

l 0

1 2

3 4

5 O.

~0

-26.31

-23.54

-21.72

-20.18

-18.94 1

0.51

-0.38

-2.22

-3.97

-5.04

-6.03 2

0.91 20.09 16.85 14.02 11.34 7.92 3

1.24 29.93 26.24 22.49 18.07 12.79 4

1.5 33.83 27.91 24.53 23.55 25.42

.5 1.7 32.49 28.21 27.05 33.58 44.17

'6 1.87 27.43 28.6 30.66 42.95 60.21 7

2.01 21.43 25.17 32.65 46.97 64.95 8

2.14 16.79 23.32 33.24 48.59 66.19 9

2.28 14.56 21.63 33.98 48.34 62.07 AIIAxli DataA~ll AlR=D DataAIII (5)

A~llD= DataAII Developed by:

Verified by:

IDeveloped by.,

Verified by. I

Entergy Operatons Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 4 of 10 Engineering Report M-EP-2003-002-01 100 75 uA

'A 50 25

-25

-500.

0 0.5 1

1.5 2

2.5 3

Axial Distance above Bottom [inch]

-ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

(

0

-26.311 -23.544 -21.718 -20.18 -18.943")

Data:=

0.506 -0.377 0.911 20.089 1.236 29.934 1.496 33.829 1.704 32.487 1.871 27.432 2.006 21.433 26.239 27.906 22.486 24.526 18.067 12.788 23.554 25.421

-2.222

-3.968 -5.036 -6.028 16.851 14.017 11.337 7.917 28.206 27.053 33.58 44.169 28.598 25.168 30.659 32.645 42.946 60.214 46.971 64.949

~2.141 16.793 23.322 33.237 48.59 66.19 )

Ax]:= Data (I)

ID: Data (5)

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

ROD:= regress(Axl, OD,3)

IDeveloped by:

Verified by:I

Entergy Operations Inc.

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

20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM 7,nn-A IDevelopedby:

Vedfied by:I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.421 1.5 2" TWCPwSCCj,3 0

0 1

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}

rtergy Model Increase in Half Length 2

C.

C.

1.5 0

0.5 0 _

0.5 1

1.5 2

2.5 3

3.5 Operating Time {Years}

4 Developed by:

Verified by:

Entergy Operations Inc.

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

t.e 200 "I

a>

100 0) r-v) uC 0

0.5 1

1.5 2

2.5 3

3.5 Operating Time {Years}

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

IDeveloped by.-

Verffied by. I Developed by:

Verified by:

Entergy Operations Inc.

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

6) =

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

30.471 34.797 34.813 34.83 34.846 34.863 34.879 34.895 34.912 34.928 34.945 34.961 34.978 34.994 35.01 35.027 Twcpwscc(j 8) 28.154 33.544 33.562 33.58 33.598 33.616 33.634 33.653 33.671 33.689 33.707 33.726 33.744 33.762 33.78 33.799 Developed by:

Verified by:

IDeveloped by Verified by I I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 44 Page 9 of 10 Engineering Report M-EP-2003-002-01 Ho o p S tre s s P lot A

2:ii X

60 40 20 0

-2 0

-4 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (inch) 250 -

0 2 00 -

j 150 1 00 -

a 50 -

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

0 1

2 3

4 0 P eratfing Ti m e~ (yea rs)f Developed by:

Verified by:

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 4 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.5 I

0 5 0.0 2

3 0 perating Time

( years)

IDeveloped by:

Verified by:.

Entergy Operations Inc.

Central Engineenng Programs Appendix "C"; Attachment 45 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw beveloped by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when R,, 5Id/t is between 2.0 and 5.0 (Thickwall Cylinder)

Refrences:

1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model)
2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -'8"Degree Nozzle, 67.5 degree from Downhill Azimuth, Augmented Analysis 1.544 inch above Nozzle Bottom Calculation

Reference:

MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric 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 Dnput is to locate the Reference tine (eg. top of the Blind Zone).

The throughwall flaw "Upper Tip" is located at the Reference tine.

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

BZ:= 1.544 This is the as-built blind zone providing a propagation length of.421 inch; freespan is 0.421 inch The Second Xtput 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.

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

Developed by:

Verified by:

Entergy Operations Inc.

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

L :=.794 od:= 4.05 id:= 2.728 Pint:= 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 atoc:= 2.67 10 12 Qg := 31.0 Trf := 617

- Qg

(

l Lo Li

.103* 10 3T+459.67 Tef+459.67)I C0e

.IC 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 ad Ro:= -2 id R:= id t:= Ro - Ri Rm:= Ri + -2 CFinhr:= IA17-105 Cbk=Timlopr Cbik FPmtblk:=

5 I

L 2

IDeveloped by.,

Veiffied by.- I De eo e by eife y

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 3 of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.

