ML032690687
| ML032690687 | |
| 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: ML032690687 (116) | |
Text
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 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. &ray Note: Only for use when Re5t1 d/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49"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 Dout is to locate the Reference Line (eg. top of the Blind Zone).
The throughwall flow "Upper rip'-
is located at the Reference Line.
Enter the eevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist:= 4.034 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by Venfied by. I
[ Deeoe y
Vrfe y
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 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 Ilim:= 1500 T := 604 v := 0.307 Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F ac := 2.67. 10 12 Qg:= 31.0 Tref := 617 Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Co:=eL' 1.03.I 3( T+459.67 Tref+459.67).
1 aoc Timlopr= Years-365-24 RO= od 2
Ri:= id 2
t := Ro - Ri Rm:= Ri + 2 2
CFinhr:= 1.417-105 Timopr Cblk :='r hlim Pmtbik:= l j I
L 2
IDeveloped by Verified by I Developed by:
Verified by:~~~~
~ ~ ~
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 3 of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "0" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (kst)
Column "5ff = OD Stress data at each Elevation (ksi)
DataAII :=
_=0 e
1 f=At2 3
-4 547=0 007V:0; O 0 0
17.35 8.19 2.28
-3.06
-8.64 F 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 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 AIIAxli=DataAII(0 MUID := DataAll (5)
AIMOD DataAII IDeveloped by:
Verified by;
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 4 of 10 Engineering Report M-EP-2003-002-01 40 26.67 13.33 v)4 0
-13.33
-26.67
-40 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
5.5 6
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 17.354 8.186 2.284
-3.064 -8.637)
Data:=
1.091 6.892 1.47 1.964 5.781 2.359 2.664 10.289 7.148 3.225 12.243 7.028 3.674 6.579 4.659 4.034 -5.621
-1.296 4.176 -12.251
-6.006 4.317 -15.641
-9.131 4.459 -18.614 -11.785
-2.224 -5.444 -7.199 0.754
-0.955 -3.232 5.324 3.428 0.494 6.829 7.244 5.952 5.865 12.453 16.377 4.184 17.859 24.278 2.741 20.517 31.88 2.2 21.496 30.446 1.319 20.216 30.786 (4.601
-21.257 -13.548 0.574 19.393 32.088)
Axl:= Data D :
ID:=Data (5)
OD:=Data RID := regress(Axl, ID,3)
ROD:= regress(Axl, OD,3)
Developed by:
Verified by:
IDeveloped by Verified by: I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr := BZ - I Flaw Center above Nozzle Bottom UI-Strs.Dist - BZ IncStrs.avg :=
20 No User Input required beyond this Point R. Sat Aug 09 11:44:49 AM 2003 Developed by:
Venfied by:~~~~~~~~~~
IDeveloped by Verified by: I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 2.49 1.5
."' TWCJWSC
- j,3 0
0.5 0
-0.5 )0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWSCC( j)I )
Operating Time (years)
Entergy Model Increase in Half Length 2
iU U2 U5 1.5 0.5 0
0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years) 4 Developed by:
Verified by:
IDeveloped by.
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 0
U, 0
Cr 200 100 0
.............................................................................................................................................................................................................................................................. I........
0 0.5 I
1.5 2
Operating Time (Years) 2.5 3
3.5 4
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average Developed by:
Verified by:
C-t
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCC(j 6) =
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817 TWCPWSCc(j 7) =
4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 TWCpwscc (.8) =
1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 Deeoe y
Vrfe y
IDeveloped by Verffied by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 9of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 30 SI 10 1 0
-3 0 2
3 4
Distan ce from Nozzle Bot1om
{inch) 0 D S urfa c e S IF ID S u rfa ce S IF A v e ra'g e S IF 0
Ur f0-Q I
-2 ws X
g(o-2 0
1 2
O pearatin g T imea (y aars )
3 4
De eoeiy Vrfe y
IDeveloped by:
Verified by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 10 of 10 Engineering Report M-EP-2003-002-01 I
0.5 -
0.3 -
01 -
-0.1 -
.3 -
-0.
Il l
0 I
2 0 p e re tin g Tim.
{y * *rs)
T I
3 4
Developed by:
Verified by:
IDeveloped by Venfied by. I
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 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: J. S. Brihmodesam 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 -"49" Degree Nozzle, Downhill Azimuth, Augmented Analysis 1.043" 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 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 := 1.043 This allows a 0.25 inch freespan below bottom of weld To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "T-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 ekvation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.293 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 Engineering Programs Input Data :-
Appendix "C"; Attachment 29 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 Pjnt := 2.235 Years := 4 11im := 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 :=
id Rid:= 2 t:= Ro-Rid t
Rm :=Rid+ -
Timopr := Years-365-24 CFnhr:
1.417-105 Timopr Cblk:= -u
'=im Pmtblk =
5 L
2 Rm
-Q g
.(
I I
1.103 10-3 T+459.67 Tref+459.67 C01 := e aTOc Temperature Correction for Coefficient Alpha Co:= C01 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Brhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 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 N(si)
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 12 3
4 5 -
0 0
-28.32
-18.3
-12.16
-6.2
-002 1
0.35
-18.79
-12.49
-6.61
-1.37 365 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 70 1.44 4.78 9.56 24.9 38.18 54.09 1.59 13.25 18.57 35.28 52.81 66.52 Sri 1.74 16 22.02 39.19 62.95 75 AXLen:= AllData(°)
IDA11:= A11Data(')
0DA11 := A11Data()
Stress Distribution
,JU I
1.043 l
l CA U) v.
IDAfl ODAJI 50 t I1e'
\\ I 11
,I I11 II II 1,
I II II III II
/
I I
I i
I I
0 0 0.5 I
1.5 2
2.5 3
3.5 AXLen Axial Elevation above Bottom [inch]
Developed by:
J S. SBlhmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 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
-28.324 -18.299 -12.16 -6.201 -0.021 )
0.35
-18.794
-12.495
-6.607 -1.366 0.63
-17.838
-10.518 -4.407 -0.477 0.854 -20.517 -12.968
-5.902 -0.874 1.034 -19.663
-11.831
-5.288 0.227 1.178 -17.203
-10.587
-0.515 16.326 Data:=
3.655 2.08
-1.536 1.46 21.019 37.289 54.089 66.517 )
1.293
-8.023 1.442 4.778
-2.205 10.461 32.658 9.557 24.903 38.177 18.569 35.278 52.808 1.591 13.252 Axi := Data(0)
(3)
MD:
Data ID := Data(')
TQ :=Data(4)
QT :=Data(2)
OD:
Data(5)
RID := regress(AxI,ID,3)
RQT := regress(AxI,QT,3)
ROD:= regress(Axl,OD, 3)
RMD:= regress(Axl,MD,3)
RTQ:= regress(Axl,TQ,3)
FLCntr RefPo in t -C if Val= i Flaw center Location Location above Nozzle Bottom RefPo in t if Val = 2 RefPoint + CO otherwise UTip := FLCntr + C0 InCStrsav StrsDist UTip Developed by:
J. S. Biihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point
&SatAug 09 10:21:18AM 2003-Developed by.
J. S. Bnhmadesam Venr led by:
- 8. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 0.09 Flaw Growth in Depth Direction 0.6 s
C.5 C) 0 I-QD 0.4 r I
I I
I I
I I
I I
I I
I I
I 0.2 I 0 ))
0.5 I
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model I
u.
C) 0 0.5 0
-0.5 I
I I
I I
I I
1,5 0
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.
J. S. Bnhmadesam Verified by:
B. C Gray
Entergy Operations Inc Appendix "C"; Attachment 29 Engineering Report Central Engineering Programs Page 7 of 1 1 M-EP-2003-002-01 Stress Intensity Factors 80 l
l l
l l
60 co 40 X
20 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by.
- 1. S. Bnlhmadesam Verified by.
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix "C"; Attachment 29 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 Ln
. _n r-0.6 0.5 0.4 0.3 0.2 0.1 0
-.-... I--............................ -.-I..............-........... p----- ---------------------------------------------- ------------- --------- ----------
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 Ia" - Tip -- Cubic "c" - Tip -- Uniform
'V-Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Brihmadesam Verified by.
B. C. Gray CC3
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 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) 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 CGRsambi(k 5) 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 Developed by.
J S. S Bhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs 80 X
80 f
40
~~~Rel 0
2 0 I
0
-20
-40 0.0 0 5 0.3 U
D 0.1 0
I
-0 1 CO 0 n o Appendix "C"; Attachment 29 Page 10 of 11 Engineering Report M-EP-2003-002-01 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (inches}
-u.o 0.5 2
3 4
o p e ra tin g T im e
{y e a rs }
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
5 -
c 0 ~3 S
I
-5 0.1 C,
-0 3i -
0 5
-0 3
0 1
2 p e rstin g T im e
( e a rs )
3 4
6.
6.5 -
r 65 a4 "o 5.0 -
4~5-l___
Surface Point ("c"-tip)
Depth Point {"a"- tip) I I
0 1
2 O pe ratin g Time (years) 3 4
Developed by:
J. S. Bnhhmadesam Verified by:
B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 1 of 10 Engineenng 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 RtSjd/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, Downhill Azimuth, Augmented Analysis 1.043 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 InpWt is to locate the Reference Line (eg. top of the Blind Zone). The throLghwall flow "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzk bottom in inches.
BZ:= 1.043 Location of Blind Zone above nozzle bottom (inch)
This allows a 0 25 inch freespan below bottom of weld The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist :=1.293 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 30 Page 2 of tO Engineering Report M-EP-2003-002.-1 Input Data :
L := 0.25 od := 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 lim := 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 CO:=eLl 103 10 -
3 T+459.67 Tie+459.67J 0
Co := e
.aoC Tiniopr:= Years 365 24 od Ro := -
Ri:= id 2
t := Ro - Ri Rm:= Ri + -2 CFinhr:= 1.417 10 Cblk:Tip
'lim
'lim Pmntblk:=15 I
L 2
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 3 of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "O" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAIl :
0 12 3
4 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 AIIAxi:
DataAlII0 AIIID DataAIl AIIOD:= DataAIl 5 Developed by:
Venfied by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 4 of 10 Engineering Report M-EP-2003-002-01 100 75
-1 tr 50 25 1-043 1-294
,...~
~ ~ ~~~..........
10 0o
-25
-50 D 0.5 I
1.5 2
2.5 3
3.5 Axial Distance above Bottom [inch]
ID Distribution
- - --.... OD distribution Observing the stress distribution select the region in the table above labeled Data^Aj 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
-28.324 0.35
-18.794 0.63
-17.838 0.854 -20.517 1.034 -19.663 1.178 -17.203 1.293
-8.023 1.442 4.778 1.591 13.252
-18.299
-12.495
-10.518
-12.968
-11.831
-10.587
-2.205 9.557 18.569
-12.16
-6.201 -0.021 )
-6.607 -1.366 3.655
_4.407 -0.477 2.08
-5.902 -0.874
-1.536
-5.288 0.227 1.46
-0.515 16.326 21.019 10.461 32.658 37.289 24.903 38.177 54.089 35.278 52.808 66.517 )
Axl:= Datai ID := Datal OD := Data RID := regress(Axl, ID,3)
ROD := regress(AxLOD,3) lIDeveloped by:
Verffied by: l
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ I
Flaw Center above Nozzle Botom
_ULStrsDist
- BZ Inc Strs.avg 20 No User Input required beyond this Point l
Sat Aug 09 11:44:49 AM Developed by:
Verified by:~~~~
IDeveloped by:
Venfied by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.25 Flaw Length vs. Time 1.5 C
- 5 PWC j.3 0
l 1.5
.16 0.5 0
-0.5 0
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWSCC (j I )
Operating Time {years}
Entergy Model Increase in Half Length 2
U rUu 1.5 0.5 0
0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time XYears,'
IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 C._
0 200 0
Cd 100 a
Cn u
0 0.5 l
I. 5 2
Operating Time {Years}
2.5 3
3.5 4
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average Developed by:
Verified by:
COG
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPIvSCC6 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 TWCpwsC (j 7)
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1 TWCpWSC
- scj, X)
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132 IDeveloped by-Venfied by: I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t B0 60 2
40 e
jZ 2 D 20 0
-2 0
-40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istanCe from N ozzle Bottom (inch) 4 O D S u rfa ce S IF ID S u rfa c e S IF A v e ra g e S IF I
a Z,
'I
-6
-1 1 0
1I 2
0 p e ra tin g T im e (y e a rs )
3 4
Developed by:
Verified by:
C7
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 10 of 10 Engineering Report M-EP-2003-002-01 0.5 -r-0.3 zX 0.1 i-0.1 (3
-0.3 -
-0 5 0
I 2
O p era ling Time (years) 3 4
Developed by:
Verified by:
IDeveloped by-Verified by I
Entergy Operations Inc Central Engineering Prograrns Appendix "C"; Attachment 31 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 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 -"28.8" Degree Nozzle, 22.5 degress rotated from Downhill, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the 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 :=l1.544 Normal blind zone To place the flow with repsect to the reference point, the flow tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "C-tip" located at the reference point (Enter 3).