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

Cloumn "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 (ksW)

DataAII :=

-1 4

0 1

2 3

4 5

0 0

-25.24

-22.71

-21.18

-19.87

-18.8 1

0.53

-1.27

-2.96

-4.4

-5.69

-6.83 2

0.96 21.94 17.09 13.36 10.18 6.33 3

1.3 30.02 26.37 22.21 17.12 11.24 4

1.57 34.09 28.09 24.31 22.83 23.83 5

1.79 32.72 28.04 26.61 32.92 43.29 6

1.97 27.6 28.45 30.15 42.18 58.89 7

2.11 21.46 24.92 31.94 46.1 63.87 8

2.24 16.73 22.99 32.59 47.9 65.05 9

2.38 14.34 21.26 33.41 47.85 61.2 AIIAxI =Data 11(0 All1D:=DataAlIW (5)

A~llD= DataAII lDeveloped by:

Verified by:

Entergy Operations Inc.

Cenfral Engineering Programs Appendix "C"; Attachment 45 Page 4 of 10 Engineering Report M-EP-2003-002-01 100 75 u,U, 50 25 0

-25;

-50F0 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 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

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

-2.963

-4.403

-5.689

-6.833 0.959 21.942 17.089 13.361 10.182 6.327 1.301 30.023 26.373 22.21 17.121 11.241 Data:=

1.575 34.094 28.085 24.306 22.834 23.834 1.794 32.716 28.035 26.605 32.916 43.289 1.97 27.602 28.447 30.151 42.181 58.888 2.106 21.457 24.92 31.944 46.103 63.871 2.242 16.731 22.988 32.591 47.9 65.049)

(: )

Axi:

Data (II ID: Data (5)

OD: Data RID := regress(Axl, ID, 3)

ROD:= regress(Axl, OD, 3)

Developed by:

Verified by:

Developed by I

Verffied by I

Entergy Operatons Inc.

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

20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM 2003 IDeveloped by.,

Verified by. I Developed by:

Verified by:~~

Entergy Operatons Inc.

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

.,, Twcpwc j,3 0

I 0.5 0 -

-0.5 0 0.5 1

Entergy Model 1.5 2

2.5 3

3.5 4

4.5 5

TWC p,(s OperatingTime(years I)

Operating Time {years}

Increase in Half Length z

Uz C9 1.5 0.5 0

0.5 I

1.5 2

2.5 3

3.5 4

Operating Time {Years}

IDeveloped by:

Verified by:.

Progl~~,-~

~,

A P P en d lv " -., A ttac h m nt 4 r ----

p a~~~~~~~ge 7 of ent4 E

R~~eport

'L'E Oi6 2-0J1 OD Sjp-tntey Mo0del

~ID SIp - Enter SIP Average gyModel 4

Verified by

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCC

=16)

=

23.707 29.582 29.6 29.618 29.636 29.654 29.672 29.691 29.709 29.727 29.745 29.764 29.782 29.8 29.816 29.837 TWCpwsc(j7) =

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

Verified by:

IDeveloped by.,

Verffled by I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 9 of 10 Engineering Report M-EP-2003-002-01 Ho o p S tre s s P lot 6 0 40 20 0

-2 0

-40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom din)ch 250 -

p 2 0 0 -

a RI t

1 5 0 -

4P

.I 1 00 -

i 50 0-SO D su rfa c e S IF ID S u rfa ce S IF I -

AAverage SIF I

I 7 ~

I 7

=

v I

a 1

2 3

4 O pea ra tin g Timre (ye arsI lDeveloped by:

Verified by:

I

Entergy Operations Inc.

Central Engineering Programs Appendix "C"; Attachment 45 Page 10 of 10 Engineering Report M-EP-2003-002-01 I1

.5 I

1.0 X 0.5 0.0 0 p e ra tin g T im e (y e a rs I IDeveloped by.

Veriffied by I Developed by:

Verified by:

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

1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -`8" Degree Nozzle, 67.5 dgeree from Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.

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

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

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

Refpoint := 1.544 This is the as-built blind zone providing a propagation length of 0.167 inch; freespan of 0.3274 inch To place the flaw with repsect to the reference point, the flow tips and center can be located as follows:

1) The pper "C-tip" located at the reference point (Enter V)
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 ipper Limit to be selected for stress distribution (e.g. Weld bottom ).

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

Developedby:V y

J. S. Bnfhradesam VenTied by S. C. Gra.y

Entergy Operations Inc Central EngineMng Programs Input Data :-

Appendix "C"; Attachment 46 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him := 1500 T := 604 aOc := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)

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

Reference Temperature for normalizing Data deg. F R.

od R0 2

Rid := id Rid :

t Ro - Rid Rm :=Rid +

Timopr := Years-365-24 C~inr :=1.417-105 Timopr Cblk:=

r Ihim.

Pmtblk =

50 L

0.