Val := 2 Upper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.8317 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
Venlfed by:
J. S. Bnhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 31 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 4im = 1500 T := 604 aOC, := 2.67 10- 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od R := -
id Rid2-t:= Ro-Rid i
Rm :
i+-
Timopr := Years-365-24 CFnhr := 1.417-105 Timopr Cblk:=
- H1im, Prntblk =
50 L
2 0
Rm Rt :=-
_Q g
I I
103[ 10-3 2
T+459.67 Tref+45967)
C0 1 :
Co 0
Co0 Stress Inout Data
)] 0C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 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 'On = Axial distance from minumum to maximum recorded on data sheet(inches)
Column 'I" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
-14.21
-11.51
-9.79
-8.24
-6.72 1
0.5
-6.49
-5.19
-4.42
-3.8
-3.18 2
0.89 1.55 1.02 0.56 0.26
-0.08 3
1.21 8.43 7.98 7.2 6.19 5.29 4
1.46 10.25 12.71 12.22 11.35 8.36 5
1.67 15.66 18.34 18.7 20.84 29.7 6
1.83 24.32 24.53 26.71 44.52 57.73 7
1.95 31.5 28.7 31.23 53.02 63.55 8
2.07 31.98 30.11 35.63 59.45 69.03 9
2.19 26.83 29.95 38.37 61.12 72.69 10 2.31 20.84 27.29 38.5 59.95 75.04 11 2.43 15.99 24.67 38.16 58.17 73.85 AXLen:= AllData(°)
ID
- = A1IData( I)
All OD
- = AIJData (5
All Stress Distribution 100
-ie
'A
'A t)
(A IDAII ODAII 50 0 0 0.5 1.5 2
2.5 3
3.5 AXLen Axial Elevation above Bottom [inch]
Developed by J. S. Bnhmadesam Verified by:
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 4 of 1 1 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAle that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(0
-14.205 -11.506
-9.79
-8.243 -6.722)
Data :=
0.495
-6.493
-5.188
-4.425 -3.796 -3.176 0.892 1.555 1.021 0.565 0.257
-0.076 1.21 8.43 7.98 7.199 6.186 5.292 1.464 10.247 12.709 12.22 11.35 8.364 1.668 15.665 18.335 18.703 20.835 29.697 1.832 24.321 24.532 26.71 44.525 57.729 1.951 31.496 28.696 31.228 53.015 63.555 2.071 31.975 30.109 35.633 59.449 69.026 2.19 26.833 29.946 38.369 61.124 72.691 2.31 20.84 27.287 38.5 59.952 75.043 k
)
I -
AxI := Data(0)
MD:= Data(3)
ID :=Data( I)
TQ := Data(4)
QT:= Data(2)
OD: Data (5)
RID := regress(Axi,ID,3)
RQT := regress(Axi, QT,3)
ROD := regress(Axl, OD,3)
RMD := regress(Axl,MD,3)
RTQ := regress(Axl,TQ,3)
FLCntr RefPoint O
if Val= I Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + c0 otherwise ULStrs.Dist - UTip UTip := FLCntr+ C0 I nCStrs.avg =
20 Developed by.
J. S. Bnhmadesam Verified by.
- 8. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point M Sat Aug 09 10:21:18 AM 2003 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 6 of 1 1 Engineering Report M-EP-2003-002-01 ProPLength -
0.128 Flaw Growth in Depth Direction 0.6
-C r-0 Q
U-0.41 I
I I
I I
I I
I I
I I
I I
I 0.2 0 D CI 0.5 l
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Q
C 0
0.81-0.61-I I ~~~~
~~~~I I
I I
I 1,5
.376 I
I I
I 0.41-0.2L 0 -0I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed by:
J S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Prograins Appendix "C"; Attachment 31 Page 7 of 11 Engineering Report M-EP-2003-002-01 4'n U,
LV r-~
80 60 40 20 Stress Intensity Factors I
I I
I I
I I
I I
III U0 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. Blihmadesam Venfied by:
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 0
fCA 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 "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 ot
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 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 6) 13.267 14.419 14.423 14.427 14.43 14.434 14.437 14.441 14.445 14.448 14.452 14.455 14.459 14.462 14.466 14.47 CG Rsambi (k, 5) 9.64 10.474 10.478 10.482 10.485 10.489 10.493 10.497 10.5 10.504 10.508 10.512 10.516 10.519 10.523 10.527 Developed by.
J. S. Bnhmadesam Vendfed by:
S. C Gray
Entergy Operations Inc Central Engineering Programs 80 l
o ID Dil ODD 60 240-I r2 20
-2I0
-20 0.0 a
_ 0.20 u 0.15 r 0.10 e°05
)0.05
/
0.00 Appendix "C"; Attachment 31 Page 10of 11 Engineering Report M-EP-2003-002-01 1.0 1.5 2.0 2.
Distance from Nozzle Bottom (inches) 0 1
2 3
4 Operating Time (years)
Developed by.
J. S. Srihmadesam Verified by B. C. Gray
(-o9
Entergy Operations Inc Central Engineering Programs 0.2 0 R
2
- 1) 0 1 500 e
0 r
Appendix "C"; Attachment 31 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
3 4
O perating Time {years}
30 6 25 i 20
.t 0I 10~
P-i"' ""-
=.int
('!a ltpj)]
5-.-,
I l
0 1
2 3
4 Operating Tiyte {yearsl Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray cIO
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 32 Page 1 of 1 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. 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 -'49" Degree Nozzle, Downhill Azimuth, Augmented Analysis 1.043" 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 This Attachment is Intentionally Blank M Sat Aug 09 10:21:18 AM 2003 -
Developed by:
J. S. Brihmadesam Verified by.
B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 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. 5. Brihmadesam Verified by: B. C. Gray Note: Only for use when Rat=,d/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"O"degree Nozzle, All Azimuth, Augmented Analysis 1.25 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 Tip" is located at the Reference tine.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.25 Location of Blind Zone above nozzle bottom (inch)
Note: Lowered BZ. This allows a Freespan of 0-546 inch to bottom of weld The Second Input is the Upper Limit for the evaluation, which is the bottom of the file t weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzk bottom) below.
LLStr,.Di~sl 1.796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Deeoe by eife y
IDeveloped by Verified by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 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 lim,:= 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 TIrf:= 617
[) = eL1.103 10 11+459.67 Tret+459.67) 1 C0 := e aoc Constant in MRP PWSCC Model for 1-600 Wrought c 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Timopr:= Years-36524 od id 2
t:= R0 -R Rm:= Ri + -
2 CFinhr:= 1.417-I05 Chlk:
Tilmopr
'lim llimI Prntblk :=
l I
L 2
Developed by:
Verified by:
IDeveloped by--
Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 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 "I" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAII :=
I o0 I
2 3
4 Is 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 10 2.34 17.56 22.68 33.81 47.49 63.56 AIIAxli=DataA11W AIIID DataAIl l AIIOD:= DataAI15 IDeveloped by Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 4of O Engineering Report M-EP-2003-002-01 4
-25
-50 0
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 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
-25.088 -27.546 -27.787 -25.624 -23.763)
Data:=
0.485
-0.563 0.874 21.515 1.186 32.751 1.436 35.667 1.635 34.244 1.796 29.45 1.932 23.674 2.068 18.928
-0.539
-2.111
-4.851
-6.157 18.635 17.122 14.843 10.089 28.494 24.136 19.645 14.45 29.598 26.166 25.589 28.417 29.574 28.286 35.408 45.379 29.814 31.385 43.337 61.713 26.502 33.261 47.609 64.65 24.564 22.854 33.968 34.789 49.071 49.525 65.876 1 62.795 )
y2.204 16.541 Ax[:= DataW ID:= Data
( )5 OD:= Data RID := regress(Axi, ID, 3)
ROD:= regress(AxlOD,3)
Developed by:
Verified by:
IDeveloped by.-
Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCt,:= BZ - I Flaw Center above Nozzle Bottom Ul-Strs.Dist - BZ lnCStrs.avg :=
20 No User Input required beyond this Point t
Sat Aug 09 11:44:49 AM 2003 Developed by:
Ven fled by:~~~~~~
IDeveloped by.
Vefified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0-546 Flaw Length vs. Time 1.5
(-R ITwcpwscc i
J,3 0
I 0.5 0
-0.5 L
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWSCC I 1)
Operating Time 1years)
Entergy Model Increase in Half Length 2
C~
r-C5 01au 1.5 I
0.5 0
0 0.5 I
1.5 2
2.5 3
3.5 4
OperatingTime (Years; IDeveloped by Verified by I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 7 of 10 Engineering Report M-EP-2003-002-01 C:
C.)
Cd
?:U 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time { Years }
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 4
IDeveloped by Verified by:
Cal
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCpWscc/
hj6) 15.871 23.129 23.139 23.149 23.159 23.169 23.179 23.189 23.199 23.21 23.22 23.23 23.24 23.25 23.26 23.271 TWCpWSCC 0
=
24.273 29.738 29.748 29.758 29.768 29.777 29.787 29.797 29.807 29.817 29.827 29.837 29.847 29.857 29.867 29.878 TWCpwSCC 8
21.089 27.647 27.658 27.669 27.68 27.691 27.702 27.713 27.723 27.734 27.745 27.756 27.767 27.778 27.789 27.8 Developed by:
Verified by:
IDeveloped by Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot 60 40
' 20 S
c, 0
-20
-40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (bc) 200 C150 isa
~.
100 a
50 0-OD Surface SIF I ID Surface SIF Average SIF 0
1 2
Operating Time (years) 3 4
Developed by:
Verified by:
IDeveloped by Verified by I cjf2-
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 10 of 10 Engineering Report M-EP-2003-002-01 i 2 a
0.8 0 0 2
3 p e reatin g T im e (ye ars )
Developed by:
Ven fled by:
IDeveloped by.-
Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 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. Cray Note: Only for use when R,^stc(1 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, Downhill Azimuth, Augmented Analysis 1.25 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/1hr.
Through Wall Axial Flaw The first Input is to locate the Reference line (eg. top of the Blind Zone).
The throughwall flaw "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.25 Location of Blind Zone above nozzle bottom (inch)
Note :- BZ lowered; This increases the freespan length to 0.536 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.Di,,t := 1.786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Developed by.
Verified by:~~~
IDeveloped by.