2 Rm t

L(

=e o1.103(T+459.67 Tref+459.67 Co:= Co0 Stress InDut Data Developed by:

J. S. Bifhmadesam

)]-0C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Verifed by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 3 of 1I Engineering Report M-EP-2003-002-01 Input all available Nodal stress data in the table below. The column designations are as follows:

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

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

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

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

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

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

AllData :=

0 1

2 3

4 5

0o

-25.24

-22.71

-21.18

-19.87

-18.8 0.53

-1.27

-2.96

-4.4

-5.69

-6.83 2

0.96 21.94 17.09 13.36 10.18 6.33 3

1.3 30.02 26.37 22.21 17.12 11.24 4

1.57 34.09 28.09 24.31 22.83 23.83 5

1.79 32.72 28.04 26.61 32.92 43.29 6

1.97 27.6 28.45 30.15 42.18 58.89 7

2.11 21.46 24.92 31.94 46.1 63.87 8

2.24 16.73 22.99 32.59 47.9 65.05 9

2.38 14.34 21.26 33.41 47.85 61.2 AXLen := AllData(O)

ID

= AllData(l)

All 0DAll:= AllData()

Stress Distribution 100 IDAll Wc ODAII U,

50

-50 '

0 0.5 1

1.5 2

2.5 3

3.5 AXLen Axial Elevation above Bottom [inch]

Developed by:e J. S. Bn'hmadesam Vedried by S. C. Gray

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

-25.236 -22.713

-21.175

-19.868 -18.802) 0.533

-1.267

-2.963

-4.403

-5.689

-6.833 0.959 1.301 21.942 30.023 34.094 17.089 13.361 10.182 6.327 26.373 22.21 17.121 11.241 28.085 24.306 22.834 23.834 Data :=

1.575 1.794 32.716 28.035 26.605 32.916 43.289 1.97 27.602 28.447 30.151 42.181 58.888 2.106 21.457 24.92 31.944 46.103 63.871 k2.242 16.731 22.988 32.591 47.9 65.049 )

AxI := Data(O)

MD: DatP)~

ID:= Dat(1)

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 Refp;t -co if Val = 1 Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + c0 otherwise UTip := FLCntr + C0 InCStrs.avg =

2S0s.Dis-UTip Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ff Sat Aug 09 10:21:18 AM 2003EI Developed by:

J. S. Brihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProLength = 0.263 0.6 Q

C-P.-

0.4 t Flaw Growth in Depth Direction I

I I

I I

I I

I I

II 0.2 1 O

0 0.5 1

1.5 2

2.5 3

3.5 Operating Time {years}

Entergy-CEP Model 4

Q C

C 0

0.8b 0.6h I

I I

I I

I I

.263

-- -F-- - --- -- -- - ----

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

I I

I 0.41-0.2h A0 0.5 l

1.5 2

2.5 3

3.5 4

Operating Time (years)

Entergy-CEP Model Developedby J. S. Brimadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 7 of 11 Engineering Report M-EP-2003-002-01 0~

C, 4)

Cr U,

80 60 I Stress Intensity Factors I

I I

I I

I I

~~~~~~~.........-.-.-..-...

~~~~~~.-...-.~~~~~~~~~~~~~~~...

40 1 20 O

CI 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 Verfied by:

B. C. Gray

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

'A r-

'A:

.E ct)

I1ran U;

r-0.6

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

0.5 0.4 0.3 0.2 0.1 A

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

I 0 0.5 1

-"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

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

I.......

1.5 2

2.5 3

3.5 4

Operating time {years}

Developed by:

J. S. Blihmadesam Verified by.

B. C. Gray U

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 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 0.828 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 CGRsambi(k, 6) 13.362 14.331 14.334 14.338 14.341 14.345 14.348 14.351 14.355 14.358 14.362 14.365 14.369 14.372 14.376 14.379 CGRsambi(k 5 9.842 10.506 10.51 10.513 10.517 10.52 10.524 10.528 10.531 10.535 10.539 10.542 10.546 10.55 10.553 10.557 Developed by:

J. S. Blihmadesam Verified by:

B. C. Gray

Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 46 Page 10 of I1 Engineering Report M-EP-2003-002-01 I

tj 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from NozIe Bottom finches}

0.20 -

111

.0.15 -

005 0

1 2

OPetIMn Tku (YearS1 3

4 Developed by-J. S. Brfhmadesam Venfled by:

B. C. Gray

Entergy Operations Inc Centra I Engineering Programs Appendix "C"; Attachment 46 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.~2 0 c

2 rim 0.1 0 To f

0.05 C

.)

0 A00 2

3 O peara tin g T ime

{y a ars}

Surface Point ('c"-tip)

Depth Point "a"- tip) 25 v

20 I

IS 0 10 - f7 I I 0'

0 1 ~~, '

2 3

4

~~~~~N `

I 00 tln6 lm (yar I

Developed by:

J. S. Brdhmadesam Verified by.

B. C. Gray

Retrieved from "https://kanterella.com/w/index.php?title=ML032790033&oldid=5413204"