Venfied by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 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 llim:= 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(
Co= eL1 103 103 LT+459.67 Tre4+459.67Jj Tirkopr:= Years-365-24 od Ro :=-
id Ri := -
t:= Ro -Ri Rm:= R + -
2 CFinhr:= 1.417-10O Timopr Cblk :=
hirn Ilimi Prntblk =15 1
L I: -
2 IDeveloped by Verified by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 3of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "O" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAl :=
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 AllAxli DataAII(0 AIMi= DataAlII AIIOD:= DataAlI5 Developed by:
Verified by:
IDeveloped by--
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 4 of 10 Engineering Report M-EP-2003-002-01 a)
(r
-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 DataAl, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-27.404 -24.356 -22.209 -20.407 -18.9788 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
-1.486
-3.599 16.422 14.61 12.415 9.376 26.049 22.723 18.95 14.201 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
-4.44
-5.268 t2.183 14.834 22.263 34.779 49.055 63.377 )
(: )
Axli Data (I)
ID:
Data (5)
OD:=Data RID:= regress(Axl, ID,3)
ROD:= regress(Axl,OD,3)
Developed by:
Verified by:~~~~~~
IDeveloped by:
Venfied by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 5 of 10 Engineering Report M-EP-2003-002-01 FL(,ltr := BZ - I Flaw Center above Nozzle Bottom
__ ULStrs.Dist - BZ ICstrs axg. :=
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 Engineering Programs Appendix "C"; Attachment 34 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.536 Flaw Length vs. Time 1.5
.< TWCPWSC 0
QZ I
0.5 0
-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 Increase in Half Length 2
U r-oIJ cLb U
1.5 I
0.5 0 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time (Years)
IDeveloped by.-
Veiffied by: I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 C
U:
cj7 200 100 0
0 0.5 1
1.5 2
2.5 3
3.5 Operating Time { Years }
............ ID SIF - Entergy Model SIF Average 4
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC TWCp\\\\SCC(j.6) 15.478 22-634 22.643 22.652 22.661 22.67 22.679 22.688 22.697 22.706 22.715 22.724 22.733 22.742 22.751 22.76 TWCpwsC( 7 22.524 27.819 27.828 27.836 27.845 27.854 27.863 27.871 27.88 27.889 27.897 27.906 27.915 27.924 27.932 27.941 TWCPwSCc(.8 19.938 26.353 26.363 26.372 26.382 26.392 26.401 26.411 26.42 26.43 26.44 26.449 26.459 26.469 26.478 26.488 Developed by:
Verified by:
IDeveloped by Venfied by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 80 40 9
u 2 0 I
-2 0
-40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D is tan ce from N o zz le Bo Ito m
{inch }
2 00 -
v E 1 S 0-100 e
I I
0 -
Z5 O D S u rfa c e S IF ID S urfac e SIF I --
A v e rage S IF 0
0 1
2 3
4 O p e ra tin g T ime a(ye ars Developed by:
Verified by:I CILtF
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.2 S 0.8 SI 0
0 -4 0.0 2
3 4
0 p e ra tin g T im e (y e a rs }
Developed by:
Verified by:~~~
IDeveloped by Verified by: I
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 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: 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, 22.5 degree from Downhill Azimuth, Augmented Analysis; 1.30" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow both for the initial flow and for a growing flaw This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPoint 13 This is the reduced Blind zone for augmented analysis; permits a 0.2504 inch free span & 0.09 inch Propogation Length 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 value below ULLStrs.Dist := 1.5504 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by Verified by:
J. S. Brihmadesam B. C. Gray
Entergy Operations Inc Cettral Engineering Programns Input Data :-
Appendix "C"; Attachment 35 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 (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
id Rid 2
t:= Ro -Rid t
Rm:id+2 Timopr := Years*365-24 CFifl=r1.417*105 Timopr Cblk
'=-
Ihim Prntblk =
50 L
2 Rm Rt :=-
1-103-lo 3 T
re9.7
.f+459.671 cI-0 l
e re l a Temperature Correction for Coefficient Alpha Co:= Co0 75 th percentile MRP-55 Revision 1 Developed by.:
J S. Brihmadesam Vefffledby:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 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 "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
-19.3
-12.52
-8.3
-4 31
-0.29 1
0.42
-13.15
-8.57
-4.68
-1.25 1.83 2
0.75
-11.83
-6.96
-2.68 0.03 1.46 3
1.02
-14.15
-8.31
-3.17 1.1 1.22 4
1.24
-12.13
-6.55 0
5.78 7.86 5
1.41
-5.38
-2.41 7.5 23.29 28.72 6
1.55 4.33 6.48 17.84 35.67 42.75 7
1.7 13.64 15.67 27.16 40.65 53.56 8
1.85 18.3 21.2 32.42 50.34 61.38 9
2 18.32 22.29 34.21 53.26 63.46 10 2.14 14.52 21.82 35.09 51.48 61.5 11 2.29 9.62 20.82 34.51 47.88 53.88 12 2.44 6.18 19.92 32.26 40.25 44.06 AXLen A= ID=W~"
IDAII:= AI]Data( ')
ODAII=: A1lData (5)
Stress Distribution 8(1 1.544
- 6) I
._i v]
V)
I IDAfl ODAIf 4(1)1 I
II II 11 "I
I I
I III II I
I I
I 20 1
()
0.5 I
1.5 2.5 3
3.5 AXILen Axial Elevation above Bottom [inch]
Developed by:
J. S. Brihmadesam Venfied by S. C. Gray
Entergy Operations Inc Central Engineering Progrants Appendix "C"; Attachment 35 Page 4 of 1 1 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
-19.301
-12.523
-8.304
-4.314 -0.289) 0.419 -13.153 0.755 -11.834 1.024 -14.146 1.239 -12.132
-8.572
-6.958
-8.315
-4.68
-1.255 1.834
-2.685 0.028 1.463
-3.168 1.103 1.221
-6.552 3.002 X 10- 3 5.78 7.858 Data :=
1.412
-5.38
-2.413 7.498 23.29 28.718 1.55 4.331 6.478 17.842 35.67 42.747 1.699 13.644 15.667 27.164 40.65 53.563 1.847 18.304 21.201 32.424 50.345 61.379
\\.1.996 18.316 22.292 34.208 53.258 63.464)
Axl := Data(0)
(3)
MD:
Data ID:= Data(])
TQ := Data(4)
QT := Data(2)
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 - cO if Val=
Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + c0 otherwise UTi p := FLCntr +co Developed by:
J. S. Brihmadesam InlcStrs~av2 ULStrs.Dist - UTiP Xla Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 5 of 11 Engineering Report M-EP-2003-002-01 we No User Input is required beyond this Point M Sat Aug 09 10:21:18 AM 2003 Developed by:
J. S. Bnomadesam Verified by:
- 8. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 6 of 1 1 Engineering Report M-EP-2003-002-01 ProPLength 0.09 0.6 0~
0-0.4 1 Flaw Growth in Depth Direction I
I I
I I
I I
I I
III 0.2 [
O 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model I -
4 I
0 S-1 Q:
S..
3 0.5 ~
0 I
I I
I I
I I
1,5 i
0.09 l
l l
l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-0.5 f
-I 0 0.5 I
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model Developed by:
J. S. Bnhmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors Cr
'A 80 60 I
I I
I I
I I
..................................................... I.....
- 40).
20 t (I (1 0.5 l
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model
- ---. Surtace Point Entergy-CEP model Developed by:
J. S. Brahmadesam Venfied by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 14 0
.°A E
en 0
0 1E r-0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.5 1
"a" - Tip -- Uniform "a" - Tip -- Linear a" - Tip -- Quadratic I"a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic
-.--- t"c" - Tip -- Cubic 1.5 2
2.5 3
3.5 Operating time {years}
4 Developed by:
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central IEngineering Programs Appendix "C"; Aftachment 35 Page 9 of 11 Engineering Report M-EP-2003-002-O1 CGRsambi (k.8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 0.83 CGRsambi (k, 6) 10.711 11.761 11.763 11.766 11.768 11.77 11.772 11.774 11.776 11.778 11.78 11.782 11.784 11.786 11.788 11.79 CGRsambi 7.9 8.672 8.674 8.677 8.68 8.683 8.685 8.688 8.691 8.693 8.696 8.699 8.702 8.704 8.707 8.71 Developed by J. S. Brihmadesam Verified by B. C Gray
Entergy Operations Inc Central Engineering Programs 60 -
I -
i e 40 A20 I
Appendix "C"; Attachment 35 Page 10 of 11 Engineering Report M-EP-2003-002-01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Distance hfom Nozzle Bottom (inches) 0.12 -
i5 eSj E 0.04 0
-I 0.00 0
1 Operating Time (years) 3 4
Developed by:
J. S. Bnhmadesam Verified by:
S. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 11 of 11 Engineering Report M-EP-2003-002-01 0 1 2 0
I 2 0.0 8 ai 0
- 2. o 0 4 e
o o 2
3 4
O p e ra tin g T inn e
{y e a rs }
Surfaw Point ("e.-tip)
I =
Depth Point ( I. a"- tip) 20 -
t 15-jO 21 hio 0
1 2
3 4
Operating Time {years}
Developed by.
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page I 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. 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 -'49" Degree Nozzle, 45 degree from Downhill Azimuth, Augmented Analysis; 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmdt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzk end.
RefPoint := 1.544 This is the as-biult Blind Zone To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper IC-ti;p" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "C-tip" located at the reference point (Enter 3).
Val := 2 Upper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 2.1632 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 Progranis Input Data :-
Appendix "C"; Attachment 36 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt := 2.235 Years := 4 11im := 1500 T := 604
°Xoc := 2.67 10 12 QT := 31.0 TFref := 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 :=-
id Rid t = Ro - Rid i
Rm :=Rd +-
Timopr := Years-365-24 CFinhr = 1.417 lo' Timopr
'Jim Pmtbik =
50 LTo:
Rm Rt :=-
--Q,4
(
I I
C 0 '
l l113 101 T+459.67 Tre4i-h97) 01 -
0 Co := C0
) eOc Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by.
J. S. Bnhmadesam Verified by:
B C Gray
Entergy Operations Inc Central I Engineering Programs Appendix "C"; Attachment 36 Page 3 of I1 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 "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 f
g o-
-if;
- 1 t ~^
C~4tt 3.-
~ $ 7~ 74 if 0; 4
-6 5 0
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 10 275 3.59 10.95 19.96 31.01 38.94
.711 2.9
-0.98 8.74 18.34 28.35 33.45 12 3.04
-2.94 7.02 18.06 26 29.85 AXLen:= AllData(0)
ID
- = A11Data (1)
All OD
- = A11Data (5)
All Stress Distribution 60 40
-IDAII
-D 20 0
-20 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
3.5 4
Developed by:
J. 5. Bnhmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAbl that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. 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 Data :=
0.585
-1.256 1.053 - 1.023 1.429 -1.559 1.729 4.165 1.97 16.258 2.163 21.131 2.31 21.593
-1.488 -1.714
-0.223 0.347 0.622 2.583 4.315 8.86 12.541 16.926
-1.95 0.516 4.895 13.38 28.26
-3.157 )
-2.073
-0.495 4.258 15.252 32.667 36.98 41.718 41.213 )
17.131 20.087 34.279 19.093 21.933 34.049
\\.2-457 17.702 17.82 22.18 34.468 AxI := Data(o)
MD := Data 3)
ID := Datal)
TQ :=Data (4)
QT -
Data(2)
OD:
Data 5 RID := regress(AxiID,3)
RQT := regress(AxI,QT,3)
ROD := regress(Axl,OD,3)
RMD := re-ress(AxI,MD,3)
RTQ := regress(AxlTQ,3)
FLCntr RefPoint -
if Val = i Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + co otherwise UJTip = FLC'ntr+ C0 Developed by:
J. S. Brihmadesam Uil-Strs.Dist -
U~Tip IlncStrs~avC- -
~
Verified by.
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point gf Sat Aug 09 10:21:18 AM 2003 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength 2 0459 Flaw Growth in Depth Direction
-a C.
a-Ci) 0
-c M
0.4 -
0.2 -
0l I
00.5 1
Fntergyv-CFP Model 1.5 2
2.5 Operating Time lyearsk 4
I C)
-C C:
-E U-0.5 0s, 1.5 0.459 I
I I
-I 0
1.5 2
Operating Time
.'5 X'years,'
3 4
Entergv-CFP Model Developed by J. S. Bnlhmadesam Verified by B. C Gray
Entergy Operations Inc Appendix "C"; Attachment 36 Engineering Report Central Engineering Programs Page 7 of 11 M-EP-2003-002-01 Stress Intensity Factors 80 l
60 40 Q
40__
t 20 m
0 0 0.5 1
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. Biihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 Cn v:
r-0
-o
.)
.U 4E 0U c)Qd Q
5-c 0.6 0.5 0.4 0.3 0.2 0.1
--................ ---------------------------------- ----------------------- ----------------------- ----------- -.-I........................... I-----------
0 0 0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
ia" - 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. B&hmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 9 of I1 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) 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 CGRsambi (k, 5) 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5201 5.201 5.201 Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs 40-
[
30 20 1
I0 0
-1 0 Appendix "C"; Attachment 36 Page 10 of 11 Engineering Report M-EP-2003-002-01 1
2 3
D istance from N ozzle B ottom
{inches) 0 S5 -
0 3 -
I 0
is
-0 1 -
2 C,
c u- 0.3
-0.5 0
1 0 p a i Ti e
b ar 2
0 p era ting T im e {y ea rs I 3
4 Developed by.
J. S. Brihmadesam Verified by.
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.3 0 3 I
It Z0 F
-O 5
-0.3 Go0.5 0
I 2
O pera tin g Time
{yea ars}I 3
4 Surface Point {"c"-tip) l l1 Depth Point {"a"- tip) i
! 6.5 F
5 6i t, 6.0 5.0 0
1 2
O perating Time {years}
3 4
Developed by:V J. S. BrIhmadesam Verified by B. C Gray
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 37 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 RotSid/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, 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 throughwal/ flaw "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.3 This is the reduced blind zone location for augmented analysis; allows a propagation length of 0.25 inch an a freespan length of 0.0.25 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.Pist :_ 1.5504 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
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Central Engineering Programs Appendix "C"; Attachment 37 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :
L := 0.25 od := 4.05 id:= 2.728 Plt := 2.235 Years:= 4 li, := 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 Bloc := 2.67-10 12 Qg:= 31.0 Tref:= 617 K
Qg I
I-)
=
I103 10o T+459.67 Irer459.67)J Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Timopr:= Years 365-24 ad Ro :=-2 id 2
t:= Ro-Ri Rm= R + -
2 CFinhr:z= 1.417. 05 Cblk:=Tmp
'lirn rimn Pmtblk:=
-50 L
I: -
2 Developed by:
Verified by:
IDeveloped by Verified by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page3of10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "0" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataA1 :
0 1
2 3
4 5
0 0
-19.3
-12.52
-8.3
-4.31
-0.29 1
0.42
-13.15
-8.57
-4.68
-1.25 1.83 2
0.75
-11.83
-6.96
-2.68 0.03 1.46 3
1.02
-14.15
-8.31
-3.17 1.1 1.22 4
1.24
-12.13
-6.55 0
5.78 7.86 5
1.41
-5.38
-2.41 7.5 23.29 28.72 6
1.55 4.33 6.48 17.84 35.67 42.75 7
1.7 13.64 15.67 27.16 40.65 53.56 8
1.85 18.3 21.2 32.42 50.34 61.38 9
2 18.32 22.29 34.21 53.26 63.46 10 2.14 14.52 21.82 35.09 51.48 61.5 11 2.29 9.62 20.82 34.51 47.88 53.88 AJIAxlI Data 11W (I)
AIIID:
Dataxill (5)
A110D:z= DataAll IDeveloped by Verified by I Developed by Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 4 of 10 Engineering Report M-EP-2003-002-01 c) v:~
-20 0
0.5 1
1.5 2
2.5 3
Axial Distance above Bottom [inch]
3.5 ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled 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
-19.301 -12.523
-8.304
-4.314 -0.289) 0.419 -13.153
-8.572 0.755 -11.834
-6.958
-4.68
-1.255 1.834
-2.685 0.028 1.463
-3.168 1.103 1.221 1.024 -14.146
-8.315 Data:= j 1.239
-12.132 -6.552 3.002x 103 5.78 7.858 1.412
-5.38 1.55 4.331 1.699 13.644 1.847 18.304
-2.413 6.478 15.667 21.201 22.292 7.498 23.29 28.718 17.842 35.67 42.747 27.164 40.65 53.563 32.424 50.345 61.379 1.996 18.316 34.208 53.258 63.464)
Axl:= Data ° ID:= Data OD:= Data RID:= regress(Axl, ID, 3)
ROD:=regress(Axi, OD, 3)
Developed by:
Verified by:
IDeveloped by:
Verified by.- I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 5 of 10 Engineering Report M-EP-2003-002-01 FL(i nr 3BZ I Flaw Center above Nozzle Bottom U'LStrsIDist BZ 20 No User Input required beyond this Point l
Sat Aug 09 11:44:49 AM 2003 Developed by Venfied by:
IDeveloped by Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 0.25 Flaw Length vs. Time 1.5
.~TWCPSCC
.5
~~~j,3 C
0.5 1.5
.25
-0.5 --
0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCpWSCC 0 I )
Operating Time (years}
Entergy Model Increase in Half Length 2
U
-C 1.5 0.5 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time (Years) 4 IDeveloped by:
Verified by I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 7 of 10 Engineering Report M-EP-2003-002-01 IAn.
our
- r vL
.7 v) vU 200 100 O ;.....................................................................................................................................
0 0.5 I
1.5 2
Operating Time (Years}
2.5 3
3.5 4
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average D e e l p e b y V e.
.e y
IDeveloped by Venfied by I C-lu
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCpVscc
.6) 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 TWCPWSCC( j 7)
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835 TWCp 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 Deeoe by Velie y
IDeveloped by Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 9of10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 60 40 j2 0
1 I
-2 0 II 0T 1.0 1.5 2.0 2
D istance from Nozzle Botto m (in ch)
O 0 S u rfa c e S IF ID S u rfac e S IF A ve ra g e S IF 0
.8 i
(0 0
-5 0
1 2
0 pera tin g Timea
{y aars I 3
4 IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 10 of 10 Engineering Report M-EP-2003-002-01 zI f.14
E I0 0.5 0.3 -
0.1 -
-0.1 -
-03
-0.5 -
0 1
2 0 peraltin g T ime yea ars )
3 4
IDeveloped by.
Venfied by I Developed by:
Verified by:
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 bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when RlO,,tid/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 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 throughwall flow "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
[3Z := 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 This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
L'1-Str.,.Pis1 :- 2.1632 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
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Entergy Operations Inc.
Central 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 hlim := 1500 T:= 604 v := 0.307 aoc:= 2.67 10 12 Qg:= 31.0 Trmf := 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 L~ ~----Te+
I-)
C0:= e 1
.103459.6 Te+59.67)Jaoc Timopr:= Years 365 24 od Ro :=-
2 t:= Ro - Ri Rm:= Ri + 2 CFinhr= 1.417 105 Timfpr lim Irim Prntblk :
I L
2 IDeveloped by.-
Venfied by I Developed 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 '"0 = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataII:
0 1
2 3
4 5
0 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 AIIAxI:=Dt 1
A11ID := DataXll i)
AIIOD:= Data 11 5 IDeveloped by Verified by: I Developed by:
Verified by:
Entergy Operations Inc.
Cenral Engineering Programs Appendix "C"; Attachment 38 Page 4 of 10 Engineering Report M-EP-2003-002-01
-10 X
0 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 Datas1 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 0.585 1.053 1.429 1.729 1.97 2.163 2.31 2.457
-0.414
-1.256
-1.023
-1.559 4.165 16.258 21.131 21.593 17.702
-1.359
-1.488
-0.223 0.622 4.315 12.541 17.131 19.093 17.82
-1.842
-1.714 0.347 2.583 8.86 16.926 20.087 21.933 22.18
-2.369
-1.95 0.516 4.895 13.38 28.26 34.279 34.049 34.468
-3.157)
-2.073
-0.495 4.258 15.252 32.667 36.98 41.718 41.213)
Axl:= Data ID:
Data~1 (5)
OD:=Data RID:= regress(Axl, ID,3)
ROD:= regress(Axl, OD, 3)
D I Developed by Verified by. I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 38 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLC~tr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist -BZ SncStrs.avg =
20 No User Input required beyond this Point l Sat Aug 09 11:44:49 AM 2003 Developed by:
Verified by:
IDevekped by.
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Entergy Operatons 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 z
"I TWCpwscc,3 0
0.5
.619 0
-0.5 0
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWScjC I)
Operating Time (years)
Entergy Model Increase in Half Length 2
5 t
1.5 1
0.5 0 CI 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time (Years)
De eo e y V rfe y
IDeveloped by.,
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Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 38 Page 7 of 10 Engineering Report M-EP-2003-002-01 11AA Juv r0.
rJ.
200 100 0
0 0.5 l
1.5 2
Operating Time {Years}
2.5 3
3.5 4
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average D
IDeveloped by.-
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Central Engineering Programs Appendix "C"; Attachment 38 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC pwscc(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 TWCpwsc( j7)=
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 CPWSCC(i8) 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:
Verfired 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 lo t 40 30 I
i 20 B
1 0 0
-1 0 7
6 05 a) 4 3-0 1
2 Distance from Nozzle Bottom (inch)
I nfl
~uf.,
~F ID S u rfa c e S IF A v e ra g e S IF 0
I 2
O pe ratin g T ime
{y ea rsI 3
4 Developed by:
Venfied by
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 38 Page 10 of 10 Engineering Report M-EP-2003-002-01 I
I 0.5 -
0.3 -
0.1 -
-0.1 -
-0.3 -
-0.5 -
0 I
2 0 p oeatin g Time ye a re) 3 4
IDeveloped by.
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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 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 -"0" Degree Nozzle, All Azimuth, Augmented Analysis 1.25" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flow. This is defined as the reference point. Enter a number (inch) that represnets the referene point elevation measured upward from the nobzle 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 flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "e-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 U'pper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.796 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engieering Programs Input Data :-
Appendix "C"; Attachment 39 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 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 :=2 Rid := id Rid :=2 t:= Ro -Rid t
Rm= Rid+ 2 Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk
'=im Pmtblk :=
50 L
Co := 2 Rm Rt:=-
[
Q ~g -
J l lo3-lo-3 (T+459.67 Tref2459.67i)]
C01
= e' X aOc TemperatureCorrectionforCoefficientAlpha Co:= Co0 Stress InDut Data 75 e] percentile MRP-55 Revision 1 Developed by:
J. S. Brihmadesam Verfied 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 Po0 = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "1" = ID Stress data at each Elevation (ksl)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4W
= Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4
-5i- - -I 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 := AlIData(o)
IDA11:= AlIData(')
ODA11
- =AIData K5)
Stress Distribution 100 r'
IDAII I-.I II I
1.$44 14796 I
I -
I I
I I
I I
I I
I
-50 _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 DataAll that represents the Developed by:
J. S. BEnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 4 of 11 Engineering Report M-EP-2003.002-01
. I
. J If'-
P¶9 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).
-25.088 -27.546 -27.787 -25.624 -23.763 )
0.485
-0.563
-0.539
-2.111
-4.851
-6.157 0.874 21.515 18.635 17.122 14.843 10.089 1.186 32.751 28.494 24.136 19.645 14.45 1.436 35.667 29.598 26.166 25.589 28.417 Data :=
1.635 1.796 34.244 29.45 29.574 29.814 28.286 31.385 35.408 43.337 45.379 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)
MD:= Data(3 ID:= Data(i)
TQ :=Data(4)
QT := Data(2)
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 - c0 if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint +
otherwise ULStrs.Dist - UTip UTip FLCntr + C0 IfCStis.avg 20 Developed by:
J. S. Brihmadesam VeT/fied 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 n Sat Aug 09 10:21:18 AM 2003-Developed by:
J1 S. Btihmadesam Veified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength 0.386 0.6 0
0 0.4 I Flaw Growth in Depth Direction I
I I
I III I
I I
I III 0.2 [
0 _0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model 0
0.8 I 0.6 r I
I I
II I
I 1,'5 I
.386
~-r-------------------------------------__---
I ~ ~ ~ ~
~ ~ ~ ~ ~ ~
I I
I I
I 0.4 r 0.2 I 0 0 0.5 I
1.5 2
2.5 3
Operating Time {years}
3.5 4
Entergy-CEP Model Developed by:
.1. S. Brihmadesam Veirifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 39 Page 7 of 1 1 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 0~
0 S-c#2 80 60 I
.I...........
40 201 0 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
J. S. Bdhmadesam Vetnied 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
...................................................................... 11,
......................................................... I...............................................................................................................................
CA) 0 C.)
E C.U C.)-
C-)
V.
0.6 0.5 0.4 I
---------------------------------------------- ----- I----------------- ---------------------------------------------- ----------
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 "a" - Tip -- Linear
"at" - Tip -- Quadratic Ila" - Tip -- Cubic tic" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic tic" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray C-Z~
i,
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:
J. S. Bnihmadesam Veried by:
B. C Gray
Entergy Operations Inc Central Engineering Programs F-ID is 60-I OD 40 -
i 20 0,
S Appendix "C"; Attachment 39 Page 10 of 11 Engineering Report M-EP-2003-002-01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 istance from Nozzle Bottorn {inches) 0.12 2* 0.10 O 0.08-a
.0.06 0
O 0.04 o 0.02 0.00 0
1 2
Operating Time {years) 3 4
Developed by.
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs 0.12-0 01 8
, 0.0 86 0.
2 0 A 4-00 0 2 0.00 20 -i
- 18 4, 16 14 c12 r
10 r
8 Appendix "C"; Attachment 39 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
O peara tin g T im e {yea ars )
Surface Point ("ca-tip)
Depth Point {"a': tip) 0 1
2 Operabng Time (years) 3 4
Developed by:
J. S. Brihmadesam Verified by' B. C. Gray